Mathletics Ontario Curriculum Alignment Grades 1 8

Transcription

1 Mathletics Ontario Curriculum Alignment Grades 1 8 Supported by independent evidence-based research and practice. Follows provincial curricula Powerful reporting Student centred

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3 Content Ontario Kindergarten 02 Ontario, Applied (MFM2P) 110 Ontario Grade 1 Ontario Grade Ontario Grade 11, (MCR3U) 118 Ontario Grade 3 20 Ontario Grade 11, and Applications (MCF3M) 125 Ontario Grade 4 Ontario Grade Ontario Grade 11, Foundations for College Mathematics (MBF3C) 131 Ontario Grade 6 Ontario Ontario Grade 11, Mathematics for Work and Everyday Life (MEL3E) 137 Ontario 69 Ontario, Academic (MPM1D) 78 Ontario, Applied (MFM1P) 91 Ontario, Academic (MPM2D) 102

4 Mathletics and the At Mathletics, we are committed to providing students, teachers and schools with high-quality learning resources that align with the most up-to-date curricula. Mathletics includes over 1300 individual adaptive practice activities. Our team of educational publishers has created a course that follows the revised, Grades 1 8 (Mathematics), You can be assured that students have access to relevant and targeted content. Courses consist of topics that follow the strands of the curriculum. Activities within each topic provide adaptive practice and each topic has a pre- and post-test. This document outlines this mapping and acts as a useful guide when using Mathletics in your school. 3P Learning Canada Engage Target Diagnose Assess Report Fluency Mobile 1 3P Learning

5 Ontario Kindergarten ONK.NS1.1 ONK.NS1.2 ONK.NS1.3 ONK.NS1.4 ONK.NS1.5 ONK.NS1.6 ONK.NS1.7 ONK.NS1.8 ONK.NS1.9 ONK.NS1.10 Investigate the idea that quantity is greater when counting forward and less when counting backwards. Investigate some concepts of quantity through identifying and comparing sets with more, fewer, or the same number of objects. Begin to make use of one-to-one correspondence in counting objects and matching groups of objects. Demonstrate understanding of the counting concepts of stable order and of order irrelevance. Recognize some quantities without having to count, using a variety of tools or strategies. Begin to use information to estimate the number in a small set. Demonstrate an understanding of number relationships for numbers from 0 to 10, through investigation. Use ordinal numbers in a variety of everyday contexts. Use, read, and represent whole numbers to 10 in a variety of meaningful contexts a hundreds chart to read whole numbers; use magnetic and sandpaper numerals to represent the number of objects in a set; put the house number on a house built at the block centre; find. Explore different Canadian coins, using coin manipulatives. How Many? More or Less? More, less or the same to 10 How many dots? How Many? Count to 5 Matching s to 10 Order s to 10 Comparing Groups of Objects Order s to 10 How many dots? How Many? Order s to 10 Ordinal s Kindergarten s and Patterns Kindergarten s and Patterns Kindergarten s and Patterns Kindergarten s and Patterns Kindergarten s and Patterns Kindergarten s and Patterns Kindergarten s and Patterns Kindergarten s and Patterns Kindergarten Time, Money and 3P Learning 2

6 Ontario Kindergarten Geometry Geometry Properties Properties ONK.NS1.11 ONK.NS1.12 ONK.M2.1 ONK.M2.2 ONK.M2.3 ONK.G3.1 ONK.G3.2 Investigate and develop strategies for composing and decomposing quantities to 10. Investigate addition and subtraction in everyday activities through the use of manipulatives, visual models, or oral exploration. Compare and order two or more objects according to an appropriate measure and use measurement terms. Demonstrate, through investigation, an awareness of non-standard measuring devices and standard measuring devices and strategies for using them. Demonstrate, through investigation, a beginning understanding of nonstandard units that are the same type but not always the same size. Explore, sort, and compare traditional and non-traditional two-dimensional shapes and three-dimensional figures. Identify and describe, using common geometric terms, two-dimensional shapes and three-dimensional figures through investigation with concrete materials. Model Addition Model Subtraction Subtracting from Ten Adding to 5 Subtracting From 5 Adding to make 5 and 10 Adding to Ten Everyday Length Compare Length Hot or Cold? Biggest Shape Everyday Mass Which Holds More? Filling Fast! Balancing Act Everyday Mass Compare Length Measuring length with blocks Collect the Shapes Collect Simple Shapes Collect the Objects Match the Solid 1 Match the Solid 2 Sort It Same and Different Collect the Shapes Collect Simple Shapes Collect the Objects Match the Solid 1 Match the Solid 2 Sort It Same and Different Kindergarten s and Patterns Kindergarten Operations with Kindergarten Kindergarten Space and Shape Kindergarten Space and Shape 3 3P Learning

7 Ontario Kindergarten Geometry Geometry Geometry Geometry Patterns Patterns Location and Movement Collection and Organization of Collection and Organization of Collection and Organization of Collection and Organization of ONK.G3.3 ONK.G3.4 ONK.G3.5 ONK.G3.6 ONK.P4.1 ONK.P4.2 ONK.DM5.1 ONK.DM5.2 ONK.DM5.3 ONK.DM5.4 Compose pictures, and build designs, shapes, and patterns, using two-dimensional shapes, and decompose two-dimensional shapes into smaller shapes, using various tools or strategies. Build three-dimensional structures using a variety of materials and begin to recognize the threedimensional figures their structure contains. Investigate the relationship between two-dimensional shapes and threedimensional figures in objects that they have made. Demonstrate an understanding of basic spatial relationships and movements. Identify, create, reproduce, and extend repeating patterns through investigation, using a variety of materials and actions. Identify and describe informally the repeating nature of patterns in everyday contexts, using oral expressions and gestures. Sort, classify, and compare objects and describe the attributes used. Collect objects and data and make representations of their observations, using concrete graphs. Respond to and pose questions about data collection and graphs. Use mathematical language in informal discussions to describe probability. Following Directions Left or Right? Where is it? Colour Patterns Simple Patterns Missing it! Complete the Pattern Sort It Same and Different Make Graphs Making Graphs Who has the Goods? Make Graphs Making Graphs Kindergarten Space and Shape Kindergarten Space and Shape Kindergarten Space and Shape Kindergarten Space and Shape Kindergarten s and Patterns Kindergarten s and Patterns Grade 1 Chance and Grade 1 Chance and Grade 1 Chance and 3P Learning 4

8 Ontario Grade 1 ON1.NS1.1 Represent, compare, and order whole numbers to 50, using a variety of tools and contexts. Arranging s 1 to 30 Order s to 20 Compare s to 20 Compare s to 50 Counting up to 20 Counting back within 20 Before, After and Between to 20 Balance s to 20 Making s Count Make Big s Count Lines Making Teen s Counting Forward Counting Backward Grade 1 s ON1.NS1.2 Read and print in words whole numbers to ten, using meaningful contexts. Matching s to 10 Grade 1 s ON1.NS1.3 Demonstrate, using concrete materials, the concept of conservation of number. Adding In Any Order Grade 1 s ON1.NS1.4 Relate numbers to the anchors of 5 and 10. Grade 1 s ON1.NS1.5 Identify and describe various coins. Everyday Money Grade 2 Time and Money ON1.NS1.6 Represent money amounts to 20, through investigation using coin manipulatives. Grade 2 Time and Money ON1.NS1.7 Estimate the number of objects in a set, and check by counting. Grade 1 s ON1.NS1.8 ON1.NS1.9 Compose and decompose numbers up to 20 in a variety of ways, using concrete materials. Divide whole objects into parts and identify and describe, through investigation, equal-sized parts of the whole, using fractional names. Balance s to 20 Complements to 10, 20, 50 Is it Half? Halves Grade 1 s Grade 1 Operations with 5 3P Learning

9 Ontario Grade 1 Counting Counting Counting Counting ON1.NS2.1 ON1.NS2.2 ON1.NS2.3 ON1.NS2.4 Demonstrate, using concrete materials, the concept of one-to-one correspondence between number and objects when counting. Count forward by 1 s, 2 s, 5 s, and 10 s to 100, using a variety of tools and strategies. Count backwards by 1 s from 20 and any number less than 20, with and without the use of concrete materials and number lines. Count backwards from 20 by 2 s and 5 s, using a variety of tools. How Many? Make s Count Count by Twos Make Big s Count Going Up Counting Forwards Skip Counting with coins Counting Forward Counting Backward How Many? Count by Fives Count by Tens Count by 2, 5s and 10s Counting Backwards Count backward within 20 Counting Backwards Grade 1 s Grade 1 s Grade 1 s Grade 1 s Counting ON1.NS2.5 Use ordinal numbers to thirtyfirst in meaningful contexts. Ordinal s 1st to 31st Grade 1 s Operational ON1.NS3.1 Solve a variety of problems involving the addition and subtraction of whole numbers to 20, using concrete materials and drawings. 1 more, 2 less Doubles and Halves to 10 Doubles and Halves to 20 Doubles and Near Doubles Model Addition Model Subtraction Addition Facts to 18 Subtraction Facts to 18 All about Twenty Composing s to 10 Composing Additions to 20 Simple Subtraction Related Facts 1 Fact Families: Add and Subtract Grade 1 Operations with 3P Learning 6

10 Ontario Grade 1 Operational ON1.NS3.2 Operational ON1.NS3.3 Attributes, Units, and ON1.M1.1 Solve problems involving the addition and subtraction of singledigit whole numbers, using a variety of mental strategies. Add and subtract money amounts to 10, using coin manipulatives and drawings. Demonstrate an understanding of the use of non-standard units of the same size for measuring. Fact Families: Add and Subtract Addition Adding to 10 Word Addition Facts to 18 Add and Subtract Addictive Addition Doubles and Near Doubles Simple Subtraction Measuring length with blocks Grade 1 Operations with Grade 2 Time and Money Grade 3 Attributes, Units, and ON1.M1.2 Estimate, measure, and record lengths, heights, and distances. Compare Length Everyday Length Measuring Length How Long is That? Grade 3 Attributes, Units, and Attributes, Units, and Attributes, Units, and Attributes, Units, and Attributes, Units, and ON1.M1.3 ON1.M1.4 ON1.M1.5 ON1.M1.6 ON1.M1.7 Construct, using a variety of strategies, tools for measuring lengths, heights, and distances in non-standard units. Estimate, measure, and describe area, through investigation using non-standard units. Estimate, measure, and describe the capacity and/or mass of an object, through investigation using non-standard units. Estimate, measure, and describe the passage of time, through investigation using non-standard units. Read demonstration digital and analogue clocks, and use them to identify benchmark times and to tell and write time to the hour and half-hour in everyday settings. Measuring length with blocks Compare Length Biggest Shape Which Holds More? Everyday Mass How Full? Filling Fast! Hour Times Half Hour Times Grade 3 Grade 2 Space and Shape Grade 3 Grade 2 Time and Money Grade 2 Time and Money 7 3P Learning

11 Ontario Grade 1 Attributes, Units, and Attributes, Units, and Spatial Spatial Spatial Spatial Properties Properties Properties Properties ON1.M1.8 ON1.M1.9 ON1.M2.1 ON1.M2.3 ON1.M2.4 ON1.M2.5 ON1.GS1.1 ON1.GS1.2 ON1.GS1.3 ON1.GS1.4 Name the months of the year in order, and read the date on a calendar. Relate temperature to experiences of the seasons. Compare two or three objects using measurable attributes, and describe the objects using relative terms. Compare and order objects by their linear measurements, using the same non-standard unit. Use the metre as a benchmark for measuring length, and compare the metre with nonstandard units. Describe, through investigation using concrete materials, the relationship between the size of a unit and the number of units needed to measure length. Identify and describe common two-dimensional shapes and sort and classify them by their attributes, using concrete materials and pictorial representations. Trace and identify the twodimensional faces of threedimensional figures, using concrete models. Identify and describe various three-dimensional figures and sort and classify them by their geometric properties, using concrete materials. Describe similarities and differences between an everyday object and a three-dimensional figure. Using a Calendar Months of the Year How Full? Filling Fast! Hot or Cold? Which Holds More? Compare Length Collect the Shapes Collect the Shapes 1 Collect Simple Shapes Relate Shapes and Solids Collect the Objects Collect the Objects 1 Collect the Objects 2 Match the Object Match the Solid 1 Match the Solid 2 Grade 2 Time and Money Grade 3 Grade 3 Grade 3 Grade 3 Grade 3 Grade 2 Space and Shape Grade 2 Space and Shape Grade 2 Space and Shape Grade 2 Space and Shape 3P Learning 8

12 Ontario Grade 1 Spatial Properties ON1.GS1.5 Locate shapes in the environment that have symmetry, and describe the symmetry. Symmetry Symmetry or Not? Grade 2 Space and Shape Spatial ON1.GS2.1 Compose patterns, pictures, and designs, using common twodimensional shapes. Simple Patterns Grade 1 Spatial ON1.GS2.2 Identify and describe shapes within other shapes. Grade 2 Space and Shape Spatial Spatial Spatial Spatial Spatial Patterning and Location and Movement Location and Movement Location and Movement ON1.GS2.3 ON1.GS2.4 ON1.GS3.1 ON1.GS3.2 ON1.GS3.3 ON1.PA1.1 Build three-dimensional structures using concrete materials, and describe the two-dimensional shapes the structures contain. Cover outline puzzles with twodimensional shapes. Describe the relative locations of objects or people using positional language. Describe the relative locations of objects on concrete maps created in the classroom. Create symmetrical designs and pictures, using concrete materials, and describe the relative locations of the parts. Identify, describe, and extend, through investigation, geometric repeating patterns involving one attribute. Where is it? Left or Right? Following Directions Symmetry or Not? Symmetry Missing it! Colour Patterns Simple Patterns Grade 2 Space and Shape Grade 2 Space and Shape Grade 3 Grade 3 Grade 2 Space and Shape Grade 1 Patterning and ON1.PA1.2 Identify and extend, through investigation, numeric repeating patterns. Increasing Patterns Decreasing Patterns Grade 1 9 3P Learning

13 Ontario Grade 1 Patterning and Patterning and Patterning and Patterning and Patterning and Patterning and Patterning and and Probability and Probability and Probability Expressions and Equality Expressions and Equality Expressions and Equality Collection and Organization of Collection and Organization of ON1.PA1.3 ON1.PA1.4 ON1.PA1.5 ON1.PA1.6 ON1.PA2.1 ON1.PA2.2 ON1.PA2.3 ON1.DMP1.1 ON1.DMP1.2 ON1.DMP2.1 Describe numeric repeating patterns in a hundreds chart. Identify a rule for a repeating pattern. Create a repeating pattern involving one attribute. Represent a given repeating pattern in a variety of ways. Create a set in which the number of objects is greater than, less than, or equal to the number of objects in a given set. Demonstrate examples of equality, through investigation, using a balance model. Determine, through investigation using a balance model and whole numbers to 10, the number of identical objects that must be added or subtracted to establish equality. Demonstrate an ability to organize objects into categories by sorting and classifying objects using one attribute, and by describing informal sorting experiences. Collect and organize primary data that is categorical, and display the data using one-toone correspondence, prepared templates of concrete graphs and pictographs, and a variety of recording methods. Read primary data presented in concrete graphs and pictographs, and describe the data using comparative language. Increasing Patterns Decreasing Patterns Increasing Patterns Decreasing Patterns Balancing Act Balancing Objects Balance s to 10 Sort It Making Graphs Tallies Who has the Goods? More or Less? Read Graphs Picture Graphs: Single-unit scale Grade 1 Grade 1 Grade 1 Grade 1 Grade 1 s Grade 1 s Grade 1 s Grade 2 Space and Shape Grade 2 Chance and Grade 2 Chance and 3P Learning 10

14 Ontario Grade 1 and Probability ON1.DMP2.2 Pose and answer questions about collected data. Who has the Goods? More or Less? Read Graphs Add and Subtract Using Graphs Grade 2 Chance and and Probability Probability ON1.DMP3.1 Describe the likelihood that everyday events will occur, using mathematical language. Will it Happen? Grade 2 Chance and 11 3P Learning

15 Ontario Grade 2 ON2.NS1.1 Represent, compare, and order whole numbers to 100, including money amounts to 100, using a variety of tools. Going Up Lines Line Order Going Down Compare s to 100 Making Big s Count Model s Skip Counting with Coins Skip Counting with coins Counting on a 100 grid Greater or Less to more, 10 less Counting Forward Counting Backward Grade 2 s ON2.NS1.2 Read and print in words whole numbers to twenty, using meaningful contexts. Matching s to 20 Grade 2 s ON2.NS1.3 ON2.NS1.4 ON2.NS1.5 ON2.NS1.6 ON2.NS1.7 ON2.NS1.8 Compose and decompose twodigit numbers in a variety of ways, using concrete materials. Determine, using concrete materials, the ten that is nearest to a given two-digit number, and justify the answer. Determine, through investigation using concrete materials, the relationship between the number of fractional parts of a whole and the size of the fractional parts. Regroup fractional parts into wholes, using concrete materials. Compare fractions using concrete materials, without using standard fractional notation. Estimate, count, and represent the value of a collection of coins with a maximum value of one dollar. Place Value 1 Repartition Two-digit s Nearest 10? Shape Fractions Model Fractions What Fraction is Shaded? Halves Halves and Quarters Uneven partitioned shapes 1 Identifying Fractions on a Line Grade 2 s Grade 2 s Grade 3 Fractions Grade 3 Fractions Grade 3 Fractions Grade 2 Time and Money 3P Learning 12

16 Ontario Grade 2 Counting Counting ON2.NS2.1 ON2.NS2.2 Count forward by 1 s, 2 s, 5 s, 10 s, and 25 s to 200, using number lines and hundreds charts, starting from multiples of 1, 2, 5, and 10. Count backwards by 1 s from 50 and any number less than 50, and count backwards by 10 s from 100 and any number less than 100, using number lines and hundreds charts. Counting by Twos Counting by Fives Counting Backward Grade 2 s Grade 2 s Counting ON2.NS2.3 Locate whole numbers to 100 on a number line and on a partial number line. Line Order Lines Grade 2 s Operational ON2.NS3.1 Solve problems involving the addition and subtraction of whole numbers to 18, using a variety of mental strategies. Addition Addictive Addition Subtraction Facts to 18 Simple Subtraction Grade 2 Operations with Operational ON2.NS3.2 Describe relationships between quantities by using whole-number addition and subtraction. : Add and Subtract Grade 2 Operations with Operational Operational ON2.NS3.3 ON2.NS3.4 Represent and explain, through investigation using concrete materials and drawings, multiplication as the combining of equal groups. Represent and explain, through investigation using concrete materials and drawings, division as the sharing of a quantity equally. Making Equal Groups Divide Into Equal Groups Groups of Two Groups of Five Groups of Ten Dividing Fives Dividing Tens Dividing Twos Making Equal Groups Divide Into Equal Groups Grade 2 Operations with Grade 2 Operations with 13 3P Learning

17 Ontario Grade 2 Operational Operational Attributes, Units, and Attributes, Units, and Attributes, Units, and Attributes, Units, and Attributes, Units, and Attributes, Units, and ON2.NS3.5 ON2.NS3.6 ON2.M1.1 ON2.M1.2 ON2.M1.3 ON2.M1.4 ON2.M1.5 ON2.M1.6 Solve problems involving the addition and subtraction of two-digit numbers, with and without regrouping, using concrete materials, studentgenerated algorithms, and standard algorithms. Add and subtract money amounts to 100 using a variety of tools. Choose benchmarks in this case, personal referents for a centimetre and a metre to help them perform measurement tasks. Estimate and measure length, height, and distance, using standard units and non-standard units. Record and represent measurements of length, height, and distance in a variety of ways. Select and justify the choice of a standard unit or a nonstandard unit to measure length. Estimate, measure, and record the distance around objects, using non-standard units. Estimate, measure, and record area, through investigation using a variety of non-standard units. Bar Model 1 Bar Model 2 2 Digit Differences Column Addition Columns that Subtract How much Change? Add s: Regroup a Ten Subtract s Subtract s: Regroup Complements to 10, 20, 50 Doubles and Halves to 20 1 more, 2 less 1 more, 10 less Doubles and Near Doubles How much Change? Measuring length with blocks How Long is That? Measuring Length Comparing Length How Long is That? Measuring length with blocks Perimeter Perimeter of Shapes Equal Areas Grade 2 Operations with Grade 2 Time and Money Grade 3 Grade 3 Grade 3 Grade 3 Grade 4 Length, Area and Perimeter Grade 3 Grade 4 Length, Area and Perimeter 3P Learning 14

18 Ontario Grade 2 Attributes, Units, and Attributes, Units, and Attributes, Units, and Attributes, Units, and Attributes, Units, and Spatial Spatial Properties Properties ON2.M1.7 ON2.M1.8 ON2.M1.9 ON2.M1.10 ON2.M1.11 ON2.M2.1 ON2.M2.2 ON2.M2.3 ON2.GS1.1 ON2.GS1.2 Estimate, measure, and record the capacity and/or mass of an object, using a variety of nonstandard units. Tell and write time to the quarter-hour, using demonstration digital and analogue clocks. Construct tools for measuring time intervals in non-standard units. Describe how changes in temperature affect everyday experiences. Use a standard thermometer to determine whether temperature is rising or falling. Describe, through investigation, the relationship between the size of a unit of area and the number of units needed to cover a surface. Compare and order a collection of objects by mass and/or capacity, using non-standard units. Determine, through investigation, the relationship between days and weeks and between months and years. Distinguish between the attributes of an object that are geometric properties and the attributes that are not geometric properties, using a variety of tools. Identify and describe various polygons and sort and classify them by their geometric properties, using concrete materials and pictorial representations. Filling Fast! Half Hour Times Quarter to and Quarter past Temperature Temperature Area of Shapes Equal Areas Everyday Mass Filling Fast! Days of the Week Months of the Year Using a Calendar Count Sides and Corners Grade 3 Grade 2 Time and Money Grade 3 Grade 4 Length, Area and Perimeter Grade 3 Grade 2 Time and Money Grade 2 Space and Shape Grade 2 Space and Shape 15 3P Learning

19 Ontario Grade 2 Spatial Spatial Spatial Spatial Spatial Spatial Spatial Spatial Spatial Spatial Properties Properties Properties Location and Movement Location and Movement Location and Movement ON2.GS1.3 ON2.GS1.4 ON2.GS1.5 ON2.GS2.1 ON2.GS2.2 ON2.GS2.3 ON2.GS2.4 ON2.GS3.1 ON2.GS3.2 ON2.GS3.3 Identify and describe various three-dimensional figures and sort and classify them by their geometric properties, using concrete materials. Create models and skeletons of prisms and pyramids, using concrete materials, and describe their geometric properties. Locate the line of symmetry in a two-dimensional shape. Compose and describe pictures, designs, and patterns by combining two-dimensional shapes. Compose and decompose twodimensional shapes. Cover an outline puzzle with two-dimensional shapes in more than one way. Build a structure using threedimensional figures, and describe the two-dimensional shapes and three-dimensional figures in the structure. Describe the relative locations and the movements of objects on a map. Draw simple maps of familiar settings, and describe the relative locations of objects on the maps. Create and describe symmetrical designs using a variety of tools. How many Faces? How many Edges? How many Corners? Collect the Objects Collect the Objects 2 Relate Shapes and Solids Symmetry Symmetry or Not? Line of Symmetry Relate Shapes and Solids Relate Shapes and Solids Map Coordinates Following Directions Coordinate Meeting Place Using a Key Grade 2 Space and Shape Grade 2 Space and Shape Grade 2 Space and Shape Grade 2 Space and Shape Grade 2 Space and Shape Grade 2 Space and Shape Grade 2 Space and Shape 3P Learning 16

20 Ontario Grade 2 Patterning and Patterning and Patterning and Patterning and Patterning and Patterning and Patterning and Patterning and Patterning and Expressions and Equality Expressions and Equality ON2.PA1.1 ON2.PA1.2 ON2.PA1.3 ON2.PA1.4 ON2.PA1.5 ON2.PA1.6 ON2.PA1.7 ON2.PA2.1 ON2.PA2.2 Identify and describe, through investigation, growing patterns and shrinking patterns generated by the repeated addition or subtraction of 1 s, 2 s, 5 s, 10 s, and 25 s on a number line and on a hundreds chart. Identify, describe, and create, through investigation, growing patterns and shrinking patterns involving addition and subtraction, with and without the use of calculators. Identify repeating, growing, and shrinking patterns found in real-life contexts. Represent a given growing or shrinking pattern in a variety of ways. Create growing or shrinking patterns. Create a repeating pattern by combining two attributes. Demonstrate, through investigation, an understanding that a pattern results from repeating an operation or making a repeated change to an attribute. Demonstrate an understanding of the concept of equality by partitioning whole numbers to 18 in a variety of ways, using concrete materials. Represent, through investigation with concrete materials and pictures, two number expressions that are equal, using the equal sign. Increasing Patterns Increasing Patterns 1 Decreasing Patterns Count Forward Patterns Count Backward Patterns Increasing Patterns Increasing Patterns 1 Decreasing Patterns Count Forward Patterns Count Backward Patterns Increasing Patterns Increasing Patterns 1 Decreasing Patterns Count Forward Patterns Count Backward Patterns Balance s to 20 Grade 2 Grade 2 Grade 2 Grade 2 Grade 2 Grade 2 Grade 2 Grade P Learning

21 Ontario Grade 2 Patterning and Patterning and Patterning and and Probability and Probability and Probability and Probability Expressions and Equality Expressions and Equality Expressions and Equality Collection and Organization of Collection and Organization of Collection and Organization of ON2.PA2.3 ON2.PA2.4 ON2.PA2.5 ON2.DMP1.1 ON2.DMP1.2 ON2.DMP1.3 ON2.DMP2.1 Determine the missing number in equations involving addition and subtraction to 18, using a variety of tools and strategies. Identify, through investigation, and use the commutative property of addition to facilitate computation with whole numbers. Identify, through investigation, the properties of zero in addition and subtraction. Commutative Property of Addition Adding In Any Order : Add and Subtract Commutative Property of Addition Demonstrate an ability to organize objects into categories, Sorting by sorting and classifying objects using two attributes Tallies simultaneously. Gather data to answer a question, using a simple survey with a limited number of responses. Collect and organize primary data that is categorical or discrete, and display the data using one-to-one correspondence in concrete graphs, pictographs, line plots, simple bar graphs, and other graphic organizers, with appropriate titles and labels and with labels ordered appropriately along horizontal axes, as needed. Read primary data presented in concrete graphs, pictographs, line plots, simple bar graphs, and other graphic organizers, and describe the data using mathematical language. Sorting 1 Tallies Making Graphs Bar Graphs 1 Bar Graphs 2 Read Graphs Dot Plots Reading From a Bar Chart Pictographs Grade 2 Operations with Grade 2 Operations with Grade 2 Operations with Grade 2 Chance and Grade 2 Chance and Grade 2 Chance and 3P Learning 18

