Connected Mathematics 3 (CMP3)

Transcription

1 A Correlation of (CMP3) 2014 To the Pennsylvania Common Core Standards in Mathematics Grades 6-8

2 A Correlation of, 2014, to the Introduction This document demonstrates how (CMP3), 2014 meets the, grades 6-8. Correlation references are to the pages of the Student and Teacher s Editions. The goal of is to help students develop mathematical knowledge, conceptual understanding, and procedural skills, along with an awareness of the rich connections between math topics across grades and across Common Core content areas. Through the Launch-Explore-Summarize model, students investigate and solve problems that develop rigorous higher-order thinking skills and problem-solving strategies. Curriculum development for CMP3 has been guided by an important mathematical idea: All students should be able to reason and communicate proficiently in mathematics. They should have knowledge of and skill in the use of the vocabulary, forms of representation, materials, tools, techniques, and intellectual methods of mathematics. This includes the ability to define and solve problems with reason, insight, inventiveness, and technical proficiency. CMP3 uses technology to help teachers implement with fidelity, thus raising student achievement. Easy-to-use mobile tools help with classroom management and capture student work on the go. ExamView delivers a full suite of assessment tools, and MathXL provides individualized skills practice. 21st century social networking technology connects CMP3 teachers, while students benefit from interactive digital student pages that allow for instantaneous sharing and effective group work. Copyright 2014 Pearson Education, Inc. or its affiliate(s). All rights reserved

3 A Correlation of, 2014 to the Table of Contents Grade Grade Grade 8... Error! Bookmark not defined. Copyright 2014 Pearson Education, Inc. or its affiliate(s). All rights reserved

4 A Correlation of, 2014 to the Grade Numbers and Operations D) Ratios and Proportional Relationships CC D.1 Understand ratio concepts and use ratio reasoning to solve problems. Grade 6, 2014 Comparing Bits and Pieces: 2.1: Equal Shares; 2.2: Unequal Shares; 2.3: Making Comparisons With Rate Tables; 4.1: Who is the Best? Making Sense of Percents; 4.2: Genetic Traits; 4.3: The Art of Comparison Decimal Operations: 4.1: What s the Tax on This Item?; 4.2: Computing Tips; 4.3: Percent Discounts; 4.4: Putting Operations Together Variables and Patterns: 3.1: Visit to Wild World; 3.2: Moving, Texting, and Measuring; 3.3: Group Discounts and a Bonus Card; 3.4: Getting the Calculation Right M06.A-R.1.1.1: Use ratio language and notation (such as 3 to 4, 3:4, 3/4) to describe a ratio relationship between two quantities. Example 1: The ratio of girls to boys in a math class is 2:3 because for every 2 girls there are 3 boys. Example 2: For every five votes candidate A received, candidate B received four votes. M06.A-R.1.1.2: Find the unit rate a/b associated with a ratio a:b (with b 0) and use rate language in the context of a ratio relationship. Example 1: This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. Example 2: We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. M06.A-R.1.1.3: Construct tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and/or plot the pairs of values on the coordinate plane. Use tables to compare ratios. Comparing Bits and Pieces: 2.1: Equal Shares; 2.2: Unequal Shares; 2.3: Making Comparisons With Rate Tables; 4.1: Who is the Best? Making Sense of Percents; 4.2: Genetic Traits; 4.3: The Art of Comparison Decimal Operations: 4.1: What s the Tax on This Item?; 4.2: Computing Tips; 4.3: Percent Discounts; 4.4: Putting Operations Together Comparing Bits and Pieces: 2.3: Making Comparisons With Rate Tables Comparing Bits and Pieces: 2.1: Equal Shares; 2.2: Unequal Shares; 2.3: Making Comparisons With Rate Tables; Variables and Patterns: 3.1: Visit to Wild World; 3.2: Moving, Texting, and Measuring 1

5 A Correlation of, 2014 to the Grade 6 M06.A-R.1.1.4: Solve unit rate problems including those involving unit pricing and constant speed. Example: If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? M06.A-R.1.1.5: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percentage. E) The Number System CC E.1 Apply and extend previous understandings of multiplication and division to divide fractions by fractions. M06.A-N.1.1.1: Interpret and compute quotients of fractions (including mixed numbers), and solve word problems involving division of fractions by fractions. Example 1: Given a story context for (2/3) (3/4), explain that (2/3) (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) (c/d) = (a/b) (d/c) = ad/bc.) Example 2: How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Example 3: How many 2 1/4-foot pieces can be cut from a 15 1/2-foot board? CC E.2 Identify and choose appropriate processes to compute fluently with multi digit numbers. Grade 6, 2014 Comparing Bits and Pieces: 2.3: Making Comparisons With Rate Tables Variables and Patterns: 3.1: Visit to Wild World; 3.2: Moving, Texting, and Measuring; 3.3: Group Discounts and a Bonus Card; 3.4: Getting the Calculation Right Comparing Bits and Pieces: 4.1: Who is the Best? Making Sense of Percents; 4.2: Genetic Traits; 4.3: The Art of Comparison Decimal Operations: 4.1: What s the Tax on This Item?; 4.2: Computing Tips; 4.3: Percent Discounts; 4.4: Putting Operations Together Let s Be Rational: 2.1: How Much of the Pan Have We Sold?; 2.2: Modeling Multiplication Situations; 2.3: Changing Forms; 3.1: Preparing Food; 3.2: Into Pieces; 3.3: Sharing a Prize; 3.4: Examining Algorithms for Dividing Fractions Let s Be Rational: 3.1: Preparing Food; 3.2: Into Pieces; 3.3: Sharing a Prize; 3.4: Examining Algorithms for Dividing Fractions Prime Time: Factors and Multiples: 1.1: Playing the Factor Game; 1.2: Playing to Win; 1.3: The Product Game; 1.4: Rectangles and Factor Pairs; 2.1: Riding Ferris Wheels; 2.2: Looking at Cicada Cycles; 2.3: Bagging Snacks; 3.1: The Product Puzzle; 3.2: Finding the Longest Factor String; 3.3: Using Prime Factorizations; 3.4: Unraveling the Locker Problem; 4.1: Reasoning With Even and Odd Numbers; 4.2: Using the Distributive Property; 4.3: Ordering Operations; 4.4: Choosing an Operation 2

