Minnesota Academic Standards for Mathematics 2007 Grade 7

Transcription

1 A Correlation of 2014 To the for Mathematics 2007

2 to the 2007 Table of Contents Number & Operation... 1 Algebra... 5 Geometry & Measurement Data Analysis & Probability Copyright 2015 Pearson Education, Inc. or its affiliate(s). All rights reserved

3 to the 2007 Number & Operation Read, write, represent and compare positive and negative rational numbers, expressed as integers, fractions and decimals Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. Recognize that π is not rational, but that it can be approximated by rational numbers such as 22/7 and Extending the Number Line 1.3 From Sauna to Snowbank, Using a Number Line 2.1 Extending Addition to 2.2 Extending Subtraction to 2.3 The "+/-" Connection 2.4 Fact Families 3.1 Multiplication Patterns With Integers 3.2 Multiplication of 3.3 Division of 3.4 Playing the Integer Product Game, Applying Multiplication and Division of Integers 4.1 Order of Operations 4.2 The Distributive Property 4.3 What Operations Are Needed? 4 Unit Project, Dealing Down Understand that division of two integers will always result in a rational number. Use this information to interpret the decimal result of a division problem when using a calculator. For example: 125/30 gives on a calculator. This answer is not exact. The exact answer can be expressed as 4 1/6, which is the same as The calculator expression does not guarantee that the 6 is repeated, but that possibility should be anticipated Locate positive and negative rational numbers on a number line, understand the concept of opposites, and plot pairs of positive and negative rational numbers on a coordinate grid. 1.2 Extending the Number Line 3.3 Division of 1.2 Extending the Number Line 1.3 From Sauna to Snowbank, Using a Number Line 2.1 Extending Addition to 2.2 Extending Subtraction to Compare positive and negative rational numbers expressed in various forms using the symbols <, >, =,,. For example: -1/2 < Playing Math Fever, Using Positive and Negative Numbers 1.2 Extending the Number Line 1

4 to the Recognize and generate equivalent representations of positive and negative rational numbers, including equivalent fractions. For example: 40 = 120 = 10 = Extending the Number Line 2.1 Extending Addition to 2.2 Extending Subtraction to 2.3 The "+/-" Connection 2.4 Fact Families 3.2 Multiplication of 3.3 Division of 4.2 The Distributive Property 4.3 What Operations Are Needed? Calculate with positive and negative rational numbers, and rational numbers with whole number exponents, to solve real-world and mathematical problems Add, subtract, multiply and divide positive and negative rational numbers that are integers, fractions and terminating 1.1 Playing Math Fever, Using Positive and decimals; use efficient and generalizable Negative Numbers procedures, including standard algorithms; 1.2 Extending the Number Line raise positive rational numbers to wholenumber exponents. Line 1.3 From Sauna to Snowbank, Using a Number For example: 3 4 x (1/2) 2 = 8 1/ In the Chips, Using a Chip Model 2.1 Extending Addition to 2.2 Extending Subtraction to 2.3 The "+/-" Connection 2.4 Fact Families 3.1 Multiplication Patterns With Integers 3.2 Multiplication of 3.3 Division of 3.4 Playing the Integer Product Game, Applying Multiplication and Division of Integers 4.1 Order of Operations 4.2 The Distributive Property 4.3 What Operations Are Needed? 4 Unit Project, Dealing Down Use real-world contexts and the inverse relationship between addition and subtraction to explain why the procedures of arithmetic with negative rational numbers make sense. For example: Multiplying a distance by -1 can be thought of as representing that same distance in the opposite direction. Multiplying by -1 a second time reverses directions again, giving the distance in the original direction. 2.1 Extending Addition to 2.2 Extending Subtraction to 2.3 The "+/-" Connection 2.4 Fact Families 3.1 Multiplication Patterns With Integers 3.2 Multiplication of 3.3 Division of 3.4 Playing the Integer Product Game, Applying Multiplication and Division of Integers 4 Unit Project, Dealing Down 2

