Topic: Topic 1-Numeration

Transcription

1 Suggested Blocks of Instruction: 10 days /September Use place value understanding and properties of operations to perform multi-digit arithmetic. 3.NBT.1. Use place value understanding to round whole numbers to the nearest 10 or NBT.2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Topic: Topic 1-Numeration /Enduring How are greater numbers read and written? How can whole numbers be compared and ordered? Our number system is based on groups of ten. Whenever we get 10 in one place value, we move to the next greater place value. The place-value periods ones, thousands, millions, and so forth, are used to read and write large numbers. Place value can be used to name numbers in different ways. Uses of numbers include telling how many and showing a date or an address. Each whole number can be associated with a unique point on the number line. Zero is the least whole number on the number line and there is no greatest number. The distance between any two consecutive whole numbers on a given number line is the same. Equal distances on the number line must correspond to equal differences in the numbers. The scale on some graphs is a number line. Place value can be used to compare whole numbers. Place value can be used to order whole numbers. 1.1 Representing Numbers 1.2 Ways to Name Numbers 1.3 Greater Numbers 1.4 Understanding Number Lines 1.5 Counting on the Number Line 1.6 Comparing Numbers 1.7 Ordering Numbers 1.8 Make an Organized List End of module performance assessment

2 Suggested Blocks of Instruction: 11 days /September /October Topic: Topic 2-Number Sense: Addition and Subtraction Objectives / CPI s/standards Use place value understanding and properties of operations to perform multi-digit arithmetic. 3.NBT.1. Use place value understanding to round whole numbers to the nearest 10 or NBT.2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. / How can sums and differences be found mentally? How can sums and differences be estimated? Some real-world problems involving joining, separating, part-part-whole, or comparison can be solved using addition or subtraction. Fact families show addition and subtraction relationships. Two numbers can be added in any order; the sum of any number and 0 is that number; and three or more numbers can be grouped and added in any order. There is more than one way to do a mental calculation. Techniques for doing addition or subtraction calculations mentally involve changing the numbers or the expressions so the calculation is easy to do mentally. Rounding is a process for finding the multiple of 10, 100, etc. closest to a given number. There is more than one way to estimate a sum or difference. Rounding and substituting compatible numbers are two ways to estimate sums and differences. Different numerical expressions can have the same value. Or, the value of one expression can be less than the value of the other expression. An equation shows a balance between what is on the right side and what is on the left side of the equal sign. 2.1 Addition Meaning & Properties 2.2 Subtraction Meanings 2.3 Using Mental Math to Add 2.4 Using Mental Math to Subtract 2.5 Rounding 2.6 Estimating Sums 2.7 Estimating Differences 2.8 Making Sense of Addition & Subtraction Equations 2.9 Reasonableness End of module performance assessment

3 Suggested Blocks of Instruction: 12 days /October Use place value understanding and properties of operations to perform multi-digit arithmetic. 3.NBT.2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Multiply and divide within OA.8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Topic: Topic 3- Using Place Value to Add and Subtract /Enduring What are standard procedures for adding and subtracting whole numbers? The expanded algorithm for adding 3-digit numbers breaks the addition problem into a series of easier problems based on place value. Answers to the simpler problems are added together to determine the final sum. Models and the standard algorithm for adding 3- digit numbers are just an extension to the hundreds place of the models and standard algorithm for adding 2-digit numbers. The expanded algorithm for subtracting 3-digit numbers breaks the subtraction problem into a series of easier problems based on place value. Answers to the simpler problems are used to find the final difference. Models and the standard algorithm for subtracting 3-digit numbers are just an extension to the hundreds place of the models and standard algorithm for subtracting 2-digit numbers. Place-value relations can help simplify subtracting across zero Three or more whole numbers can be grouped and added in any order. 3.1 Adding with an Expanded Algorithm 3.2 Models for Adding 3-Digits Numbers 3.3 Adding 3-Digit Number 3.4 Adding 3 or More Numbers 3.5 Draw a Picture 3.6 Subtracting with an Expanded Algorithm 3.7 Models for Subtracting 3-Digits Numbers 3.8 Subtracting 3-Digit Numbers 3.9 Subtracting Across Zero 3.10 Draw a Picture and Write a Number Sentence End of module performance assessment