6 A Correlation of, 2014 to the Grade 6 M06.A-N.2.1.1: Solve problems involving operations (+,,, and ) with whole numbers, decimals (through thousandths), straight computation, or word problems. Grade 6, 2014 Prime Time: Factors and Multiples: 1.1: Playing the Factor Game; 1.2: Playing to Win; 1.3: The Product Game; 1.4: Rectangles and Factor Pairs; 2.1: Riding Ferris Wheels; 2.2: Looking at Cicada Cycles; 2.3: Bagging Snacks; 3.1: The Product Puzzle; 3.2: Finding the Longest Factor String; 3.3: Using Prime Factorizations; 3.4: Unraveling the Locker Problem Comparing Bits and Pieces: 1.1: Fundraising; 1.2: Fundraising Thermometers; 1.3: Equivalent Fractions on the Line; 1.4: Measuring Progress; 1.5: Comparing Fundraising Goals; 2.1: Equal Shares; 2.2: Unequal Shares; 2.3: Making Comparisons With Rate Tables; 3.1: Extending the Number Line; 3.2: Estimating and Ordering Rational Numbers; 3.3: Sharing 100 Things; 3.4: Decimals on the Number Line; 3.5: Earthquake Relief; 4.1: Who is the Best? Making Sense of Percents; 4.2: Genetic Traits; 4.3: The Art of Comparison Let s Be Rational: 1.1: Getting Close; 1.2: Estimating Sums and Differences; 1.3: Land Sections; 1.4: Visiting the Spice Shop; 2.1: How Much of the Pan Have We Sold?; 2.2: Modeling Multiplication Situations; 2.3: Changing Forms; 3.1: Preparing Food; 3.2: Into Pieces; 3.3: Sharing a Prize; 3.4: Examining Algorithms for Dividing Fractions; 4.1: Just the Facts; 4.2: Multiplication and Division Fact Families; 4.3: Becoming an Operations Sleuth Decimal Operations: 1.1: Out to Lunch; 1.2: Getting Close; 1.3: Take a Hike; 2.1: Getting Things in the Right Place; 2.2: What s the Difference?; 2.3: Connecting Operations; 3.1: It s Decimal Time(s); 3.2: It Works Every Time; 3.3: How Many Times?; 3.4: Going the Long Way; 3.5: Challenging Cases; 4.1: What s the Tax on This Item?; 4.2: Computing Tips; 4.3: Percent Discounts; 4.4: Putting Operations Together CC E.3 Develop and/or apply number theory concepts to find common factors and multiples. Prime Time: Factors and Multiples: 2.1: Riding Ferris Wheels; 2.2: Looking at Cicada Cycles; 2.3: Bagging Snacks Let s Be Rational: 1.3: Land Sections; 1.4: Visiting the Spice Shop 3

7 A Correlation of, 2014 to the Grade 6 M06.A-N.2.2.1: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. M06.A-N.2.2.2: Apply the distributive property to express a sum of two whole numbers, 1 through 100, with a common factor as a multiple of a sum of two whole numbers with no common factor. Example: Express as 4(9 + 2). A Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials. CC E.4 Apply and extend previous understandings of numbers to the system of rational numbers. Grade 6, 2014 Prime Time: 2.3: Bagging Snacks Let s Be Rational: 1.3: Land Sections; 1.4: Visiting the Spice Shop Prime Time: Factors and Multiples: 4.2: Using the Distributive Property; 4.3: Ordering Operations Prime Time: Factors and Multiples: 2.3: Bagging Snacks Let s Be Rational: 1.3: Land Sections; 1.4: Visiting the Spice Shop Comparing Bits and Pieces: 1.1: Fundraising; 1.2: Fundraising Thermometers; 1.3: Equivalent Fractions on the Line; 1.4: Measuring Progress; 1.5: Comparing Fundraising Goals; 3.1: Extending the Number Line; 3.2: Estimating and Ordering Rational Numbers; 3.3: Sharing 100 Things; 3.4: Decimals on the Number Line; 3.5: Earthquake Relief; 4.1: Who is the Best? Making Sense of Percents; 4.2: Genetic Traits; 4.3: The Art of Comparison Let s Be Rational: 1.1: Getting Close; 1.2: Estimating Sums and Differences; 1.3: Land Sections; 1.4: Visiting the Spice Shop; 2.1: How Much of the Pan Have We Sold?; 2.2: Modeling Multiplication Situations; 2.3: Changing Forms; 3.1: Preparing Food; 3.2: Into Pieces; 3.3: Sharing a Prize; 3.4: Examining Algorithms for Dividing Fractions; 4.1: Just the Facts; 4.2: Multiplication and Division Fact Families; 4.3: Becoming an Operations Sleuth Decimal Operations: 1.1: Out to Lunch; 1.2: Getting Close; 1.3: Take a Hike; 2.1: Getting Things in the Right Place; 2.2: What s the Difference?; 2.3: Connecting Operations; 3.1: It s Decimal Time(s); 3.2: It Works Every Time; 3.3: How Many Times?; 3.4: Going the Long Way; 3.5: Challenging Cases; 4.1: What s the Tax on This Item?; 4.2: Computing Tips; 4.3: Percent Discounts; 4.4: Putting Operations Together 4

8 A Correlation of, 2014 to the Grade 6 M06.A-N.3.1.1: Represent quantities in realworld contexts using positive and negative numbers, explaining the meaning of 0 in each situation (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge). M06.A-N.3.1.2: Determine the opposite of a number and recognize that the opposite of the opposite of a number is the number itself (e.g., ( 3) = 3; 0 is its own opposite). M06.A-N.3.1.3: Locate and plot integers and other rational numbers on a horizontal or vertical number line; locate and plot pairs of integers and other rational numbers on a coordinate plane. M06.A-N.3.2.1: Write, interpret, and explain statements of order for rational numbers in real-world contexts. Example: Write 3 C > 7 C to express the fact that 3 C is warmer than 7 C. Grade 6, 2014 Comparing Bits and Pieces: 3.1: Extending the Number Line; 3.2: Estimating and Ordering Rational Numbers; 3.4: Decimals on the Number Line Comparing Bits and Pieces: 3.1: Extending the Number Line Comparing Bits and Pieces: 3.1: Extending the Number Line; 3.2: Estimating and Ordering Rational Numbers; 3.4: Decimals on the Number Line Comparing Bits and Pieces: 3.2: Estimating and Ordering Rational Numbers; 3.3: Sharing 100 Things; 3.4: Decimals on the Number Line; 3.5: Earthquake Relief M06.A-N.3.2.2: Interpret the absolute value of a rational number as its distance from 0 on the number line and as a magnitude for a positive or negative quantity in a real-world situation. Example: For an account balance of 30 dollars, write 30 = 30 to describe the size of the debt in dollars, and recognize that an account balance less than 30 dollars represents a debt greater than 30 dollars. Comparing Bits and Pieces: 3.1: Extending the Number Line M06.A-N.3.2.3: Solve real-world and mathematical problems by plotting points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Covering and Surrounding: 2.1: Triangles on Grids; 3.4: Polygons on Coordinate Grids Variables and Patterns: 1.1: Getting Ready to Ride; 1.2: From Atlantic City to Lewes; 1.3: From Lewes to Chincoteague Island; 1.4: From Chincoteague to Colonial Williamsburg 5