5 to the Understand that calculators and other computing technologies often truncate or round numbers. For example: A decimal that repeats or terminates after a large number of digits is truncated or rounded Solve problems in various contexts involving calculations with positive and negative rational numbers and positive integer exponents, including computing simple and compound interest. For related content, please see: 3.1 Multiplication Patterns With Integers 3.2 Multiplication of 3.3 Division of 3.4 Playing the Integer Product Game, Applying Multiplication and Division of Integers 4.1 Order of Operations 4.2 The Distributive Property 4.3 What Operations Are Needed? 4 Unit Project, Dealing Down 4.1 Order of Operations 3

6 to the Use proportional reasoning to solve problems involving ratios in various contexts. For example: A recipe calls for milk, flour and sugar in a ratio of 4:6:3 (this is how recipes are often given in large institutions, such as hospitals). How much flour and milk would be needed with 1 cup of sugar? 1.3 Time to Concentrate, Scaling Ratios 1.4 Keeping Things in Proportion, Scaling to Solve Proportions 2.1 Sharing Pizza, Comparison Strategies 2.2 Comparing Pizza Prices, Scaling Rates 2.3 Finding Costs, Unit Rate and Constant of Proportionality 3.1 Commissions, Markups, and Discounts, Proportions With Percents 3.2 Measuring to the Unit, Measurement Conversions 3.3 Mixing it Up: Connecting Ratios, Rates, Moving Straight Ahead, Linear Relationships 1.1 Walking Marathons, Finding and Using Rates 1.2 Walking Rates and Linear Relationships, Tables, Graphs, and Equations 1.3 Raising Money, Using Linear Relationships 1.4 Using the Walkathon Money, Recognizing Linear Relationships 4.1 Climbing Stairs, Using Rise and Run Filling and Wrapping, Three-Dimensional Measurement 1.4 Compost Containers, Scaling Up Prisms 3.1 Going Around in Circles, Circumference 3.2 Pricing Pizza 3.3 Squaring a Circle to Find Its Area 3.4 Connecting Circumference and Area 4.2 Wrapping Paper, Volume of Cylinders 4.3 Comparing Juice Containers, Comparing Surface Areas 4.4 Filling Cones and Spheres Demonstrate an understanding of the relationship between the absolute value of a rational number and distance on a number line. Use the symbol for absolute value. For example: -3 represents the distance from -3 to 0 on a number line or 3 units; the distance between 3 and 9/2 on the number line is 3-9/2 or 3/ Extending Subtraction to 4

7 to the 2007 Algebra Understand the concept of proportionality in real-world and mathematical situations, and distinguish between proportional and other relationships Understand that a relationship between two variables, x and y, is proportional if it can be expressed in the form y/x = k or y = kx. Distinguish proportional relationships from other relationships, including inversely proportional relationships (xy = k or y = k/x). For example: The radius and circumference of a circle are proportional, whereas the length x and the width y of a rectangle with area 12 are inversely proportional, since xy = 12 or equivalently, y = 12/x. 2.2 Comparing Pizza Prices, Scaling Rates 2.3 Finding Costs, Unit Rate and Constant of Proportionality 3.3 Mixing it Up: Connecting Ratios, Rates, Moving Straight Ahead, Linear Relationships 1.1 Walking Marathons, Finding and Using Rates Walking Rates and Linear Relationships, Tables, Graphs, and Equations 1.3 Raising Money, Using Linear Relationships 1.4 Using the Walkathon Money, Recognizing Linear Relationships 4.1 Climbing Stairs, Using Rise and Run Filling and Wrapping, Three-Dimensional Measurement 3.1 Going Around in Circles, Circumference 3.2 Pricing Pizza 3.3 Squaring a Circle to Find Its Area 3.4 Connecting Circumference and Area Understand that the graph of a proportional relationship is a line through the origin whose slope is the unit rate (constant of proportionality). Know how to use graphing technology to examine what happens to a line when the unit rate is changed. 2.3 Finding Costs, Unit Rate and Constant of Proportionality 3.3 Mixing it Up: Connecting Ratios, Rates, Moving Straight Ahead, Linear Relationships 1.1 Walking Marathons, Finding and Using Rates 1.2 Walking Rates and Linear Relationships, Tables, Graphs, and Equations 1.3 Raising Money, Using Linear Relationships 1.4 Using the Walkathon Money, Recognizing Linear Relationships 4.1 Climbing Stairs, Using Rise and Run 5

