Bits and Pieces 3 27 Days Data About Us 5 Days MCAS Review Order of Operations, Integer +,-, etc How Likely Is It? 12 Days Math Topics ( p drive)

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1 Grade 6 Calendar Computation Strategies Packet 2 Days Benchmark Test 2 Days Prime Time 17 Days Bits and Pieces 1 26 Days Shapes and Designs 17 Days Bits and Pieces 2 25 Days CMP2 Covering and Surrounding 23 Days Bits and Pieces 3 27 Days Data About Us 5 Days MCAS Review Order of Operations, Integer +,-, etc How Likely Is It? 12 Days Math Topics ( p drive) Sep-10 S M T W T F S Bench 8 Bench Oct-10 Nov-10 Dec-10 S M T W T F S S M T W T F S S M T W T F S Jan-11 Feb-11 Mar-11 S M T W T F S S M T W T F S S M T W T F S Apr-11 May-11 Jun-11 S M T W T F S S M T W T F S S M T W T F S

2 Grade 6 Curriculum Map MCAS Questions for most books are in a file named Grade 6 MCAS by Book - located in the p-drive BEGIN YEAR WITH MULTIPLICATION AND DIVISION PACKET - located in p-drive 2 days PRIME TIME 17 Days Curriculum Map Investigations CMP 2 Notes Standards Essential skills Objectives / Goals Playing the Factor Game Playing to Win the Factor Game The Product Game 1.3 Finding Patterns 2.1 Reasoning With Even and Odd Numbers 2.2 Combine 2.2, 2.3 Classifying Numbers 2.3 Riding Ferris Wheels 3.1 Combine 3.1, P.1 Become familiar with the factors of the numbers 2 to 30. Review multiplication and division of small whole numbers. Recognize the difference between prime numbers and composite numbers. Relate dividing and finding factors. Classify numbers as prime or composite. Recognize that some numbers are rich in factors, while others have few factors. Review multiplication facts. Develop understanding of factors and multiples and the relationships between them. Understand that some products are the result of more than one factor pair. Review multiplication facts. Recognize that factors come in pairs and that once one factor is found, another can also be found. Visualize and represent a factor pair as the dimensions of a rectangle. Determine whether a number is prime/composite, square/non-square, and even/odd based on its factor pairs. Develop an informal sense of which factors must be checked to be sure all the factors of a number are found. Make conjectures about the result of operations on odd numbers, on even numbers, and on combinations of odd and even numbers, and create arguments to show which conjectures are valid and which are not. Determine whether a product is even or odd based on its factors. Determine whether a sum is even or odd based on its addends. Classify numbers by their characteristics using Venn diagrams as a tool for sorting and classifying. Develop understanding of factors and multiples, common factors and common multiples, and the relationship among them. Recognize situations in which finding common multiples of whole numbers is important. Develop strategies for finding common multiples. Observe patterns in common multiples of numbers and use patterns to reason about and predict future occurrences and solve problems. 6/16/2010 1

3 Looking at Cicada Cycles 3.2 Bagging Snacks 3.3 Planning a Picnic 3.4 The Product Puzzle Finding the Longest Factor String Combine 3.3, P.1 6.P.1 6.P Introduce term relatively prime Recognize situations in which finding common multiples of whole numbers is important. Develop strategies for finding common multiples. Observe patterns in common multiples of numbers and use patterns to reason about and predict future occurrences and solve problems. Recognize situations in which finding common multiples of whole numbers is important. Begin to develop strategies for finding common multiples. Observe patterns in common multiples of numbers and use patterns to reason about and predict future occurrences and solve problems. Recognize situations in which finding common multiples of whole numbers is important. Develop strategies for finding common multiples. Observe patterns in common multiples of numbers and use patterns to reason about and predict future occurrences and solve problems. Find factorizations of numbers and then break them down into prime factorizations. Understand that prime numbers are the essential multiplicative building blocks for whole numbers. Develop a systematic strategy for finding prime factorizations. Recognize that numbers may have several different factorizations but, except for order, each whole numbers greater than 1 has exactly one factorization in to a product of prime numbers (the Fundamental Theorem of Arithmetic). OMIT Using Prime Factorizations 4.3 OMIT Unraveling the Locker Problem 5.1 Supplement exponents and exponential form with practice problems on exponents Bits and Pieces I 26 Days Curriculum Map Investigations CMP 2 Notes Standards Essential Skills Big Ideas/Objectives 6/16/2010 2