9 A Correlation of, 2014 to the Grade Algebraic Concepts B) Expressions & Equations CC B.1 Apply and extend previous understandings of arithmetic to algebraic expressions. M06.B-E.1.1.1: Write and evaluate numerical expressions involving whole-number exponents. Grade 6, 2014 Covering and Surrounding: 4.2: Filling the Boxes; 4.3: Designing Gift Boxes Variables and Patterns: 3.1: Visit to Wild World; 3.2: Moving, Texting, and Measuring; 3.3: Group Discounts and a Bonus Card; 3.4: Getting the Calculation Right; 4.1: Taking the Plunge; 4.2: More Than One Way to Say It; 4.3: Putting It All Together; 4.4: Finding the Unknown Value; 4.5: It s Not Always Equal Prime Time: Factors and Multiples: 3.2: Finding the Longest Factor String; 3.3: Using Prime Factorizations; 3.4: Unraveling the Locker Problem Covering and Surrounding: 4.2: Filling the Boxes; 4.3: Designing Gift Boxes M06.B-E.1.1.2: Write algebraic expressions from verbal descriptions. Example: Express the description five less than twice a number as 2y 5. M06.B-E.1.1.3: Identify parts of an expression using mathematical terms (e.g., sum, term, product, factor, quotient, coefficient, quantity). Example: Describe the expression 2(8 + 7) as a product of two factors. Variables and Patterns: 3.1: Visit to Wild World; 3.2: Moving, Texting, and Measuring; 3.3: Group Discounts and a Bonus Card; 3.4: Getting the Calculation Right; 4.1: Taking the Plunge; 4.2: More Than One Way to Say It; 4.3: Putting It All Together; 4.4: Finding the Unknown Value; 4.5: It s Not Always Equal Prime Time: 3.1: The Product Puzzle; 3.2: Finding the Longest Factor String; 3.3: Using Prime Factorizations; 3.4: Unraveling the Locker Problem; 4.2: Using the Distributive Property; 4.3: Ordering Operations; 4.4: Choosing an Operation M06.B-E.1.1.4: Evaluate expressions at specific values of their variables, including expressions that arise from formulas used in real-world problems. Example: Evaluate the expression b2 5 when b = 4. Covering and Surrounding: 4.2: Filling the Boxes; 4.3: Designing Gift Boxes Variables and Patterns: 3.1: Visit to Wild World; 3.2: Moving, Texting, and Measuring; 3.3: Group Discounts and a Bonus Card; 3.4: Getting the Calculation Right; 4.1: Taking the Plunge; 4.2: More Than One Way to Say It; 4.3: Putting It All Together; 4.4: Finding the Unknown Value; 4.5: It s Not Always Equal 6

10 A Correlation of, 2014 to the Grade 6 M06.B-E.1.1.5: Apply the properties of operations to generate equivalent expressions. Example 1: Apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x. Example 2: Apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y). Example 3: Apply properties of operations to y + y + y to produce the equivalent expression 3y. CC B.2 Understand the process of solving a one variable equation or inequality and apply it to real world and mathematical problems. M06.B-E.2.1.1: Use substitution to determine whether a given number in a specified set makes an equation or inequality true. M06.B-E.2.1.2: Write algebraic expressions to represent real-world or mathematical problems. M06.B-E.2.1.3: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all non-negative rational numbers. M06.B-E.2.1.4: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem and/or represent solutions of such inequalities on number lines. CC B.3 Represent and analyze quantitative relationships between dependent and independent variables. Grade 6, 2014 Prime Time: Factors and Multiples: 4.2: Using the Distributive Property; 4.3: Ordering Operations; 4.4: Choosing an Operation Variables and Patterns: 4.1: Taking the Plunge; 4.2: More Than One Way to Say It; 4.3: Putting It All Together; 4.4: Finding the Unknown Value; 4.5: It s Not Always Equal Variables and Patterns: 4.1: Taking the Plunge; 4.2: More Than One Way to Say It; 4.3: Putting It All Together; 4.4: Finding the Unknown Value; 4.5: It s Not Always Equal Variables and Patterns: 4.1: Taking the Plunge; 4.4: Finding the Unknown Value; 4.5: It s Not Always Equal Variables and Patterns: 3.1: Visit to Wild World; 3.2: Moving, Texting, and Measuring; 3.3: Group Discounts and a Bonus Card; 3.4: Getting the Calculation Right; 4.1: Taking the Plunge; 4.2: More Than One Way to Say It; 4.3: Putting It All Together; 4.4: Finding the Unknown Value; 4.5: It s Not Always Equal Variables and Patterns: 4.1: Taking the Plunge; 4.2: More Than One Way to Say It; 4.3: Putting It All Together; 4.4: Finding the Unknown Value Variables and Patterns: 4.5: It s Not Always Equal Variables and Patterns: 1.1: Getting Ready to Ride; 1.2: From Atlantic City to Lewes; 1.3: From Lewes to Chincoteague Island; 1.4: From Chincoteague to Colonial Williamsburg; 2.1: Renting Bicycles; 2.2: Finding Customers; 2.3: Predicting Profits; 2.4: What s the Story?; 3.1: Visit to Wild World; 3.2: Moving, Texting, and Measuring; 3.3: Group Discounts and a Bonus Card; 3.4: Getting the Calculation Right 7