8 to the 2007 Recognize proportional relationships in real-world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols and graphs; solve problems involving proportional relationships and explain results in the original context Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations. For example: Larry drives 114 miles and uses 5 gallons of gasoline. Sue drives 300 miles and uses 11.5 gallons of gasoline. Use equations and graphs to compare fuel efficiency and to determine the costs of various trips. Stretching and Shrinking, Understanding 1.1 Solving a Mystery, An Introduction to 1.2 Scaling Up and Down, Corresponding Sides and Angles 2.1 Drawing Wumps, Making Similar Figures 2.2 Hats Off to the Wumps, Changing a Figure's Size and Location 2.3 Mouthing Off and Nosing Around, Scale Factors 3.1 Rep-Tile Quadrilaterals, Forming Rep-Tiles With Similar Quadrilaterals 3.2 Rep-Tile Triangles, Forming Rep-Tiles With 3.3 Designing Under Constraints, Scale Factors and Similar Shapes 3.4 Out of Reach, Finding Lengths With Similar Triangles 4.1 Ratios Within Similar Parallelograms 4.2 Ratios Within 4.3 Finding Missing Parts, Using to Find Measurements 4.4 Using Shadows to Find Heights, Using 4 Unit Project, Shrinking or Enlarging Pictures 1.1 Surveying Opinions, Analyzing Comparison Statements 1.2 Mixing Juice, Comparing Ratios 1.3 Time to Concentrate, Scaling Ratios 1.4 Keeping Things in Proportion, Scaling to Solve Proportions 2.1 Sharing Pizza, Comparison Strategies 2.2 Comparing Pizza Prices, Scaling Rates 2.3 Finding Costs, Unit Rate and Constant of Proportionality 3.1 Commissions, Markups, and Discounts, Proportions With Percents 3.2 Measuring to the Unit, Measurement Conversions 3.3 Mixing it Up: Connecting Ratios, Rates, 6

9 to the 2007 (Continued) Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations. For example: Larry drives 114 miles and uses 5 gallons of gasoline. Sue drives 300 miles and uses 11.5 gallons of gasoline. Use equations and graphs to compare fuel efficiency and to determine the costs of various trips. Moving Straight Ahead, Linear Relationships 1.1 Walking Marathons, Finding and Using Rates Walking Rates and Linear Relationships, Tables, Graphs, and Equations 1.3 Raising Money, Using Linear Relationships 1.4 Using the Walkathon Money, Recognizing Linear Relationships 4.1 Climbing Stairs, Using Rise and Run Filling and Wrapping, Three-Dimensional Measurement 3.1 Going Around in Circles, Circumference 3.2 Pricing Pizza 3.3 Squaring a Circle to Find Its Area 3.4 Connecting Circumference and Area Solve multi-step problems involving proportional relationships in numerous contexts. For example: Distance-time, percent increase or decrease, discounts, tips, unit pricing, lengths in similar geometric figures, and unit conversion when a conversion factor is given, including conversion between different measurement systems. Another example: How many kilometers are there in 26.2 miles? Stretching and Shrinking, Understanding 1.1 Solving a Mystery, An Introduction to 1.2 Scaling Up and Down, Corresponding Sides and Angles 2.1 Drawing Wumps, Making Similar Figures 2.2 Hats Off to the Wumps, Changing a Figure's Size and Location 2.3 Mouthing Off and Nosing Around, Scale Factors 3.1 Rep-Tile Quadrilaterals, Forming Rep-Tiles With Similar Quadrilaterals 3.2 Rep-Tile Triangles, Forming Rep-Tiles With 3.3 Designing Under Constraints, Scale Factors and Similar Shapes 3.4 Out of Reach, Finding Lengths With Similar Triangles 4.1 Ratios Within Similar Parallelograms 4.2 Ratios Within 4.3 Finding Missing Parts, Using to Find Measurements 4.4 Using Shadows to Find Heights, Using 4 Unit Project, Shrinking or Enlarging Pictures 7