22 Ontario Grade 2 and Probability and Probability and Probability and Probability and Probability ON2.DMP2.2 ON2.DMP2.3 ON2.DMP2.4 Probability ON2.DMP3.1 Probability ON2.DMP3.2 Pose and answer questions about class generated data in concrete graphs, pictographs, line plots, simple bar graphs, and tally charts. Distinguish between numbers that represent data values and numbers that represent the frequency of an event. Demonstrate an understanding of data displayed in a graph, by comparing different parts of the data and by making statements about the data as a whole. Describe probability as a measure of the likelihood that an event will occur, using mathematical language. Describe the probability that an event will occur, through investigation with simple games and probability experiments and using mathematical language. Add and Subtract Using Graphs Bar Graphs 1 Bar Graphs 2 Read Graphs Dot Plots Reading from a Bar Chart Pictographs What are the Chances? Will it Happen? Most Likely and Least Likely What are the Chances? Will it Happen? Most Likely and Least Likely What Are the Chances? Grade 2 Chance and Grade 2 Chance and Grade 3 Chance and Grade 3 Chance and Grade 3 Chance and 19 3P Learning

23 Ontario Grade 3 ON3.NS1.1 ON3.NS1.2 ON3.NS1.3 ON3.NS1.4 ON3.NS1.5 ON3.NS1.6 ON3.NS1.7 ON3.NS1.8 ON3.NS.1.9 Represent, compare, and order whole numbers to 1000, using a variety of tools. Read and print in words whole numbers to one hundred, using meaningful contexts. Identify and represent the value of a digit in a number according to its position in the number. Compose and decompose three-digit numbers into hundreds, tens, and ones in a variety of ways, using concrete materials. Round two-digit numbers to the nearest ten, in problems arising from real-life situations. Represent and explain, using concrete materials, the relationship among the numbers 1, 10, 100, and Divide whole objects and sets of objects into equal parts, and identify the parts using fractional names, without using numbers in standard fractional notation. Represent and describe the relationships between coins and bills up to $10. Estimate, count, and represent the value of a collection of coins and bills with a maximum value of $10. Model s Which is Bigger? Which is Smaller? Understanding Place value 1 Place value 2 Place Value to Thousands Understanding Place value 1 Place Value Partitioning Partition Puzzles 2 Repartition Two-digit s Place value 2 Place Value to Thousands Nearest 10? Understanding Place value 1 Place value 2 Place Value to Thousands What Fraction Is Shaded? Shape Fractions Fraction Fruit Sets 1 Fraction Length Models 1 Fraction Length Models 2 Model Fractions Everyday Money Who has the Money? Money Everyday Money Who s got the money? Grade 3 Reading and Understanding Whole s Grade 3 Reading and Understanding Whole s Grade 3 Reading and Understanding Whole s Grade 3 Reading and Understanding Whole s Grade 3 Reading and Understanding Whole s Grade 3 Reading and Understanding Whole s Grade 3 Fractions 3P Learning 20

24 Ontario Grade 3 Counting Counting ON3.NS1.10 ON3.NS2.1 ON3.NS2.2 Operational ON3.NS3.1 Operational ON3.NS3.2 Solve problems that arise from real-life situations and that relate to the magnitude of whole numbers up to Count forward by 1 s, 2 s, 5 s, 10 s, and 100 s to 1000 from various starting points, and by 25 s to 1000 starting from multiples of 25, using a variety of tools and strategies. Count backwards by 2 s, 5 s, and 10 s from 100 using multiples of 2, 5, and as starting points, and count backwards by 100 s from 1000 and any number less than 1000, using a variety of tools and strategies. Solve problems involving the addition and subtraction of two-digit numbers, using a variety of mental strategies. Add and subtract three-digit numbers, using concrete materials, student generated algorithms, and standard algorithms. : Add and Subtract Counting by Twos Counting by Fives Counting by Tens Count by 2s, 5s and 10s Counting by Twos Counting by Fives Counting by Tens Counting Backward Magic Mental Addition Magic Mental Subtraction 3-Digit Differences Add 3-Digit s Add 3-Digit s: Regroup Add Two 2-Digit s Add Two 2-Digit s: Regroup 2-Digit Differences: Regroup 3-Digit Differences: 1 Regrouping 3-Digit Differences: 2 Regroupings 3-Digit Differences with Zeros Add Multi-Digit s 1 Add Three 3-Digit s: Regroup Grade 3 Addition and Subtraction Grade 2 s Grade 2 s Grade 3 Addition and Subtraction Grade 3 Addition and Subtraction 21 3P Learning

25 Ontario Grade 3 Operational ON3.NS3.3 Operational ON3.NS3.4 Operational ON3.NS3.5 Operational ON3.NS3.6 Attributes, Units, and Attributes, Units, and Attributes, Units, and ON3.M1.1 ON3.M1.2 ON3.M1.3 Use estimation when solving problems involving addition and subtraction, to help judge the reasonableness of a solution. Add and subtract money amounts, using a variety of tools, to make simulated purchases and change for amounts up to $10. Relate multiplication of onedigit numbers and division by one-digit divisors to real life situations, using a variety of tools and strategies. Multiply to 7 x 7 and divide to 49 7, using a variety of mental strategies. Estimate, measure, and record length, height, and distance, using standard units. Draw items using a ruler, given specific lengths in centimetres. Read time using analogue clocks, to the nearest five minutes, and using digital clocks, and represent time in 12-hour notation. Estimate Sums Estimate Differences How much Change? Related Facts 2 Multiplication Arrays Times Tables Groups of Two Groups of Three Groups of Four Groups of Five Groups of Six Groups of Seven Arrays 1 Multiplication Grids Model Multiplication to 5 x 5 Frog Jump Multiplication Dividing Twos Dividing Threes Dividing Fours Dividing Fives Dividing Sixes Dividing Sevens How Long is That? Perimeter Perimeter of Shapes How Long is That? Perimeter Perimeter of Shapes Five Minute Times Quarter to and Quarter past Grade 3 Addition and Subtraction Grade 3 Addition and Subtraction Grade 3 Multiplication and Division Grade 3 Multiplication and Division Grade 3 Grade 3 Grade 3 Time 3P Learning 22

26 Ontario Grade 3 Attributes, Units, and Attributes, Units, and Attributes, Units, and Attributes, Units, and ON3.M1.4 ON3.M1.5 ON3.M1.6 ON3.M1.7 Estimate, read, and record positive temperatures to the nearest degree Celsius. Identify benchmarks for freezing, cold, cool, warm, hot, and boiling temperatures as they relate to water and for cold, cool, warm, and hot temperatures as they relate to air. Estimate, measure, and record the perimeter of twodimensional shapes, through investigation using standard units. Estimate, measure, and record area. Temperature Temperature Perimeter of Shapes Perimeter Calculate Perimeter of Squares and Rectangles Bigger or Smaller Shape Perimeter: Triangles Perimeter Detectives 1 Area of Shapes Equal Areas Grade 3 Grade 3 Attributes, Units, and ON3.M1.8 Choose benchmarks for a kilogram and a litre to help them perform measurement tasks. Kilogram Conversions Everyday Mass Using a Litre Litre Conversions Grade 3 Attributes, Units, and Attributes, Units, and ON3.M1.9 ON3.M1.10 ON3.M2.1 ON3.M2.2 Estimate, measure, and record the mass of objects, using the standard unit of the kilogram or parts of a kilogram. Estimate, measure, and record the capacity of containers, using the standard unit of the litre or parts of a litre. Compare standard units of length, and select and justify the most appropriate standard unit to measure length. Compare and order objects on the basis of linear measurements in centimetres and/or metres in problemsolving contexts. Kilogram Conversions Everyday Mass Using a Litre Litre Conversions Which Measuring Tool? Which Unit of? Which Unit of? Which Measuring Tool? Grade 3 Grade P Learning

27 Ontario Grade 3 Compare and order various shapes ON3.M2.3 by area, using congruent shapes and grid paper for measuring. Describe, through investigation using grid paper, the relationship between ON3.M2.4 the size of a unit of area and the number of units needed to cover a surface. Spatial Spatial Spatial Spatial Spatial Spatial Spatial Properties Properties Properties Properties Properties ON3.M2.5 ON3.M2.6 ON3.G1.1 ON3.G1.2 ON3.G1.3 ON3.G1.4 ON3.G1.5 ON3.G2.1 ON3.G2.2 Compare and order a collection of objects, using standard units of mass and/or capacity. Solve problems involving the relationships between minutes and hours, hours and days, days and weeks, and weeks and years, using a variety of tools. Use a reference tool to identify right angles and to describe angles as greater than, equal to, or less than a right angle. Identify and compare various polygons and sort them by their geometric properties. Compare various angles, using concrete materials and pictorial representations, and describe angles as bigger than, smaller than, or about the same as other angles. Compare and sort prisms and pyramids by geometric properties, using concrete materials. Construct rectangular prisms, and describe geometric properties of the prisms. Solve problems requiring the greatest or least number of two-dimensional shapes needed to compose a larger shape. Explain the relationships between different types of quadrilaterals. Equal Areas Bigger or Smaller Shape Equal Areas Bigger or Smaller Shape Equal Areas Right Angle Relation Comparing Angles Equal Angles Collect the Polygons Count Sides and Corners Faces, Edges and Vertices Equal Angles Comparing Angles How many Faces? How many Edges? How many Corners? Faces, Edges and Vertices Collect the Objects Relate Shapes and Solids Grade 3 Grade 3 Grade 3 Grade 2 Time Grade 5 Geometry Grade 5 Geometry Grade 5 Geometry Grade 5 Geometry Grade 5 Geometry Grade 5 Geometry 3P Learning 24

28 Ontario Grade 3 Spatial Spatial Spatial Spatial Spatial Spatial Patterning and Patterning and Patterning and Location and Movement Location and Movement Location and Movement ON3.G2.3 ON3.G2.4 ON3.G2.5 ON3.G3.1 ON3.G3.2 ON3.G3.3 ON3.PA1.1 ON3.PA1.2 ON3.PA1.3 Identify and describe the twodimensional shapes that can be found in a three-dimensional figure. Describe and name prisms and pyramids by the shape of their base. Identify congruent twodimensional shapes by manipulating and matching concrete materials. Describe movement from one location to another using a grid map. Identify flips, slides, and turns, through investigation using concrete materials and physical motion, and name flips, slides, and turns as reflections, translations, and rotations. Complete and describe designs and pictures of images that have a vertical, horizontal, or diagonal line of symmetry. Identify, extend, and create a repeating pattern involving two attributes, using a variety of tools. Identify and describe, through investigation, number patterns involving addition, subtraction, and multiplication, represented on a number line, on a calendar, and on a hundreds chart. Extend repeating, growing, and shrinking number patterns. Relate Shapes and Solids Grade 5 Geometry What Pyramid am I? What Prism am I? Collect the Objects Congruent Figures Following Directions Using a Key Flip, Slide, Turn Transformations Symmetry Symmetry or Not? Simple Patterns Pattern Error Missing it! Complete the Pattern Simple Patterns Pattern Error Missing it! Complete the Pattern Increasing Patterns Decreasing Patterns Pick the Next Count Forward Patterns Count Backward Patterns Grade 5 Geometry Grade 5 Geometry Grade 5 Geometry Grade 5 Geometry Grade P Learning

29 Ontario Grade 3 Patterning and Patterning and Patterning and Patterning and Patterning and Patterning and Patterning and and Probability and Probability Expressions and Equality Expressions and Equality Expressions and Equality Expressions and Equality Collection and Organization of Collection and Organization of ON3.PA1.4 ON3.PA1.5 ON3.PA1.6 ON3.PA2.1 ON3.PA2.2 ON3.PA2.3 ON3.PA2.4 ON3.DP1.1 ON3.DP1.2 Create a number pattern involving addition or subtraction, given a pattern represented on a number line or a pattern rule expressed in words. Represent simple geometric patterns using a number sequence, a number line, or a bar graph. Demonstrate, through investigation, an understanding that a pattern results from repeating an action, repeating an operation, using a transformation, or making some other repeated change to an attribute. Determine, through investigation, the inverse relationship between addition and subtraction. Determine, the missing number in equations involving addition and subtraction of one and twodigit numbers, using a variety of tools and strategies. Identify, through investigation, the properties of zero and one in multiplication. Identify, through investigation, and use the associative property of addition to facilitate computation with whole numbers. Demonstrate an ability to organize objects into categories, by sorting and classifying objects using two or more attributes simultaneously. Collect data by conducting a simple survey about themselves, their environment, issues in their school or community, or content from another subject. Increasing Patterns Decreasing Patterns Pick the Next Count Forward Patterns Count Backward Patterns Increasing Patterns Decreasing Patterns Pick the Next Count Forward Patterns Count Backward Patterns Describing Patterns Related Facts 1 Missing s Missing Values Concept of Zero Commutative Property of Addition Addition Properties Sort It Sort It Sorting 1 Grade 3 Grade 3 Grade 3 Grade 3 Addition and Subtraction Grade 3 Addition and Subtraction Grade 3 Addition and Subtraction Grade 3 Addition and Subtraction Grade 3 Chance and Grade 3 Chance and 3P Learning 26

30 Ontario Grade 3 and Probability and Probability and Probability and Probability and Probability Collection and Organization of Probability ON3.DP1.3 ON3.DP2.1 ON3.DP2.2 ON3.DP2.3 ON3.DP3.1 Collect and organize categorical or discrete primary data and display the data in charts, tables, and graphs, with appropriate titles and labels and with labels ordered appropriately along horizontal axes, as needed, using many-to-one correspondence. Read primary data presented in charts, tables, and graphs, then describe the data using comparative language, and describe the shape of the data. Interpret and draw conclusions from data presented in charts, tables, and graphs. Demonstrate an understanding of mode, and identify the mode in a set of data. Predict the frequency of an outcome in a simple probability experiment or game, then perform the experiment, and compare the results with the predictions, using mathematical language. Making Picture Graphs: With Scale Sorting Pictographs Bar Graphs 1 Interpreting Tables Bar Graphs 2 Reading from a Bar Chart Mode Mode from Frequency Table Simple Probability Most Likely and Least Likely Grade 3 Chance and Grade 3 Chance and Grade 3 Chance and Grade 6 Representation Grade 3 Chance and and Probability Probability ON3.DP3.2 Demonstrate, through investigation, an understanding of fairness in a game and relate this to the occurrence of equally likely outcomes. What are the Chances? Most Likely and Least Likely Simple Probability Fair Games Grade 3 Chance and 27 3P Learning

31 Ontario Grade 4 ON4.NS1.1 ON4.NS1.2 ON4.NS1.3 ON4.NS1.4 ON4.NS1.5 ON4.NS1.6 Represent, compare, and order whole numbers to , using a variety of tools. Demonstrate an understanding of place value in whole numbers and decimal numbers from 0.1 to , using a variety of tools and strategies. Read and print in words whole numbers to one thousand, using meaningful contexts. Round four-digit whole numbers to the nearest ten, hundred, and thousand, in problems arising from real-life situations. Represent, compare, and order decimal numbers to tenths, using a variety of tools and using standard decimal notation. Represent fractions using concrete materials, words, and standard fractional notation, and explain the meaning of the denominator as the number of the fractional parts of a whole or a set, and the numerator as the number of fractional parts being considered. Place Value to Thousands Ascending Order Descending Order Greater Than or Less Than? Place value 3 Which Is Greater? Which Is Less? Place Value to Thousands Understanding Place Value 3 Greater Than or Less Than? Place value 3 Which Is Greater? Which Is Less? Expanding s Place Value to Thousands Greater Than or Less Than? Place value 3 Which Is Greater? Which Is Less? Nearest Thousand? Identifying fractions beyond 1 Counting with Fractions on a Line Halves and Quarters What Fraction is Shaded? Identifying Fractions on a Line Grade 4 Reading and Understanding Whole s Grade 4 Reading and Understanding Whole s Grade 4 Reading and Understanding Whole s Grade 4 Reading and Understanding Whole s Grade 4 Fractions 3P Learning 28

32 Ontario Grade 4 Strand Substrand Expectation Expectation Description ON4.NS1.7 ON4.NS1.8 Compare and order fractions by considering the size and the number of fractional parts. Compare fractions to the benchmarks of 0, 1/2, and 1. Activities ebooks Fraction Fruit Sets 1 Ordering Fractions Comparing Fractions 1a Comparing Fractions 1b Equivalent Fractions Ordering Fractions Comparing Fractions 1 Comparing Fractions 1a Comparing Fractions 1b Comparing Fractions 2 Compare Fractions 2 Equivalent Fractions Grade 4 Fractions Grade 4 Fractions ON4.NS1.9 Demonstrate and explain the relationship between equivalent fractions, using concrete materials and drawings. Equivalent Fractions on a Line 1 Shading Equivalent Fractions Equivalent Fractions Equivalent Fraction Wall 1 Fraction Wall Labelling 1 Grade 4 Fractions Counting Counting ON4.NS1.10 ON4.NS1.11 ON4.NS2.1 ON4.NS2.2 Read and represent money amounts to $100 Solve problems that arise from real-life situations and that relate to the magnitude of whole numbers up to Count forward by halves, thirds, fourths, and tenths to beyond one whole, using concrete materials and number lines. Count forward by tenths from any decimal number expressed to one decimal place, using concrete materials and number lines. Money Everyday Money Who has the Money? Word with Letters Counting with Fractions on a Line Identifying fractions beyond 1 Grade 4 Addition and Subtraction Grade 4 Addition and Subtraction Grade 4 Fractions 29 3P Learning

33 Ontario Grade 4 Operational Operational ON4.NS3.1 ON4.NS3.2 Add and subtract twodigit numbers, using a variety of mental strategies. Solve problems involving the addition and subtraction of four-digit numbers, using studentgenerated algorithms and standard algorithms. Mental Addition Add Three 2-Digit s: Regroup Add Three 3-Digit s: Regroup Mental Addition Magic Mental Subtraction Add Two 2-Digit s Add Two 2-Digit s: Regroup Add Three 2-Digit s 2-Digit Differences 2-Digit Differences: Regroup Magic Symbols 1 Magic Symbols 2 Adding Colossal Columns Subtracting Colossal Columns Add 3-Digit s Add 3-Digit s: Regroup 3-Digit Differences with Zeros 3-Digit Differences: 1 Regrouping 3-Digit Differences: 2 Regroupings Estimate Sums Estimate Differences Grade 4 Addition and Subtraction Grade 4 Addition and Subtraction Operational ON4.NS3.3 Add and subtract decimal numbers to tenths, using concrete materials and student-generated algorithms. Add Decimals 1 Subtract Decimals 1 Grade 4 Fractions, Decimal and Percentages Operational Operational ON4.NS3.4 ON4.NS3.5 Add and subtract money amounts by making simulated purchases and providing change for amounts up to $100, using a variety of tools. Multiply to 9 x 9 and divide to 81 9, using a variety of mental strategies. How much Change? Fact Families: Multiply and Divide Arrays 2 Groups of Eight Groups of Nine Dividing Eights Dividing Nines Times Tables Grade 4 Addition and Subtraction Grade 4 Multiplication and Division 3P Learning 30

34 Ontario Grade 4 Operational Operational Operational Operational Operational Proportional ON4.NS3.6 ON4.NS3.7 ON4.NS3.8 ON4.NS3.9 ON4.NS3.10 ON4.NS4.1 Solve problems involving the multiplication of one-digit whole numbers, using a variety of mental strategies. Multiply whole numbers by 10, 100, and 1000, and divide whole numbers by 10 and 100, using mental strategies. Multiply two-digit whole numbers by one-digit whole numbers, using a variety of tools, student-generated algorithms, and standard algorithms. Divide two-digit whole numbers by one digit whole numbers, using a variety of tools and student-generated algorithms. Use estimation when solving problems involving the addition, subtraction, and multiplication of whole numbers, to help judge the reasonableness of a solution. Describe relationships that involve simple whole-number multiplication. Multiplication Facts Fact Families: Multiply and Divide Groups of Eight Groups of Nine Times Tables Multiplying by 10, 100, 1000 Dividing Tens Multiply Multiples of 10 Estimation: Multiply and Divide Multiply: 1-Digit : Regroup Multiply: 1-Digit Multiply: 2-Digit by 1-Digit Equivalent Facts: Multiply Multiply and Divide 1 Multiplication 1 Missing s: x and facts Dividing Eights Remainders by Arrays Division Facts 1 Halve it! Division Facts Remainders by Arrays Divide: 1-Digit Divisor 1 Dividing Nines Divide: 1-Digit Divisor 2 Divide: 1-Digit Divisor, Remainder Estimation: Multiply and Divide Estimate Differences Estimate Sums Estimate Products Multiply: 1-Digit Multiply: 2-Digit by 1-Digit Fact Families: Multiply and Divide Grade 4 Multiplication and Division Grade 4 Multiplication and Division Grade 4 Multiplication and Division Grade 4 Multiplication and Division Grade 4 Addition and Subtraction Grade 4 Multiplication and Division 31 3P Learning

35 Ontario Grade 4 and and Proportional Proportional Attributes, Units and ON4.NS4.2 ON4.NS4.3 ON4.M1.1 Determine and explain, through investigation, the relationship between fractions and decimals to tenths, using a variety of tools and strategies. Demonstrate an understanding of simple multiplicative relationships involving unit rates, through investigation using concrete materials and drawings. Estimate, measure, and record length, height, and distance, using standard units. How Long is That? Measuring Length Grade 4 Length, Area and Perimeter Attributes, Units and ON4.M1.2 Draw items using a ruler, given specific lengths in millimetres or centimetres. Attributes, Units and ON4.M1.3 Estimate, measure, and represent time intervals to the nearest minute. Time Mentals Elapsed Time What Time Will it Be? Grade 3 Time Attributes, Units and ON4.M1.4 Estimate and determine elapsed time, with and without using a time line, given the durations of events expressed in fiveminute intervals, hours, days, weeks, months, or years. Time Mentals Elapsed Time What Time Will it Be? Grade 3 Time Attributes, Units and ON4.M1.5 Estimate, measure using a variety of tools and strategies, and record the perimeter and area of polygons. Perimeter of Shapes Perimeter Perimeter: Squares and Rectangles Perimeter Detectives 1 Perimeter: Triangles Area of Shapes Equal Areas Area: Squares and Rectangles Area: Quadrilaterals Grade 4 Length, Area and Perimeter 3P Learning 32

36 Ontario Grade 4 Attributes, Units and Attributes, Units and Attributes, Units and ON4.M1.6 ON4.M1.7 ON4.M1.8 ON4.M2.1 ON4.M2.2 Estimate, measure, and record the mass of objects, using the standard units of the kilogram and the gram. Estimate, measure, and record the capacity of containers, using the standard units of the litre and the millilitre. Estimate, measure using concrete materials, and record volume, and relate volume to the space taken up by an object. Describe, through investigation, the relationship between various units of length. Select and justify the most appropriate standard unit to measure the side lengths and perimeters of various polygons. How Heavy? Grams and Kilograms Kilogram Conversions Using a Litre Comparing Volume Centimetres and Metres Converting cm and mm Kilometre Conversions Metres and Kilometres Which Measuring Tool? Grade 4 Volume, Capacity and Mass Grade 4 Volume, Capacity and Mass Grade 4 Volume, Capacity and Mass Grade 4 Length, Area and Perimeter Grade 4 Length, Area and Perimeter ON4.M2.3 Determine, through investigation, the relationship between the side lengths of a rectangle and its perimeter and area. Perimeter of Shapes Perimeter Perimeter: Squares and Rectangles Area: Squares and Rectangles Grade 4 Length, Area and Perimeter ON4.M2.4 Pose and solve meaningful problems that require the ability to distinguish perimeter and area. Perimeter of Shapes Perimeter Perimeter: Squares and Rectangles Perimeter: Triangles Area: Squares and Rectangles Calculate Perimeter of Squares and Rectangles Grade 4 Length, Area and Perimeter 33 3P Learning

37 Ontario Grade 4 Spatial Spatial Properties Properties ON4.M2.5 ON4.M2.6 ON4.M2.7 ON4.M2.8 ON4.M2.9 ON4.M2.10 ON4.GS1.1 ON4.GS1.2 Compare and order a collection of objects, using standard units of mass and/or capacity. Determine, through investigation, the relationship between grams and kilograms. Determine, through investigation, the relationship between millilitres and litres. Comparing Volume Kilogram Conversions Grams and Kilograms Litre Conversions Using a Litre Millilitres and Litres Select and justify the most appropriate standard unit to measure mass and the Which measuring most appropriate standard tool? unit to measure the capacity of a container. Solve problems involving the relationship between years and decades, and between decades and centuries. Compare, using a variety of tools, two-dimensional shapes that have the same perimeter or the same area. Which measuring tool? Which measuring tool? Draw the lines of symmetry of twodimensional shapes, Symmetry or Not? Symmetry through investigation using a variety of tools and Lines of Symmetry strategies. Identify and compare different types of quadrilaterals and sort Collect the Shapes 2 and classify them by their geometric properties. Grade 4 Volume, Capacity and Mass Grade 4 Volume, Capacity and Mass Grade 4 Volume, Capacity and Mass Grade 4 Space, Shape and Position 3P Learning 34

38 Ontario Grade 4 Spatial Spatial Spatial Spatial Spatial Spatial Properties Properties Properties ON4.GS1.3 ON4.GS1.4 ON4.GS1.5 ON4.GS2.1 ON4.GS2.2 ON4.GS2.3 Identify benchmark angles, using a reference tool, and compare other angles to these benchmarks. Relate the names of the benchmark angles to their measures in degrees. Identify and describe prisms and pyramids and classify them by their geometric properties. Construct a threedimensional figure from a picture or model of the figure, using connecting cubes. Construct skeletons of three-dimensional figures, using a variety of tools, and sketch the skeletons. Draw and describe nets of rectangular and triangular prisms. Right Angle Relation Classifying Angles Comparing Angles Measuring Angles Estimating Angles Right Angle Relation Classifying Angles Comparing Angles Measuring Angles Estimating Angles Equal Angles Prisms and Pyramids Faces, Edges and Vertices Grade 4 Space, Shape and Position Grade 4 Space, Shape and Position Grade 4 Space, Shape and Position Grade 5 Geometry Grade 5 Geometry Spatial ON4.GS2.4 Construct prisms and pyramids from given nets. Grade 5 Geometry Spatial Spatial Spatial Location and Movement Location and Movement ON4.GS2.5 ON4.GS3.1 ON4.GS3.2 Construct threedimensional figures, using only congruent shapes. Identify and describe the general location of an object using a grid system. Identify, perform, and describe reflections using a variety of tools. Congruent Figures Map Coordinates Coordinate Meeting Place Flip, Slide, Turn Grade 5 Geometry Grade 4 Space, Shape and Position Grade 5 Geometry 35 3P Learning

39 Ontario Grade 4 Spatial Patterning and Patterning and Patterning and Patterning and Patterning and Patterning and Patterning and Location and Movement Expressions and Equality Expressions and Equality ON4.GS3.3 ON4.PA1.1 ON4.PA1.2 ON4.PA1.3 ON4.PA1.4 ON4.PA1.5 ON4.PA2.1 ON4.PA2.2 Create and analyse symmetrical designs by reflecting a shape, or shapes, using a variety of tools, and identify the congruent shapes in the designs. Extend, describe, and create repeating, growing, and shrinking number patterns. Connect each term in a growing or shrinking pattern with its term number, and record the patterns in a table of values that shows the term number and the term. Create a number pattern involving addition, subtraction, or multiplication, given a pattern rule expressed in words. Make predictions related to repeating geometric and numeric patterns. Extend and create repeating patterns that result from reflections, through investigation using a variety of tools. Determine, through investigation, the inverse relationship between multiplication and division. Determine the missing number in equations involving multiplication of one and twodigit numbers, using a variety of tools and strategies. Congruent Figures Pick the Next Increasing Patterns Decreasing Patterns Table of Values Table of Values Pick the Next Increasing Patterns Decreasing Patterns I am Thinking of a Describing Patterns Related Facts 2 Find the Missing 1 Magic Symbols 1 Magic Symbols 2 Grade 5 Geometry Grade 4 Grade 4 Grade 4 Grade 4 Grade 4 Grade 4 Multiplication and Division Grade 4 3P Learning 36