11 A Correlation of, 2014 to the Grade 6 M06.B-E.3.1.1: Write an equation to express the relationship between the dependent and independent variables. Example: In a problem involving motion at a constant speed of 65 units, write the equation d = 65t to represent the relationship between distance and time. M06.B-E.3.1.2: Analyze the relationship between the dependent and independent variables using graphs and tables and/or relate these to an equation. Grade 6, 2014 Variables and Patterns: 3.1: Visit to Wild World; 3.2: Moving, Texting, and Measuring; 3.3: Group Discounts and a Bonus Card; 3.4: Getting the Calculation Right Covering and Surrounding: 1.3: Fencing In Spaces Variables and Patterns: 1.1: Getting Ready to Ride; 1.2: From Atlantic City to Lewes; 1.3: From Lewes to Chincoteague Island; 1.4: From Chincoteague to Colonial Williamsburg; 2.1: Renting Bicycles; 2.2: Finding Customers; 2.3: Predicting Profits; 2.4: What s the Story?; 3.1: Visit to Wild World; 3.2: Moving, Texting, and Measuring; 3.3: Group Discounts and a Bonus Card; 3.4: Getting the Calculation Right Geometry A) Geometry CC A.1 Apply appropriate tools to solve real world and mathematical problems involving area, surface area, and volume. M06.C-G.1.1.1: Determine the area of triangles and special quadrilaterals (i.e., square, rectangle, parallelogram, rhombus, and trapezoid). Formulas will be provided. M06.C-G.1.1.2: Determine the area of irregular or compound polygons. Example: Find the area of a room in the shape of an irregular polygon by composing and/or decomposing. M06.C-G.1.1.3: Determine the volume of right rectangular prisms with fractional edge lengths. Formulas will be provided. Covering and Surrounding: 1.1: Designing Bumper-Car Rides; 1.2: Building Storm Shelters; 1.3: Fencing In Spaces; 2.1: Triangles on Grids; 2.2: More Triangles; 2.3: Making Families of Triangles; 2.4: Designing Triangles Under Constraints; 3.1: Parallelograms and Triangles; 3.2: Making Families of Parallelograms; 3.3: Designing Parallelograms; 3.4: Polygons on Coordinate Grids; 4.1: Making Rectangular Boxes; 4.2: Filling the Boxes; 4.3: Designing Gift Boxes Covering and Surrounding: 2.3: Making Families of Triangles; 2.4: Designing Triangles Under Constraints; 3.1: Parallelograms and Triangles; 3.2: Making Families of Parallelograms; 3.3: Designing Parallelograms; 3.4: Polygons on Coordinate Grids Covering and Surrounding: 1.1: Designing Bumper-Car Rides; 3.1: Parallelograms and Triangles Covering and Surrounding: 4.2: Filling the Boxes; 4.3: Designing Gift Boxes 8

12 A Correlation of, 2014 to the Grade 6 M06.C-G.1.1.4: Given coordinates for the vertices of a polygon in the plane, use the coordinates to find side lengths and area of the polygon (limited to triangles and special quadrilaterals). Formulas will be provided. M06.C-G.1.1.5: Represent three-dimensional figures using nets made of rectangles and triangles. M06.C-G.1.1.6: Determine the surface area of triangular and rectangular prisms (including cubes). Formulas will be provided Measurement, Data, and Probability B) Statistics and Probability CC B.1 Demonstrate an understanding of statistical variability by displaying, analyzing, and summarizing distributions. M06.D-S.1.1.1: Display numerical data in plots on a number line, including line plots, histograms, and box-and whisker plots. M06.D-S.1.1.2: Determine quantitative measures of center (e.g., median, mean, mode) and variability (e.g., range, interquartile range, mean absolute deviation). Grade 6, 2014 Covering and Surrounding: 2.1: Triangles on Grids; 3.4: Polygons on Coordinate Grids Covering and Surrounding: 4.1: Making Rectangular Boxes; 4.3: Designing Gift Boxes Covering and Surrounding: 4.1: Making Rectangular Boxes; 4.3: Designing Gift Boxes Data About Us: 1.1: How Many Letters Are in a Name?; 1.2: Describing Name Lengths; 1.3: Describing Name Lengths; 2.1: What s a Mean Household Size?; 2.2: Comparing Distributions With the Same Mean; 2.3: Making Choices; 2.4: Who Else Is in Your Household; 3.1: Estimating Cereal Serving Sizes; 3.2: Connecting Cereal Shelf Location and Sugar; 3.3: Is It Worth the Wait?; 4.1: Traveling to School; 4.2: Jumping Rope; 4.3: How Much Taller is a 6 th Grader Than A Second Grader? Data About Us: 1.1: How Many Letters Are in a Name?; 1.2: Describing Name Lengths; 1.3: Describing Name Lengths; 2.1: What s a Mean Household Size?; 2.2: Comparing Distributions With the Same Mean; 2.3: Making Choices; 2.4: Who Else Is in Your Household; 3.1: Estimating Cereal Serving Sizes; 3.2: Connecting Cereal Shelf Location and Sugar; 3.3: Is It Worth the Wait?; 4.1: Traveling to School; 4.2: Jumping Rope; 4.3: How Much Taller is a 6 th Grader Than A Second Grader? Data About Us: 2.1: What s a Mean Household Size?; 2.2: Comparing Distributions With the Same Mean; 2.3: Making Choices; 2.4: Who Else Is in Your Household; 3.1: Estimating Cereal Serving Sizes; 3.2: Connecting Cereal Shelf Location and Sugar; 3.3: Is It Worth the Wait? 9

13 A Correlation of, 2014 to the Grade 6 M06.D-S.1.1.3: Describe any overall pattern and any deviations from the overall pattern with reference to the context in which the data were gathered. M06.D-S.1.1.4: Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Grade 6, 2014 Data About Us: 3.1: Estimating Cereal Serving Sizes; 3.2: Connecting Cereal Shelf Location and Sugar; 3.3: Is It Worth the Wait? Data About Us: 2.1: What s a Mean Household Size?; 2.2: Comparing Distributions With the Same Mean; 2.3: Making Choices; 2.4: Who Else Is in Your Household; 3.1: Estimating Cereal Serving Sizes; 3.2: Connecting Cereal Shelf Location and Sugar; 3.3: Is It Worth the Wait? 10