10 to the 2007 (Continued) Solve multi-step problems involving proportional relationships in numerous contexts. For example: Distance-time, percent increase or decrease, discounts, tips, unit pricing, lengths in similar geometric figures, and unit conversion when a conversion factor is given, including conversion between different measurement systems. Another example: How many kilometers are there in 26.2 miles? 1.3 Time to Concentrate, Scaling Ratios 1.4 Keeping Things in Proportion, Scaling to Solve Proportions 2.1 Sharing Pizza, Comparison Strategies 2.2 Comparing Pizza Prices, Scaling Rates 2.3 Finding Costs, Unit Rate and Constant of Proportionality 3.1 Commissions, Markups, and Discounts, Proportions With Percents 3.2 Measuring to the Unit, Measurement Conversions 3.3 Mixing it Up: Connecting Ratios, Rates, Use knowledge of proportions to assess the reasonableness of solutions. For example: Recognize that it would be unreasonable for a cashier to request $200 if you purchase a $225 item at 25% off. Stretching and Shrinking, Understanding 2.1 Drawing Wumps, Making Similar Figures 2.2 Hats Off to the Wumps, Changing a Figure's Size and Location 2.3 Mouthing Off and Nosing Around, Scale Factors 3.1 Rep-Tile Quadrilaterals, Forming Rep-Tiles With Similar Quadrilaterals 3.2 Rep-Tile Triangles, Forming Rep-Tiles With 3.3 Designing Under Constraints, Scale Factors and Similar Shapes 3.4 Out of Reach, Finding Lengths With Similar Triangles 4.1 Ratios Within Similar Parallelograms 4.2 Ratios Within 4.3 Finding Missing Parts, Using to Find Measurements 4.4 Using Shadows to Find Heights, Using 4 Unit Project, Shrinking or Enlarging Pictures 1.1 Surveying Opinions, Analyzing Comparison Statements 1.2 Mixing Juice, Comparing Ratios 1.3 Time to Concentrate, Scaling Ratios 1.4 Keeping Things in Proportion, Scaling to Solve Proportions 8

11 to the 2007 (Continued) Use knowledge of proportions to assess the reasonableness of solutions. For example: Recognize that it would be unreasonable for a cashier to request $200 if you purchase a $225 item at 25% off. 2.1 Sharing Pizza, Comparison Strategies 2.2 Comparing Pizza Prices, Scaling Rates 2.3 Finding Costs, Unit Rate and Constant of Proportionality 3.1 Commissions, Markups, and Discounts, Proportions With Percents 3.2 Measuring to the Unit, Measurement Conversions 3.3 Mixing it Up: Connecting Ratios, Rates, Apply understanding of order of operations and algebraic properties to generate equivalent numerical and algebraic expressions containing positive and negative rational numbers and grouping symbols; evaluate such expressions Use properties of algebra to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents. Properties of algebra include associative, commutative and distributive laws. For example: Combine like terms (use the distributive law) to write 3x 7x + 1 = (3 7)x + 1 = -4x + 1. Shapes and Designs, Two-Dimensional Geometry 2.4 The Ins and Outs of Polygons 2.1 Extending Addition to 4.1 Order of Operations 4.2 The Distributive Property Stretching and Shrinking, Understanding 1.1 Solving a Mystery, An Introduction to 1.2 Scaling Up and Down, Corresponding Sides and Angles 2.1 Drawing Wumps, Making Similar Figures 2.2 Hats Off to the Wumps, Changing a Figure's Size and Location Evaluate algebraic expressions containing rational numbers and whole number exponents at specified values of their variables. For example: Evaluate the expression 1/3(2x 5) 2 at x = Apply understanding of order of operations and grouping symbols when using calculators and other technologies. For example: Recognize the conventions of using a caret (^ raise to a power) and asterisk (* multiply); pay careful attention to the use of nested parentheses. Shapes and Designs, Two-Dimensional Geometry 2.1 Angle Sums of Regular Polygons Grade 6 Prime Time 4.3 Ordering Operations 4.4 Choosing and Operation 9