40 Ontario Grade 4 Patterning and Patterning and and Probability and Probability and Probability and Probability and Probability and Probability Expressions and Equality Expressions and Equality Collection and organization Collection and organization ON4.PA2.3 ON4.PA2.4 ON4.DMP1.1 ON4.DMP1.2 ON4.DMP2.1 ON4.DMP2.2 ON4.DMP2.3 ON4.DMP2.4 Identify, through investigation, and use the commutative property of multiplication to facilitate computation with whole numbers. Identify, through investigation, and use the distributive property of multiplication over addition to facilitate computation with whole numbers. Collect data by conducting a survey or an experiment to do with themselves, their environment, issues in their school or the community, or content from another subject, and record observations or measurements. Collect and organize discrete primary data and display the data in charts, tables, and graphs that have appropriate titles, labels, and scales that suit the range and distribution of the data, using a variety of tools. Read, interpret, and draw conclusions from primary data and from secondary data, presented in charts, tables, and graphs. Demonstrate, through investigation, an understanding of median, and determine the median of a set of data. Describe the shape of a set of data across its range of values, using charts, tables, and graphs. Compare similarities and differences between two related sets of data, using a variety of strategies. Arithmetic Laws Multiplication Properties Solve : Multiply, Divide 1 Bar Chart Divided Bar Graphs Bar Graphs 1 Reading from a Bar Chart Divided Bar Graphs Mode Mode from Stem and Leaf Plot Stem and Leaf Introduction Stem-and-Leaf Plots Median The Median Median from Stem and Leaf Plot Median The Median Median from Stem and Leaf Plot Median The Median Median from Stem and Leaf Plot Grade 4 Addition and Subtraction Grade 4 Multiplication and Division Grade 4 Chance and Grade 5 Representation 37 3P Learning

41 Ontario Grade 4 and Probability and Probability Probability Probability ON4.DMP3.1 ON4.DMP3.2 Predict the frequency of an outcome in a simple probability experiment, explaining their reasoning conduct the experiment and compare the result with the prediction. Determine, through investigation, how the number of repetitions of a probability experiment can affect the conclusions drawn. Possible Outcomes Probability Scale Introductory Probability Possible Outcomes Probability Scale Grade 4 Chance and Grade 4 Chance and 3P Learning 38

42 Ontario Grade 5 and and and and ON5.NS1.1 ON5.NS1.2 ON5.NS1.3 ON5.NS1.4 Represent, compare, and order whole numbers and decimal numbers from 0 to , using a variety of tools. Demonstrate an understanding of place value in whole numbers and decimal numbers from 0 to , using a variety of tools and strategies. Read and print in words whole numbers to ten thousand, using meaningful contexts. Round decimal numbers to the nearest tenth, in problems arising from reallife situations. Nearest Whole Place Value Partitioning Comparing Decimals 1 Decimal Order 1 Place Value to Thousands Greater Than or Less Than? Greater Than or Less? Expanding s Decimal Place Value Understanding Place Value 3 Place Value 1 (x 10 and 10) Nearest Whole Comparing Decimals 1 Decimal Order 1 Decimal Place Value Place Value to Thousands Greater Than or Less Than? Greater Than or Less? Expanded Notation Expanding s Decimals from Words to Digits 1 Place value 3 s in Words Rounding Decimals 1 Nearest Whole Grade 5 Reading and Understanding Whole s Grade 5 Reading and Understanding Whole s Grade 5 Reading and Understanding Whole s Grade 5 Fractions, Decimals and Percentages 39 3P Learning

43 Ontario Grade 5 ON5.NS1.5 ON5.NS1.6 ON5.NS1.7 ON5.NS1.8 ON5.NS1.9 Counting ON5.NS2.1 Represent, compare, and order fractional amounts with like denominators, including proper and improper fractions and mixed numbers, using a variety of tools and using standard fractional notation. Demonstrate and explain the concept of equivalent fractions, using concrete materials. Demonstrate and explain equivalent representations of a decimal number, using concrete materials and drawings. Read and write money amounts to $1000. Solve problems that arise from real-life situations and that relate to the magnitude of whole numbers up to Count forward by hundredths from any decimal number expressed to two decimal places, using concrete materials and number lines. Fraction Wall Labelling 1 Equivalent Fraction Wall 1 Mixed and Improper Fractions on a Line Identifying Fractions Beyond 1 Fractions on a Line What Mixed Is Shaded? Identifying Fractions on a Line Mixed to Improper Improper to Mixed Ordering Fractions Comparing Fractions 1 Comparing Fractions 2 Compare Fractions 1a Compare Fractions 1b Compare Fractions 2 Part-Whole Rods 1 Part-Whole Rods 2 Equivalent Fractions Shading Equivalent Fractions Equivalent Fractions on a Line 1 Equivalent Fractions on a Line 2 Decimals to Fractions 2 Fractions to Decimals 2 Money Who s got the Money? How much Change? Word : Multiply and Divide : Multiply and Divide Multiply and Divide 1 : Add and Subtract 1 Word with Letters Decimals on a Line Decimals on the Line Decimal Place Value Grade 5 Fractions, Decimals and Percentages Grade 5 Fractions, Decimals and Percentages Grade 5 Fractions, Decimals and Percentages Grade 5 Fractions, Decimals and Percentages 3P Learning 40

44 Ontario Grade 5 Operational Operational Operational ON5.NS3.1 ON5.NS3.2 ON5.NS3.3 Solve problems involving the addition, subtraction, and multiplication of whole numbers, using a variety of mental strategies Add and subtract decimal numbers to hundredths, including money amounts, using concrete materials, estimation, and algorithms. Multiply two-digit whole numbers by two-digit whole numbers, using estimation, studentgenerated algorithms, and standard algorithms. Magic Mental Addition Magic Mental Subtraction Adding Colossal Columns Repartition to Subtract Compensation-Add Compensation-Subtract Subtracting Colossal Columns Mental Methods Multiplication 1 Mental Methods Multiplication 2 Mental Methods Multiplication 3 Bump Add and Subtract Jump Add and Subtract Multiply: 2-Digit by 1-Digit Multiply: 1-Digit, Regroup Multiply: 2-Digit, Regroup Money Add Decimals 1 Subtract Decimals 1 Decimal Complements Adding Decimals Subtracting Decimals Adding and Subtracting Decimals Arrays 2 Contracted Multiplication Multiply: 1-Digit Long Multiplication Multiply: 2 Digit, Regroup Multiply: 2-Digit by 1-Digit Multiply: 1-Digit, Regroup Mental Methods Multiplication 1 Multiply Multiples of 10 Multiplying by 10, 100, 1000 Mental Methods Multiplication 1 Mental Methods Multiplication 2 Mental Methods Multiplication 3 Multiply 2 Digits Area Model Double and Halve to Multiply Double and Halve to Multiply Multiply 3 single-digit numbers Estimate Products Grade 5 Addition and Subtraction Grade 5 Multiplication and Division Grade 5 Fractions, Decimals and Percentages Grade 5 Multiplication and Division 41 3P Learning

45 Ontario Grade 5 and and and and and Operational Operational Operational Proportional Proportional ON5.NS3.4 ON5.NS3.5 ON5.NS3.6 ON5.NS4.1 ON5.NS4.2 Divide three-digit whole numbers by one-digit whole numbers, using concrete materials, estimation, studentgenerated algorithms, and standard algorithms. Multiply decimal numbers by 10, 100, 1000, and , and divide decimal numbers by 10 and 100, using mental strategies. Use estimation when solving problems involving the addition, subtraction, multiplication, and division of whole numbers, to help judge the reasonableness of a solution. Describe multiplicative relationships between quantities by using simple fractions and decimals. Determine and explain, through investigation using concrete materials, drawings, and calculators, the relationship between fractions and their equivalent decimal forms. Divide: 1-Digit Divisor 1 Divide: 1-Digit Divisor 2 Estimate Quotients Short Division Long Division Long Division by Whole s Divide: 1-Digit Divisor, Remainder Estimation: Multiply and Divide Estimate Quotients Mental Methods Division Mental Methods Division 2 Mental Methods Division 3 Division Facts to Twelve Estimate Quotients Multiply Decimals: 10, 100, 1000 Multiply Decimals and Powers of 10 Divide Decimals: 10, 100, 1000 Divide by Powers of 10 Divide decimals by powers of Estimation: Add and Subtract Estimate Sums Estimate Differences Estimate Quotients Estimate Products Estimation: Multiply and Divide Fractions to Decimals 2 Decimals to Fractions 2 Grade 5 Multiplication and Division Grade 5 Multiplication and Division Grade 5 Fractions, Decimals and Percentages Grade 5 Addition and Subtraction Grade 5 Multiplication and Division Grade 5 Fractions, Decimals and Percentages 3P Learning 42

46 Ontario Grade 5 and Proportional Attributes, Units, and Attributes, Units, and Attributes, Units, and ON5.NS4.3 ON5.M1.1 ON5.M1.2 ON5.M1.3 Demonstrate an understanding of simple multiplicative relationships involving whole-number rates, through investigation using concrete materials and drawings. Estimate, measure, and represent time intervals to the nearest second. Estimate and determine elapsed time, with and without using a time line, given the durations of events expressed in minutes, hours, days, weeks, months, or years. Measure and record temperatures to determine and represent temperature changes over time. Rates Word Rates Elapsed Time Time Mentals 24 Hour Time Time Mentals Elapsed Time What Time Will it Be? Temperature Grade 4 Time Grade 4 Time ON5.M1.4 Estimate and measure the perimeter and area of regular and irregular polygons, using a variety of tools and strategies. Perimeter of Shapes Perimeter Perimeter: Triangles Area: Squares and Rectangles Perimeter: Squares and Rectangles 1 Area of Shapes Perimeter Detectives 1 Grade 5 Length, Area and Perimeter ON5.M2.1 Select and justify the most appropriate standard unit to measure length, height, width, and distance, and to measure the perimeter of various polygons. Perimeter of Shapes Perimeter Perimeter: Squares and Rectangles 1 Perimeter: Triangles Perimeter Detectives 1 Grade 5 Length, Area and Perimeter 43 3P Learning ON5.M2.2 Solve problems requiring conversion from metres to centimetres and from kilometres to metres. Kilometre Conversions Converting cm and mm Grade 5 Length, Area and Perimeter

47 Ontario Grade 5 ON5.M2.3 ON5.M2.4 ON5.M2.5 ON5.M2.6 ON5.M2.7 ON5.M2.8 ON5.M2.9 Solve problems involving the relationship between a 12-hour clock and a 24- hour clock. Create, through investigation using a variety of tools and strategies, twodimensional shapes with the same perimeter or the same area. Determine, through investigation using a variety of tools and strategies, the relationships between the length and width of a rectangle and its area and perimeter, and generalize to develop the formulas. Solve problems requiring the estimation and calculation of perimeters and areas of rectangles. Determine, through investigation, the relationship between capacity and volume, by comparing the volume of an object with the amount of liquid it can contain or displace. Determine, through investigation using stacked congruent rectangular layers of concrete materials, the relationship between the height, the area of the base, and the volume of a rectangular prism, and generalize to develop the formula. Select and justify the most appropriate standard unit to measure mass. 24 Hour Time Grade 4 Time Perimeter: Squares and Rectangles 1 Area: Squares and Rectangles Perimeter: Squares and Rectangles 1 Area: Squares and Rectangles Volume: Rectangular Prisms 2 Volume: Rectangular Prisms 1 Volume: Rectangular Prisms 2 Volume: Rectangular Prisms 1 Grams and Kilograms Which measuring tool? Grade 5 Length, Area and Perimeter Grade 5 Length, Area and Perimeter Grade 5 Volume, Capacity and Mass Grade 5 Volume, Capacity and Mass Grade 5 Length, Area and Perimeter Grade 5 Volume, Capacity and Mass 3P Learning 44

48 Ontario Grade 5 Spatial Spatial Spatial Spatial Spatial Spatial Spatial Spatial Spatial Spatial Spatial Properties Properties Properties Properties Properties Properties Location and Movement Location and Movement Location and Movement ON5.GS1.1 ON5.GS1.2 ON5.GS1.3 ON5.GS1.4 ON5.GS1.5 ON5.GS1.6 ON5.GS2.1 ON5.GS2.2 ON5.GS3.1 ON5.GS3.2 ON5.GS3.3 Distinguish among polygons, regular polygons, and other two-dimensional shapes. Distinguish among prisms, right prisms, pyramids, and other three-dimensional figures. Identify and classify acute, right, obtuse, and straight angles. Measure and construct angles up to 90º, using a protractor. Identify triangles, and classify them according to angle and side properties. Construct triangles, using a variety of tools, given acute or right angles and side measurements. Identify prisms and pyramids from their nets. Construct nets of prisms and pyramids, using a variety of tools. Locate an object using the cardinal directions and a coordinate system. Compare grid systems commonly used on maps. Identify, perform, and describe translations, using a variety of tools. Collect More Shapes Collect the Polygons Prisms and Pyramids Collect the Objects 1 Collect the Objects 2 Right and Oblique Objects What Type of Angle? Classifying Angles Measuring Angles Estimating Angles Triangle Tasters Triangles: Acute, Right, Obtuse Triangle Tasters Triangles: Acute, Right, Obtuse What Direction was That? More Directions! Map Coordinates Coordinate Meeting Place What Direction was That? More Directions! Map Coordinates Coordinate Meeting Place Flip, Slide, Turn Transformations Rotational Symmetry Grade 5 Geometry Grade 5 Geometry Grade 5 Geometry Grade 5 Geometry Grade 5 Geometry Grade 5 Geometry Grade 5 Geometry Grade 5 Geometry Grade 5 Position Grade 5 Position Grade 5 Geometry 45 3P Learning

49 Ontario Grade 5 Spatial Patterning and Patterning and Patterning and Patterning and Patterning and Patterning and Patterning and Location and Movement Variables, Expressions and Variables, Expressions and ON5.GS3.4 ON5.PA1.1 ON5.PA1.2 ON5.PA1.3 ON5.PA1.4 ON5.PA1.5 ON5.PA2.1 ON5.PA2.2 Create and analyse designs by translating and/or reflecting a shape, or shapes, using a variety of tools. Create, identify, and extend numeric and geometric patterns, using a variety of tools. Build a model to represent a number pattern presented in a table of values that shows the term number and the term. Make a table of values for a pattern that is generated by adding or subtracting a number to get the next term, or by multiplying or dividing by a constant to get the next term, given either the sequence or the pattern rule in words. Make predictions related to growing and shrinking geometric and numeric patterns. Flip, Slide, Turn Transformations Rotational Symmetry Pattern Error Describing Patterns Table of Values Find the Missing 1 Missing Values Find the Function Rule Missing s: Variables Increasing Patterns Decreasing Patterns Extend and create repeating patterns that Increasing Patterns result from translations, through investigation using Decreasing Patterns a variety of tools. Demonstrate, through investigation, an understanding of variables as changing quantities, given equations with letters or other symbols that describe relationships involving simple rates. Demonstrate, through investigation, an understanding of variables as unknown quantities represented by a letter or other symbol. Write an Equation: Word Write an Equation: Word Grade 5 Geometry Grade 5 Grade 5 Grade 5 Grade 5 Grade 5 Grade 5 Grade 5 3P Learning 46

50 Ontario Grade 5 Patterning and and Probability and Probability and Probability and Probability Variables, Expressions and Collection and Organization of Collection and Organization of Collection and Organization of Collection and Organization of ON5.PA2.3 ON5.DMP1.1 ON5.DMP1.2 ON5.DMP1.3 ON5.DMP1.4 Determine the missing number in equations involving addition, subtraction, multiplication, or division and one or two digit numbers, using a variety of tools and strategies. Distinguish between discrete data and continuous data. Collect data by conducting a survey or an experiment to do with themselves, their environment, issues in their school or community, or content from another subject, and record observations or measurements. Collect and organize discrete or continuous primary data and secondary data and display the data in charts, tables, and graphs that have appropriate titles, labels, and scales that suit the range and distribution of the data, using a variety of tools. Demonstrate an understanding that sets of data can be samples of larger populations. Missing Values Find the Missing 1 : Add and Subtract 1 Missing s: Variables : Add and Subtract : Multiply and Divide Mass Word Stem and Leaf Introduction Stem-and-Leaf Plots Tally Charts Bar Chart Circle Graphs Reading from a Bar Chart Line Graphs: Interpretation Pie Charts Tally Charts Bar Chart Reading from a Bar Chart Line Graphs: Interpretation Grade 5 Grade 5 Representation Grade 5 Representation 47 3P Learning

51 Ontario Grade 5 and Probability and Probability and Probability and Probability and Probability and Probability and Probability Collection and Organization of Probability Probability Probability ON5.DMP1.5 ON5.DMP2.1 ON5.DMP2.2 ON5.DMP2.3 ON5.DMP3.1 ON5.DMP3.2 ON5.DMP3.3 Describe, through investigation, how a set of data is collected and explain whether the collection method is appropriate. Read, interpret, and draw conclusions from primary data and from secondary data, presented in charts, tables, and graphs. Calculate the mean for a small set of data and use it to describe the shape of the data set across its range of values, using charts, tables, and graphs. Compare similarities and differences between two related sets of data, using a variety of strategies. Determine and represent all the possible outcomes in a simple probability experiment, using systematic lists and area models. Represent, using a common fraction, the probability that an event will occur in simple games and probability experiments. Pose and solve simple probability problems, and solve them by conducting probability experiments and selecting appropriate methods of recording the results. Pie Charts Tally Charts Bar Chart Reading from a Bar Chart Line Graphs: Interpretation Pie Charts Tally Charts Bar Chart Reading from a Bar Chart Line Graphs: Interpretation Stem and Leaf Introduction Stem-and-Leaf Plots Mean Median Mode Mean from Frequency Table Finding the Average Mean Mean from Frequency Table Mode Median Finding the Average Mean Mean from Frequency Table Possible Outcomes Simple Probability Find the Probability Fair Games Possible Outcomes Simple Probability Find the Probability Probability Scale Fair Games Possible Outcomes Simple Probability Find the Probability Probability Scale Grade 5 Representation Grade 5 Representation Grade 5 Representation Grade 5 Representation Grade 5 Chance and Probability Grade 5 Chance and Probability Grade 5 Chance and Probability 3P Learning 48

52 Ontario Grade 6 ON6.NS1.1 ON6.NS1.2 ON6.NS1.3 ON6.NS1.4 Represent, compare, and order whole numbers and decimal numbers from to , using a variety of tools. Demonstrate an understanding of place value in whole numbers and decimal numbers from to , using a variety of tools and strategies. Read and print in words whole numbers to one hundred thousand, using meaningful contexts. Represent, compare, and order fractional amounts with unlike denominators, including proper and improper fractions and mixed numbers, using a variety of tools and using standard fractional notation. Understanding Place Value 3 Comparing Decimals Decimal Order Decimal Order 2 Decimals on a Line Understanding Place Value 3 Place Value 2 (x 10 and 10) Expanded Notation Decimals from Words to Digits 1 Decimals from Words to Digits 2 s from Words to Digits 1 s from Words to Digits 2 s in Words Comparing Fractions 1 Comparing Fractions 2 Ordering Fractions 1 Converting Mixed and Improper Equivalent Fractions on a Line 2 Equivalent Fraction Wall 2 Fraction Wall Labelling 2 Unit Fractions Identifying fractions beyond 1 Mixed and Improper Fractions on a Line Simplifying Fractions Grade 6 Fractions, Decimals and Percentages Grade 6 Fractions, Decimals and Percentages Grade 6 Reading and Understanding Whole s Grade 6 Fractions, Decimals and Percentages ON6.NS1.5 Estimate quantities using benchmarks of 10%, 25%, 50%, 75%, and 100%. 49 3P Learning

53 Ontario Grade 6 Operational ON6.NS1.6 ON6.NS1.7 ON6.NS2.1 Solve problems that arise from real-life situations and that relate to the magnitude of whole numbers up to Identify composite numbers and prime numbers, and explain the relationship between them. Use a variety of mental strategies to solve addition, subtraction, multiplication, and division problems involving whole numbers. Word with Letters Ratio Word Rates Word Multiplication 1 Multiply and Divide 1 Word : Multiply and Divide Product of Prime Factors Prime Factoring Prime or Composite? Magic Mental Addition Magic Mental Subtraction Adding Colossal Columns Subtracting Colossal Columns 3-Digit Differences 3-Digit Differences with Zeros 3-Digit Differences: 1 Regrouping Compensation-Add Compensation-Subtract 3-Digit Differences: 2 Regroupings Add 3-Digit s Add Three 3-Digit s: Regroup Jump Add and Subtract Mental Methods Multiplication 1 Mental Methods Multiplication 2 Mental Methods Multiplication 3 Multiply: 2-Digit, Regroup Multiply More Multiples of 10 Multiplication Properties Mental Methods Division 1 Mental Methods Division 2 Mental Methods Division 3 Divide: 2-Digit Divisor, Remainder Double and Halve to Multiply Multiply 2 Digits Area Model Estimate Sums Estimate Differences Grade 6 Fractions, Decimals and Percentages Grade 6 Reading and Understanding Whole s Grade 6 Addition and Subtraction Grade 6 Multiplication and Division 3P Learning 50

54 Ontario Grade 6 Operational Operational Operational ON6.NS2.2 ON6.NS2.3 ON6.NS2.4 Solve problems involving the multiplication and division of whole numbers, using a variety of tools and strategies. Add and subtract decimal numbers to thousandths, using concrete materials, estimation, algorithms, and calculators. Multiply and divide decimal numbers to tenths by whole numbers, using concrete materials, estimation, algorithms, and calculators. Rounding s for Division Estimation: Multiply and Divide Estimate Products Estimate Quotients Adding Decimals Add Decimals 2 Subtracting Decimals Subtract Decimals 2 Estimate Decimal Differences 1 Estimate Decimal Sums 1 Estimate Decimal Differences 2 Estimate Decimal Sums 2 Divide Decimal by Whole Decimal by Whole Grade 6 Reading and Understanding Whole s Grade 6 Fractions, Decimals and Percentages Grade 6 Fractions, Decimals and Percentages Operational ON6.NS2.5 Multiply whole numbers by 0.1, 0.01, and using mental strategies. Operational Operational Operational ON6.NS2.6 ON6.NS2.7 ON6.NS2.8 Multiply and divide decimal numbers by 10, 100, 1000, and using mental strategies. Use estimation when solving problems involving the addition and subtraction of whole numbers and decimals, to help judge the reasonableness of a solution. Explain the need for a standard order for performing operations, by investigating the impact that changing the order has when performing a series of operations. Multiply Decimals: 10, 100, 1000 Divide Decimals: 10, 100, 1000 Divide by Powers of 10 Multiply Decimals and Powers of 10 Estimate Sums Estimate Differences Estimate Decimal Sums 1 Estimate Decimal Sums 2 Estimate Decimal Differences 1 Estimate Decimal Differences 2 Order of Operations 1 (BEDMAS) Grade 6 Fractions, Decimals and Percentages Grade 6 Fractions, Decimals and Percentages Grade 6 Reading and Understanding Whole s 51 3P Learning

55 Ontario Grade 6 and and and Proportional Proportional Proportional Attributes, Units, and Attributes, Units, and ON6.NS3.1 ON6.NS3.2 ON6.NS3.3 ON6.M1.1 ON6.M1.2 ON6.M2.1 Represent ratios found in real-life contexts, using concrete materials, drawings, and standard fractional notation. Determine and explain, through investigation using concrete materials, drawings, and calculators, the relationships among fractions, decimal numbers, and percents. Represent relationships using unit rates. Demonstrate an understanding of the relationship between estimated and precise measurements, and determine and justify when each kind is appropriate. Estimate, measure, and record length, area, mass, capacity, and volume, using the metric measurement system. Select and justify the appropriate metric unit to measure length or distance in a given real-life situation. Ratio Word Fractions of a Collection Decimals to Fractions 1 Decimals to Fractions 2 Convert Decimals to Fractions 2 Percents and Decimals Match Decimals and Percentages Decimal to Percentage Percentage to Fraction Percents to Fractions Rates Rates Word Unitary Method Simplify Ratios: 2 Whole s Equivalent Ratios Grams and Kilograms Converting cm and mm Millilitres and Litres Grade 6 Length, Perimeter and Area Grade 6 Volume, Capacity and Mass Grade 6 Length, Perimeter and Area Grade 6 Volume, Capacity and Mass 3P Learning 52

56 Ontario Grade 6 ON6.M2.2 ON6.M2.3 ON6.M2.4 ON6.M2.5 ON6.M2.6 ON6.M2.7 Solve problems requiring conversion from larger to smaller metric units. Construct a rectangle, a square, a triangle, and a parallelogram, using a variety of tools, given the area and/or perimeter. Determine, through investigation using a variety of tools and strategies, the relationship between the area of a rectangle and the areas of parallelograms and triangles, by decomposing and composing. Millilitres and Litres Litre Conversions Converting Units of Length Converting Units of Mass Grams and Kilograms Capacity Addition Millilitres and Litres Litre Conversions Converting Units of Length Converting Units of Mass Grams and Kilograms Capacity Addition Millilitres and Litres Litre Conversions Converting Units of Length Converting Units of Mass Grams and Kilograms Capacity Addition Develop the formulas for the area of a Millilitres and Litres parallelogram and Litre Conversions the area of a triangle Converting Units of Length [i.e., Area of triangle = 2], using the area Converting Units of Mass relationships among Grams and Kilograms rectangles, parallelograms, Capacity Addition and triangles. Solve problems involving the estimation and calculation of the areas of triangles and the areas of parallelograms. Determine, using concrete materials, the relationship between units used to measure area, and apply the relationship to solve problems that involve conversions from square metres to square centimetres. Area: Triangles Area: Right Triangles Area: Parallelograms Converting Units of Area Grade 6 Volume, Capacity and Mass Grade 6 Volume, Capacity and Mass Grade 6 Volume, Capacity and Mass Grade 6 Volume, Capacity and Mass Grade 6 Length, Perimeter and Area Grade 6 Length, Perimeter and Area 53 3P Learning