4 Reporting Progress N.4 To assess prior knowledge of fractions Fraction Strips 1.2 Measuring Progress N.4 6.N.4 Comparing Classes N.7 Equivalent Fractions/Equal Shares 2.1 Finding Equivalent Fractions 2.2 Comparing Fractions to Benchmarks 2.3 Fractions Between Fractions N.6 6.N.7 6.N.6 6.N.7 6.N.6 6.N.7 Fractions Greater Than One N.6 Making Smaller Parts N To explore the role of numerator/denominator as part-to-whole nature of fractions. To develop strategies for folding fraction strips for benchmark fractions and investigate the equivalent fractions resulting from partitioning strategies. To use fraction strips to represent part-to-whole nature of fractions and to begin to use fractions to find fraction parts of whole number quantities. To begin to reason with fractions > 1 and understand the need to consider the size of the whole when comparing fraction amounts. To recognize the role of the numerator and denominator when partitioning and using LCM for finding equivalent fractions To develop strategies for finding equivalent fractions and understand a place on a number line can have more than 1 fraction name. A fraction can represent the length from 1 point to another on a number line. To use benchmarks to estimate the size of and to compare fractions. To develop strategies for comparing/ordering fractions. To recognize that by using smaller partitions one can find a fraction between 2 given fractions To develop strategies for representing fraction amounts as mixed #'s and improper fractions To read/write decimal and fraction #'s and extend understanding of those #'s past the hundredths value Making Even Smaller Parts N7 To develop ways to find a decimal between any 2 given decimals Decimal Benchmarks N.2 To use hundredths grids to represent fractions and decimals and find decimal equivalents for fractions Fractions to Decimals N.14 To use division to determine the value of a fraction Ordering Decimals N.7 To develop strategies for ordering and comparing decimals Who's the Best 4.1 To introduce percents a as part-to-whole relationship where the whole is scaled to 6.N.7 be "out of 100" Choosing the Best 4.2 Finding a General Strategy N.7 6.N.7 To develop strategies for using % to compare situations with different numbers of trials To develop connections between fractions, decimals and percents; compare whole amounts > and < 100 Changing Forms To convert from fractions/decimals to % and from % back to fractions/decimals 6/16/2010 3

5 6.N.7 Shapes and Designs 17 Days Curriculum Map Investigations CMP 2 Notes Standards Skills Essential Big Ideas/Objectives Sorting Shapes To sort shapes according to special properties and describe those properties. Symmetries of Shapes G.7 9 To introduce students to rotation and reflection symmetries of figures Tiling a Beehive 1.3 To decide which shapes will tile a surface and what common properties they have. Understanding Angles Developing Angle Benchmarks Using an Angle Ruler 2.3 OMIT Analyzing Measurement Errors omit Combine 2.1, 2.2 Use angle rulers and protractors To use a right angle as a benchmark to estimate the size of angles To develop angle benchmarks. 6-20, To increase the ability to reason with shapes. To practice measuring angles with an angle ruler. To give more practice with estimation. Angles and Parallel Lines 2.5 Angle Sums of Regular Polygons 3.1 Angle Sums of Any Polygon G.3 6.M G.8 6.M.7 6.G.8 6.G Angles in Tilings Exterior Angles in Polygons 3.4 Building Triangles G.3, To explore patterns among angles created when 2 or more lines are cut by another line. To develop understanding of parallel lines and parallelograms. To find the angle sums of regular polygons. To determine relationships between the # of sides and angle sum of these polygons. To find angle sums of any polygon. To develop conjectures about the relationship between the # of sides and angle sum of any polygon. To decide which regular polygons will tile by themselves or in combinations using prior knowledge about interior angles 6-20 To explore the sum of the exterior angles of a polygon. 5 To build triangles given three side lengths. To decide if any 3 lengths will make a triangle. To find that the sum of 2 side lengths must be greater than the 3rd side of the triangle. 6/16/2010 4