12 to the 2007 Represent real-world and mathematical situations using equations with variables. Solve equations symbolically, using the properties of equality. Also solve equations graphically and numerically. Interpret solutions in the original context Represent relationships in various contexts with equations involving variables and positive and negative rational numbers. Use the properties of equality to solve for the value of a variable. Interpret the solution in the original context. For example: Solve for w in the equation P = 2w + 2l when P = 3.5 and l = 0.4. Another example: To post an Internet website, Mary must pay $300 for initial set up and a monthly fee of $12. She has $842 in savings, how long can she sustain her website? Shapes and Designs, Two-Dimensional Geometry 2.1 Angle Sums of Regular Polygons 2.2 Angle Sums of Any Polygon 2.4 The Ins and Outs of Polygons 3.4 Parallel Lines and Transversals Moving Straight Ahead, Linear Relationships 1.3 Raising Money, Using Linear Relationships 1.4 Using the Walkathon Money, Recognizing Linear Relationships 2.1 Henri and Emile's Race, Finding the Point of Intersection 2.2 Crossing the Line, Using Tables, Graphs, and Equations 2.3 Comparing Cost, Comparing Relationships 2.4 Connecting Tables, Graphs, and Equations 3.1 Solving Equations Using Tables and Graphs 3.2 Mystery Pouches in the Kingdom of Montarek, Exploring Equality 3.3 From Pouches to Variables, Writing Equations 3.4 Solving Linear Equations 3.5 Finding the Point of Intersection, Equations and Inequalities 4.1 Climbing Stairs, Using Rise and Run 4.2 Finding the Slope of a Line 4.3 Exploring Patterns With Lines 4.4 Pulling It All Together, Writing Equations for Linear Relationships 4 Unit Project, Conducting an Experiment Solve equations resulting from proportional relationships in various contexts. For example: Given the side lengths of one triangle and one side length of a second triangle that is similar to the first, find the remaining side lengths of the second triangle. Another example: Determine the price of 12 yards of ribbon if 5 yards of ribbon cost $ Time to Concentrate, Scaling Ratios 1.4 Keeping Things in Proportion, Scaling to Solve Proportions 3.1 Commissions, Markups, and Discounts, Proportions With Percents 3.2 Measuring to the Unit, Measurement Conversions 3.3 Mixing it Up: Connecting Ratios, Rates, 10