4 Suggested Blocks of Instruction: 7 days / October/ November Represent and solve problems involving multiplication and division. 3.OA.1.Interpret products of whole numbers. 3.OA.3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. Understand properties of multiplication and the relationship between multiplication and division. 3.OA.5. Apply properties of operations as strategies to multiply and divide. Topic: Topic 4- Meanings of Multiplication /Enduring What are different meanings for multiplication? How are multiplication and addition related? Repeated addition involves joining equal groups and is one way to think about multiplication. An array involves joining equal groups and is one way to think about multiplication. Some real-world problems involving joining or separating equal groups or comparison can be solved using multiplication. Two numbers can be multiplied in any order and the product remains the same. 4.1 Multiplication as Repeated Addition 4.2 Arrays and Multiplication 4.3 The Commutative Property 4.4 Writing Multiplication Stories 4.5 Writing to Explain End of module performance assessment

5 Suggested Blocks of Instruction: 9 days / November Topic: Topic 5- Multiplication Facts: Use Patterns Represent and solve problems involving multiplication and division. 3.OA.3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. Multiply and divide within OA.9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. Use place value understanding and properties of operations to perform multi-digit arithmetic. 3.NBT.3. Multiply one-digit whole numbers by multiples of 10 in the range (e.g., 9 80, 5 60) using strategies based on place value and properties of operations. /Enduring What patterns can be used to find certain multiplication facts? There are patterns in the products for multiplication facts with factors of 2 and 5. There are patterns in the products for multiplication facts with a factor of 9. There are patterns in the products for multiplication facts with factors of 0 and 1. There are patterns in the products for multiplication facts with factors of 2, 5, and 9. Patterns can be used to find products involving factor of 10. Basic facts and place-value patterns can be used to find products when one factor is a multiple of & 5 as Factors as a Factor 5.3 Multiplying with 0 and Patterns for Facts as a Factor 5.6 Multiplying by Multiples of Two-Question Problems End of module performance assessment

6 Suggested Blocks of Instruction: 11 days / November / December Topic: Topic 6 -Multiplication Facts: Use Known Facts Represent and solve problems involving multiplication and division. 3.OA.3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. Understand properties of multiplication and the relationship between multiplication and division. 3.OA.5. Apply properties of operations as strategies to multiply and divide. /Enduring How can unknown multiplication facts be found using known facts? The Distributive Property can be used to break a large array into two smaller arrays. Three or more numbers can be grouped and multiplied in any order. Basic multiplication facts with 3 as a factor can be found by breaking apart the unknown fact into known facts. The answers to the known facts are added to get the final product. Basic multiplication facts with 4 as a factor can be found by breaking apart the unknown fact into known fact. The answers to the known facts are added to get the final product. Basic multiplication facts with 6 or 7 as a factor can be found by breaking apart the unknown facts into known facts. The answers to the known facts are added to get the final product. Basic multiplication facts with 8 as a factor can be found by breaking apart the unknown fact into known facts. The answers to the known facts are added to get the final product. Patterns and known facts can be used to find unknown multiplication facts. Finding the number of combinations that are possible between the members of one group and the members of another group is one meaning of multiplication. 6.1 The Distributive Property as a Factor as a Factor & 7 as Factors as a Factor 6.6 Multiplying with 3 Factors 6.7 Multiplication Facts 6.8 Multiplying to Find Combinations 6.9 Multi-Step Problems End of module performance assessment

7 Suggested Blocks of Instruction: 8 days /December / January Topic: Topic 7- Meanings of Division Represent and solve problems involving multiplication and division. 3.OA.2. Interpret whole-number quotients of whole numbers, e.g., interpret 56 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. 3.OA.3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. 3.OA.4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. Understand properties of multiplication and the relationship between multiplication and division. 3.OA.6. Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8. /Enduring What are different meanings of division? How is division related to other operations? Some real-world problems involving joining or separating equal groups or comparison can be solved using division. Sharing involves separating equal groups and is one way to think about division. Repeated subtraction involves separating equal groups and is one way to think about division. Any division problem can be thought of as a multiplication fact with a missing factor. Then, an answer can be found using a multiplication table. Sharing and repeated subtraction both involve separating equal groups and are two ways to thin about division. Materials: EnVision Math 7.1 Division as Sharing 7.2 Division As Repeated Subtraction 7.3 Finding Missing # s in a Multiplication Table 7.4 Choose an Appropriate Equation 7.5 Writing Division Stories 7.6 Use Objects and Draw End of module performance assessment