6 Building Quadrilaterals 4.2 Properties of Quadrilaterals 4.3, 6.G.8, 6-22 To build quadrilaterals given 4 side lengths. To decide if any 4 side lengths will make a quadrilateral. To find that the sum of 3 side lengths must be greater than the 4 th side To use the properties of quadrilaterals to build specific quadrilaterals. BITS AND PIECES II 25 Days Curriculum Map Investigations CMP 2 Notes Standa Essential rds skills Big Ideas/Objectives Getting Close N.6 6.N.14 To use estimation to find decimal and fraction sums Estimating Sums N.14 To use estimation when an exact answer is not needed; decide if over or 6.N.16 underestimation will suffice Land Sections N.14 To develop strategies for adding/subtracting fractions Visiting the Spice Shop N.14 To use number sentences for adding/subtracting fractions and mixed numbers Just the Facts N.12 To explore the inverse relationship between adding/subtracting fractions and use efficient strategies for adding/subtracting fractions/mixed numbers Algorithms 2.4 To develop efficient algorithms for adding and subtracting fractions Additional practice workbook To practice algorithms for adding and subtracting fractions and to solve word pages problems by adding and subtracting fractions Selling Brownies N.14 To understand that finding a fraction of a fraction means multiplication and to estimate products of fractions Finding Part of a Part 3.2 Modeling Multiplication N.14 6.P.4 6.N.14 To use models to represent the product of two fractions and estimate the product of two fractions To develop strategies for multiplying fractions, whole numbers and mixed numbers and determine when to use them Changing Forms N.14 To explore the relationship between two fractions and their product Multiplication Algorithm N.14 To use an efficient algorithm to solve any fraction multiplication problem Preparing Food N.14 To divide a whole number by a fraction Fundraising Continues N.14 To divide a fraction by a whole number 6/16/2010 5

7 Summer Work N.14 To divide a fraction by a fraction Writing Division Algorithm N.12 1 To explore the inverse operations of multiplication/division and use an efficient algorithm to solve any division problem Additional practice workbook pages To practice the algorithms for multiplying and dividing fractions and to solve word problems by multiplying and dividing fractions COVERING AND SURROUNDING 23 Days Curriculum Map Investigations CMP 2 Notes Standards Designing Bumper-Car Rides Essential skills M Pricing Bumper-Car Rides M Decoding Designs M Building Storm Shelters M OPTIONAL Stretching the Perimeter Fencing Spaces 2.3 OMIT Adding Tiles to Pentominos Triangles on Grids (Day 1) Triangles on Grids (Day 2) M M M Objectives / Goals Learn that the area of a figure is the number of square units needed to cover it. Learn that the perimeter of an object is the number of units of length needed to surround it. Learn that the area of a figure is the number of square units needed to cover it. Learn that the perimeter of an object is the number of units of length needed to surround it. Understand that two figures with the same area may have different perimeters. Use the relationship between length and width to develop formulas for the area and perimeter of a rectangle. Explore questions of maximum and minimum in the context of finding the largest and smallest perimeter for rectangles of fixed area. Understand that the perimeters of rectangles with a fixed area can vary considerably. Continue to develop facility-using formulas for finding perimeter and area of rectangles. Continue to develop a conceptual understanding of area and perimeter. Understand that the perimeters of rectangles with a fixed area can vary considerably. Explore questions of maximum and minimum I the context of finding the largest and smallest perimeter for rectangles of fixed area. Continue to develop facility using formulas for finding perimeter and area of rectangles. Continue to develop a conceptual understanding of area and perimeter. Find the minimum and maximum area of a rectangle with a fixed perimeter. Understand that the areas of rectangles with a fixed perimeter can vary considerably. Construct diagrams, tables, and graphs to organize and represent data. Continue to develop facility using formulas for finding perimeter and area of rectangles. Develop and employ reasonable strategies for finding the area of a triangle. Find relationships between rectangles and triangles. 6/16/2010 6