14 A Correlation of, 2014, to the Grade Numbers and Operations D) Ratios and Proportional Relationships CC D.1 Analyze proportional relationships and use them to model and solve real world and mathematical problems. Grade 7, 2014 Stretching and Shrinking: 1.2: Scaling Up and Down; 2.3: Mouthing Off and Nosing Around; 3.1: Rep-Tile Quadrilaterals; 3.3: Designing Under Constraints; 3.4: Out of Reach; 4.1: Ratios Within Similar Parallelograms; 4.2: Ratios Within Similar Triangles; 4.3: Finding Missing Parts; 4.4: Using Shadows to Find Heights Comparing and Scaling: 1.4: Keeping Things in Proportion; 2.1: Sharing Pizza; 2.2: Comparing Pizza Prices; 2.3: Finding Costs; 3.1: Commissions, Markups, and Discounts; 3.2: Measuring to the Unit; 3.3: Mixing it Up Moving Straight Ahead: 1.1: Walking Marathons; 1.2: Walking Rates and Linear Relationships M07.A-R.1.1.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. Example: If a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2 / 1/4 miles per hour, equivalently 2 miles per hour. M07.A-R.1.1.2: Determine whether two quantities are proportionally related (e.g., by testing for equivalent ratios in a table, graphing on a coordinate plane and observing whether the graph is a straight line through the origin). Comparing and Scaling: 1.1: Surveying Opinions; 1.2: Mixing Juice; 1.3: Time to Concentrate; 2.2: Comparing Pizza Prices; 2.3: Finding Costs; 3.2: Measuring to the Unit Moving Straight Ahead: 1.1: Walking Marathons; 1.2: Walking Rates and Linear Relationships; 1.3: Raising Money; 2.1: Henri and Emile s Race; 2.2: Crossing the Line; 2.3: Comparing Costs; 2.4: Connecting Tables; Graphs, and Equations; 2.3: Comparing Costs Stretching and Shrinking: 2.3: Mouthing Off and Nosing Around; 3.1: Rep-Tile Quadrilaterals; 3.3: Designing Under Constraints; 4.1: Ratios Within Similar Parallelograms; 4.2: Ratios Within Similar Triangles Comparing and Scaling: 1.4: Keeping Things in Proportion; 2.1: Sharing Pizza M07.A-R.1.1.3: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Comparing and Scaling: 2.2: Comparing Pizza Prices; 2.3: Finding Costs; 3.2: Measuring to the Unit Moving Straight Ahead: 1.1: Walking Marathons; 1.2: Walking Rates and Linear Relationships 11

15 A Correlation of, 2014, to the Grade 7 M07.A-R.1.1.4: Represent proportional relationships by equations. Example: If total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. M07.A-R.1.1.5: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r), where r is the unit rate. M07.A-R.1.1.6: Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease. Grade 7, 2014 Stretching and Shrinking: 4.3: Finding Missing Parts; 4.4: Using Shadows to Find Heights Comparing and Scaling: 1.4: Keeping Things in Proportion; 2.2: Comparing Pizza Prices; 2.3: Finding Costs; 3.2: Measuring to the Unit; 3.3: Mixing it Up Moving Straight Ahead: 2.1: Henri and Emile s Race; 2.2: Crossing the Line Stretching and Shrinking: 1.2: Scaling Up and Down; 3.1: Rep-Tile Quadrilaterals; 3.4: Out of Reach; 4.1: Ratios Within Similar Parallelograms; 4.2: Ratios Within Similar Triangles; 4.3: Finding Missing Parts; 4.4: Using Shadows to Find Heights Comparing and Scaling: 1.1: Surveying Opinions; 1.4: Keeping Things in Proportion; 2.1: Sharing Pizza; 2.2: Comparing Pizza Prices; 2.3: Finding Costs; 3.1: Commissions, Markups, and Discounts; 3.2: Measuring to the Unit; 3.3: Mixing it Up E) The Number System CC E.1 Apply and extend previous understandings of operations with fractions to operations with rational numbers. Accentuate the Negative: 1.2: Extending the Number Line; 2.1: Extending Addition to Rational Numbers; 2.2 Extending Subtraction to Rational Numbers; 3.2: Multiplication of Rational Numbers; 3.3 Division of Rational Numbers; 4.1 Order of Operations Comparing and Scaling: 3.1: Commissions, Markups, and Discounts M07.A-N.1.1.1: Apply properties of operations to add and subtract rational numbers, including real-world contexts. M07.A-N.1.1.2: Represent addition and subtraction on a horizontal or vertical number line. Accentuate the Negative: 1.1: Playing Math Fever; 1.2: Extending the Number Line; 1.3 From Sauna to Snowbank; 1.4: In the Chips; 2.1: Extending Addition to Rational Numbers; 2.2 Extending Subtraction to Rational Numbers; 2.3: The +/- Connection; 2.4: Fact Families; 4.1 Order of Operations Accentuate the Negative: 1.2: Extending the Number Line; 1.3 From Sauna to Snowbank; 2.1: Extending Addition to Rational Numbers; 2.2 Extending Subtraction to Rational Numbers 12

16 A Correlation of, 2014, to the Grade 7 M07.A-N.1.1.3: Apply properties of operations to multiply and divide rational numbers, including real-world contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats. Grade 7, 2014 Accentuate the Negative: 3.1: Multiplication Patterns; 3.2: Multiplication of Rational Numbers; 3.3 Division of Rational Numbers; 3.4: Playing the Integer Product Game; 4.3 What Operations Are Needed? Comparing and Scaling: 3.1: Commissions, Markups, and Discounts 2.2 Algebraic Concepts B) Expressions & Equations CC B.1 Apply properties of operations to generate equivalent expressions. Accentuate the Negative: 4.1 Order of Operations; 4.2: The Distributive Property; 4.3 What Operations Are Needed? Moving Straight Ahead: 3.3: From Pouches to Variables; 3.4: Solving Linear Equations M07.B-E.1.1.1: Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients. Example 1: The expression 1/2 (x + 6) is equivalent to 1/2 x + 3. Example 2: The expression 5.3 y is equivalent to 9.5 y (or y + 9.5). Example 3: The expression 4w 10 is equivalent to 2(2w 5). CC B.3 Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations. M07.B-E.2.1.1: Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. Example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50 an hour (or 1.1 $25 = $27.50). Moving Straight Ahead: 3.3: From Pouches to Variables; 3.4: Solving Linear Equations Moving Straight Ahead: 1.1: Walking Marathons; 1.2: Walking Rates and Linear Relationships; 1.3: Raising Money; 1.4: Using the Walkathon Money; 2.1: Henri and Emile s Race; 2.2: Crossing the Line; 2.3: Comparing Costs; 2.4: Connecting Tables; Graphs, and Equations; 3.1: Solving Equations Using Tables and Graphs; 3.2: Mystery Pouches in the Kingdom of Montarek; 3.3: From Pouches to Variables; 3.4: Solving Linear Equations; 3.5: Finding the Points of Intersection; 4.1: Climbing Stairs; 4.2: Finding the Slope of a Line; 4.3: Exploring Patterns With Lines; 4.4: Pulling it All Together Comparing and Scaling: 1.2: Mixing Juice; 1.3: Time to Concentrate Comparing and Scaling: 3.1: Commissions, Markups, and Discounts; 3.2: Measuring to the Unit; 3.3: Mixing it Up 13