57 Ontario Grade 6 ON6.M2.8 ON6.M2.9 Determine, through investigation using a variety of tools and strategies, the relationship between the height, the area of the base, and the volume of a triangular prism, and generalize to develop the formula. Determine, through investigation using a variety of tools and strategies, the surface area of rectangular and triangular prisms. Volume: Triangular Prisms Volume: Triangular Prisms Surface Area: Rectangular Prisms Grade 6 Volume, Capacity and Mass Grade 6 Volume, Capacity and Mass ON6.M2.10 Solve problems involving the estimation and calculation of the surface area and volume of triangular and rectangular prisms. Volume: Rectangular Prisms 1 Volume: Rectangular Prisms 2 Volume: Triangular Prisms Surface Area: Rectangular Prisms 1 Grade 6 Length, Perimeter and Area Grade 6 Volume, Capacity and Mass Spatial Spatial Spatial Spatial Spatial Properties Properties Properties Properties ON6.GS1.1 ON6.GS1.2 ON6.GS1.3 ON6.GS1.4 ON6.GS2.1 Sort and classify quadrilaterals by geometric properties related Properties of Quadrilaterals to symmetry, angles, and sides, through investigation using a Triangle Tasters variety of tools and strategies. Sort polygons according to the number of lines of symmetry and the order of rotational symmetry, through investigation using a variety of tools. Measure and construct angles up to 180 using a protractor, and classify them as acute, right, obtuse, or straight angles. Construct polygons using a variety of tools, given angle and side measurements. Build three-dimensional models using connecting cubes, given isometric sketches or different views of the structure. Symmetry or Not? Rotational Symmetry What Type of Angle? Labelling Angles Classifying Angles Measuring Angles What Type of Angle? Labelling Angles Classifying Angles Properties of Solids Nets Grade 6 Geometry Grade 6 Geometry Grade 6 Geometry Grade 6 Geometry Solids 3P Learning 54

58 Ontario Grade 6 Spatial Spatial Spatial Spatial Patterning and Patterning and Patterning and Patterning and Location and Movement Location and Movement Location and Movement ON6.GS2.2 ON6.GS3.1 ON6.GS3.2 ON6.GS3.3 ON6.PA1.1 ON6.PA1.2 ON6.PA1.3 ON6.PA1.4 Sketch, using a variety of tools, isometric perspectives and different views of threedimensional figures built with interlocking cubes. Explain how a coordinate system represents location, and plot points in the first quadrant of a Cartesian coordinate plane. Identify, perform, and describe, through investigation using a variety of tools, rotations of 180º and clockwise and counterclockwise rotations of 90º, with the centre of rotation inside or outside the shape. Create and analyse designs made by reflecting, translating, and/or rotating a shape, or shapes, by 90º or 180º. Identify geometric patterns, through investigation using concrete materials or drawings, and represent them numerically. Make tables of values for growing patterns, given pattern rules in words, then list the ordered pairs and plot the points in the first quadrant, using a variety of tools. Determine the term number of a given term in a growing pattern that is represented by a pattern rule in words, a table of values, or a graph. Describe pattern rules that generate patterns by adding or subtracting a constant, or multiplying or dividing by a constant, to get the next term, then distinguish such pattern rules from pattern rules, given in words, that describe the general term by referring to the term number. Properties of Solids Coordinate Graphs: 1st Quadrant Rotations: Coordinate Plane Flip, Slide, Turn Transformations Rotational Symmetry Describing Patterns Table of Values Function Rules and Tables Table of Values Table of Values Solids Grade 6 Position Grade 6 Position Grade 6 Geometry Grade 6 Grade 6 Grade 6 Grade P Learning

59 Ontario Grade 6 Patterning and Patterning and Patterning and Patterning and Patterning and Patterning and and Probability and Probability Variables, Expressions, and Variables, Expressions, and Variables, Expressions, and Variables, Expressions, and Collection and Organization of Collection and Organization of ON6.PA1.5 ON6.PA1.6 ON6.PA2.1 ON6.PA2.2 ON6.PA2.3 ON6.PA2.4 ON6.DMP1.1 ON6.DMP1.2 Determine a term, given its term number, by extending growing and shrinking patterns that are generated by adding or subtracting a constant, or multiplying or dividing by a constant, to get the next term. Extend and create repeating patterns that result from rotations, through investigation using a variety of tools. Demonstrate an understanding of different ways in which variables are used. Identify, through investigation, the quantities in an equation that vary and those that remain constant. Solve problems that use two or three symbols or letters as variables to represent different unknown quantities. Determine the solution to a simple equation with one variable, through investigation using a variety of tools and strategies. Collect data by conducting a survey or an experiment to do with themselves, their environment, issues in their school or community, or content from another subject, and record observations or measurements. Collect and organize discrete or continuous primary data and secondary data and display the data in charts, tables, and graphs that have appropriate titles, labels, and scales that suit the range and distribution of the data, using a variety of tools. Table of Values Table of Values Mass Word Solve : Add, Subtract 1 Solve : Add, Subtract 2 Write an Equation: Word Find the Missing 2 Missing Values: Decimals Missing s: Variables I am Thinking of a! Histograms Tally Charts Divided Bar Graphs Grade 6 Grade 6 Grade 6 Grade 6 Grade 6 Grade 6 Grade 6 Representation Grade 6 Representation 3P Learning 56

60 Ontario Grade 6 and Probability and Probability and Probability and Probability and Probability and Probability Collection and Organization of Collection and Organization of ON6.DMP1.3 ON6.DMP1.4 ON6.DMP2.1 ON6.DMP2.2 ON6.DMP2.3 ON6.DMP2.4 Select an appropriate type of graph to represent a set of data, graph the data using technology, and justify the choice of graph. Determine, through investigation, how well a set of data represents a population, on the basis of the method that was used to collect the data. Read, interpret, and draw conclusions from primary data and from secondary data, presented in charts, tables, and graphs. Compare, through investigation, different graphical representations of the same data. Explain how different scales used on graphs can influence conclusions drawn from the data. Demonstrate an understanding of mean, and use the mean to compare two sets of related data, with and without the use of technology. Histograms Tally Charts Divided Bar Graphs Histograms Tally Charts Divided Bar Graphs Mean from Frequency Table Stem and Leaf Introduction Stem-and-Leaf Plots Interpreting Tables Line Graphs: Interpretation Divided Bar Graphs Tally Charts Histograms Stem and Leaf Introduction Stem-and-Leaf Plots Interpreting Tables Line Graphs: Interpretation Divided Bar Graphs Tally Charts Histograms Stem and Leaf Introduction Stem-and-Leaf Plots Interpreting Tables Line Graphs: Interpretation Divided Bar Graphs Tally Charts Histograms Mean Median Mode Finding the Average Mean from Frequency Table Grade 6 Representation Grade 6 Representation Grade 6 Representation Grade 6 Representation Grade 6 Representation Grade 6 Representation 57 3P Learning

61 Ontario Grade 6 and Probability and Probability and Probability and Probability Probability Probability Probability ON6.DMP2.5 ON6.DMP3.1 ON6.DMP3.2 ON6.DMP3.3 Demonstrate, through investigation, an understanding of how data from charts, tables, and graphs can be used to make inferences and convincing arguments. Express theoretical probability as a ratio of the number of favourable outcomes to the total number of possible outcomes, where all outcomes are equally likely. Represent the probability of an event, using a value from the range of 0 to 1. Predict the frequency of an outcome of a simple probability experiment or game, by calculating and using the theoretical probability of that outcome. Mean Median Mode Finding the Average Mean from Frequency Table Probability Scale Venn Diagrams Dice and Coins Find the Probability Simple Probability Complementary Events Possible Outcomes Fair Games Probability Scale Venn Diagrams Dice and Coins Find the Probability Simple Probability Complementary Events Possible Outcomes Fair Games Probability Scale Venn Diagrams Dice and Coins Find the Probability Simple Probability Complementary Events Possible Outcomes Fair Games Relative Frequency Grade 6 Representation Grade 6 Representation Grade 6 Chance and Probability Grade 6 Chance and Probability 3P Learning 58

62 Ontario ON7.NS1.1 Represent, compare, and order decimals to hundredths and fractions, using a variety of tools. Generate multiples and ON7.NS1.2 factors, using a variety of tools and strategies. Identify and compare ON7.NS1.3 integers found in real-life contexts. Represent and order ON7.NS1.4 integers using a variety of tools. ON7.NS1.5 Select and justify the most appropriate representation of a quantity (i.e., fraction, decimal, percent) for a given context. Represent perfect squares ON7.NS1.6 and square roots, using a variety of tools. Decimals on a Line Decimal Order Decimal Place Value Compare Decimals Compare Decimals 1 Compare Decimals 2 Identifying Fractions on a Line Mixed and Improper Fractions on a Line Compare Fractions 1a Compare Fractions 1b Compare Fractions 2 Multiples Least Common Multiple Factors Find the Factor Greatest Common Factor Product of Prime Factors Prime Factoring Prime or Composite? Comparing Integers Integers on a Line Ordering Integers ( Line) Ordering Integers Comparing Integers Integers: Order of Operations (BEDMAS) Decimal to Percentage Percentage to Fraction Fraction to Terminating Decimal Fraction to Decimal 1 Decimal to Fraction Square Roots Estimate Square Roots Decimals Fractions Whole s Directed s Directed s Decimals Percentage Basics Fractions Whole s 59 3P Learning

63 Ontario ON7.NS1.7 Operational Operational Operational ON7.NS2.1 ON7.NS2.2 ON7.NS2.3 Explain the relationship between exponential notation and the measurement of area and volume. Divide whole numbers by simple fractions and by decimal numbers to hundredths, using concrete materials. Use a variety of mental strategies to solve problems involving the addition and subtraction of fractions and decimals. Solve problems involving the multiplication and division of decimal numbers to thousandths by one-digit whole numbers, using a variety of tools. Converting Units of Area Converting Volume Divide Whole by Fraction Divide Fractions Visual Model Add Subtract Fractions 1 Add Like Fractions Subtract Like Fractions Add subtract fractions 1 Fraction by Whole Subtract Decimals 1 Subtract Decimals 2 Add Unlike Fractions Subtract Unlike Fractions Add Decimals: Same Sign Subtracting Decimals Adding Decimals Add and Subtracting Decimals Decimal Complements Divide Decimal by Whole Decimal by Whole Whole s Fractions Decimals Fractions Decimals Decimals Operational ON7.NS2.4 Solve multi-step problems arising from real-life contexts and involving whole numbers and decimals, using a variety of tools. to Solve Write an Equation: Word Percentage Word Rate Word Rates Word Ratio Word Best Buy Whole s Decimals 3P Learning 60

64 Ontario 61 3P Learning Operational Operational Operational Operational Operational ON7.NS2.5 ON7.NS2.6 ON7.NS2.7 ON7.NS2.8 ON7.NS2.9 Proportional ON7.NS3.1 Use estimation when solving problems involving operations with whole numbers, decimals, and percents, to help judge the reasonableness of a solution. Evaluate expressions that involve whole numbers and decimals, including expressions that contain brackets, using order of operations. Estimate Decimal Differences 1 Estimate Decimal Differences 2 Estimate Decimal Sums 1 Estimate Decimal Sums 2 Estimate Decimal Operations Estimate Sums Estimate Differences Estimate Products Estimate Quotients Estimation: Add and Subtract Estimation: Multiply and Divide Solve : Add, Subtract 1 Solve : Add, Subtract 2 Solve : Multiply, Divide 1 Solve Percent to Solve Write an Equation: Word Order of Operations 1 (BEDMAS) Add and subtract fractions with simple like and unlike Add Unlike Fractions denominators, using a variety Subtract Unlike Fractions of tools. Demonstrate, using concrete materials, the relationship between the repeated addition of fractions and the multiplication of that fraction by a whole number. Add and subtract integers, using a variety of tools. Determine, through investigation, the relationships among fractions, decimals, percents, and ratios. Subtract Integers Add Integers Integers: Subtraction More with Integers Integers: Add and Subtract Integers: Order of Operations (BEDMAS) Decimal to Percentage Percentage to Fraction Fraction to Terminating Decimal Decimals to Fractions 1 Decimals to Fractions 2 Fraction to Decimal 1 Percentage of a Percent Increase and Decrease Fractions to Decimals 1 Whole s Decimals Percentage Basics Basics Fractions Fractions Directed s Grade 6 Fractions, Decimals and Percentages

65 Ontario Proportional Proportional Proportional Attributes, Units, and ON7.NS3.2 ON7.NS3.3 ON7.NS3.4 ON7.M1.1 ON7.M2.1 ON7.M2.2 ON7.M2.3 ON7.M2.4 Solve problems that involve determining whole number percents, using a variety of tools. Demonstrate an understanding of rate as a comparison, or ratio, of two measurements with different units. Solve problems involving the calculation of unit rates. Research and report on real-life applications of area measurements. Sketch different polygonal prisms that share the same volume. Solve problems that require conversion between metric units of measure. Solve problems that require conversion between metric units of area. Determine, through investigation using a variety of tools (e.g., concrete materials, dynamic geometry software) and strategies, the relationship for calculating the area of a trapezoid, and generalize to develop the formula [i.e., Area = (sum of lengths of parallel sides x height) 2]. Solve Percent Percentage Word Unitary Method Solve Proportions Equivalent Ratios Rates Ratios Simplify Ratios: 2 Whole s Simplify Ratios: Fractions Simplify Ratios: Mixed s Rate Calculations Rate Word Rates Word Ratio Word Best Buy Converting cm and mm Metres and Kilometres Converting Units of Length Converting Units of Mass Mass Addition Capacity Addition Converting Units of Area Area: Parallelograms (Metric) Area: Quadrilaterals Percentage Basics Solids Solids Grade 6 Volume, Capacity and Mass Converting Units Converting Units Area and Perimeter 3P Learning 62

66 Ontario Spatial Spatial Properties Properties ON7.M2.5 ON7.M2.6 ON7.M2.7 ON7.M2.8 ON7.M2.9 ON7.GS1.1 ON7.GS1.2 Solve problems involving the estimation and calculation of the area of a trapezoid. Estimate and calculate the area of composite two-dimensional shapes by decomposing into shapes with known area relationships. Determine, through investigation using a variety of tools and strategies (e.g., decomposing right prisms; stacking congruent layers of concrete materials to form a right prism), the relationship between the height, the area of the base, and the volume of right prisms with simple polygonal bases (e.g., parallelograms, trapezoids), and generalize to develop the formula. Determine, through investigation using a variety of tools (e.g., nets, concrete materials, dynamic geometry software, Polydrons), the surface area of right prisms. Solve problems that involve the surface area and volume of right prisms and that require conversion between metric measures of capacity and volume. Construct related lines (i.e., parallel; perpendicular; intersecting at 30º, 45º, and 60º), using angle properties and a variety of tools. Sort and classify triangles and quadrilaterals by geometric properties related to symmetry, angles, and sides, through investigation using a variety of tools. Area: Parallelograms (Metric) Area: Quadrilaterals Area: Composite Shapes Volume: Rectangular Prisms 1 Volume: Rectangular Prisms 2 Volume: Prisms Volume: Triangular Prisms Surface Area: Rectangular Prisms Using Similar Triangles Similar Figures Measuring Solids Perimeter and Area Solids Solids Solids Converting Units Angles Angles and Polygons Similarity and Congruence Spatial Properties ON7.GS1.3 Construct angle bisectors and perpendicular bisectors, using a variety of tools. Constructions 63 3P Learning

67 Ontario Spatial Spatial Properties Properties ON7.GS1.4 ON7.GS2.1 Investigate, using concrete materials, the angles between the faces of a prism, and identify right prisms. Identify, through investigation, the minimum side and angle information (i.e., side-side-side; side-angle-side; angle-side angle) needed to describe a unique triangle. Triangle Tasters Using Similar Triangles Solids Similarity and Congruence Spatial Properties ON7.GS2.2 Determine, through investigation using a variety of tools (e.g., dynamic geometry software, concrete materials, geoboard), relationships among area, perimeter, corresponding side lengths, and corresponding angles of congruent shapes. Using Similar Triangles Similar Figures Congruent Figures Scale Factor Congruent Figures: Find Values Congruent Triangles Similarity and Congruence Spatial Spatial Spatial Spatial Spatial Properties Properties Location and Movement Location and Movement Location and Movement ON7.GS2.3 ON7.GS2.4 ON7.GS3.1 ON7.GS3.2 ON7.GS3.3 Demonstrate an understanding that enlarging or reducing twodimensional shapes creates similar shapes. Distinguish between and compare similar shapes and congruent shapes, using a variety of tools (e.g., pattern blocks, grid paper, dynamic geometry software) and strategies (e.g., by showing that dilatations create similar shapes and that translations, rotations, and reflections generate congruent shapes). Plot points using all four quadrants of the Cartesian coordinate plane. Identify, perform, and describe dilatations (i.e., enlargements and reductions), through investigation using a variety of tools. Create and analyse designs involving translations, reflections, dilatations, and/or simple rotations of twodimensional shapes, using a variety of tools. Scale Factor Similar Figures Congruent Figures Symmetry Rotational Symmetry Transformations Flip, Slide, Turn Transformations: Coordinate Plane Rotations: Coordinate Plane Ordered Pairs Coordinate Graphs: 1st Quadrant Coordinate Graphs Scale Factor Transformations Transformations: Coordinate Plane Rotations: Coordinate Plane Flip, Slide, Turn Similarity and Congruence Similarity and Congruence The Plane Similarity and Congruence Polygons 3P Learning 64

68 Ontario Spatial Location and Movement ON7.GS3.4 Determine, through investigation using a variety of tools polygons or combinations of polygons that tile a plane, and describe the transformation(s) involved. Polygons Patterning and ON7.PA1.1 Represent linear growing patterns, using a variety of tools and strategies. Graphing from a Table of Values Patterning and Patterning and Patterning and Patterning and Patterning and Patterning and Variables, Expressions, and Variables, Expressions, and Variables, Expressions, and ON7.PA1.2 ON7.PA1.3 ON7.PA1.4 ON7.PA2.1 ON7.PA2.2 ON7.PA2.3 Make predictions about linear growing patterns, through investigation with concrete materials. Develop and represent the general term of a linear growing pattern, using algebraic expressions involving one operation. Compare pattern rules that generate a pattern by adding or subtracting a constant, or multiplying or dividing by a constant, to get the next term. Model real-life relationships involving constant rates where the initial condition starts at 0 (e.g., speed, heart rate, billing rate), through investigation using tables of values and graphs. Model real-life relationships involving constant rates (e.g., speed, heart rate, billing rate), using algebraic equations with variables to represent the changing quantities in the relationship. Translate phrases describing simple mathematical relationships into algebraic expressions using concrete materials (e.g., algebra tiles, pattern blocks, counters). Graphing from a Table of Values Writing ic Expressions and Inequalities Basics Basics Basics 65 3P Learning

69 Ontario Patterning and Patterning and Patterning and and Probability and Probability and Probability and Probability Variables, Expressions, and Variables, Expressions, and Variables, Expressions, and Collection and Organization of Collection and Organization of Collection and Organization of Collection and Organization of ON7.PA2.4 ON7.PA2.5 ON7.PA2.6 ON7.DMP1.1 ON7.DMP1.2 ON7.DMP1.3 ON7.DMP1.4 Evaluate algebraic expressions by substituting natural numbers for the variables. Make connections between evaluating algebraic expressions and determining the term in a pattern using the general term. Solve linear equations of the form ax= c or c=ax and ax + b=c or variations such as b + ax=c and c=bx + a (where a, b, and c are natural numbers) by modelling with concrete materials, by inspection, or by guess and check, with and without the aid of a calculator. Collect data by conducting a survey or an experiment to do with themselves, their environment, issues in their school or community, or content from another subject and record observations or measurements. Collect and organize categorical, discrete, or continuous primary data and secondary data and display the data in charts, tables, and graphs that have appropriate titles, labels, and that suit the range and distribution of the data, using a variety of tools. Select an appropriate type of graph to represent a set of data, graph the data using technology, and justify the choice of graph. Distinguish between a census and a sample from a population. Simple Substitution 1 Simple Substitution 2 Tally Charts Interpreting Tables Dot Plots Frequency Histograms Line Graphs: Interpretation Divided Bar Graphs Step Graphs Sector Graphs Sector Graph Calculations Table of Values Basics Grade 6 Representation Grade 6 Representation Grade 6 Representation 3P Learning 66

70 Ontario and Probability and Probability and Probability and Probability and Probability and Probability and Probability and Probability 67 3P Learning Collection and Organization of Probability Probability ON7.DMP1.5 ON7.DMP2.1 ON7.DMP2.2 ON7.DMP2.3 ON7.DMP2.4 ON7.DMP2.5 ON7.DMP3.1 ON7.DMP3.2 Identify bias in data collection methods. Read, interpret, and draw conclusions from primary data and from secondary presented in charts, tables, and graphs. Identify, through investigation, graphs that present data in misleading ways. Determine, through investigation, the effect on a measure of central tendency (i.e., mean, median, and mode) of adding or removing a value or values. Identify and describe trends, based on the distribution of the data presented in tables and graphs, using informal language. Make inferences and convincing arguments that are based on the analysis of charts, tables, and graphs. Research and report on real-world applications of probabilities expressed in fraction, decimal, and percent form. Make predictions about a population when given a probability. Tally Charts Interpreting Tables Dot Plots Frequency Histograms Line Graphs: Interpretation Divided Bar Graphs Step Graphs Sector Graphs Sector Graph Calculations Mean Median Mode Mean from Frequency Table Mode from Frequency Table Cumulative Frequency Table Relative Frequency Interpreting Tables Table of Values Simple Probability Dice and Coins Fair Games Probability Scale Find the Probability Complementary Events Grade 6 Representation Chance

71 Ontario and Probability and Probability Probability Probability ON7.DMP3.3 ON7.DMP3.4 Represent in a variety of ways all the possible outcomes of a probability experiment involving two independent events, and determine the theoretical probability of a specific outcome involving two independent events. Perform a simple probability experiment involving two independent events, and compare the experimental probability with the theoretical probability of a specific outcome. Possible Outcomes Simple Probability Dice and Coins Fair Games Find the Probability Probability Scale Complementary Events Chance Chance 3P Learning 68

72 Ontario and and and and and and Operational ON8.NS1.1 ON8.NS1.2 ON8.NS1.3 ON8.NS1.4 ON8.NS1.5 ON8.NS2.1 Express repeated multiplication using exponential notation. Represent whole numbers in expanded form using powers of ten. Represent, compare, and order rational numbers (i.e., positive and negative fractions and decimals to thousandths). Translate between equivalent forms of a number (i.e., decimals, fractions, percents). Determine common factors and common multiples using the prime factorization of numbers. Solve multi-step problems arising from real-life contexts and involving whole numbers and decimals, using a variety of tools and strategies. Exponents Exponent Notation Exponent Form to s Properties of Exponents The Zero Exponent Prime Factoring: Exponents Scientific Notation Decimal Order 2 Comparing Decimals 2 Comparing Fractions with Signs Ordering Fractions Decimals to Fractions 1 Decimals to Fractions 2 Fractions to Decimals 1 Fractions to Decimals 2 Percents and Decimals Percents to Fractions Prime or Composite? Prime Factoring Product of Prime Factors Least Common Multiple Greatest Common Factor Find the Factor Percentage Word Rates Word Ratio Word Unitary Method Best Buy Simplifying Exponents Simplifying Exponents Decimals Fractions Directed s Grade 6 Fractions, Decimals and Percentages Decimals Percentage Calculations Expanding and Factoring Decimals 69 3P Learning

73 Ontario and and and and and Operational Operational Operational Operational Operational ON8.NS2.2 ON8.NS2.3 ON8.NS2.4 ON8.NS2.5 ON8.NS2.6 Solve problems involving percents expressed to one decimal place and wholenumber percents greater than 100. Use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, and fractions, to help judge the reasonableness of a solution. Represent the multiplication and division of fractions, using a variety of tools and strategies. Solve problems involving addition, subtraction, multiplication, and division with simple fractions. Represent the multiplication and division of integers, using a variety of tools. Percentage Word Estimate Decimal Operations Estimate Decimal Differences 1 Estimate Decimal Differences 2 Estimate Decimal Sums 1 Estimate Decimal Sums 2 Estimate Sums Estimate Differences Estimate Products Estimate Quotients Estimate Products with Fractions Estimate Square Roots Divide Fractions: Visual Model Add Like Fractions Add Unlike Fractions Converting Mixed and Improper Add Like Mixed s Add Mixed s: Same Sign Add Unlike Mixed s Subtract Like Mixed s Subtract Unlike Mixed s Multiply Mixed s Divide Mixed s Improper to Mixed Mixed to Improper Subtract Like Fractions Subtract Unlike Fractions Fraction by Whole Multiply Two Fractions 1 Multiply Two Fractions 2 Divide Fractions by Fractions 1 Divide Fractions by Fractions 2 Integers: Multiply and Divide Percentage Calculations Grade 6 Fractions, Decimals and Percentages Decimals Fractions Fractions Directed s 3P Learning 70

74 Ontario 71 3P Learning Operational Operational Operational Operational Proportional Proportional Proportional Proportional ON8.NS2.7 ON8.NS2.8 ON8.NS2.9 ON8.NS2.10 ON8.NS3.1 ON8.NS3.2 ON8.NS3.3 ON8.NS3.4 Solve problems involving operations with integers, using a variety of tools. Evaluate expressions that involve integers, including expressions that contain brackets and exponents, using order of operations. Multiply and divide decimal numbers by various powers of ten. Estimate, and verify using a calculator, the positive square roots of whole numbers, and distinguish between whole numbers that have wholenumber square roots (i.e., perfect square numbers) and those that do not. Identify and describe reallife situations involving two quantities that are directly proportional. Solve problems involving proportions, using concrete materials, drawings, and variables. Solve problems involving percent that arise from real-life contexts. Solve problems involving rates. Integers: Subtraction Integers: Add and Subtract More with Integers Integers: Order of Operations (BEDMAS) Order of Operations 1 (BEDMAS) Multiply Decimals and Powers of 10 Divide by Powers of 10 Divide Decimals: 10, 100, 1000 Multiply Decimals: 10, 100, 1000 Decimal by Whole Decimal by Decimal Divide Decimal by Whole Divide Decimal by Decimal Percentage of a Square Roots Estimate Square Roots Best Buy Unitary Method Solve Proportions Simplify Ratios: 2 Whole s Percentage Word Rates Word Ratio Word Ratios Equivalent Ratios Dividing a into a Ratio Rates Rates Calculations Directed s Simplifying Decimals Whole s Percentage Calculations Percentage Calculations Percentage Calculations

75 Ontario Attributes, Units, and ON8.M1.1 ON8.M2.1 ON8.M2.2 ON8.M2.3 ON8.M2.4 ON8.M2.5 ON8.M2.6 ON8.M2.7 Research, describe, and report on applications of volume and capacity measurement. Solve problems that require conversions involving metric units of area, volume, and capacity. Measure the circumference, radius, and diameter of circular objects, using concrete materials. Determine, through investigation using a variety of tools and strategies, the relationships for calculating the circumference and the area of a circle, and generalize to develop the formulas. Solve problems involving the estimation and calculation of the circumference and the area of a circle. Determine, through investigation using a variety of tools and strategies the relationship between the area of the base and height and the volume of a cylinder, and generalize to develop the formula (i.e., Volume = area of base x height). Determine, through investigation using concrete materials, the surface area of a cylinder. Solve problems involving the surface area and the volume of cylinders, using a variety of strategies. Converting Units of Area Converting Volume Capacity Word Capacity Addition Converting cm and mm Metres and Kilometres Converting Units of Length Converting Units of Mass Converting cm and mm Centimetres and Metres Grams and Kilograms Circumference: Circles Area:Circles 1 Circumference: Circles Area:Circles 1 Volume: Cylinders Similar Areas and Volumes Surface Area: Cylinders Volume: Cylinders Surface Area: Cylinders Measuring Solids Converting Units Perimeter and Area Perimeter and Area Perimeter and Area Measuring Solids Measuring Solids Measuring Solids 3P Learning 72