8 Suggested Blocks of Instruction: 11 days /January Represent and solve problems involving multiplication and division. 3.OA.3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. Multiply and divide within OA.7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division. Topic: Topic 8-Division /Enduring How can an unknown division fact be found by thinking of a related multiplication fact? Multiplication and division have an inverse relationship. The inverse relationship between multiplication and division can be used to find division facts; every division fact has a related multiplication fact. Patterns and known facts can be used to find unknown multiplication facts. Division facts can be found by thinking of a related multiplication fact. Any number (except 0) divided by itself is equal to 1. Any number divided by 1 is that number. Zero divided by any number (except 0) is zero. Zero cannot be a divisor. Different numerical expressions can have the same value. Or, the value of one expression can be less than (or greater than) the value of the other expression. An equation shows a balance between what is on the right side and what is on the left side of the equal sign. An equation shows a balance between what is on the right side and what is on the left side of the equal sign. 8.1 Relating Multiplication & Division 8.2 Fact Families with 2,3,4 & Fact Families with 6 & Fact Families with 8 & Multi-Step Problems 8.6 Making Sense of Multiplication & Division Facts 8.7 Dividing with 0 & Multiplication & Division Facts 8.9 Draw a Picture and Write a# Sentence End of module performance assessment

9 Suggested Blocks of Instruction: 10 days /January / February Topic: Topic 9-Understanding Fractions / Develop understanding of fractions as numbers. 3.NF.1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. 3.NF.2. Understand a fraction as a number on the number line; represent fractions on a number line diagram. 2a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. 2b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. Represent and solve problems involving multiplication and division. 3.OA.3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. What are different interpretations of a fraction? A region can be divided into equal-sized parts in different ways. Equal-sized parts of a region have the same area but not necessarily the same shape. A fraction describes the division of a whole (region, set, segment) into equal parts. The bottom number in a fraction tells how many equal parts the whole is divided into. The top number tells how many equal parts are indicated. A fraction is relative to the size of the whole. Finding a unit-fractional part of a whole is the same as dividing the whole by the denominator of the fraction. Some points between whole numbers on a number line can be labeled with fractions or mixed numbers. The denominator of the fraction can be determined by counting the number of equal parts between two consecutive whole numbers. Fractions can be approximated by other fractions that are close. 9.1 Dividing Regions into Equal parts 9.2 Fractions & Regions 9.3 Fractions & Sets 9.4 Fractional Parts of a Set 9.5 Locating Fractions on the # Line 9.6 Benchmark Fractions 9.7 Fractions & Length 9.8 Make a Table and Look for a Pattern End of module performance assessment

10 Suggested Blocks of Instruction: Topic: Topic 10-Fraction Comparison and Equivalence 11 days /February / Develop understanding of fractions as numbers. 3.NF.2. Understand a fraction as a number on the number line; represent fractions on a number line diagram. 2a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. 2b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. 3.NF.3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. 3a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. 3c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. 3d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. What are different ways to compare fractions? If two fractions have the same denominator, the fraction with the greater numerator is the greater fraction. If two fractions have the same numerator, the fraction with the lesser denominator is the greater fraction. Fractions can be compared to each other by comparing them to benchmark numbers such as 0, ½, and 1. Number lines can be used to compare fractions with like denominator or the numerators. A fraction is relative to the size of the whole Models can be used to compare fractional amounts. Number lines can be used to compare fractions with like denominators or like numerators. Equivalent fractions name the same point on a number line. If a fraction aligns with a whole number on a number line or to a whole number fraction strip, the whole number is equivalent to that fraction. The same fractional amount can be represented by an infinite set of different but equivalent fractions. Equivalent fractions name the same point on a number line. If a fraction aligns with a whole number on a number line or to a whole number fraction strip, the whole number is equivalent to that fraction. Materials: 10.1 Using Models to Compare Fractions: Same Denominator 10.2 Using Models to Compare Fractions: Same Numerator 10.3 Comparing Fractions Using Benchmarks 10.4 Comparing Fractions on the Number Line 10.5 Finding Equivalent Fractions 10.6 Equivalent Fractions and the Number Line 10.7 Whole Numbers & Fractions 10.8 Using Fractions 10.9 Draw a Picture End of module performance assessment

11 Suggested Blocks of Instruction: 11 days / February/March Topic: Topic 11-Two-Dimensional Shapes and Their Attributes /Enduring Reason with shapes and their attributes. 3.G.1. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. 3.G.2. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. How can two-dimensional shapes be described, analyzed, and classified? Lines and line segments are sets of points in space that can be used to describe parts of other geometric lines, shapes and solids. An angle is formed by two rays with a common endpoint. Angles can be classified by their size. Plane shapes have many properties that make them different from one another. Polygons can be described and classified by their sides and angles. Polygons can be put together or taken apart to make other polygons Lines & Line Segments 11.2 Angles 11.3 Polygons 11.4 Triangles 11.5 Quadrilaterals 11.6 Combining & Separating Shapes 11.7 Making New Shapes 11.8 Solve a Simpler Problem 11.9 Make & Test Generalizations End of module performance assessment