17 A Correlation of, 2014, to the Grade 7 M07.B-E.2.2.1: Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Example: The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? M07.B-E.2.2.2: Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers, and graph the solution set of the inequality. Example: A salesperson is paid $50 per week plus $3 per sale. This week she wants her pay to be at least $100. Write an inequality for the number of sales the salesperson needs to make and describe the solutions. M07.B-E.2.3.1: Determine the reasonableness of answer(s) or interpret the solution(s) in the context of the problem. Example: If you want to place a towel bar that is 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. A Use estimation to solve problems. Grade 7, 2014 Moving Straight Ahead: 3.1: Solving Equations Using Tables and Graphs; 3.2: Mystery Pouches in the Kingdom of Montarek; 3.3: From Pouches to Variables; 3.4: Solving Linear Equations Accentuate the Negative: 1.2: Extending the Number Line; Moving Straight Ahead: 3.1: Solving Equations Using Tables and Graphs Moving Straight Ahead: 3.5: Finding the Points of Intersection; 4.4: Pulling it All Together Filling and Wrapping: 2.2: Packing A Prism; 3.2: Pricing Pizza; 3.4: Connecting Circumference and Area 14

18 A Correlation of, 2014, to the Grade Geometry A) Geometry CC A.1 Solve real world and mathematical problems involving angle measure, area, surface area, circumference, and volume. Grade 7, 2014 Shapes and Designs: 1.2: In a Spin; 1.3: Estimating Measures of Rotations and Angles; 1.4: Measuring Angles; 1.5: Design Challenge; 2.1: Angle Sums of Regular Polygons; 2.2 Angle Sums of Any Polygon; 2.3: The Bees Do It; 2.4: The Ins and Outs of Polygons; 3.2: Design Challenge II; 3.3: Building Quadrilaterals; 3.4: Parallel Lines and Transversals Stretching and Shrinking: 1.2: Scaling Up and Down; 3.1: Rep-Tile Quadrilaterals; 3.3: Designing Under Constraints Filling and Wrapping: 1.1: How Big Are Those Boxes?; 1.2: Optimal Containers I; 1.3: Optimal Containers II; 1.4: Compost Containers; 2.1: Folding Paper; 2.2: Packing A Prism; 2.3: Slicing Prisms and Pyramids; 3.1: Going Around in Circles; 3.2: Pricing Pizza; 3.3: Squaring a Circle to Find Its Area; 3.4: Connecting Circumference and Area; 4.1: Networking; 4.2: Wrapping Paper; 4.3: Comparing Juice Containers; 4.4: Filling Cones and Spheres; 4.5: Comparing Volumes of Spheres, Cylinders, and Cones M07.C-G.2.1.1: Identify and use properties of supplementary, complementary, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. M07.C-G.2.1.2: Identify and use properties of angles formed when two parallel lines are cut by a transversal (e.g., angles may include alternate interior, alternate exterior, vertical, corresponding). M07.C-G.2.2.1: Find the area and circumference of a circle. Solve problems involving area and circumference of a circle(s). Formulas will be provided. Shapes and Designs: 1.4: Measuring Angles; 2.4: The Ins and Outs of Polygons; 3.4: Parallel Lines and Transversals Shapes and Designs: 3.4: Parallel Lines and Transversals Stretching and Shrinking: 3.4: Out of Reach Filling and Wrapping: 3.1: Going Around in Circles; 3.2: Pricing Pizza; 3.3: Squaring a Circle to Find Its Area; 3.4: Connecting Circumference and Area 15

19 A Correlation of, 2014, to the Grade 7 M07.C-G.2.2.2: Solve real-world and mathematical problems involving area, volume, and surface area of two and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Formulas will be provided. CC A.2 Visualize and represent geometric figures and describe the relationships between them. Grade 7, 2014 Stretching and Shrinking: 3.1: Rep-Tile Quadrilaterals; 3.3: Designing Under Constraints; 3.4: Out of Reach Filling and Wrapping: 1.1: How Big Are Those Boxes?; 1.2: Optimal Containers I; 1.3: Optimal Containers II; 1.4: Compost Containers; 2.1: Folding Paper; 2.2: Packing A Prism; 2.3: Slicing Prisms and Pyramids; 3.1: Going Around in Circles; 3.2: Pricing Pizza; 3.3: Squaring a Circle to Find Its Area; 3.4: Connecting Circumference and Area; 4.1: Networking; 4.2: Wrapping Paper; 4.3: Comparing Juice Containers; 4.4: Filling Cones and Spheres; 4.5: Comparing Volumes of Spheres, Cylinders, and Cones Shapes and Designs: 1.1: Sorting and Sketching Polygons; 1.2: In a Spin; 1.3: Estimating Measures of Rotations and Angles; 1.4: Measuring Angles; 1.5: Design Challenge; 2.1: Angle Sums of Regular Polygons; 2.2 Angle Sums of Any Polygon; 2.3: The Bees Do It; 2.4: The Ins and Outs of Polygons; 3.1: Building Triangles; 3.2: Design Challenge II; 3.3: Building Quadrilaterals; 3.4: Parallel Lines and Transversals Stretching and Shrinking: 1.1: Solving a Mystery; 1.2: Scaling Up and Down; 2.1: Drawing Wumps; 2.2: Hats Off to the Wumps; 2.3: Mouthing Off and Nosing Around; 3.1: Rep- Tile Quadrilaterals; 3.2: Rep-Tile Triangles; 3.3: Designing Under Constraints; 3.4: Out of Reach; 4.1: Ratios Within Similar Parallelograms; 4.2: Ratios Within Similar Triangles; 4.3: Finding Missing Parts; 4.4: Using Shadows to Find Heights Moving Straight Ahead: 4.1: Climbing Stairs; 4.2: Finding the Slope of a Line; 4.3: Exploring Patterns With Lines; 4.4: Pulling it All Together 16