13 to the 2007 Geometry & Measurement Use reasoning with proportions and ratios to determine measurements, justify formulas and solve real-world and mathematical problems involving circles and related geometric figures Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is π. Calculate the circumference and area of circles and sectors of circles to solve problems in various contexts. Filling and Wrapping, Three-Dimensional Measurement 3.1 Going Around in Circles, Circumference 3.2 Pricing Pizza 3.3 Squaring a Circle to Find Its Area 3.4 Connecting Circumference and Area Calculate the volume and surface area of cylinders and justify the formulas used. For example: Justify the formula for the surface area of a cylinder by decomposing the surface into two circles and a rectangle. Filling and Wrapping, Three-Dimensional Measurement 4.1 Networking, Surface Area of Cylinders 4.2 Wrapping Paper, Volume of Cylinders 4.5 Comparing Volumes of Spheres, Cylinders, and Cones 4 Unit Project, The Package Design Contest Analyze the effect of change of scale, translations and reflections on the attributes of twodimensional figures , Describe the properties of similarity, Stretching and Shrinking, Understanding compare geometric figures for similarity, and determine scale factors. 2.3 Mouthing Off and Nosing Around, Scale For example: Corresponding angles in similar Factors geometric figures have the same measure. 3.1 Rep-Tile Quadrilaterals, Forming Rep-Tiles With Similar Quadrilaterals 3.2 Rep-Tile Triangles, Forming Rep-Tiles With 3.3 Designing Under Constraints, Scale Factors and Similar Shapes 3.4 Out of Reach, Finding Lengths With Similar Triangles 4.1 Ratios Within Similar Parallelograms 4.2 Ratios Within 4.3 Finding Missing Parts, Using to Find Measurements 4.4 Using Shadows to Find Heights, Using 4 Unit Project, Shrinking or Enlarging Pictures 1.4 Keeping Things in Proportion, Scaling to Solve Proportions 11

14 to the 2007 (Continued) Use knowledge of proportions to assess the reasonableness of solutions. For example: Recognize that it would be unreasonable for a cashier to request $200 if you purchase a $225 item at 25% off. Filling and Wrapping, Three-Dimensional Measurement 1.4 Compost Containers, Scaling Up Prisms 4.2 Wrapping Paper, Volume of Cylinders 4.3 Comparing Juice Containers, Comparing Surface Areas 4.4 Filling Cones and Spheres Apply scale factors, length ratios and area ratios to determine side lengths and areas of similar geometric figures. For example: If two similar rectangles have heights of 3 and 5, and the first rectangle has a base of length 7, the base of the second rectangle has length 35/3. Stretching and Shrinking, Understanding 1.1 Solving a Mystery, An Introduction to 1.2 Scaling Up and Down, Corresponding Sides and Angles 2.1 Drawing Wumps, Making Similar Figures 2.2 Hats Off to the Wumps, Changing a Figure's Size and Location 2.3 Mouthing Off and Nosing Around, Scale Factors 3.1 Rep-Tile Quadrilaterals, Forming Rep-Tiles With Similar Quadrilaterals 3.2 Rep-Tile Triangles, Forming Rep-Tiles With 3.3 Designing Under Constraints, Scale Factors and Similar Shapes 3.4 Out of Reach, Finding Lengths With Similar Triangles 4.1 Ratios Within Similar Parallelograms 4.2 Ratios Within 4.3 Finding Missing Parts, Using to Find Measurements 4.4 Using Shadows to Find Heights, Using 4 Unit Project, Shrinking or Enlarging Pictures 1.4 Keeping Things in Proportion, Scaling to Solve Proportions Filling and Wrapping, Three-Dimensional Measurement 1.4 Compost Containers, Scaling Up Prisms 4.2 Wrapping Paper, Volume of Cylinders 4.3 Comparing Juice Containers, Comparing Surface Areas 4.4 Filling Cones and Spheres 12

15 to the Use proportions and ratios to solve problems involving scale drawings and conversions of measurement units. For example: 1 square foot equals 144 square inches. Another example: In a map where 1 inch represents 50 miles, 1/2 inch represents 25 miles. Stretching and Shrinking, Understanding 1.1 Solving a Mystery, An Introduction to 1.2 Scaling Up and Down, Corresponding Sides and Angles 2.1 Drawing Wumps, Making Similar Figures 2.2 Hats Off to the Wumps, Changing a Figure's Size and Location 2.3 Mouthing Off and Nosing Around, Scale Factors 3.1 Rep-Tile Quadrilaterals, Forming Rep-Tiles With Similar Quadrilaterals 3.2 Rep-Tile Triangles, Forming Rep-Tiles With 3.3 Designing Under Constraints, Scale Factors and Similar Shapes 3.4 Out of Reach, Finding Lengths With Similar Triangles 4.1 Ratios Within Similar Parallelograms 4.2 Ratios Within 4.3 Finding Missing Parts, Using to Find Measurements 4.4 Using Shadows to Find Heights, Using 4 Unit Project, Shrinking or Enlarging Pictures 1.4 Keeping Things in Proportion, Scaling to Solve Proportions Filling and Wrapping, Three-Dimensional Measurement 1.4 Compost Containers, Scaling Up Prisms 4.2 Wrapping Paper, Volume of Cylinders 4.3 Comparing Juice Containers, Comparing Surface Areas 4.4 Filling Cones and Spheres Graph and describe translations and reflections of figures on a coordinate grid and determine the coordinates of the vertices of the figure after the transformation. For example: The point (1, 2) moves to (-1, 2) after reflection about the y-axis. Stretching and Shrinking, Understanding 2.1 Drawing Wumps, Making Similar Figures 2.2 Hats Off to the Wumps, Changing a Figure's Size and Location 2.3 Mouthing Off and Nosing Around, Scale Factors 4 Unit Project, Shrinking or Enlarging Pictures 13