8 3.1 6.M More Triangles M What's the Area? M OMIT Designing Triangles Under Constraints Finding Measures of Parallelograms 3.4 Cover surface area e.g painting a room Discovery Ed has some 5 minute videos on S A M Find relationships between rectangles and triangles. Use these relationships to develop techniques for finding the area of a triangle. Distinguish among base, height, and side lengths of triangles. Understand that depending upon how you position a given triangles, it has more than one base and height, but only one area. Explore how triangles with the same base and height can look different but have the same area. Develop and employ reasonable strategies for finding the areas and perimeters of parallelograms. Parallelograms from Triangles M.1 6.M Find area relationships between rectangles, triangles, and parallelograms. Use relationships between parallelograms and triangles to develop techniques for finding the areas of parallelograms. Distinguish among the base, height, and side lengths of a parallelogram. Understand that a parallelogram may be positioned in more than one way, and thus may have more than one base-height pair, but only one area. OMIT Designing Parallelograms Under Constraints 4.3 Parks, Hotels, and Quilts M.1 6.M Measuring Lakes Surrounding a Circle M Apply techniques for finding the areas and perimeters of parallelograms to a variety of problem situations. Develop techniques for estimating areas and perimeters of irregular figures. Use ideas about area and perimeter to solve practical problems. Continue to develop a conceptual understanding of area and perimeter. Discover that it takes slightly more than three diameters to equal the circumference of a circle. Use this discovery to develop a formula for circumference of a circle. Develop strategies for organizing and comparing data. 6/16/2010 7

9 Pricing Pizzas M "Squaring" a Circle M Develop techniques for estimating the area of a circle. Develop strategies for organizing and comparing data. Use ideas about area and perimeter to solve practical problems. Continue to develop a conceptual understanding of area and perimeter. Discover that it takes slightly more than three radius squares to equal the area of a circle. Use this discovery to develop a formula for area of a circle. BITS AND PIECES III 27 Days Curriculum Map Investigations CMP 2 Standards Essential skills Big Ideas/Objectives About How Much? 1.1 To use decimal/fraction relationship to estimate decimal sums. Add/Subtract Decimals 1.2 To develop place-value understanding of decimal addition and subtraction Using Fractions to Add/Subtract 1.3 Algorithms 1.4 Relating Fraction/Decimal Mult. 2.1 Missing Factors N.12 6.N.3 6.N.2 Finding Decimal Products 2.3 Factor-Product Relationships 2.4 Deciphering Decimal Situations 3.1 The Great Equalizer 3.2, To connect strategies for adding/subtracting of decimals to adding/subtracting fractions with multiples of 10 as denominators To develop algorithms for adding/subtracting decimals; to explore the inverse relationship between adding/subtracting To estimate the size of and develop place-value understanding of decimal products; to solve decimal multiplication problems To use place value to explore the relationship between factors and products in decimal multiplication To use estimation as a strategy for finding decimal products To develop an algorithm for multiplying decimals in which the decimal point is placed into a product by counting/adding decimal places. To identify when to add, subtract, multiply or divide decimals; to use models to solve division problems To use the relationship between decimals and fractions AND the common denominator approach to develop algorithm for dividing decimals 6/16/2010 8

10 Exploring Dividing Decimals 3.3 Representing Fractions as Decimals Determining Tax 4.1 Computing Tips 4.2 Finding Bargains 4.3 Clipping Coupons 5.1 How Much Can We Spend 5.2, To use knowledge about fractions to develop an algorithm for dividing decimals and explore the inverse relationship between multiplication/division in fact families To predict the decimal representation of a fraction (terminating or repeating) To understand that a percent is a decimal fraction with a denominator of 100; to represent percents as decimals; to use decimal computation to compute percents To represent % as decimals and explore the relationship between 1% and 10% use this to compute 5%, 15% and 20% To use % in estimating/computing tax, tips and discounts; to find what percent one number is of another; solve percent problems To find a strategy for finding the percent of a discount To use percents in estimating a given amount and solve problems with percents Making Circle Graphs 5.3 To make and interpret circle graphs to represent data; solve problems with percent DATA ABOUT US 5 Days Curriculum Map Investigations CMP 2 Notes Standards Essential skills Objectives / Goals Organizing and Interpreting Data Useful Statistics 1.2 Experimenting With the Median /2 Day 6.D.1 6.D Describe data distributions. Use line plots and bar graphs to display data distributions. Use mode, median, how data vary from the least to the greatest values, and range to describe what is typical about a data distribution. Use tables and line plots to display data distributions. Recognizing how the median, as a measure of center, responds to changes in the number and magnitude of data values. Use line plots to display data distributions. Using Different Data Types 1.4 For homework 6.D Identify whether data are categorical or numerical. Use bar graphs to display data distributions. Understand how median, mode, and range relate to numerical and categorical data. 6/16/2010 9