76 Ontario Spatial Spatial Spatial Spatial Spatial Spatial Spatial 73 3P Learning Properties Properties Properties ON8.GS1.1 ON8.GS1.2 ON8.GS1.3 ON8.GS2.1 ON8.GS2.2 ON8.GS2.3 ON8.GS2.4 Sort and classify quadrilaterals by geometric properties, including those based on diagonals, through investigation using a variety of tools. Construct a circle, given its centre and radius, or its centre and a point on the circle, or three points on the circle. Investigate and describe applications of geometric properties in the real world. Determine, through investigation using a variety of tools relationships among area, perimeter, corresponding side lengths, and corresponding angles of similar shapes. Determine, through investigation using a variety of tools and strategies, the angle relationships for intersecting lines and for parallel lines and transversals, and the sum of the angles of a triangle. Solve angle-relationship problems involving triangles (e.g., finding interior angles or complementary angles), intersecting lines (e.g., finding supplementary angles or opposite angles), and parallel lines and transversals. Determine the Pythagorean relationship, through investigation using a variety of tools and strategies. Floor Plans Perimeter: Triangles Perimeter: Composite Shapes Similar Figures Perimeter of Shapes Perimeter: Squares and Rectangles Perimeter Area: Quadrilaterals Perimeter: Composite Shapes Using Similar Triangles Angle Sum of a Triangle Equal, Complement or Supplement? Angles and Parallel Lines Measuring Angles Labeling Angles Classifying Angles Pythagoras Theorem Pythagorean Triads Find Slant Height Polygons Constructions Perimeter and Area Similarity and Congruence Polygons and Angles Angles Polygons and Angles Angles Polygons and Angles Pythagorus Theorem

77 Ontario Geometry and Spatial Geometry and Spatial Geometry and Spatial Geometry and Spatial Patterning and Patterning and Patterning and Location and Movement Location and Movement ON8.GS2.5 ON8.GS2.6 ON8.GS3.1 ON8.GS3.2 ON8.PA1.1 ON8.PA1.2 ON8.PA1.3 Solve problems involving right triangles geometrically, using the Pythagorean relationship. Determine, through investigation using concrete materials, the relationship between the numbers of faces, edges, and vertices of a polyhedron (i.e., number of faces + number of vertices=number of edges + 2). Graph the image of a point, or set of points, on the Cartesian coordinate plane after applying a transformation to the original point(s). Identify, through investigation, realworld movements that are translations, reflections, and rotations. Represent, through investigation with concrete materials, the general term of a linear pattern, using one or more algebraic expressions. Represent linear patterns graphically (i.e., make a table of values that shows the term number and the term, and plot the coordinates on a graph), using a variety of tools. Determine a term, given its term number, in a linear pattern that is represented by a graph or an algebraic equation. Pythagoras Theorem Pythagorean Triads Find Slant Height Euler s Formula Coordinate Graphs Coordinate Graphs: 1st Quadrant Coordinate Methods in Geometry Rotations: Coordinate Plane Transformations: Coordinate Plane Flip, Slide, Turn Ordered Pairs Which Straight Line? Equation of a Line 1 Pattern Rules and Tables Find the Pattern Rule Determining a Rule for a Line Graphing from a Table of Values Reading Values from a Line Determining a Rule for a Line y = ax Pythagorus Theorem The Plane 3P Learning 74

78 Ontario Patterning and Patterning and Patterning and Patterning and Patterning and Patterning and and Probability 75 3P Learning Variables, Expressions, and Variables, Expressions, and Variables, Expressions, and Variables, Expressions, and Variables, Expressions, and Variables, Expressions, and Collection and Organization of ON8.PA2.1 ON8.PA2.2 ON8.PA2.3 ON8.PA2.4 ON8.PA2.5 ON8.PA2.6 ON8.DMP1.1 Describe different ways in which algebra can be used in real-life situations. Model linear relationships using tables of values, graphs, and equations, through investigation using a variety of tools. Translate statements describing mathematical relationships into algebraic expressions and equations. Evaluate algebraic expressions with up to three terms, by substituting fractions, decimals, and integers for the variables. Make connections between solving equations and determining the term number in a pattern, using the general term. Solve and verify linear equations involving a one-variable term and having solutions that are integers, by using inspection, guess and check, and a balance model. Collect data by conducting a survey or an experiment to do with themselves, their environment, issues in their school or community, or content from another subject, and record observations or measurements. Pattern Rules and Tables Find the Pattern Rule Graphing from a Table of Values Writing ic Expressions to Solve More Simple Substitution 2 Simple Substitution 3 Simple Solve Multi-Step with Grouping Symbols to Solve with Fractions 2 Solve Two-Step Solve Percent with Decimals : Variables, Both Sides Find the Pattern Rule Checking Solutions Find the Mistake Simplifying Simplifying Simplifying Simplifying

79 Ontario and Probability and Probability and Probability and Probability and Probability and Probability Collection and Organization of Collection and Organization of Collection and Organization of Collection and Organization of ON8.DMP1.2 ON8.DMP1.3 ON8.DMP1.4 ON8.DMP1.5 ON8.DMP2.1 ON8.DMP2.2 Organize into intervals a set of data that is spread over a broad range. Collect and organize categorical, discrete, or continuous primary data and secondary data, and display the data in charts, tables, and graphs (including histograms and scatter plots) that have appropriate titles, labels, and scales that suit the range and distribution of the data, using a variety of tools. Select an appropriate type of graph to represent a set of data, graph the data using technology, and justify the choice of graph. Explain the relationship between a census, a representative sample, sample size, and a population. Read, interpret, and draw conclusions from primary data and from secondary data, presented in charts, tables, and graphs. Determine, through investigation, the appropriate measure of central tendency (i.e., mean, median, or mode) needed to compare sets of data. Dot Plots Histograms Cumulative Frequency Histograms Histograms Scatter Plots Circle Graphs Divided Bar Graphs Step Graphs Sector Graphs Column Graphs Tally Charts Bar Graphs 2 Travel Graphs Compound Bar Chart Dot Plots Cumulative Frequency Histogram Analysis: Scatter Plots Line Graphs: Interpretation Mean Median Mode Mode from Frequency Table Median from Frequency Table Mean from Frequency Table Median and Cumulative Frequency Grouped Frequency Median from Stem and Leaf Plot Mode from Stem and Leaf Plot Grade 6 Representation Grade 6 Representation 3P Learning 76

80 Ontario and Probability and Probability and Probability and Probability and Probability ON8.DMP2.3 ON8.DMP2.4 ON8.DMP2.5 ON8.DMP2.6 ON8.DMP2.7 Demonstrate an understanding of the Histograms appropriate uses of bar graphs and histograms by comparing Bar Graphs 2 their characteristics. Compare two attributes or characteristics (e.g., height versus arm span), using a scatter plot, and determine whether or not the scatter plot suggests a relationship. Identify and describe trends, based on the rate of change of data from tables and graphs, using informal language. Make inferences and convincing arguments that are based on the analysis of charts, tables, and graphs. Compare two attributes or characteristics, using a variety of data management tools and strategies. Scatter Plots Analysis: Scatter Plots Line Graphs: Interpretation Caroll Diagram and Probability Probability ON8.DMP3.1 Compare, through investigation, the theoretical probability of an event with experimental probability, and explain why they might differ. Simple Probability Find the Probability Counting Techniques 1 Counting Techniques 2 Probability Probability and Probability and Probability Probability Probability ON8.DMP3.2 ON8.DMP3.3 Determine, through investigation, the tendency of experimental probability to approach theoretical probability as the number of trials in an experiment increases, using classgenerated data and technology-based simulation models. Identify the complementary event for a given event, and calculate the theoretical probability that a given event will not occur. Find the Probability Complementary Events Probability Probability Probability Probability 77 3P Learning

81 Ontario, Academic (MPM1D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Operating with Exponents Operating with Exponents Operating with Exponents Operating with Exponents Manipulating Expressions and ON9AC.NS1.1 ON9AC.NS1.2 ON9AC.NS1.3 ON9AC.NS1.4 ON9AC.NS2.1 Substitute into and evaluate algebraic expressions involving exponents (i.e., evaluate expressions involving naturalnumber exponents with rational-number bases [e.g., evaluate (3/2) 3 by hand and by using a calculator]). (Sample problem: A movie theatre wants to compare the volumes of popcorn in two containers, a cube with edge length 8.1 cm and a cylinder with radius 4.5 cm and height 8.0 cm. Which container holds more popcorn?) Describe the relationship between the algebraic and geometric representations of a single-variable term up to degree three [i.e., length, which is one dimensional, can be represented by x; area, which is two dimensional, can be represented by (x)(x) or x 2 ; volume, which is three dimensional, can be represented by (x)(x)(x), (x 2 )(x), or x 3 ]. Derive, through the investigation and examination of patterns, the exponent rules for multiplying and dividing monomials, and apply these rules in expressions involving one and two variables with positive exponents. Extend the multiplication rule to derive and understand the power of a power rule, and apply it to simplify expressions involving one and two variables with positive exponents. Simplify numerical expressions involving integers and rational numbers, with and without the use of technology. Exponents Area, Surface Area, and Volume Exponents Exponents Expressions and Exponent Form to s The Zero Exponent Zero Exponent and Perimeter, Area, Dimension Change Properties of Exponents Simplifying with Exponent Laws 1 Exponent Laws and Multiplication with Exponents Factoring with Exponents Properties of Exponents Exponent Laws with Brackets Exponents Measuring Solids Exponents Exponents Add Like Fractions Add Unlike Fractions Subtract Like Fractions Subtract Unlike Fractions Whole ic Fractions 1 s Divide Fractions by Fractions 1 Fractions Divide Fractions by Fractions 2 Decimals Multiply Two Fractions 1 Multiply Two Fractions 2 Operations with Fractions 3P Learning 78

82 Ontario, Academic (MPM1D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Manipulating Expressions and Manipulating Expressions and Manipulating Expressions and Manipulating Expressions and Manipulating Expressions and ON9AC.NS2.2 ON9AC.NS2.3 ON9AC.NS2.4 ON9AC.NS2.5 ON9AC.NS2.6 Solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion. Relate their understanding of inverse operations to squaring and taking the square root, and apply inverse operations to simplify expressions and solve equations. Add and subtract polynomials with up to two variables [e.g., (2x 5) + (3x + 1), (3x 2 y + 2xy 2 ) + (4x 2 y 6xy 2 )], using a variety of tools (e.g., algebra tiles, computer algebra systems, paper and pencil). Multiply a polynomial by a monomial involving the same variable [e.g., 2x(x + 4), 2x 2 (3x 2 2x + 1)], using a variety of tools (e.g., algebra tiles, diagrams, computer algebra systems, paper and pencil). Expand and simplify polynomial expressions involving one variable [e.g., 2x(4x + 1) 3x(x + 2)], using a variety of tools (e.g., algebra tiles, computer algebra systems, paper and pencil). Percent, Ratio, Rate, and Proportion Polynomials Polynomials Polynomials Polynomials Percent Increase and Decrease Percentage Change: Increase and Decrease Percentage to Fraction Percentage Word Solve Percent Rates Rates Calculations Rates Word Equivalent Ratios Ratio Word Solve Proportions Proportional with Square Roots Like Terms: Add and Subtract ic Fractions 1 ic Multiplication Expanding Brackets Expanding with Negatives Expand then Simplify Expanding Binomial Products Special Binomial Products Percentage Basics Percentage Calculations Rates and Ratios and Inequalities Basics Basics Expanding and Factorizing 79 3P Learning

83 Ontario, Academic (MPM1D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Manipulating Expressions and Manipulating Expressions and Manipulating Expressions and ON9AC.NS2.7 ON9AC.NS2.8 ON9AC.NS2.9 Solve first-degree equations, including equations with fractional coefficients, using a variety of tools (e.g., computer algebra systems, paper and pencil) and strategies (e.g., the balance analogy, algebraic strategies). Rearrange formulas involving variables in the first degree, with and without substitution (e.g., in analytic geometry, in measurement) (Sample problem: A circular garden has a circumference of 30 m. What is the length of a straight path that goes through the centre of this garden? Solve problems that can be modelled with first-degree equations, and compare algebraic methods to other solution methods (Sample problem: Solve the following problem in more than one way: Jonah is involved in a walkathon. His goal is to walk 25 km. He begins at 9:00 a.m. and walks at a steady rate of 4 km/h. How many kilometres does he still have left to walk at 1:15 p.m. if he is to achieve his goal? First- Degree First- Degree First- Degree Solve : Add, Subtract 1 Solve : Add, Subtract 2 Solve : Multiply, Divide 1 Solve : Multiply, Divide 2 Simple Solve Two-Step More Solve Multi-Step with Grouping Symbols with Decimals with Fractions Changing the Subject Writing Write an Equation: Word and Inequalities Under Review and Inequalities 3P Learning 80

84 Ontario, Academic (MPM1D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Using to Investigate Using to Investigate Using to Investigate ON9AC.LR1.1 ON9AC.LR1.2 ON9AC.LR1.3 Interpret the meanings of points on scatter plots or graphs that represent linear relations, including scatter plots or graphs in more than one quadrant [e.g., on a scatter plot of height versus age, interpret the point (13, 150) as representing a student who is 13 years old and 150 cm tall; identify points on the graph that represent students who are taller and younger than this student] (Sample problem: Given a graph that represents the relationship of the Celsius scale and the Fahrenheit scale, determine the Celsius equivalent of 5 F.) Pose problems, identify variables, and formulate hypotheses associated with relationships between two variables (Sample problem: Does the rebound height of a ball depend on the height from which it was dropped?) Design and carry out an investigation or experiment involving relationships between two variables, including the collection and organization of data, using appropriate methods, equipment, and/or technology (e.g., surveying; using measuring tools, scientific probes, the Internet) and techniques (e.g., making tables, drawing graphs) (Sample problem: Design and perform an experiment to measure and record the temperature of ice water in a plastic cup and ice water in a thermal mug over a 30 min period, for the purpose of comparison. What factors might affect the outcome of this experiment? How could you design the experiment to account for them? Under review Under review Conversion Graphs Gradients for Real Basics The Plane 81 3P Learning

85 Ontario, Academic (MPM1D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Using to Investigate Understanding Characteristics of Understanding Characteristics of ON9AC.LR1.4 ON9AC.LR2.1 ON9AC.LR2.2 Describe trends and relationships observed in data, make inferences from data, compare the inferences with hypotheses about the data, and explain any differences between the inferences and the hypotheses (e.g., describe the trend observed in the data. Does a relationship seem to exist? Of what sort? Is the outcome consistent with your hypothesis? Identify and explain any outlying pieces of data. Suggest a formula that relates the variables. How might you vary this experiment to examine other relationships?) (Sample problem: Hypothesize the effect of the length of a pendulum on the time required for the pendulum to make five full swings. Use data to make an inference. Compare the inference with the hypothesis. Are there other relationships you might investigate involving pendulums?) Construct tables of values, graphs, and equations, using a variety of tools (e.g., graphing calculators, spreadsheets, graphing software, paper and pencil), to represent linear relations derived from descriptions of realistic situations (Sample problem: Construct a table of values, a graph, and an equation to represent a monthly cellphone plan that costs $25, plus $0.10 per minute of airtime.) Construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools (e.g., spreadsheets, graphing software, graphing calculators, paper and pencil), for linearly related and non-linearly related data collected from a variety of sources (e.g., experiments, electronic secondary sources, patterning with concrete materials) (Sample problem: Collect data, using concrete materials or dynamic geometry software, and construct a table of values, a scatter plot, and a line or curve of best fit to represent the following relationships: the volume and the height for a square-based prism with a fixed base; the volume and the side length of the base for a square-based prism with a fixed height.) Modelling Modelling Function Rules and Tables y=ax Analysis: Scatter Plots Basics The Plane Under Review 3P Learning 82

86 Ontario, Academic (MPM1D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Understanding Characteristics of Understanding Characteristics of Understanding Characteristics of Connecting Various Representations of Connecting Various Representations of 83 3P Learning ON9AC.LR2.3 ON9AC.LR2.4 ON9AC.LR2.5 ON9AC.LR3.1 ON9AC.LR3.2 Identify, through investigation, some properties of linear relations (i.e., numerically, the first difference is a constant, which represents a constant rate of change; graphically, a straight line represents the relation), and apply these properties to determine whether a relation is linear or non-linear. Compare the properties of direct variation and partial variation in applications, and identify the initial value (e.g., for a relation described in words, or represented as a graph or an equation) (Sample problem: Yoga costs $20 for registration, plus $8 per class. Tai chi costs $12 per class. Which situation represents a direct variation, and which represents a partial variation? For each relation, what is the initial value? Explain your answers.) Determine the equation of a line of best fit for a scatter plot, using an informal process (e.g., using a movable line in dynamic statistical software; using a process of trial and error on a graphing calculator; determining the equation of the line joining two carefully chosen points on the scatter plot). Determine values of a linear relation by using a table of values, by using the equation of the relation, and by interpolating or extrapolating from the graph of the relation (Sample problem: The equation H =300 60t represents the height of a hot air balloon that is initially at 300 m and is descending at a constant rate of 60 m/min. Determine algebraically and graphically how long the balloon will take to reach a height of 160 m.) Describe a situation that would explain the events illustrated by a given graph of a relationship between two variables (Sample problem: The walk of an individual is illustrated in the given graph, produced by a motion detector and a graphing calculator. Describe the walk [e.g., the initial distance from the motion detector, the rate of walk]. Under review Under review Slope of a Line Find the Function Rule y=ax Modelling Determining a Rule for a Line y=ax Find the Function Rule Modelling Determining a Rule for a Line Reading Values from a Line Function Rules and Tables Table of Values Straight Lines Straight Lines Under Review Basics Under Review

87 Ontario, Academic (MPM1D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Connecting Various Representations of Connecting Various Representations of ON9AC.LR3.3 ON9AC.LR3.4 Strand: Analytic Geometry Investigating the hip Between the Equation of a Relation and the Shape of Its Graph Investigating the hip Between the Equation of a Relation and the Shape of Its Graph ON9AC.AG1.1 ON9AC.AG1.2 Determine other representations of a linear relation, given one representation (e.g., given a numeric model, determine a graphical model and an algebraic model; given a graph, determine some points on the graph and determine an algebraic model). Describe the effects on a linear graph and make the corresponding changes to the linear equation when the conditions of the situation they represent are varied (e.g., given a partial variation graph and an equation representing the cost of producing a yearbook, describe how the graph changes if the cost per book is altered, describe how the graph changes if the fixed costs are altered, and make the corresponding changes to the equation). Determine, through investigation, the characteristics that distinguish the equation of a straight line from the equations of nonlinear relations (e.g., use a graphing calculator or graphing software to graph a variety of linear and non-linear relations from their equations; classify the relations according to the shapes of their graphs; connect an equation of degree one to a linear relation). Identify, through investigation, the equation of a line in any of the forms y=mx + b, Ax + By + C=0, x=a, y=b. Under review Function Rules and Tables Find the Function Rule Graphing from a Table of Values 2 Which Straight Line? Equation of a Line 1 Determing a Rule for a Line Modelling Gradients for Real General Form of a Line Horizontal and Vertical Lines Straight Lines Under Review Under Review Straight Lines 3P Learning 84

88 Ontario, Academic (MPM1D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Analytic Geometry Investigating the hip Between the Equation of a Relation and the Shape of Its Graph Investigating the Properties of Slope Investigating the Properties of Slope Investigating the Properties of Slope Investigating the Properties of Slope Using the Properties of to Solve ON9AC.AG1.3 ON9AC.AG2.1 ON9AC.AG2.2 ON9AC.AG2.3 ON9AC.AG2.4 ON9AC.AG3.1 Express the equation of a line in the form y=mx + b, given the form Ax + By + C=0. Determine, through investigation, various formulas for the slope of a line segment or a line (e.g., m=rise/ run, m=(the change in y)/(the change in x) or m= y/ x, m=(y 2 y 1 )/(x 2 x 1 )), and use the formula to determine the slope of a line segment or a line. Identify, through investigation with technology, the geometric significance of m and b in the equation y=mx + b. Determine, through investigation, connections among the representations of a constant rate of change of a linear relation (e.g., the cost of producing a book of photographs is $50, plus $5 per book, so an equation is C=50 + 5p; a table of values provides the first difference of 5; the rate of change has a value of 5, which is also the slope of the corresponding line; and 5 is the coefficient of the independent variable, p, in this equation). Identify, through investigation, properties of the slopes of lines and line segments (e.g., direction, positive or negative rate of change, steepness, parallelism, perpendicularity), using graphing technology to facilitate investigations, where appropriate. Graph lines by hand, using a variety of techniques (e.g., graph y=(2/3)x 4 using the y-intercept and slope; graph 2x + 3y=6 using the x- and y-intercepts). Analytic Geometry General Form of a Line Slope of a Line Equation from Two Points Slope of a Line y=ax Intercepts Which Straight Line? Gradients for Real Modelling Are they Parallel? Are they Perpendicular? Perpendicular and Parallel Lines Equation of a Line 3 Graphing from a Table of Values 2 Which Straight Line? y=ax Straight Lines Straight Lines Straight Lines Coordinate Geometry Straight Lines Straight Lines 85 3P Learning

89 Ontario, Academic (MPM1D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Analytic Geometry Using the Properties of to Solve Using the Properties of to Solve Using the Properties of to Solve Using the Properties of to Solve ON9AC.AG3.2 ON9AC.AG3.3 ON9AC.AG3.4 ON9AC.AG3.5 Determine the equation of a line from information about the line (e.g., the slope and y-intercept; the slope and a point; two points) (Sample problem: Compare the equations of the lines parallel to and perpendicular to y=2x 4, and with the same x-intercept as 3x 4y=12. Verify using dynamic geometry software.) Describe the meaning of the slope and y-intercept for a linear relation arising from a realistic situation (e.g., the cost to rent the community gym is $40 per evening, plus $2 per person for equipment rental; the vertical intercept, 40, represents the $40 cost of renting the gym; the value of the rate of change, 2, represents the $2 cost per person), and describe a situation that could be modelled by a given linear equation (e.g., the linear equation M=50 + 6d could model the mass of a shipping package, including 50 g for the packaging material, plus 6 g per flyer added to the package). Identify and explain any restrictions on the variables in a linear relation arising from a realistic situation (e.g., in the relation C= n, C is the cost of holding a party in a hall and n is the number of guests; n is restricted to whole numbers of 100 or less, because of the size of the hall, and C is consequently restricted to $50 to $2550). Determine graphically the point of intersection of two linear relations, and interpret the intersection point in the context of an application (Sample problem: A video rental company has two monthly plans. Plan A charges a flat fee of $30 for unlimited rentals; Plan B charges $9, plus $3 per video. Use a graphical model to determine the conditions under which you should choose Plan A or Plan B.). Analytic Geometry Under review Analytic Geometry Equation from Point and Gradient Equation from Two Points Are they Parallel? Are they Perpendicular? Perpendicular and Parallel Lines Equation of a Line 3 Gradients for Real Solve Systems by Graphing Simultaneous 1 Simultaneous 2 Simultaneous Breakeven Points Modelling Straight Lines Under Review Under Review 3P Learning 86

90 Ontario, Academic (MPM1D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: and Geometry Investigating the Optimal Values of s Investigating the Optimal Values of s Investigating the Optimal Values of s Investigating the Optimal Values of s Investigating the Optimal Values of s ON9AC.MG1.1 ON9AC.MG1.2 ON9AC.MG1.3 ON9AC.MG1.4 ON9AC.MG1.5 Determine the maximum area of a rectangle with a given perimeter by constructing a variety of rectangles, using a variety of tools (e.g., geoboards, graph paper, toothpicks, a pre-made dynamic geometry sketch), and by examining various values of the area as the side lengths change and the perimeter remains constant. Determine the minimum perimeter of a rectangle with a given area by constructing a variety of rectangles, using a variety of tools (e.g., geoboards, graph paper, a premade dynamic geometry sketch), and by examining various values of the side lengths and the perimeter as the area stays constant. Identify, through investigation with a variety of tools (e.g. concrete materials, computer software), the effect of varying the dimensions on the surface area [or volume] of square-based prisms and cylinders, given a fixed volume [or surface area.] Explain the significance of optimal area, surface area, or volume in various applications (e.g., the minimum amount of packaging material; the relationship between surface area and heat loss.) Pose and solve problems involving maximization and minimization of measurements of geometric shapes and figures e.g., determine the dimensions of the rectangular field with the maximum area that can be enclosed by a fixed amount of fencing, if the fencing is required on only three sides) (Sample problem: Determine the dimensions of a square-based, opentopped prism with a volume of 24 cm 3 and with the minimum surface area.). Area, Surface Area, and Volume Area, Surface Area, and Volume Area, Surface Area, and Volume Under Review Under review Area of Squares and Rectangles Perimeter of Squares and Rectangles Area of Squares and Rectangles Perimeter of Squares and Rectangles Surface Area: Rectangular Prisms Surface Area: Cylinders Volume: Rectangular Prisms 1 Volume: Cylinders Under Review Area and Perimeter Area and Perimeter Solids Measuring Solids Under Review Under Review 87 3P Learning

91 Ontario, Academic (MPM1D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: and Geometry Involving Perimeter, Area, Surface Area, and Volume Involving Perimeter, Area, Surface Area, and Volume Involving Perimeter, Area, Surface Area, and Volume Involving Perimeter, Area, Surface Area, and Volume Involving Perimeter, Area, Surface Area, and Volume ON9AC.MG2.1 ON9AC.MG2.2 ON9AC.MG2.3 ON9AC.MG2.4 ON9AC.MG2.5 Relate the geometric representation of the Pythagorean theorem and the algebraic representation a 2 + b 2 =c 2. Solve problems using the Pythagorean theorem, as required in applications (e.g., calculate the height of a cone, given the radius and the slant height, in order to determine the volume of the cone). Solve problems involving the areas and perimeters of composite two-dimensional shapes (i.e., combinations of rectangles, triangles, parallelograms, trapezoids, and circles) (Sample problem: A new park is in the shape of an isosceles trapezoid with a square attached to the shortest side. The side lengths of the trapezoidal section are 200 m, 500 m, 500 m, and 800 m, and the side length of the square section is 200 m. If the park is to be fully fenced and sodded, how much fencing and sod are required?) Develop, through investigation (e.g., using concrete materials), the formulas for the volume of a pyramid, a cone, and a sphere (e.g., use threedimensional figures to show that the volume of a pyramid [or cone] is 1/3 the volume of a prism [or cylinder] with the same base and height, and therefore that Vpyramid=Vprism/3 or Vpyramid=(area of base)(height)/3. Determine, through investigation, the relationship for calculating the surface area of a pyramid (e.g., use the net of a square based pyramid to determine that the surface area is the area of the square base plus the areas of the four congruent triangles). Pythagorean Theorem Pythagorean Theorem Pythagorean Theorem Area, Surface Area, and Volume Area, Surface Area, and Volume Pythagorean Theorem Pythagorean Theorem Pythagoras and Perimeter Pythagorean Triads Cone and Pyramid Dimensions Pythagoras and Perimeter Volume: Pyramids Volume: Cones Volume: Spheres Surface Area: Square Pyramids Surface Area: Rectangular Pyramids Pythagoras' Theorem Pythagoras' Theorem Measuring Solids Pythagoras' Theorem Perimeter and Area Measuring Solids Measuring Solids 3P Learning 88