20 A Correlation of, 2014, to the Grade 7 (Continued) CC A.2 Visualize and represent geometric figures and describe the relationships between them. M07.C-G.1.1.1: Solve problems involving scale drawings of geometric figures, including finding length and area. M07.C-G.1.1.2: Identify or describe the properties of all types of triangles based on angle and side measures. Grade 7, 2014 Filling and Wrapping: Filling and Wrapping: 1.1: How Big Are Those Boxes?; 1.2: Optimal Containers I; 1.3: Optimal Containers II; 1.4: Compost Containers; 2.1: Folding Paper; 2.2: Packing A Prism; 2.3: Slicing Prisms and Pyramids; 3.1: Going Around in Circles; 3.2: Pricing Pizza; 3.3: Squaring a Circle to Find Its Area; 3.4: Connecting Circumference and Area; 4.1: Networking; 4.2: Wrapping Paper; 4.3: Comparing Juice Containers; 4.4: Filling Cones and Spheres; 4.5: Comparing Volumes of Spheres, Cylinders, and Cones Stretching and Shrinking: 1.1: Solving a Mystery; 1.2: Scaling Up and Down; 2.1: Drawing Wumps; 2.2: Hats Off to the Wumps; 2.3: Mouthing Off and Nosing Around; 3.1: Rep-Tile Quadrilaterals; 3.3: Designing Under Constraints; 3.4: Out of Reach; 4.1: Ratios Within Similar Parallelograms; 4.2: Ratios Within Similar Triangles; 4.3: Finding Missing Parts Shapes and Designs: 1.1: Sorting and Sketching Polygons; 2.1: Angle Sums of Regular Polygons; 2.2 Angle Sums of Any Polygon; 3.1: Building Triangles; 3.2: Design Challenge II; 3.5: Design Challenge III Stretching and Shrinking: 3.2: Rep-Tile Triangles; 3.4: Out of Reach; 4.2: Ratios Within Similar Triangles; 4.4: Using Shadows to Find Heights M07.C-G.1.1.3: Use and apply the triangle inequality theorem. M07.C-G.1.1.4: Describe the two-dimensional figures that result from slicing threedimensional figures. Example: Describe plane sections of right rectangular prisms and right rectangular pyramids. 2.4 Measurement, Data, and Probability B) Statistics and Probability CC B.1 Draw inferences about populations based on random sampling concepts. Shapes and Designs: 3.1: Building Triangles Filling and Wrapping: 2.3: Slicing Prisms and Pyramids; 4.1: Networking; 4.3: Comparing Juice Containers Samples and Populations: 2.1: Asking About Honesty; 2.2: Selecting a Sample; 2.3: Choosing Random Samples; 2.4: Growing Samples 17

21 A Correlation of, 2014, to the Grade 7 M07.D-S.1.1.1: Determine whether a sample is a random sample given a real-world situation. Grade 7, 2014 Samples and Populations: 2.1: Asking About Honesty; 2.2: Selecting a Sample; 2.3: Choosing Random Samples; 2.4: Growing Samples M07.D-S.1.1.2: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Example 1: Estimate the mean word length in a book by randomly sampling words from the book. Example 2: Predict the winner of a school election based on randomly sampled survey data. Samples and Populations: 2.2: Selecting a Sample; 2.3: Choosing Random Samples; 2.4: Growing Samples CC B.2 Draw informal comparative inferences about two populations. Samples and Populations: 1.1: Comparing Performances; 1.2: Which Team Is Most Successful?; 1.3: Pick Your Preference; 1.4: Are Steel-Frame Coasters Faster Than Wood-Frame Coasters? M07.D-S.2.1.1: Compare two numerical data distributions using measures of center and variability. Example 1: The mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team. This difference is equal to approximately twice the variability (mean absolute deviation) on either team. On a line plot, note the difference between the two distributions of heights. Example 2: Decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth grade science book. CC B.3 Investigate chance processes and develop, use, and evaluate probability models. Samples and Populations: 1.1: Comparing Performances; 1.2: Which Team Is Most Successful?; 1.3: Pick Your Preference; 1.4: Are Steel-Frame Coasters Faster Than Wood-Frame Coasters? What Do You Expect?: 1.1: Choosing Cereal; 1.2: Tossing Paper Cups; 1.3 One More Try; 1.4 Analyzing Events; 2.1 Predicting to Win; 2.2 Choosing Marbles; 2.3: Designing a Fair Game; 2.4: Winning the Bonus Prize; 3.1: Designing a Spinner to Find Probabilities; 3.2: Making Decisions; 3.3: Roller Derby; 3.4: Scratching Spots; 4.1: Drawing Area Models to Find the Sample Space; 4.2: Making Purple; 5.1: Guessing Answers; 5.2: Ortonville; 5.3: A Baseball Series 18

22 A Correlation of, 2014, to the Grade 7 M07.D-S.3.1.1: Predict or determine whether some outcomes are certain, more likely, less likely, equally likely, or impossible (i.e., a probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event). M07.D-S.3.2.1: Determine the probability of a chance event given relative frequency. Predict the approximate relative frequency given the probability. Example: When rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times but probably not exactly 200 times. Grade 7, 2014 What Do You Expect?: 1.4 Analyzing Events; 2.1 Predicting to Win; 2.2 Choosing Marbles; 2.3: Designing a Fair Game What Do You Expect?: 1.1: Choosing Cereal; 1.2: Tossing Paper Cups; 1.3 One More Try; 1.4 Analyzing Events; 2.1 Predicting to Win; 3.1: Designing a Spinner to Find Probabilities; 3.2: Making Decisions; 3.3: Roller Derby; 3.4: Scratching Spots M07.D-S.3.2.2: Find the probability of a simple event, including the probability of a simple event not occurring. Example: What is the probability of not rolling a 1 on a number cube? What Do You Expect?: 1.1: Choosing Cereal; 1.2: Tossing Paper Cups; 1.3 One More Try; 1.4 Analyzing Events; 2.1 Predicting to Win; 2.2 Choosing Marbles; 2.3: Designing a Fair Game; 2.4: Winning the Bonus Prize; 3.1: Designing a Spinner to Find Probabilities; 3.2: Making Decisions; 3.3: Roller Derby; 3.4: Scratching Spots; 4.1: Drawing Area Models to Find the Sample Space; 4.2: Making Purple; 4.3: One-and- One Free Throws; 4.4: Finding Expected Value M07.D-S.3.2.3: Find probabilities of independent compound events using organized lists, tables, tree diagrams, and simulation. What Do You Expect?: 2.1 Predicting to Win; 2.3: Designing a Fair Game; 2.4: Winning the Bonus Prize; 5.1: Guessing Answers; 5.2: Ortonville; 5.3: A Baseball Series A Find probabilities for compound events (e.g., find probability of red and blue, find probability of red or blue) and represent as a fraction, decimal or percent). What Do You Expect?: 2.3: Designing a Fair Game; 2.4: Winning the Bonus Prize; 4.1: Drawing Area Models to Find the Sample Space; 4.2: Making Purple; 4.3: One-and-One Free Throws; 4.4: Finding Expected Value; 5.1: Guessing Answers; 5.2: Ortonville; 5.3: A Baseball Series 19