11 Vertical Bar Graphs and Horizontal Bar Graphs Traveling to School For homework For homework Jumping Rope 2.2 1/2 Day Relating Height to Arm Span Relating Travel Time to Distance 6.D.1 6.D /2 Day Distinguish between vertical and horizontal bar graphs. Distinguish how numerical data or categorical data are shown on a horizontal bar graph. Answer questions using both kinds of bar graphs. Group numerical data in equal intervals and display their distribution using a stemand-leaf plot. Find measures of center and variation, including range and how data vary from the least to the greatest values, when a distribution is displayed using a stem-and-leaf plot. Compare two distributions displayed using back-to-back stem-and-leaf plots. Compare two distributions using statistics, such as median, range, and how the data vary from least to greatest values. Identify outliers in a distribution. Display distributions of paired-data values on coordinate graphs. Explore relationships between paired-data values whose distributions are displayed using coordinate graphs. Explore intervals for scaling the vertical axis (y-axis0 and the horizontal axis (x-axis). Explore relationships between paired-data values whose distributions are displayed using coordinate graphs. Explore intervals for scaling the vertical axis (y-axis) and the horizontal axis (x-axis). Finding the Mean D Understand the mean as a number that "evens out" or "balances" a distribution. Data With the Same Mean Using the Mean 3.3 1/2 Day 3.2 1/2 Day 6.D D Create distributions with designated means. Recognize that data with the same mean may have different distributions. Reason with a model that clarifies the development of the algorithm for finding the mean. Experiment with how the mean, as a measure of center, responds to changes in the number and magnitude of data values. HOW LIKELY IS IT? 12 Days Curriculum Map Investigations CMP 2 Notes Standard s Essential skills Objectives / Goals Choosing Cereal D Develop an intuitive sense of probability through a coin-tossing experiment. Tossing Paper Cups D Continue to develop an intuitive sense of probability through a cup tossing experiment. Understand that probabilities are useful for predicting what will happen over the long run. Toss cups to find an experimental probability where the outcomes are not equally likely. One More Try D Develop strategies for finding experimental probabilities for a situation that involves tossing two coins. Begin to explore the notion of fair and unfair. 6/16/

12 Analyzing Events D Understand the concepts of equally likely and not equally likely. Predicting to Win D Find the theoretical probability by analyzing the possible equally likely outcomes involved in a game of guessing the color of a block. Compare the experimental and theoretical probabilities. Exploring Probabilities D Observe some properties of probability. Winning the Bonus Prize D Use organized lists and tree diagrams to find theoretical probabilities. Understand that experimental probabilities are better estimates of theoretical probabilities when based on larger numbers of trials. Deepen understanding of equally likely and not equally likely. Understand that a Pondering Possible and D game of chance is fair only if each player has the same chance of winning, not just a Probable possible chance of winning. Designing a Spinner D Develop strategies for finding experimental and theoretical probabilities in situations involving spinners. Making Decisions D Analyze probability situations. Use probability to make decisions. Decide whether the probability situations are fair or unfair. Scratching Spots D Develop strategies for finding both experimental (using a simulation of a scratch-off prize card) and theoretical probabilities (analyzing the scratch-off prize card). OPTIONAL Genetic Traits D Use class and survey data to find the experimental probabilities for certain genetic traits. OPTIONAL Tracing Traits D.3 6.D Appreciate the power of probability for making predictions. Develop strategies (for example, using a chart or table) for finding theoretical probabilities involving genetics. Roller Derby D.3 6.M Appreciate the power of probability for determining strategies for winning a game. Develop strategies (for example, using a chart or table) for finding both experimental and theoretical probabilities of winning a game. 6/16/