92 Ontario, Academic (MPM1D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: and Geometry Involving Perimeter, Area, Surface Area, and Volume Investigating and Applying Investigating and Applying 89 3P Learning ON9AC.MG2.6 ON9AC.MG3.1 ON9AC.MG3.2 Solve problems involving the surface areas and volumes of prisms, pyramids, cylinders, cones, and spheres, including composite figures (Sample problem: Break-bit Cereal is sold in a single-serving size, in a box in the shape of a rectangular prism of dimensions 5 cm by 4 cm by 10 cm. The manufacturer also sells the cereal in a larger size, in a box with dimensions double those of the smaller box. Compare the surface areas and the volumes of the two boxes, and explain the implications of your answers.). Determine, through investigation using a variety of tools (e.g., dynamic geometry software, concrete materials), and describe the properties and relationships of the interior and exterior angles of triangles, quadrilaterals, and other polygons, and apply the results to problems involving the angles of polygons (Sample problem: With the assistance of dynamic geometry software, determine the relationship between the sum of the interior angles of a polygon and the number of sides. Use your conclusion to determine the sum of the interior angles of a 20-sided polygon.) Determine, through investigation using a variety of tools (e.g., dynamic geometry software, paper folding), and describe some properties of polygons (e.g., the figure that results from joining the midpoints of the sides of a quadrilateral is a parallelogram; the diagonals of a rectangle bisect each other; the line segment joining the midpoints of two sides of a triangle is half the length of the third side), and apply the results in problem solving (e.g., given the width of the base of an A-frame tree house, determine the length of a horizontal support beam that is attached half way up the sloping sides). Area, Surface Area, and Volume Properties of Polygons Properties of Polygons Surface Area: Rectangular Prisms Surface Area: Cylinders Surface Area: Square Pyramids Surface Area: Rectangular Pyramids Surface Area: Cones Surface Area: Spheres Volume: Rectangular Prisms 1 Volume: Cylinders Volume: Pyramids Volume: Cones Volume: Spheres Volume: Composite Figures Angle Measures in a Triangle Angle Sum of a Triangle Angle Sum of a Quadrilateral Exterior Angles of a Triangle Interior and Exterior Angles Plane Figure Theorems Ratio of Intercepts Measuring Solids Angles and Polygons Polygons and Angles Polygons

93 Ontario, Academic (MPM1D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: and Geometry Investigating and Applying Investigating and Applying ON9AC.MG3.3 ON9AC.MG3.4 Pose questions about geometric relationships, investigate them, and present their findings, using a variety of mathematical forms (e.g., written explanations, diagrams, dynamic sketches, formulas, tables) (Sample problem: How many diagonals can be drawn from one vertex of a 20-sided polygon? How can I find out without counting them?) Illustrate a statement about a geometric property by demonstrating the statement with multiple examples, or deny the statement on the basis of a counterexample, with or without the use of dynamic geometry software (Sample problem: Confirm or deny the following statement: If a quadrilateral has perpendicular diagonals, then it is a square.) Under review Properties of Polygons Plane Figure Theorems Under Review Polygons 3P Learning 90

94 Ontario, Applied (MFM1P) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Involving Proportional Reasoning Involving Proportional Reasoning Involving Proportional Reasoning Involving Proportional Reasoning Involving Proportional Reasoning ON9AP.NS1.1 ON9AP.NS1.2 ON9AP.NS1.3 ON9AP.NS1.4 ON9AP.NS1.5 Illustrate equivalent ratios, using a variety of tools (e.g., concrete materials, diagrams, dynamic geometry software) (e.g., show that 4:6 represents the same ratio as 2:3 by showing that a ramp with a height of 4 m and a base of 6 m and a ramp with a height of 2 m and a base of 3 m are equally steep). Represent, using equivalent ratios and proportions, directly proportional relationships arising from realistic situations (Sample problem: You are building a skateboard ramp whose ratio of height to base must be 2:3. Write a proportion that could be used to determine the base if the height is 4.5 m.) Solve for the unknown value in a proportion, using a variety of methods (e.g., concrete materials, algebraic reasoning, equivalent ratios, constant of proportionality) (Sample problem: Solve x/4 = 15/20.) Make comparisons using unit rates (e.g., if 500 ml of juice costs $2.29, the unit rate is /ml; this unit rate is less than for 750 ml of juice at $3.59, which has a unit rate of /ml). Solve problems involving ratios, rates, and directly proportional relationships in various contexts (e.g., currency conversions, scale drawings, measurement), using a variety of methods (e.g., using algebraic reasoning, equivalent ratios, a constant of proportionality; using dynamic geometry software to construct and measure scale drawings) (Sample problem: Simple interest is directly proportional to the amount invested. If Luis invests $84 for one year and earns $1.26 in interest, how much would he earn in interest if he invested $235 for one year?) Proportional Reasoning Proportional Reasoning Proportional Reasoning Equivalent Ratios Equivalent Fractions Ratio Word Rates Solve Proportions Proportional Reasoning Ratio Word Rate Word Rates Calculations Proportional Rates and Ratios Rates and Ratios Rates and Ratios Rates and Ratios Rates and Ratios 91 3P Learning

95 Ontario, Applied (MFM1P) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Involving Proportional Reasoning Simplifying Expressions and ON9AP.NS1.6 ON9AP.NS2.1 Solve problems requiring the expression of percents, fractions, and decimals in their equivalent forms (e.g., calculating simple interest and sales tax; analysing data) (Sample problem: Of the 29 students in a math class, 13 are taking science this semester. If this class is representative of all the students in the school, estimate and calculate the percent of the 236 students who are taking science this semester. Estimate and calculate the number of students this percent represents.). Simplify numerical expressions involving integers and rational numbers, with and without the use of technology. Proportional Reasoning Numerical Expressions Ratio and Proportion Decimal to Percentage Percentage to Fraction What Percentage? Percentage of a Percentage Word Percentage Basics Percentage Calculations Add Like Fractions Add Unlike Fractions Add Like Mixed s Add Unlike Mixed s Add Mixed s: Signs Can Differ Subtract Like Fractions Subtract Unlike Fractions Subtract Like Mixed s Subtract Unlike Mixed s Subtract Mixed Fractions s: Signs Differ Multiply Two Fractions 1 Multiply Two Fractions 2 Multiplying Fractions Multiply Mixed s Divide Fractions by Fractions 1 Divide Fractions by Fractions 2 Dividing Fractions Divide Mixed s with Signs Operations with Fractions 3P Learning 92

96 Ontario, Applied (MFM1P) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Simplifying Expressions and Simplifying Expressions and Simplifying Expressions and Simplifying Expressions and Simplifying Expressions and ON9AP.NS2.2 ON9AP.NS2.3 ON9AP.NS2.4 ON9AP.NS2.5 ON9AP.NS2.6 Relate their understanding of inverse operations to squaring and taking the square root, and apply inverse operations to simplify expressions and solve equations. Describe the relationship between the algebraic and geometric representations of a single-variable term up to degree three [i.e., length, which is one dimensional, can be represented by x; area, which is two dimensional, can be represented by (x)(x) or x 2 ; volume, which is three dimensional, can be represented by (x) (x)(x), (x 2 )(x), or x 3 ] Substitute into and evaluate algebraic expressions involving exponents (i.e., evaluate expressions involving natural-number exponents with rational-number bases) [e.g., evaluate (3/2) 3 by hand and by using a calculator]) (Sample problem: A movie theatre wants to compare the volumes of popcorn in two containers, a cube with edge length 8.1 cm and a cylinder with radius 4.5 cm and height 8.0 cm. Which container holds more popcorn?); Add and subtract polynomials involving the same variable up to degree three [e.g., (2x + 1) + (x 2 3x + 4)], using a variety of tools (e.g., algebra tiles, computer algebra systems, paper and pencil). Multiply a polynomial by a monomial involving the same variable to give results up to degree three [e.g., (2x)(3x), 2x(x + 3)], using a variety of tools (e.g., algebra tiles, drawings, computer algebra systems, paper and pencil). Dimensions and Volume Numerical Expressions Polynomials Polynomials with Square Roots Perimeter, Area, Dimension Change Exponent Form to s Like Terms: Add and Subtract ic Fractions 1 ic Multiplication Expanding Brackets Expanding with Negatives Measuring Solids Exponents Basics Basics 93 3P Learning

97 Ontario, Applied (MFM1P) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Simplifying Expressions and Simplifying Expressions and ON9AP.NS2.7 ON9AP.NS2.8 Strand: Using to Investigate Using to Investigate ON9AP.LR1.1 ON9AP.LR1.2 Solve first-degree equations with nonfractional coefficients, using a variety of tools (e.g., computer algebra systems, paper and pencil) and strategies (e.g., the balance analogy, algebraic strategies) (Sample problem: Solve 2x + 7=6x 1 using the balance analogy.) Substitute into algebraic equations and solve for one variable in the first degree (e.g., in relationships, in measurement) (Sample problem: The perimeter of a rectangle can be represented as P=2l + 2w. If the perimeter of a rectangle is 59 cm and the width is 12 cm, determine the length.). Interpret the meanings of points on scatter plots or graphs that represent linear relations, including scatter plots or graphs in more than one quadrant [e.g., on a scatter plot of height versus age, interpret the point (13, 150) as representing a student who is 13 years old and 150 cm tall; identify points on the graph that represent students who are taller and younger than this student] (Sample problem: Given a graph that represents the relationship of the Celsius scale and the Fahrenheit scale, determine the Celsius equivalent of 5 F.) Pose problems, identify variables, and formulate hypotheses associated with relationships between two variables (Sample problem: Does the rebound height of a ball depend on the height from which it was dropped?) Under review Under review Simple Solve Two-Step More Solve Multi-Step with Grouping Symbols and Inequalities Conversion Graphs Gradients for Real Basics The Plane 3P Learning 94

98 Ontario, Applied (MFM1P) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Using to Investigate Using to Investigate Determining Characteristics of ON9AP.LR1.3 ON9AP.LR1.4 ON9AP.LR2.1 Carry out an investigation or experiment involving relationships between two variables, including the collection and organization of data, using appropriate methods, equipment, and/or technology (e.g., surveying; using measuring tools, scientific probes, the Internet) and techniques (e.g., making tables, drawing graphs) (Sample problem: Perform an experiment to measure and record the temperature of ice water in a plastic cup and ice water in a thermal mug over a 30 min period, for the purpose of comparison. What factors might affect the outcome of this experiment? How could you change the experiment to account for them?) Describe trends and relationships observed in data, make inferences from data, compare the inferences with hypotheses about the data, and explain any differences between the inferences and the hypotheses (e.g., describe the trend observed in the data. Does a relationship seem to exist? Of what sort? Is the outcome consistent with your hypothesis? Identify and explain any outlying pieces of data. Suggest a formula that relates the variables. How might you vary this experiment to examine other relationships?) (Sample problem: Hypothesize the effect of the length of a pendulum on the time required for the pendulum to make five full swings. Use data to make an inference. Compare the inference with the hypothesis. Are there other relationships you might investigate involving pendulums?). Construct tables of values and graphs, using a variety of tools (e.g., graphing calculators, spreadsheets, graphing software, paper and pencil), to represent linear relations derived from descriptions of realistic situations (Sample problem: Construct a table of values and a graph to represent a monthly cellphone plan that costs $25, plus $0.10 per minute of airtime.) Modelling Function Rules and Tables y=ax Basics The Plane 95 3P Learning

99 Ontario, Applied (MFM1P) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Determining Characteristics of Determining Characteristics of Investigating Constant Rate of Change Investigating Constant Rate of Change ON9AP.LR2.2 ON9AP.LR2.3 ON9AP.LR3.1 ON9AP.LR3.2 Construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools (e.g., spreadsheets, graphing software, graphing calculators, paper and pencil), for linearly related and non-linearly related data collected from a variety of sources (e.g., experiments, electronic secondary sources, patterning with concrete materials) (Sample problem: Collect data, using concrete materials or dynamic geometry software, and construct a table of values, a scatter plot, and a line or curve of best fit to represent the following relationships: the volume and the height for a square-based prism with a fixed base; the volume and the side length of the base for a square-based prism with a fixed height.) Identify, through investigation, some properties of linear relations (i.e., numerically, the first difference is a constant, which represents a constant rate of change; graphically, a straight line represents the relation), and apply these properties to determine whether a relation is linear or non-linear. Determine, through investigation, that the rate of change of a linear relation can be found by choosing any two points on the line that represents the relation, finding the vertical change between the points (i.e., the rise) and the horizontal change between the points (i.e., the run), and writing the ratio rise/run(i.e., rate of change = rise/run). Determine, through investigation, connections among the representations of a constant rate of change of a linear relation (e.g., the cost of producing a book of photographs is $50, plus $5 per book, so an equation is C=50 + 5p; a table of values provides the first difference of 5; the rate of change has a value of 5; and 5 is the coefficient of the independent variable, p, in this equation. Analysis: Scatter Plots Slope of a Line Find the Function Rule y=ax Modelling Determining a Rule for a Line Slope of a Line Equation from Two Points Equation of a Line 1 Gradients for Real Modelling Under Review Straight Lines Straight Lines 3P Learning 96

100 Ontario, Applied (MFM1P) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Investigating Constant Rate of Change Investigating Constant Rate of Change Investigating Constant Rate of Change Connecting Various Representations of and Using the Representations ON9AP.LR3.3 ON9AP.LR3.4 ON9AP.LR3.5 ON9AP.LR4.1 Compare the properties of direct variation and partial variation in applications, and identify the initial value (e.g., for a relation described in words, or represented as a graph or an equation) (Sample problem: Yoga costs $20 for registration, plus $8 per class. Tai chi costs $12 per class. Which situation represents a direct variation, and which represents a partial variation? For each relation, what is the initial value? Explain your answers.) Express a linear relation as an equation in two variables, using the rate of change and the initial value (e.g., Mei is raising funds in a charity walkathon; the course measures 25 km, and Mei walks at a steady pace of 4 km/h; the distance she has left to walk can be expressed as d=25 4t, where t is the number of hours since she started the walk). Describe the meaning of the rate of change and the initial value for a linear relation arising from a realistic situation (e.g., the cost to rent the community gym is $40 per evening, plus $2 per person for equipment rental; the vertical intercept, 40, represents the $40 cost of renting the gym; the value of the rate of change, 2, represents the $2 cost per person), and describe a situation that could be modelled by a given linear equation (e.g., the linear equation M=50 + 6d could model the mass of a shipping package, including 50 g for the packaging material, plus 6 g per flyer added to the package). Determine values of a linear relation by using a table of values, by using the equation of the relation, and by interpolating or extrapolating from the graph of the relation (Sample problem: The equation H=300 60t represents the height of a hot air balloon that is initially at 300 m and is descending at a constant rate of 60 m/min. Determine algebraically and graphically its height after 3.5 min.) y=ax Find the Function Rule Modelling Determining a Rule for a Line Modelling Determining a Rule for a Line Gradients for Real Reading Values from a Line Function Rules and Tables Table of Values Conversion Graphs Straight Lines Straight Lines Under Review Basics 97 3P Learning

101 Ontario, Applied (MFM1P) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Connecting Various Representations of and Using the Representations Connecting Various Representations of and Using the Representations Connecting Various Representations of and Using the Representations Connecting Various Representations of and Using the Representations ON9AP.LR4.2 ON9AP.LR4.3 ON9AP.LR4.4 ON9AP.LR4.5 Describe a situation that would explain the events illustrated by a given graph of a relationship between two variables (Sample problem: The walk of an individual is illustrated in the given graph, produced by a motion detector and a graphing calculator. Describe the walk [e.g., the initial distance from the motion detector, the rate of walk].) Determine other representations of a linear relation arising from a realistic situation, given one representation (e.g., given a numeric model, determine a graphical model and an algebraic model; given a graph, determine some points on the graph and determine an algebraic model). Under review Solve problems that can be modelled with first-degree equations, and compare the algebraic method to other solution methods (e.g., graphing) (Sample problem: First- Bill noticed it snowing and measured that Degree 5 cm of snow had already fallen. During the next hour, an additional 1.5 cm of snow fell. If it continues to snow at this rate, how many more hours will it take until a total of 12.5 cm of snow has accumulated?) Describe the effects on a linear graph and make the corresponding changes to the linear equation when the conditions of the situation they represent are varied (e.g., given a partial variation graph and an equation representing the cost of producing a yearbook, describe how the graph changes if the cost per book is altered, describe how the graph changes if the fixed costs are altered, and make the corresponding changes to the equation). Function Rules and Tables Find the Function Rule Graphing from a Table of Values 1 Graphing from a Table of Values 2 Which Straight Line? Equation of a Line 1 Determing a Rule for a Line Modelling Writing Write an Equation: Word Gradients for Real Under Review Straight Lines and Inequalities Under Review 3P Learning 98

102 Ontario, Applied (MFM1P) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Connecting Various Representations of and Using the Representations Connecting Various Representations of and Using the Representations ON9AP.LR4.6 ON9AP.LR4.7 Strand: and Geometry Investigating the Optimal Values of s of Rectangles Investigating the Optimal Values of s of Rectangles ON9AP.MG1.1 ON9AP.MG1.2 Determine graphically the point of intersection of two linear relations, and interpret the intersection point in the context of an application (Sample problem: A video rental company has two monthly plans. Plan A charges a flat fee of $30 for unlimited rentals; Plan B charges $9, plus $3 per video. Use a graphical model to determine the conditions under which you should choose Plan A or Plan B.) Select a topic involving a two-variable relationship (e.g., the amount of your pay cheque and the number of hours you work; trends in sports salaries over time; the time required to cool a cup of coffee), pose a question on the topic, collect data to answer the question, and present its solution using appropriate representations of the data (Sample problem: Individually or in a small group, collect data on the cost compared to the capacity of computer hard drives. Present the data numerically, graphically, and [if linear] algebraically. Describe the results and any trends orally or by making a poster display or by using presentation software.). Determine the maximum area of a rectangle with a given perimeter by constructing a variety of rectangles, using a variety of tools (e.g., geoboards, graph paper, toothpicks, a pre-made dynamic geometry sketch), and by examining various values of the area as the side lengths change and the perimeter remains constant. Determine the minimum perimeter of a rectangle with a given area by constructing a variety of rectangles, using a variety of tools (e.g., geoboards, graph paper, a premade dynamic geometry sketch), and by examining various values of the side lengths and the perimeter as the area stays constant. First-Degree Solve Systems by Graphing Simultaneous 1 Simultaneous 2 Simultaneous Breakeven Points Area, Surface Area, and Volume Dimensions and Volume Area of Squares and Rectangles Perimeter of Squares and Rectangles Area of Squares and Rectangles Perimeter of Squares and Rectangles Area and Perimeter Area and Perimeter 99 3P Learning

103 Ontario, Applied (MFM1P) Substrand Expectation Expectation Description Topic Activities ebooks Strand: and Geometry Investigating the Optimal Values of s of Rectangles Involving Perimeter, Area, and Volume Involving Perimeter, Area, and Volume Involving Perimeter, Area, and Volume Involving Perimeter, Area, and Volume ON9AP.MG1.3 ON9AP.MG2.1 ON9AP.MG2.2 ON9AP.MG2.3 ON9AP.MG2.4 Solve problems that require maximizing the area of a rectangle for a fixed perimeter or minimizing the perimeter of a rectangle for a fixed area (Sample problem: You have 100 m of fence to enclose a rectangular area to be used for a snow sculpture competition. One side of the area is bounded by the school, so the fence is required for only three sides of the rectangle. Determine the dimensions of the maximum area that can be enclosed.). Relate the geometric representation of the Pythagorean theorem to the algebraic representation a 2 + b 2 = c 2. Solve problems using the Pythagorean theorem, as required in applications (e.g., calculate the height of a cone, given the radius and the slant height, in order to determine the volume of the cone). Solve problems involving the areas and perimeters of composite two-dimensional shapes (i.e., combinations of rectangles, triangles, parallelograms, trapezoids, and circles) (Sample problem: A new park is in the shape of an isosceles trapezoid with a square attached to the shortest side. The side lengths of the trapezoidal section are 200 m, 500 m, 500 m, and 800 m, and the side length of the square section is 200 m. If the park is to be fully fenced and sodded, how much fencing and sod are required?) Develop, through investigation (e.g., using concrete materials), the formulas for the volume of a pyramid, a cone, and a sphere (e.g., use three-dimensional figures to show that the volume of a pyramid [or cone] is 1/3 the volume of a prism [or cylinder] with the same base and height, and therefore that Vpyramid=Vprism/3 or Vpyramid=(area of base)(height)/3. Under review Dimensions and Volume Dimensions and Volume Dimensions and Volume Dimensions and Volume Pythagorean Theorem Pythagorean Theorem Pythagoras and Perimeter Pythagorean Triads Cone and Pyramid Dimensions Pythagoras and Perimeter Volume: Pyramids Volume: Cones Volume: Spheres Pythagoras' Theorem Pythagoras' Theorem Measuring Solids Pythagoras' Theorem Perimeter and Area Measuring Solids 3P Learning 100

104 Ontario, Applied (MFM1P) Substrand Expectation Expectation Description Topic Activities ebooks Strand: and Geometry Involving Perimeter, Area, and Volume Investigating and Applying Investigating and Applying Investigating and Applying ON9AP.MG2.5 ON9AP.MG3.1 ON9AP.MG3.2 ON9AP.MG3.3 Solve problems involving the volumes of prisms, pyramids, cylinders, cones, and spheres (Sample problem: Break-bit Cereal is sold in a single-serving size, in a box in the shape of a rectangular prism of dimensions 5 cm by 4 cm by 10 cm. The manufacturer also sells the cereal in a larger size, in a box with dimensions double those of the smaller box. Make a hypothesis about the effect on the volume of doubling the dimensions. Test your hypothesis using the volumes of the two boxes, and discuss the result.). Determine, through investigation using a variety of tools (e.g., dynamic geometry software, concrete materials), and describe the properties and relationships of the interior and exterior angles of triangles, quadrilaterals, and other polygons, and apply the results to problems involving the angles of polygons (Sample problem: With the assistance of dynamic geometry software, determine the relationship between the sum of the interior angles of a polygon and the number of sides. Use your conclusion to determine the sum of the interior angles of a 20-sided polygon.) Determine, through investigation using a variety of tools (e.g., dynamic geometry software, concrete materials), and describe the properties and relationships of the angles formed by parallel lines cut by a transversal, and apply the results to problems involving parallel lines (e.g., given a diagram of a rectangular gate with a supporting diagonal beam, and given the measure of one angle in the diagram, use the angle properties of triangles and parallel lines to determine the measures of the other angles in the diagram). Create an original dynamic sketch, paper folding design, or other illustration that incorporates some of the geometric properties from this section, or find and report on some real-life application(s) (e.g., in carpentry, sports, architecture) of the geometric properties. Dimensions and Volume Angles Angles Under review Volume: Rectangular Prisms 1 Volume: Cylinders Volume: Pyramids Volume: Cones Volume: Spheres Volume: Composite Figures Angle Measures in a Triangle Angle Sum of a Triangle Angle Sum of a Quadrilateral Exterior Angles of a Triangle Interior and Exterior Angles Parallel Lines Angles on Parallel Lines Measuring Solids Angles and Polygons Polygons and Angles Angles 101 3P Learning

105 Ontario, Academic (MPM2D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: of the Form y=ax 2 + bx + c Investigating the Basic Properties of Investigating the Basic Properties of Investigating the Basic Properties of Investigating the Basic Properties of ON10AC.QR1.1 ON10AC.QR1.2 ON10AC.QR1.3 ON10AC.QR1.4 Collect data that can be represented as a quadratic relation, from experiments using appropriate equipment and technology (e.g., concrete materials, scientific probes, graphing calculators), or from secondary sources (e.g., the Internet, Statistics Canada); graph the data and draw a curve of best fit, if appropriate, with or without the use of technology (Sample problem: Make a 1 m ramp that makes a 15 angle with the floor. Place a can 30 cm up the ramp. Record the time it takes for the can to roll to the bottom. Repeat by placing the can 40 cm, 50 cm, and 60 cm up the ramp, and so on. Graph the data and draw the curve of best fit.) Determine, through investigation with and without the use of technology, that a quadratic relation of the form y=ax 2 + bx + c (a 0) can be graphically represented as a parabola, and that the table of values yields a constant second difference (Sample problem: Graph the relation y=x 2 4x by developing a table of values and plotting points. Observe the shape of the graph. Calculate first and second differences. Repeat for different quadratic relations. Describe your observations and make conclusions, using the appropriate terminology.) Identify the key features of a graph of a parabola (i.e., the equation of the axis of symmetry, the coordinates of the vertex, the y-intercept, the zeros, and the maximum or minimum value), and use the appropriate terminology to describe them. Compare, through investigation using technology, the features of the graph of y=x 2 and the graph of y=2 x, and determine the meaning of a negative exponent and of zero as an exponent (e.g., by examining patterns in a table of values for y=2 x ; by applying the exponent rules for multiplication and division). Graphing Parabolas Parabolas and Marbles Parabolas and Rectangles Graphing Parabolas Vertex of a Parabola Parabolas and Marbles Parabolas and Rectangles Graphing Parabolas Graphing Exponentials Parabolas Simple Nonlinear Graphs Parabolas Simple Nonlinear Graphs Parabolas Simple Nonlinear Graphs Parabolas Simple Nonlinear Graphs Exponential and Power Graphs 3P Learning 102

106 Ontario, Academic (MPM2D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: of the Form y=ax 2 + bx + c Relating the Graph of y=x 2 and Its Transformations Relating the Graph of y=x 2 and Its Transformations Relating the Graph of y=x 2 and Its Transformations Relating the Graph of y=x 2 and Its Transformations ON10AC.QR2.1 ON10AC.QR2.2 ON10AC.QR2.3 ON10AC.QR2.4 ON10AC.QR3.1 ON10AC.QR3.2 Identify, through investigation using technology, the effect on the graph of y=x 2 of transformations (i.e., translations, reflections in the x-axis, vertical stretches or compressions) by considering separately each parameter a, h, and k [i.e., investigate the effect on the graph of y=x 2 of a, h, and k in y=x 2 + k, y=(x h) 2, and y=ax 2 ]. Explain the roles of a, h, and k in y=a(x h) 2 + k, using the appropriate terminology to describe the transformations, and identify the vertex and the equation of the axis of symmetry. Sketch, by hand, the graph of y=a(x h) 2 + k by applying transformations to the graph of y=x 2 [Sample problem: Sketch the graph of y= 1/2(x 3) 2 + 4, and verify using technology.] Determine the equation, in the form y=a(x h) 2 + k, of a given graph of a parabola. Expand and simplify second-degree polynomial expressions [e.g., (2x + 5) 2, (2x y)(x + 3y)], using a variety of tools (e.g., algebra tiles, diagrams, computer algebra systems, paper and pencil) and strategies (e.g., patterning). Factor polynomial expressions involving common factors, trinomials, and differences of squares [e.g., 2x 2 + 4x, 2x 2y + ax ay, x 2 x 6, 2a a + 5, 4x 2 25], using a variety of tools (e.g., concrete materials, computer algebra systems, paper and pencil) and strategies (e.g., patterning). Under review Symmetries of Graphs 1 Vertex of a Parabola Symmetries of Graphs 1 Graphing Parabolas Symmetries of Graphs 1 Expand then Simplify Expanding Binomial Products Special Binomial Products Grouping in Pairs Factoring s 1 Factoring s 2 Parabolas Simple Nonlinear Graphs Sketching Polynomials Parabolas Simple Nonlinear Graphs Sketching Polynomials Parabolas Simple Nonlinear Graphs Parabolas Simplifying Factoring 103 3P Learning