23 A Correlation of, 2014, to the Grade Numbers and Operations E) The Number System CC E.1 Distinguish between rational and irrational numbers using their properties. M08.A-N.1.1.1: Determine whether a number is rational or irrational. For rational numbers, show that the decimal expansion terminates or repeats (limit repeating decimals to thousandths). M08.A-N.1.1.2: Convert a terminating or repeating decimal to a rational number (limit repeating decimals to thousandths). A Compare and/or order any real numbers (rational and irrational may be mixed). A Simplify square roots (e.g., 24 = 2 6). CC E.4 Estimate irrational numbers by comparing them to rational numbers. Grade 8, 2014 Looking for Pythagoras: 4.1: Analyzing the Wheel of Theodorus; 4.4: Getting Real Looking for Pythagoras: 4.3: Representing Decimals as Fractions; 4.4: Getting Real Looking for Pythagoras: 4.2: Representing Fractions as Decimals; 4.4: Getting Real Looking for Pythagoras: 4.1: Analyzing the Wheel of Theodorus; 4.4: Getting Real Looking for Pythagoras: 2.2: Square Roots; 2.3: Using Squares; 2.4: Cube Roots; 3.1: Discovering the Pythagorean Theorem; 3.3: Finding Distances; 3.4: Measuring the Egyptian Way; 4.1: Analyzing the Wheel of Theodorus Looking for Pythagoras: 4.1: Analyzing the Wheel of Theodorus; 4.4: Getting Real; 5.1: Stopping Sneaky Sally M08.A-N.1.1.3: Estimate the value of irrational numbers without a calculator (limit whole number radicand to less than 144). Example: 5 is between 2 and 3 but closer to 2. M08.A-N.1.1.4: Use rational approximations of irrational numbers to compare and order irrational numbers. M08.A-N.1.1.5: Locate/identify rational and irrational numbers at their approximate locations on a number line. A Compare and/or order any real numbers (rational and irrational may be mixed). Looking for Pythagoras: 4.1: Analyzing the Wheel of Theodorus; 4.4: Getting Real; 5.1: Stopping Sneaky Sally Looking for Pythagoras: 4.1: Analyzing the Wheel of Theodorus; 4.4: Getting Real; 5.1: Stopping Sneaky Sally Looking for Pythagoras: 4.1: Analyzing the Wheel of Theodorus; 4.4: Getting Real Looking for Pythagoras: 4.1: Analyzing the Wheel of Theodorus; 4.4: Getting Real 20

24 A Correlation of, 2014, to the Grade 8 F) Number and Quantity 2.2 Algebraic Concepts B) Expressions & Equations CC B.1 Apply concepts of radicals and integer exponents to generate equivalent expressions. M08.B-E.1.1.1: Apply one or more properties of integer exponents to generate equivalent numerical expressions without a calculator (with final answers expressed in exponential form with positive exponents). Properties will be provided. Example: = 3 3 = 1/(33) M08.B-E.1.1.2: Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of perfect squares (up to and including 122) and cube roots of perfect cubes (up to and including 53) without a calculator. Example: If x2 = 25 then x = ± 25. M08.B-E.1.1.3: Estimate very large or very small quantities by using numbers expressed in the form of a single digit times an integer power of 10 and express how many times larger or smaller one number is than another. Example: Estimate the population of the United States as and the population of the world as and determine that the world population is more than 20 times larger than the United States population. M08.B-E.1.1.4: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Express answers in scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology (e.g., interpret 4.7EE9 displayed on a calculator as ) Grade 8, 2014 Looking for Pythagoras: 2.2: Square Roots; 2.3: Using Squares; 2.4: Cube Roots Growing, Growing, Growing: 5.1: Looking For Patterns Among Exponents; 5.2: Rules of Exponents; 5.3: Extending the Rules of Exponents; 5.4: Operations With Scientific Notation Growing, Growing, Growing: 5.1: Looking For Patterns Among Exponents; 5.2: Rules of Exponents; 5.3: Extending the Rules of Exponents; 5.4: Operations With Scientific Notation Looking for Pythagoras: 2.2: Square Roots; 2.3: Using Squares; 2.4: Cube Roots; 5.1: Stopping Sneaky Sally Growing, Growing, Growing: 5.4: Operations With Scientific Notation Growing, Growing, Growing: 5.4: Operations With Scientific Notation 21

25 A Correlation of, 2014, to the Grade 8 A Simplify/evaluate expressions involving properties/laws of exponents, roots and/or absolute value to solve problems (exponents should be integers from -10 to 10). CC B.2 Understand the connections between proportional relationships, lines, and linear equations. M08.B-E.2.1.1: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. Example: Compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. M08.B-E.2.1.2: Use similar right triangles to show and explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane. M08.B-E.2.1.3: Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Grade 8, 2014 Looking for Pythagoras: 2.1: Looking for Squares; 2.2: Square Roots; 2.3: Using Squares; 2.4: Cube Roots Thinking With Mathematical Models: 2.2: Up and Down the Staircase; 2.3: Tree Top Fun; 2.4: Boat Rental Business; 2.5: Amusement Park or Movies; 4.1: Analyzing the Wheel of Theodorus; 5.1: Stopping Sneaky Sally Thinking With Mathematical Models: 2.2: Up and Down the Staircase Thinking With Mathematical Models: 2.2: Up and Down the Staircase Thinking With Mathematical Models: 2.2: Up and Down the Staircase; 2.3: Tree Top Fun; 2.4: Boat Rental Business; 2.5: Amusement Park or Movies It s In The System: 1.2: Connecting Ax + By = C and y = mx + b; 2.1: Shirts and Caps Again A Translate from one representation of a linear function to another (i.e., graph, table, and equation). Thinking With Mathematical Models: 1.3: Custom Construction Parts; 2.2: Up and Down the Staircase; 2.3: Tree Top Fun; 2.4: Boat Rental Business; 2.5: Amusement Park or Movies Say It With Symbols: 2.1: Walking Together; 2.2: Predicting Profit 22