12 Suggested Blocks of Instruction: 7 days / March Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. 3.MD.1. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. Topic: Topic 12-Time /Enduring How can lengths of time be measured and found? Time can be expressed using different units that are related to each other. The minute hand takes 5 minutes to move from one number to the next on a typical clock face. The minute hand takes 1 minute to move from one mark to the next on a typical clock face. There are different units for measuring time. Many clock times can be expressed in more than one way. The duration of an event can be measured if one knows the start and end times for the event. Learning activities/ 12.1 Time to the Half Hour and Quarter Hour 12.2 Time to the Minute 12.3 Units of Time 12.4 Elapsed Time 12.5 Work Backward End of module performance assessment

13 Suggested Blocks of Instruction: 7 days /March/April Topic: Topic 13-Perimeter Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. 3.MD.8. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. /Enduring How can perimeter be measured and found? The distance around a figure is its perimeter. To find the perimeter of a polygon, add the lengths of the sides. In a given measurement situation, the type of measuring tool and the measurement units it contains determine the appropriateness of the tool. To find the perimeter of a polygon, add the lengths of the sides. Shapes can be made with a given perimeter. Different shapes can have the same perimeter Understanding Perimeter 13.2 Tools and Units for Perimeter 13.3 Perimeter of Common Shapes 13.4 Different Shapes with the Same Perimeter 13.5 Try, Check, and Revise End of module performance assessment

14 Suggested Blocks of Instruction: 12 days /April Geometric measurement: understand concepts of area and relate area to multiplication and to addition. 3.MD.5. Recognize area as an attribute of plane figures and understand concepts of area measurement. 5a. A square with side length 1 unit, called a unit square, is said to have one square unit of area, and can be used to measure area. 3.MD.6. Measure areas by counting unit squares (square cm, square m, square in, square ft, andother units). 3.MD.7. Relate area to the operations of multiplication and addition. 7a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. 7b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world problems, and represent whole-number products as rectangular areas in mathematical reasoning. 7c.Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a b and a c. Use area models to represent the distributive property in mathematical reasoning. 7d.Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts to solve real world problems. Reason with shapes and their attributes. 3.G.2. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. Topic: Topic 14-Area /Enduring What does area mean? What are different ways o find the area of a shape? The amount of space inside a shape is its area, and area can be estimated or found using square units. Square units can be used to create shapes with given areas. Standard measurement units are used for consistence in find and communicating measurements. The amount of space inside a shape is its area and area can be estimated or found using square units. Formulas exist for finding the area of some polygons. The area of rectangles can be used to model the Distributive Property. The area of some irregular shapes can be found by breaking apart the original shape into other shapes for which the areas can be found. There are relationships between the perimeter and area of a polygon. Equal-area parts of a figure can be sued to model unit fractions Covering Regions 14.2 Area & Units 14.3 Standard Units 14.4 Area of Squares & Rectangles 14.5 Area and the Distributive Property 14.6 Solve a Simpler Problem 14.7 Area of Irregular Shapes 14.8 Same Area, Different Perimeter 14.9 Equal Areas and Fractions Selecting Appropriate Measurement Units and Tools End of module performance assessment

15 Suggested Blocks of Instruction: 7 days /April / May Topic: Topic 15-Liquid Volume and Mass Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. 3.MD.2. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). /Enduring What are the customary units for measuring capacity and weight? What are the metric units for measuring capacity and mass? Capacity is a measure of the amount of liquid a container can hold. Mass is a measure of the quantity of matter in an object. Weight and mass are different. The weight of an object is a measure of how heavy an object is Customary Units of Capacity 15.2 Metric Units of Capacity 15.3 Units of Mass 15.4 Units of Weight 15.5 Draw a Picture End of module performance assessment

16 Suggested Blocks of Instruction: 8 days / May Represent and interpret data. 3.MD.3. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step how many more and how many less problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. 3.MD.4. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters. Topic: Topic 16-Data /Enduring How can data be represented, interpreted, and analyzed? Line plots allow data to be compared more easily than in a list or a table. Line plots can be sued to organize and represent data generated by measuring lengths. Each type of graph is most appropriate for certain kinds of data. Pictographs and bar graphs help to compare data. The key for a pictograph determines the number of pictures needed to represent each number in a set of data. In a bar graph, the scale determines how long the bar needs to be to represent each number in a set of data Line Plots 16.2 Length & Line Plots 16.3 Reading Pictographs and Bar Graphs 16.4 Making Pictographs 16.5 Making Bar Graphs 16.6 Use Tables & Graphs to Draw Conclusions End of module performance assessment