107 Ontario, Academic (MPM2D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: of the Form y=ax 2 + bx + c ON10AC.QR3.3 ON10AC.QR3.4 ON10AC.QR3.5 ON10AC.QR3.6 ON10AC.QR3.7 ON10AC.QR3.8 Determine, through investigation, and describe the connection between the factors of a quadratic expression and the x-intercepts (i.e., the zeros) of the graph of the corresponding quadratic relation, expressed in the form y=a(x r)(x s). Interpret real and non-real roots of quadratic equations, through investigation using graphing technology, and relate the roots to the x-intercepts of the corresponding relations. Express y=ax 2 + bx + c in the form y=a(x h) 2 + k by completing the square in situations involving no fractions, using a variety of tools (e.g. concrete materials, diagrams, paper and pencil). Sketch or graph a quadratic relation whose equation is given in the form y=ax 2 + bx + c, using a variety of methods (e.g., sketching y=x 2 2x 8 using intercepts and symmetry; sketching y=3x 2 12x + 1 by completing the square and applying transformations; graphing h= 4.9t t using technology). Explore the algebraic development of the quadratic formula (e.g., given the algebraic development, connect the steps to a numerical example; follow a demonstration of the algebraic development [student reproduction of the development of the general case is not required]). Solve quadratic equations that have real roots, using a variety of methods (i.e., factoring, using the quadratic formula, graphing) (Sample problem: Solve x x + 16=0 by factoring, and verify algebraically. Solve x 2 + x 4=0 using the quadratic formula, and verify graphically using technology. Solve 4.9t t + 1.5=0 by graphing h= 4.9t t using technology.). 1 2 Checking Solutions Solve s: Coefficient of 1 The Formula The Discriminant Completing the Square Completing the Square 2 Graphing Parabolas The Formula Factoring s 1 Factoring s 2 The Formula Graphing Parabolas Parabolas Parabolas Parabolas Parabolas Factoring 3P Learning 104

108 Ontario, Academic (MPM2D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: of the Form y=ax 2 + bx + c Involving Involving ON10AC.QR4.1 ON10AC.QR4.2 Strand: Analytic Geometry Using Systems to Solve Using Systems to Solve ON10AC.AG1.1 ON10AC.AG1.2 Determine the zeros and the maximum or minimum value of a quadratic relation from its graph (i.e., using graphing calculators or graphing software) or from its defining equation (i.e., by applying algebraic techniques.) Solve problems arising from a realistic situation represented by a graph or an equation of a quadratic relation, with and without the use of technology (e.g., given the graph or the equation of a quadratic relation representing the height of a ball over elapsed time, answer questions such as the following: What is the maximum height of the ball? After what length of time will the ball hit the ground? Over what time interval is the height of the ball greater than 3 m?). Solve systems of two linear equations involving two variables, using the algebraic method of substitution or elimination (Sample problem: Solve y=1/2x 5, 3x + 2y= 2 for x and y algebraically, and verify algebraically and graphically). Solve problems that arise from realistic situations described in words or represented by linear systems of two equations involving two variables, by choosing an appropriate algebraic or graphical method (Sample problem: The Robotics Club raised $5000 to build a robot for a future competition. The club invested part of the money in an account that paid 4% annual interest, and the rest in a government bond that paid 3.5% simple interest per year. After one year, the club earned a total of $190 in interest. How much was invested at each rate? Verify your result.). Systems of Systems of Parabolas and Marbles Parabolas and Rectangles Completing the Square Completing the Square 2 Vertex of a Parabola Parabolas and Marbles Parabolas and Rectangles Simultaneous Simultaneous 1 Simultaneous 2 Solve Systems by Graphing Breakeven Point Parabolas Factoring Parabolas and Inequalities and Inequalities 105 3P Learning

109 Ontario, Academic (MPM2D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Analytic Geometry Involving Properties of Line Segments Involving Properties of Line Segments Involving Properties of Line Segments Involving Properties of Line Segments Involving Properties of Line Segments Using Analytic Geometry to Verify Properties ON10AC.AG2.1 ON10AC.AG2.2 ON10AC.AG2.3 ON10AC.AG2.4 ON10AC.AG2.5 ON10AC.AG3.1 Develop the formula for the midpoint of a line segment, and use this formula to solve problems (e.g., determine the coordinates of Analytic the midpoints of the sides of a triangle, given Geometry the coordinates of the vertices, and verify concretely or by using dynamic geometry software). Develop the formula for the length of a line segment, and use this formula to solve problems (e.g., determine the lengths of the line segments joining the midpoints of the sides of a triangle, given the coordinates of the vertices of the triangle, and verify using dynamic geometry software). Develop the equation for a circle with centre (0, 0) and radius r, by applying the formula for the length of a line segment. Determine the radius of a circle with centre (0, 0), given its equation; write the equation of a circle with centre (0, 0), given the radius; and sketch the circle, given the equation in the form x 2 + y 2 =r 2. Solve problems involving the slope, length, and midpoint of a line segment (e.g., determine the equation of the right bisector of a line segment, given the coordinates of the endpoints; determine the distance from a given point to a line whose equation is given, and verify using dynamic geometry software). Determine, through investigation (e.g., using dynamic geometry software, by paper folding), some characteristics and properties of geometric figures (e.g., medians in a triangle, similar figures constructed on the sides of a right triangle). Analytic Geometry Analytic Geometry Analytic Geometry Analytic Geometry Analytic Geometry Midpoint by Formula Distance Between Two Points Centre and Radius 1 Graphing Circles Centre and Radius 1 Graphing Circles Midpoint by Formula Distance Between Two Points Are They Parallel? Are They Perpendicular? Perpendicular and Parallel Lines Equation of a Line 3 Perpendicular Distance 1 Perpendicular Distance 2 Plane Figure Theorems Coordinate Geometry Coordinate Geometry Circle Graphs Circle Graphs Coordinate Geometry Coordinate Geometry 3P Learning 106

110 Ontario, Academic (MPM2D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Analytic Geometry Using Analytic Geometry to Verify Properties Using Analytic Geometry to Verify Properties ON10AC.AG3.2 ON10AC.AG3.3 Strand: Trigonometry Investigating Similarity and ON10AC.TR1.1 Involving Similar Triangles Investigating Similarity and Involving Similar Triangles Investigating Similarity and Involving Similar Triangles ON10AC.TR1.2 ON10AC.TR1.3 Verify, using algebraic techniques and analytic geometry, some characteristics of geometric figures (e.g., verify that two lines are perpendicular, given the coordinates of two points on each line; verify, by determining side length, that a triangle is equilateral, given the coordinates of the vertices). Plan and implement a multi-step strategy that uses analytic geometry and algebraic techniques to verify a geometric property (e.g., given the coordinates of the vertices of a triangle, verify that the line segment joining the midpoints of two sides of the triangle is parallel to the third side and half its length, and check using dynamic geometry software; given the coordinates of the vertices of a rectangle, verify that the diagonals of the rectangle bisect each other). Verify, through investigation (e.g., using dynamic geometry software, concrete materials), the properties of similar triangles (e.g., given similar triangles, verify the equality of corresponding angles and the proportionality of corresponding sides). Describe and compare the concepts of similarity and congruence. Solve problems involving similar triangles in realistic situations (e.g., shadows, reflections, scale models, surveying) (Sample problem: Use a metre stick to determine the height of a tree, by means of the similar triangles formed by the tree, the metre stick, and their shadows.). Analytic Geometry Under Review Similarity and Congruence Similarity and Congruence Under Review Are They Parallel? Are They Perpendicular? Under Review Similar Triangles Scale Factor Similar Triangles Similar Figures Congruent Triangles Congruent Figures (Grid) Congruent Figures: Find Values Under Review Coordinate Geometry Coordinate Geometry Similarity and Congruence Similarity and Congruence Similarity and Congruence 107 3P Learning

111 Ontario, Academic (MPM2D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Trigonometry Involving the Trigonometry of Right Triangles Involving the Trigonometry of Right Triangles Involving the Trigonometry of Right Triangles Involving the Trigonometry of Acute Triangles ON10AC.TR2.1 ON10AC.TR2.2 ON10AC.TR2.3 ON10AC.TR3.1 Determine, through investigation (e.g., using dynamic geometry software, concrete materials), the relationship between the ratio of two sides in a right triangle and the ratio of the two corresponding sides in a similar right triangle, and define the sine, cosine, and tangent ratios (e.g., sin A = opposite/hypotenuse). Determine the measures of the sides and angles in right triangles, using the primary trigonometric ratios and the Pythagorean theorem. Solve problems involving the measures of sides and angles in right triangles in real life applications (e.g., in surveying, in navigating, in determining the height of an inaccessible object around the school), using the primary trigonometric ratios and the Pythagorean theorem. Explore the development of the sine law within acute triangles (e.g., use dynamic geometry software to determine that the ratio of the side lengths equals the ratio of the sines of the opposite angles; follow the algebraic development of the sine law and identify the application of solving systems of equations [student reproduction of the development of the formula is not required]). Trigonometry Trigonometry Trigonometry Hypotenuse, Adjacent, Opposite Sin A Cos A Tan A Pythagorean Theorem Sin A Cos A Tan A Find Unknown Sides Find Unknown Angles Elevation and Depression Trigonometry 1 Trigonometry 2 Trigonometry Sine Rule 1 Trigonometry Trigonometry Trigonometry Non Right Angled Triangles 3P Learning 108

112 Ontario, Academic (MPM2D) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Trigonometry Involving the Trigonometry of Acute Triangles Involving the Trigonometry of Acute Triangles Involving the Trigonometry of Acute Triangles ON10AC.TR3.2 ON10AC.TR3.3 ON10AC.TR3.4 Explore the development of the cosine law within acute triangles (e.g., use dynamic geometry software to verify the cosine law; follow the algebraic development of the cosine law and identify its relationship to the Pythagorean theorem and the cosine ratio [student reproduction of the development of the formula is not required]). Determine the measures of sides and angles in acute triangles, using the sine law and the cosine law (Sample problem: In triangle ABC, A=35, B=65, and AC=18 cm. Determine BC. Check your result using dynamic geometry software.) Solve problems involving the measures of sides and angles in acute triangles. Trigonometry Trigonometry Trigonometry Cosine Rule 1 Cosine Rule 2 Sine Rule 1 Cosine Rule 1 Cosine Rule 2 Sine Rule 1 Cosine Rule 1 Cosine Rule 2 Non Right Angled Triangles Non Right Angled Triangles Non Right Angled Triangles 109 3P Learning

113 Ontario, Applied (MFM2P) Substrand Expectation Expectation Description Topic Activities ebooks Strand: and Trigonometry Involving Similar Triangles Involving Similar Triangles Involving Similar Triangles Involving the Trigonometry of Right Triangles Involving the Trigonometry of Right Triangles Involving the Trigonometry of Right Triangles ON10AP.MT1.1 ON10AP.MT1.2 ON10AP.MT1.3 ON10AP.MT2.1 ON10AP.MT2.2 ON10AP.MT2.3 Verify, through investigation (e.g., using dynamic geometry software, concrete materials), properties of similar triangles (e.g., given similar triangles, verify the equality of corresponding angles and the proportionality of corresponding sides). Determine the lengths of sides of similar triangles, using proportional reasoning. Solve problems involving similar triangles in realistic situations (e.g., shadows, reflections, scale models, surveying) (Sample problem: Use a metre stick to determine the height of a tree, by means of the similar triangles formed by the tree, the metre stick, and their shadows.). Determine, through investigation (e.g., using dynamic geometry software, concrete materials), the relationship between the ratio of two sides in a right triangle and the ratio of the two corresponding sides in a similar right triangle, and define the sine, cosine, and tangent ratios (e.g., sin A = opposite/ hypotenuse). Determine the measures of the sides and angles in right triangles, using the primary trigonometric ratios and the Pythagorean theorem. Solve problems involving the measures of sides and angles in right triangles in real-life applications (e.g., in surveying, in navigation, in determining the height of an inaccessible object around the school), using the primary trigonometric ratios and the Pythagorean theorem (Sample problem: Build a kite, using imperial measurements, create a clinometer to determine the angle of elevation when the kite is flown, and use the tangent ratio to calculate the height attained.) Trigonometry Similar Triangles Trigonometry Similar Triangles Under Review Trigonometry Trigonometry Trigonometry Under Review Hypotenuse, Adjacent, Opposite Sin A Cos A Tan A Pythagorean Theorem Sin A Cos A Tan A Find Unknown Sides Find Unknown Angles Elevation and Depression Trigonometry 1 Trigonometry 2 Similarity and Congruence Similarity and Congruence Similarity and Congruence Trigonometry Trigonometry Trigonometry 3P Learning 110

114 Ontario, Applied (MFM2P) Substrand Expectation Expectation Description Topic Activities ebooks Strand: and Trigonometry Involving the Trigonometry of Right Triangles Involving Surface Area and Volume, Using the Imperial and Metric Systems of Involving Surface Area and Volume, Using the Imperial and Metric Systems of Involving Surface Area and Volume, Using the Imperial and Metric Systems of ON10AP.MT2.4 ON10AP.MT3.1 ON10AP.MT3.2 ON10AP.MT3.3 Describe, through participation in an activity, the application of trigonometry in an occupation (e.g., research and report on how trigonometry is applied in astronomy; attend a career fair that includes a surveyor, and describe how a surveyor applies trigonometry to calculate distances; job shadow a carpenter for a few hours, and describe how a carpenter uses trigonometry). Use the imperial system when solving measurement problems (e.g., problems involving dimensions of lumber, areas of carpets, and volumes of soil or concrete). Perform everyday conversions between the imperial system and the metric system (e.g., millilitres to cups, centimetres to inches) and within these systems (e.g., cubic metres to cubic centimetres, square feet to square yards), as necessary to solve problems involving measurement (Sample problem: A vertical post is to be supported by a wooden pole, secured on the ground at an angle of elevation of 60, and reaching 3 m up the post from its base. If wood is sold by the foot, how many feet of wood are needed to make the pole?) Determine, through investigation, the relationship for calculating the surface area of a pyramid (e.g., use the net of a square based pyramid to determine that the surface area is the area of the square base plus the areas of the four congruent triangles). Trigonometry Surface Area and Volume Surface Area and Volume Elevation and Depression Trigonometry 1 Trigonometry 2 Perimeter: Squares and Rectangles Calculate Area of Shapes (inches, feet, yards) Customary Units of Capacity Customary Units of Length Customary Units of Weight 1 Customary Units of Capacity Customary Units of Length Customary Units of Weight 1 Converting Units of Length Converting Units of Mass Operations with Length Volume: Rectangular Prisms 2 Nets Surface Area: Square Pyramid Surface Area: Rectangular Pyramid Trigonometry Converting Units Converting Units Converting Units Measuring Solids 111 3P Learning

115 Ontario, Applied (MFM2P) Substrand Expectation Expectation Description Topic Activities ebooks Strand: and Trigonometry Involving Surface Area and Volume, Using the Imperial and Metric Systems of ON10AP.MT3.4 Strand: Modelling Manipulating and ic ON10AP.LR1.1 Solve problems involving the surface areas of prisms, pyramids, and cylinders, and the volumes of prisms, pyramids, cylinders, cones, and spheres, including problems involving combinations of these figures, using the metric system or the imperial system, as appropriate (Sample problem: How many cubic yards of concrete are required to pour a concrete pad measuring 10 feet by 10 feet by 1 foot? If poured concrete costs $110 per cubic yard, how much does it cost to pour a concrete driveway requiring 6 pads?). Solve first-degree equations involving one variable, including equations with fractional coefficients (e.g. using the balance analogy, computer algebra systems, paper and pencil) (Sample problem: Solve x/2 + 4=3x 1 and verify.) Surface Area and Volume Surface Area: Rectangular Prisms Surface Area: Triangular Prisms Surface Area: Cylinders Surface Area: Square Pyramids Surface Area: Rectangular Pyramids Volume: Rectangular Prisms 1 Volume: Rectangular Prisms 2 Volume: Triangular Prisms Volume: Prisms Volume: Pyramids Volume: Cylinders Volume: Cones Volume: Spheres Volume: Composite Figures Checking Solutions Solve : Add, Subtract 1 Solve : Add, Subtract 2 Solve : Multiply, Divide 1 Solve : Multiply, Divide 2 Simple Solve Two-Step Solve Multi-Step More with Grouping Symbols : Variables, Both Sides with Decimals with Fractions with Fractions 2 Measuring Solids and Inequalities 3P Learning 112

116 Ontario, Applied (MFM2P) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Modelling Manipulating and ic Manipulating and ic Graphing and Writing of Lines Graphing and Writing of Lines Graphing and Writing of Lines Graphing and Writing of Lines Graphing and Writing of Lines 113 3P Learning ON10AP.LR1.2 ON10AP.LR1.3 ON10AP.LR2.1 ON10AP.LR2.2 ON10AP.LR2.3 ON10AP.LR2.4 ON10AP.LR2.5 Determine the value of a variable in the first degree, using a formula (i.e., by isolating the variable and then substituting known values; by substituting known values and then solving for the variable) (e.g., in analytic geometry, in measurement) (Sample problem: A cone has a volume of 100 cm 3. The radius of the base is 3 cm. What is the height of the cone?) Express the equation of a line in the form y=mx + b, given the form Ax + By + C=0. Connect the rate of change of a linear relation to the slope of the line, and define the slope as the ratio m=rise/run. Identify, through investigation, y=mx + b as a common form for the equation of a straight line, and identify the special cases x=a, y=b. Identify, through investigation with technology, the geometric significance of m and b in the equation y=mx + b. Identify, through investigation, properties of the slopes of lines and line segments (e.g., direction, positive or negative rate of change, steepness, parallelism), using graphing technology to facilitate investigations, where appropriate. Graph lines by hand, using a variety of techniques (e.g., graph y=(2/3)x - 4 using the y-intercept and slope; graph 2x + 3y=6 using the x- and y-intercepts.) Under Review Under Review General Form of a Line Slope of a Line Gradient y=ax General Form of a Line Horizontal and Vertical Lines Slope of a Line Gradient y=ax Intercepts Which Straight Line? Equation of a Line 1 y=ax Equation of a Line 1 Are They Parallel? y=ax Which Straight Line? Graphing from a Table of Values Graphing from a Table of Values 2 Straight Lines Straight Lines Straight Lines Straight Lines Straight Lines Straight Lines

117 Ontario, Applied (MFM2P) Substrand Expectation Expectation Description Topic Activities ebooks Strand: Modelling Graphing and Writing of Lines and Interpreting Systems of and Interpreting Systems of and Interpreting Systems of ON10AP.LR2.6 ON10AP.LR3.1 ON10AP.LR3.2 ON10AP.LR3.3 Determine the equation of a line, given its graph, the slope and y-intercept, the slope and a point on the line, or two points on the line. Determine graphically the point of intersection of two linear relations (e.g., using graph paper, using technology) (Sample problem: Determine the point of intersection of y + 2x= 5 and y=(2/3)x + 3 using an appropriate graphing technique, and verify.) Solve systems of two linear equations involving two variables with integral coefficients, using the algebraic method of substitution or elimination (Sample problem: Solve y=2x + 1, 3x + 2y=16 for x and y algebraically, and verify algebraically and graphically.) Solve problems that arise from realistic situations described in words or represented by given linear systems of two equations involving two variables, by choosing an appropriate algebraic or graphical method (Sample problem: Maria has been hired by Company A with an annual salary, S dollars, given by S= a, where a represents the number of years she has been employed by this company. Ruth has been hired by Company B with an annual salary, S dollars, given by S= a, where a represents the number of years she has been employed by that company. Describe what the solution of this system would represent in terms of Maria s salary and Ruth s salary. After how many years will their salaries be the same? What will their salaries be at that time?). Systems of Systems of Systems of y=ax Which Straight Line? Determining the Rule for a Line 1 Equation of a Line 1 Equation from Point and Gradient Equation from Two Points Solve Systems by Graphing Simultaneous 1 Simultaneous 2 Simultaneous Breakeven Point Straight Lines and Inequalities and Inequalities and Inequalities 3P Learning 114

118 Ontario, Applied (MFM2P) Substrand Expectation Expectation Description Topic Activities ebooks Strand: of the Form y=ax 2 + bx + c Manipulating Expressions Manipulating Expressions Manipulating Expressions Manipulating Expressions Identifying Characteristics of ON10AP.QR1.1 ON10AP.QR1.2 ON10AP.QR1.3 ON10AP.QR1.4 ON10AP.QR2.1 Expand and simplify second-degree polynomial expressions involving one variable that consist of the product of two binomials [e.g., (2x + 3)(x + 4)] or the square of a binomial [e.g., (x + 3) 2 ], using a variety of tools (e.g., algebra tiles, diagrams, computer algebra systems, paper and pencil) and strategies (e.g. patterning). Factor binomials (e.g., 4x 2 + 8x) and trinomials (e.g., 3x 2 + 9x 15) involving one variable up to degree two, by determining a common factor using a variety of tools (e.g., algebra tiles, computer algebra systems, paper and pencil) and strategies (e.g., patterning). Factor simple trinomials of the form x 2 + bx + c (e.g., x 2 + 7x + 10, x 2 + 2x 8), using a variety of tools (e.g., algebra tiles, computer algebra systems, paper and pencil) and strategies (e.g., patterning). Factor the difference of squares of the form x 2 a 2 (e.g., x 2 16). Collect data that can be represented as a quadratic relation, from experiments using appropriate equipment and technology (e.g., concrete materials, scientific probes, graphing calculators), or from secondary sources (e.g., the Internet, Statistics Canada); graph the data and draw a curve of best fit, if appropriate, with or without the use of technology (Sample problem: Make a 1 m ramp that makes a 15 angle with the floor. Place a can 30 cm up the ramp. Record the time it takes for the can to roll to the bottom. Repeat by placing the can 40 cm, 50 cm, and 60 cm up the ramp, and so on. Graph the data and draw the curve of best fit.) Under Review Under Review Expand then Simplify Expanding Binomial Products Special Binomial Products Factoring Factoring Expressions Grouping in Pairs Factoring s 1 Factoring s 2 Under Review Under Review Simplifying Factoring Factoring Factoring Under Review 115 3P Learning

119 Ontario, Applied (MFM2P) Substrand Expectation Expectation Description Topic Activities ebooks Strand: of the Form y=ax 2 + bx + c Identifying Characteristics of Identifying Characteristics of Identifying Characteristics of ON10AP.QR2.2 ON10AP.QR2.3 ON10AP.QR2.4 Determine, through investigation using technology, that a quadratic relation of the form y=ax 2 + bx + c (a 0) can be graphically represented as a parabola, and determine that the table of values yields a constant second difference (Sample problem: Graph the quadratic relation y=x 2 4, using technology. Observe the shape of the graph. Consider the corresponding table of values, and calculate the first and second differences. Repeat for a different quadratic relation. Describe your observations and make conclusions.) Identify the key features of a graph of a parabola (i.e., the equation of the axis of symmetry, the coordinates of the vertex, the y-intercept, the zeros, and the maximum or minimum value), using a given graph or a graph generated with technology from its equation, and use the appropriate terminology to describe the features. Compare, through investigation using technology, the graphical representations of a quadratic relation in the form y=x 2 + bx + c and the same relation in the factored form y=(x r)(x s) (i.e., the graphs are the same), and describe the connections between each algebraic representation and the graph [e.g., the y-intercept is c in the form y=x 2 + bx + c; the x-intercepts are r and s in the form y=(x r)(x s)] (Sample problem: Use a graphing calculator to compare the graphs of y= x 2 + 2x 8 and y=(x + 4)(x 2). In what way(s) are the equations related? What information about the graph can you identify by looking at each equation? Make some conclusions from your observations, and check your conclusions with a different quadratic equation.). Under Review Graphing Parabolas Vertex of a Parabola Under Review Parabolas Parabolas Parabolas 3P Learning 116

120 Ontario, Applied (MFM2P) Substrand Expectation Expectation Description Topic Activities ebooks Strand: of the Form y=ax 2 + bx + c by Interpreting Graphs of by Interpreting Graphs of ON10AP.QR3.1 ON10AP.QR3.2 Solve problems involving a quadratic relation by interpreting a given graph or a graph generated with technology from its equation (e.g., given an equation representing the height of a ball over elapsed time, use a graphing calculator or graphing software to graph the relation, and answer questions such as the following: What is the maximum height of the ball? After what length of time will the ball hit the ground? Over what time interval is the height of the ball greater than 3 m?) Solve problems by interpreting the significance of the key features of graphs obtained by collecting experimental data involving quadratic relations (Sample problem: Roll a can up a ramp. Using a motion detector and a graphing calculator, record the motion of the can until it returns to its starting position, graph the distance from the starting position versus time, and draw the curve of best fit. Interpret the meanings of the vertex and the intercepts in terms of the experiment. Predict how the graph would change if you gave the can a harder push. Test your prediction.). Under Review Parabolas and Rectangles Parabolas and Marbles Under Review Parabolas Parabolas 117 3P Learning

121 Ontario Grade 11, (MCR3U) Characteristics of Characteristics of Characteristics of Characteristics of Characteristics of Characteristics of Characteristics of Characteristics of Representing Representing Representing Representing Representing Representing Representing Representing A.1.1 A.1.2 Distinguish a function from a relation that is not a function using tables and graphs. and quadratic functions using function notation. A.1.3 Domain and range Domain Function Notation 1 Function Notation 2 Function Notation 3 Find the Function Rule Determining a Rule for a Line Which Straight Line? General Form of a Line Graphing Parabolas A.1.4 Inverse of a function A.1.5 A.1.6 A.1.7 A.1.8 Determine the numeric or graphical representation of the inverse of a linear or quadratic function. Domain and range of a function and the domain and range of the inverse. ic representation of the inverse of a linear or quadratic function. Roles of the parameters a, k, d, and c in functions of the form y=af(k(x d)) + c. Domain y=ax Horizontal and Vertical Lines Graphing from a Table of Values Equation of a Line 1 General Form of a Line Equation from Point and Gradient Equation from Two Points Graphing Parabolas Vertex of a Parabola Straight Lines 3P Learning 118

122 Ontario Grade 11, (MCR3U) Characteristics of Characteristics of Characteristics of Characteristics of Characteristics of Characteristics of Representing Involving Involving Involving Involving Involving A.1.9 A.2.1 A.2.2 A.2.3 A.2.4 A.2.5 Sketch graphs of y=af(k(x d)) + c by applying one or more transformations. of zeros (i.e., x-intercepts) of a quadratic function. Maximum or minimum value of a quadratic function whose equation is given in standard form, by factoring or completing the square. Solve problems involving quadratic functions arising from real-world applications and represented using function notation. Determine the algebraic representation of a quadratic function, given the real roots of the corresponding quadratic equation and a point on the function. involving the intersection of a linear function and a quadratic function graphically and algebraically. y=ax Horizontal and Vertical Lines Graphing from a Table of Values Equation of a Line 1 General Form of a Line Equation from Point and Gradient Equation from Two Points Graphing Parabolas Vertex of a Parabola Graphing Parabolas Factoring s 1 Factoring s Vertex of a Parabola Completing the Square 2 Completing the Square Vertex of a Parabola Sum and Product of Roots Parabolas Parabolas Parabolas 119 3P Learning

123 Ontario Grade 11, (MCR3U) Characteristics of Characteristics of Characteristics of Characteristics of Exponential Exponential Exponential Determining Equivalent ic Expressions Determining Equivalent ic Expressions Determining Equivalent ic Expressions Determining Equivalent ic Expressions Representing Exponential Representing Exponential Representing Exponential A.3.1 A.3.2 A.3.3 A.3.4 B.1.1 B.1.2 B.1.3a Simplify polynomial expressions by adding, subtracting, and multiplying. Simplify radicals and radical expressions. Simplify rational expressions by adding, subtracting, multiplying, and dividing, and state the restrictions on the variable values. Determine if two given algebraic expressions are equivalent. Graphing exponential functions. Value of a power with a rational exponent. Simplify algebraic expressions containing integer and rational exponents. Recognising Like Terms Like Terms: Add and Subtract Expanding Binomial Products Special Binomial Products Using the Distributive Property Expand then Simplify Expanding with Negatives Expanding Brackets Simplifying Irrational s Adding and Subtracting Irrational s Multiplying Irrational s Expanding Irrational Expressions Rationalizing the Denominator Irrational Form to Exponent Form ic Fractions 1 ic Fractions 2 ic Fractions 3 ic Fractions 1 ic Fractions 2 ic Fractions 3 Graphing Exponentials Identifying Graphs Non Graphs Fractional Exponents Multiplication with Exponents Exponent Notation and Exponent Laws with Brackets Zero Exponent and Factoring with Exponents Properties of Exponents Simplifying Irrational s and Exponents Simplifying Simplifying Simple Non Graphs Irrational s and Exponents Irrational s and Exponents 3P Learning 120

124 Ontario Grade 11, (MCR3U) Exponential Exponential Exponential Exponential Exponential Exponential Exponential Exponential Representing Exponential Representing Exponential Connecting Graphs and of Exponential Connecting Graphs and of Exponential Connecting Graphs and of Exponential Connecting Graphs and of Exponential Connecting Graphs and of Exponential Connecting Graphs and of Exponential B1.3b B.1.4 B.2.1 B.2.2a B.2.2b B.2.3 B.2.4 B.2.5 Evaluate numeric expressions containing integer and rational exponents and rational bases. Describe key properties relating to domain and range, intercepts, increasing/decreasing intervals, and asymptotes for exponential functions. Distinguish exponential functions from linear and quadratic functions. Roles of the parameters a, k, d, and c in functions of the form y = af (k(x d)) + c. Describe these roles in terms of transformations on the graph. Sketch graphs of y = af (k(x d)) + c by applying one or more transformations. The equation of a given exponential function can be expressed using different bases. Represent an exponential function with an equation, given its graph or its properties. Exponent Notation Simplifying with Exponent Laws 1 Exponent Notation Simplifying with Exponent Laws 1 Graphing Exponentials Irrational s and Exponents Irrational s and Exponents Simple Non Graphs Exponential and Power Graphs 121 3P Learning

125 Ontario Grade 11, (MCR3U) Discrete Discrete Trigonometric Trigonometric Trigonometric Trigonometric Trigonometric Trigonometric Trigonometric Involving Financial Applications Involving Financial Applications Determining and Applying Trigonometric Ratios Determining and Applying Trigonometric Ratios Determining and Applying Trigonometric Ratios Determining and Applying Trigonometric Ratios Determining and Applying Trigonometric Ratios Determining and Applying Trigonometric Ratios Determining and Applying Trigonometric Ratios C.3.6 C.3.7 Effects of changing the conditions (i.e., the payments, the frequency of the payments, the interest rate, the compounding period) of ordinary simple annuities. Amount, the present value, and the regular payment of an ordinary simple annuity. Compound Interest Compound Interest by Formula Simple Interest Present and Future Value Tables Compound Interest Compound Interest by Formula Simple Interest Present and Future Value Tables D.1.1 Special angles Exact Trigonometric Ratios D.1.2 D.1.3 D.1.4 Values of the sine, cosine, and tangent of angles from 0º to 360º. Two angles from 0º to 360º for which the value of a given trigonometric ratio is the same. Secant, cosecant, and cotangent. Sin A Cos A Tan A Which Quadrant? Sign of the Angle Trigonometric Interest Grade 12 Series in Finance Interest Grade 12 Series in Finance Trigonometry Trigonometry Trigonometric D.1.5 Pythagorean identity D.1.5a Quotient identity (tanx=sinx/cosx). D.1.5b Reciprocal identities 3P Learning 122

126 Ontario Grade 11, (MCR3U) Trigonometric Trigonometric Trigonometric Trigonometric Trigonometric Trigonometric Trigonometric Trigonometric 123 3P Learning Determining and Applying Trigonometric Ratios Determining and Applying Trigonometric Ratios Connecting Graphs and of Sinusoidal Connecting Graphs and of Sinusoidal Connecting Graphs and of Sinusoidal Connecting Graphs and of Sinusoidal Connecting Graphs and of Sinusoidal Connecting Graphs and of Sinusoidal D.1.6 D.1.7 D.2.1 D.2.2 using the primary trigonometric ratios, the cosine law, and the sine law. involving right triangles and oblique triangles in three-dimensional settings. Describe key properties (e.g., cycle, amplitude, period) of periodic functions arising from real-world applications. Predict, by extrapolating, the future behaviour of a relationship modelled using a numeric or graphical representation of a periodic function. Find Unknown Sides Find Unknown Angles Sine Rule 1 Cosine Rule 1 Cosine Rule 2 Sine Rule 2 Elevation and Depression Trigonometry 1 Trigonometry 2 Period and Amplitude Period and Amplitude Trigonometry D.2.3 D.2.4 D.2.5 D.2.6 Graphing sin and cos functions. Roles of the parameters a, k, d, and c in functions of the form y=af(k(x d)) + c, where f(x)=sinx or f(x)=cosx (angles in degrees). Amplitude, period, phase shift, domain, and range of sinusoidal functions whose equations are given in the form f(x)=asin(k(x d)) + c or f(x)=acos(k(x d)) + c. Sine and Cosine Curves Sine and Cosine Curves Period and Amplitude Trigonometric

127 Ontario Grade 11, (MCR3U) Trigonometric Trigonometric Trigonometric Trigonometric Trigonometric Trigonometric Connecting Graphs and of Sinusoidal Connecting Graphs and of Sinusoidal Connecting Graphs and of Sinusoidal Involving Sinusoidal Involving Sinusoidal Involving Sinusoidal D.2.7 D.2.7a D.2.8 Sketch graphs of y=af(k(x d)) + c by applying one or more transformations to the graphs of f(x)=sinx and f(x)=cosx. State the domain and range of the transformed functions. Represent a sinusoidal function with an equation, given its graph or its properties. Sine and Cosine Curves Sine and Cosine Curves Sine and Cosine Curves D.3.1 D.3.2 D.3.3 Identify periodic and sinusoidal functions, including those that arise from real-world applications involving periodic phenomena, given various representations. Sinusoidal functions used to model periodic phenomena. 3P Learning 124

128 Ontario Grade 11, and Applications (MCF3M) Connecting Graphs and of A.1.1 A.1.2 A.1.3 A.1.4 A.1.5 A.1.6 A.1.7 A.1.8 A.2.1 involving quadratic relations arising from realworld applications and represented by tables of values and graphs. Represent situations (e.g., the area of a picture frame of variable width) using quadratic expressions in one variable, and expand and simplify quadratic expressions in one variable. Factor quadratic expressions in one variable. Solve quadratic equations. Factors used in solving a quadratic equation and the x-intercepts of the graph of the corresponding quadratic relation. ic development of quadratic formula Connect the number of real roots to the value of the discriminant. Real roots of a variety of quadratic equations. Distinguish a function from a relation that is not a function, through investigation of linear and quadratic relations using a variety of representations. Parabolas and Marbles Parabolas and Rectangles Parabolas and Marbles Parabolas and Rectangles Factoring s 1 Factoring s Formula 1 2 Factoring s 1 Factoring s 2 Graphing Parabolas Formula The Discriminant Roots of the Factoring s 1 Factoring s Formula The Discriminant Factoring 125 3P Learning

129 Ontario Grade 11, and Applications (MCF3M) Connecting Graphs and of Connecting Graphs and of Connecting Graphs and of Connecting Graphs and of Connecting Graphs and of Connecting Graphs and of Connecting Graphs and of Connecting Graphs and of Connecting Graphs and of A.2.2 A.2.3 A.2.4 A.2.5 Substitute into and evaluate linear and quadratic functions represented using function notation. Domain and range (quadratics) Restrictions on the domain and the range of a quadratic function in contexts arising from real-world applications. Roles of a, h, and k in quadratic functions of the form f(x)=a(x h)² + k. Function Notation 1 Function Notation 2 Domain Domain A.2.6 Sketch g(x)=a(x h)² + k Vertex of a Parabola A.2.7 A.2.8 A.2.9 A.2.10 Convert from vertex form to standard form. Completing the square Sketch graphs of quadratic functions in factored form by using the x-intercepts to determine the vertex. Describe the properties of a quadratic function. Completing the Square Completing the Square 2 Completing the Square Completing the Square 2 Graphing Parabolas Vertex of a Parabola Parabolas Simple Nonlinear Graphs Parabolas Simple Nonlinear Graphs 3P Learning 126

130 Ontario Grade 11, and Applications (MCF3M) Exponential Exponential Exponential Exponential Exponential Connecting Graphs and of Involving Involving Connecting Graphs and of Exponential Connecting Graphs and of Exponential Connecting Graphs and of Exponential Connecting Graphs and of Exponential Connecting Graphs and of Exponential A.2.11 A.3.2 A.3.3 B.1.1 B.1.2 B.1.3 B.1.4 B.1.5 Graph of a quadratic function whose equation is given in the standard form. Determine the equation of the quadratic function that best models a suitable data set graphed on a scatter plot. Solve problems arising from real-world applications. Power with a rational exponent. Numerical expressions containing integer and rational exponents and rational bases. Graph an exponential relation, given its equation. Key properties relating to domain and range, intercepts, increasing/ decreasing intervals, and asymptotes. Exponent rules for power of a power, multiplying and dividing numeric expressions involving exponents. Graphing Parabolas Fractional Exponents Irrational Form to Exponent Form Multiplication with Exponents More Fraction Properties of Exponents Graphing Exponentials Identifying Graphs Graphing Exponentials Identifying Graphs Multiplication with Exponents Dividing Expressions Exponent Laws and Exponent Laws with Brackets Zero Exponent and Simplifying with Exponent Laws 1 Simplifying with Exponent Laws 2 Parabolas Simple Nonlinear Graphs Irrational s and Exponents Exponents Exponential and Power Graphs Exponential and Power Graphs Exponential and Power Graphs Exponents 127 3P Learning

131 Ontario Grade 11, and Applications (MCF3M) Exponential Exponential Exponential Exponential Exponential Exponential Exponential Exponential Connecting Graphs and of Exponential Involving Exponential Involving Exponential Involving Exponential Financial Involving Exponential Financial Involving Exponential Financial Involving Exponential Financial Involving Exponential B.1.6 B.2.2a B.2.2b B.2.3 B.3.1 B.3.2 B.3.3 B.3.4 Distinguish exponential functions from linear and quadratic functions. Identify exponential functions, including those that arise from real-world applications involving growth and decay. Explain any restrictions that the context places on the domain and range. Solve problems using given graphs or equations of exponential functions arising from a variety of real-world applications. Compound interest as exponential growth. of compounding periods, n, using the compound interest formula. Non Regions Exponential Growth and Decay Exponential Growth and Decay Conversion Graphs Modelling Modelling Simple Interest Terms: Arithmetic Progressions Sum: Arithmetic Progressions Compound Interest Compound Interest by Formula Present and Future Value Tables Terms: Progressions 1 Terms: Progressions 2 Sigma Notation 1 Sigma Notation 2 Compound Interest Compound Interest Compound Interest by Formula Simple Nonlinear Graphs Grade 12 Series in Finance Grade 12 Series in Finance Interest Interest 3P Learning 128

132 Ontario Grade 11, and Applications (MCF3M) Exponential Exponential Exponential Trigonometric Trigonometric Trigonometric Trigonometric Trigonometric Financial Involving Exponential Financial Involving Exponential Financial Involving Exponential Applying the Sine Law and the Cosine Law in Acute Triangles Applying the Sine Law and the Cosine Law in Acute Triangles Applying the Sine Law and the Cosine Law in Acute Triangles Applying the Sine Law and the Cosine Law in Acute Triangles Connecting Graphs and of Sine B.3.5 B.3.6 B.3.7 C.1.1 C.1.2 C.1.4 C.1.5 C.2.1 Ordinary simple annuities Effects of changing the conditions (i.e., the payments, the frequency of the payments, the interest rate, the compounding period) of ordinary simple annuities. Amount, the present value, and the regular payment of an ordinary simple annuity. Determining the measures of the sides and angles of right triangles. Solve problems involving two right triangles in two dimensions. Use sine and cosine to calculate sides and angles in acute triangles. Solve problems that require the use of the sine law or the cosine law in acute triangles. Describe key properties (e.g., cycle, amplitude, period) of periodic functions arising from realworld applications. Future Value of an Annuity Present Value of an Annuity Future Value of an Annuity Present Value of an Annuity Future Value of an Annuity Present Value of an Annuity Find Unknown Sides Find Unknown Angles Hypotenuse of a Right Triangle Find Unknown Sides Find Unknown Angles Elevation and Depression Trigonometry 1 Trigonometry 2 Sine Rule 1 Cosine Rule 1 Cosine Rule 2 Sine Rule 2 Sine Rule 1 Cosine Rule 1 Cosine Rule 2 Sine Rule 2 Area Rule 1 Area Rule 2 Period and Amplitude Sine and Cosine Curves Interest Grade 12 Series in Finance Interest Grade 12 Series in Finance Interest Grade 12 Series in Finance Trigonometry Trigonometry Non Right Angled Triangles Non Right Angled Triangles Trigonometric 129 3P Learning

133 Ontario Grade 11, and Applications (MCF3M) Trigonometric Trigonometric Trigonometric Trigonometric Trigonometric Trigonometric Trigonometric Connecting Graphs and of Sine Connecting Graphs and of Sine Connecting Graphs and of Sine Connecting Graphs and of Sine Connecting Graphs and of Sine Connecting Graphs and of Sine Connecting Graphs and of Sine C.2.2 C.2.3 C.2.4 Predict, by extrapolating, the future behaviour of a relationship modelled using a numeric or graphical representation of a periodic function. Graphing the relationship between angles from 0º to 360º and the corresponding sine ratios. Graph of f(x)=sinx for angle measures expressed in degrees, and determine and describe its key properties. Period and Amplitude Sine and Cosine Curves Sine and Cosine Curves Sine and Cosine Curves Trigonometric Trigonometric Trigonometric C.2.5 C.2.6a C.2.6b C.2.7 Roles of the parameters a, c, and d in functions in the form f(x)=asinx, f(x)=sinx + c, and f(x)=sin(x d). Describe these roles in terms of transformations. Sketch graphs of f(x)=asinx, f(x)=sinx + c, and f(x)=sin(x d) by applying transformations to the graph of f(x)=sinx. Sine and Cosine Curves 3P Learning 130

134 Ontario Grade 11, Foundations for College Mathematics (MBF3C) Mathematical Models Mathematical Models Mathematical Models Mathematical Models Mathematical Models Mathematical Models Mathematical Models Connecting Graphs and of Connecting Graphs and of Connecting Graphs and of Connecting Graphs and of Connecting Graphs and of Connecting Graphs and of Connecting Graphs and of A.1.1 A.1.2 A.1.3 A.1.4 A.1.5 A.1.6 A.1.7 Tables of values and graph quadratic relations arising from real-world applications. Determine and interpret meaningful values of the variables, given a graph of a quadratic relation arising from a real-world application. Roles of a, h, and k in quadratic relations of the form y=a(x h)² + k, and describe these roles in terms of transformations. Sketch graphs of quadratic relations represented by the equation y=a(x h)² + k. Expand and simplify quadratic expressions. Express the equation of a quadratic relation in the standard form given the vertex form. Factor trinomials with leading coefficient 1. Parabolas and Rectangles Parabolas and Marbles Parabolas and Rectangles Parabolas and Marbles Completing the Square Completing the Square 2 Completing the Square Completing the Square 2 Expanding Binomial Products Special Binomial Products Expand then Simplify Simplifying Binomial Expressions Factoring s 1 Factoring s 2 Expanding Binomial Products Special Binomial Products Expand then Simplify Simplifying Binomial Expressions Factoring s 1 Factoring s 2 Factoring s 1 Factoring s 2 Simple Non Graphs Simple Non Graphs Parabolas Sketching Polynomials Parabolas Sketching Polynomials Expanding and Factoring Simplifying Simple Non Graphs Factoring 131 3P Learning

135 Ontario Grade 11, Foundations for College Mathematics (MBF3C) Mathematical Models Mathematical Models Mathematical Models Mathematical Models Mathematical Models Mathematical Models Mathematical Models Mathematical Models Connecting Graphs and of Connecting Graphs and of Connecting Graphs and of Exponential Connecting Graphs and of Exponential Connecting Graphs and of Exponential Connecting Graphs and of Exponential Connecting Graphs and of Exponential Involving Exponential A.1.8 A.1.9 A.2.1 A.2.2 A.2.3 A.2.4 A.2.6 A.3.4 Solve quadratic problems Negative exponents and of zero as an exponent. Numeric expressions containing integer exponents and rational bases. Exponent rules for power of a power, multiplying and dividing numeric expressions involving exponents. Graph simple exponential relations. Distinguish exponential relations from linear and quadratic relations. Growth and decay Reducible to s Roots of the 1 2 Formula The Discriminant Integer Exponents The Zero Exponent Zero Exponent and Exponent Laws and Exponent Laws with Brackets Multiplication with Exponents Exponent Form to s Zero Exponent and Exponent Laws and Simplifying with Exponent Laws 1 Simplifying with Exponent Laws 2 Graphing Exponentials Conversion Graphs Modelling Modelling Exponential Growth and Decay Exponents Exponents Exponents Exponential and Power Graphs 3P Learning 132

136 Ontario Grade 11, Foundations for College Mathematics (MBF3C) Personal Finance Personal Finance Personal Finance Personal Finance Personal Finance Personal Finance Personal Finance Involving Compound Interest Involving Compound Interest Involving Compound Interest Involving Compound Interest Involving Compound Interest Involving Compound Interest Comparing Financial Services B.1.1 Compare the simple and compound interest for a given principal. Simple Interest Compound Interest Compound Interest by Formula Present and Future Value Tables Interest B.1.2 B.1.3 B.1.4 B.1.5 B.1.6 B.2.5 Calculation of the amount, future value or the principal the compound interest formula. Total interest earned on an investment or paid on a loan by determining the difference between the amount and the principal. Calculation of the interest rate per compounding period, i, or the number of compounding periods, n, in the compound interest formula. Effect on the future value of a compound interest investment or loan of changing the total length of time, the interest rate, or the compounding period. Solve problems involving applications of the compound interest formula to determine the cost of making a purchase on credit. Simple Interest Compound Interest Compound Interest by Formula Effective Interest Rate Future Value of Investments 1 Future Value of Investments 2 Present and Future Value Tables Effective Interest Rate Present and Future Value Tables Comparing Home Loans Comparing Loans Credit Card Repayments Future Value of an Annuity Present Value of an Annuity Interest Interest Interest Interest Interest Grade 12 Series in Finance 133 3P Learning

137 Ontario Grade 11, Foundations for College Mathematics (MBF3C) Strand Substrand Expectation Trigonometry Trigonometry Trigonometry Trigonometry Trigonometry Trigonometry Trigonometry Representing Two-Dimensional Shapes and Three-Dimensional Figures Representing Two-Dimensional Shapes and Three-Dimensional Figures Representing Two-Dimensional Shapes and Three-Dimensional Figures Applying the Sine Law and the Cosine Law in Acute Triangles Applying the Sine Law and the Cosine Law in Acute Triangles Applying the Sine Law and the Cosine Law in Acute Triangles Applying the Sine Law and the Cosine Law in Acute Triangles C.1.2 C.1.3 Expectation Description Represent threedimensional objects. Create nets, plans, and patterns from physical models arising from a variety of real-world applications. Activities ebooks Properties of Solids Nets Solids Measuring Solids C.1.4 C.2.1 Determining the measures of the sides and angles of right triangles using the primary trigonometric ratios. Find Unknown Sides Find Unknown Angles Sin A Cos A Tan A Elevation and Depression Trigonometry 1 Trigonometry 2 Trigonometry C.2.2 C.2.3 C.2.4 Working With One-Variable D.1.1 Sine law and the cosine law. Frequency Sine Rule 1 Sine Rule 2 Cosine Rule 1 Cosine Rule 2 Area Rule 1 Area Rule 2 Frequency Histograms Histograms Tally Charts Cumulative Frequency Table Relative Frequency Cumulative Frequency Histogram Terms Non Right Angled Triangles Interpreting 3P Learning 134

138 Ontario Grade 11, Foundations for College Mathematics (MBF3C) Working With One-Variable Working With One-Variable Working With One-Variable Working With One-Variable Working With One-Variable D.1.4 D.1.5 D.1.6 D.1.7a D.1.7b Describe and compare sampling techniques (e.g., random, stratified, clustered, convenience, voluntary). Identify different types of one-variable data (i.e., categorical, discrete, continuous). Identify and describe properties associated with common distributions of data (e.g., normal, bimodal, skewed). Measures of central tendency. Measures of spread Frequency Histograms Histograms Tally Charts Cumulative Frequency Table Relative Frequency Cumulative Frequency Histogram Terms Frequency Histograms Histograms Tally Charts Cumulative Frequency Table Relative Frequency Cumulative Frequency Histogram Terms Frequency Histograms Histograms Tally Charts Cumulative Frequency Table Relative Frequency Cumulative Frequency Histogram Terms Mean Median Mode Mean from Frequency Table Mode from Frequency Table Median from Frequency Calculating Standard Deviation Interpreting Standard Deviation Interpreting Interpreting Interpreting 135 3P Learning

139 Ontario Grade 11, Foundations for College Mathematics (MBF3C) Working With One-Variable Working With One-Variable Working With One-Variable Working With One-Variable Applying Probability Applying Probability D.1.7c Variance Calculating Standard Deviation Interpreting Standard Deviation Interpreting D.1.8 D.1.9 Compare two or more sets of one-variable data, using measures of central tendency and measures of spread. Calculating Standard Deviation Interpreting Standard Deviation Interpreting D.1.10 D.2.2 Determine the theoretical probability of an event. Simple Probability Find the Probability Probability Scale Fair Games Probability Tables Probability With Replacement Probability Without Replacement Complementary Events Dice and Coins Probability D.2.3 Frequency distribution Frequency Histograms 3P Learning 136

140 Ontario Grade 11, Mathematics for Work and Everyday Life (MEL3E) Earning and Purchasing Earning and Purchasing Earning and Purchasing Earning and Purchasing Earning and Purchasing Earning and Purchasing Earning and Purchasing Earning and Purchasing Earning and Purchasing Earning and Purchasing Saving, Investing and Borrowing Earning Describing Purchasing Power Describing Purchasing Power Describing Purchasing Power Purchasing A.1.4 A.2.1 A.2.2 A.2.3 A.3.2 Different remuneration methods (e.g., hourly rate, overtime rate, job or project rate, commission, salary, gratuities). Deductions Percent of total earnings deducted through government payroll deductions for various benchmarks. Gross pay, net pay, and payroll deductions. Estimate the sale price before taxes when making a purchase. Piecework and Royalties Profit and Loss Wages and Salaries Commission Working Overtime Bonuses and Leave Loading Special Allowances Best Buy Budgeting Successive Discounts Deductions and Tax Instalments Deductions and Tax Instalments Budgeting Earning Money Taxation Taxation Earning Money Earning Money Purchasing A.3.3 Estimating sales tax Taxation Purchasing Purchasing Purchasing A.3.4 A.3.6 A.3.7 Calculate discounts, sale prices, and after-tax costs. Estimate the change from an amount offered to pay a How much Change? charge. Make the correct change from an amount offered to How much Change? pay a charge, using currency manipulatives. Percentage Calculations Purchasing A.3.8 Best buy Best Buy Comparing Financial Services Saving, Comparing Investing and Financial Borrowing Services 137 3P Learning B.1.1 Compare information about the various savings alternatives commonly available from financial institutions. B.1.3 Various financial statements Comparing Loans Reading from a Bill Graphs from Bills

141 Ontario Grade 11, Mathematics for Work and Everyday Life (MEL3E) Saving, Investing and Borrowing Saving, Investing and Borrowing Saving, Investing and Borrowing Saving, Investing and Borrowing Saving, Investing and Borrowing Saving, Investing and Borrowing Saving, Investing and Borrowing Transportation and Travel Transportation and Travel Transportation and Travel Saving and Investing Saving and Investing Saving and Investing Borrowing Borrowing Borrowing Borrowing Owning and Operating a Vehicle B.2.1 B.2.4 B.2.5 B.3.1 B.3.2 B.3.3 B.3.4 C.1.7 Solve problems involving applications of simple interest. Effect on the future value of a compound interest investment of changing the total length of time, the interest rate, or the compounding period. Applications of compound interest to saving and investing. Effects of carrying an outstanding balance on a credit card at current interest rates. Information describing the features (e.g., interest rates, flexibility) and conditions (e.g., eligibility, required collateral) of various personal loans. Total interest paid over the life of a personal loan, given the principal, the length of the loan, and the periodic payments. Effect of the length of time taken to repay a loan on the principal and interest components of a personal loan repayment. Solve problems that involve the fixed costs (e.g., licence fee, insurance) and variable costs (e.g., maintenance, fuel) of owning and operating a vehicle. Travelling by Automobile C.2.1 Determine distances represented on maps. Travelling by Automobile C.2.3 Estimated costs (e.g., gasoline, accommodation, food, entertainment, tolls, car rental) involved in a trip by automobile. Simple Interest Profit and Loss Compound Interest Compound Interest by Formula Present and Future Value Tables Effective Interest Rate Comparing Loans Future Value of Investments 1 Future Value of Investments 2 Credit Card Repayments Comparing Loans Comparing Home Loans Comparing Loans Comparing Home Loans Future Value of an Annuity Present Value of an Annuity Comparing Loans Comparing Home Loans Present and Future Value Tables Scale Scale Coordinate Meeting Place Map Coordinates Scale Scale Coordinate Meeting Place Map Coordinates Interest Interest Interest Grade 12 Series in Finance Depreciation Depreciation Interest Grade 12 Series in Finance Interest Grade 12 Series in Finance 3P Learning 138

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