16 to the 2007 Data Analysis & Probability Use mean, median and range to draw conclusions about data and make predictions Design simple experiments and Moving Straight Ahead, Linear collect data. Determine mean, median and Relationships range for quantitative data and from data 4 Unit Project, Conducting an Experiment represented in a display. Use these quantities to draw conclusions about the data, compare different data sets, and make predictions. What Do You Expect? Probability and For example: By looking at data from the Expected Value past, Sandy calculated that the mean gas 1.1 Choosing Cereal, Tossing a Coin to Find mileage for her car was 28 miles per gallon. Probabilities She expects to travel 400 miles during the 1.3 One More Try, Finding Experimental next week. Predict the approximate number Probabilities of gallons that she will use. 3.1 Designing a Spinner to Find Probabilities 3.2 Making Decisions, Analyzing Fairness 3.3 Roller Derby, Analyzing Fairness 3.4 Scratching Spots, Designing and Using a Simulation 4.2 Making Purple, Area Models and Probability 4.3 One-and-One Free Throws, Simulating a Probability Simulation 5.1 Guessing Answers, Finding More Expected Values 5 Unit Project, The Carnival Game Samples and Populations, Making Comparisons and Predictions 1.1 Comparing Performances, Using Center and Spread 1.2 Which Team Is Most Successful? Using the MAD to Compare Samples 1.3 Pick Your Preference, Distinguishing Categorical Data From Numerical Data 1.4 Are Steel-Frame Coasters Faster Than Wood-Frame Coasters? Using the IQR to Compare Samples 2.1 Asking About Honesty, Using a Sample to Draw Conclusions 2.2 Selecting a Sample, Different Kinds of Samples 2.3 Choosing Random Samples, Comparing Samples Using Center and Spread 2.4 Growing Samples, What Size Sample to Use? 3.1 Solving an Archeological Mystery, Comparing Samples Using Box Plots 3.2 Comparing Heights of Basketball Players, Using Means and MADs 14

17 to the 2007 (Continued) Design simple experiments and collect data. Determine mean, median and range for quantitative data and from data represented in a display. Use these quantities to draw conclusions about the data, compare different data sets, and make predictions. For example: By looking at data from the past, Sandy calculated that the mean gas mileage for her car was 28 miles per gallon. She expects to travel 400 miles during the next week. Predict the approximate number of gallons that she will use. 3.3 Five Chocolate Chips in Every Cookie, Using Sampling in a Simulation 3.4 Estimating a Deer Population, Using Samples t Estimate the Size of a Population Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Know how to create data displays using a spreadsheet to examine this impact. For example: How does dropping the lowest test score affect a student's mean test score? Samples and Populations, Making Comparisons and Predictions 2.3 Choosing Random Samples, Comparing Samples Using Center and Spread 2.4 Growing Samples, What Size Sample to Use? 3.3 Five Chocolate Chips in Every Cookie, Using Sampling in a Simulation 3.4 Estimating a Deer Population, Using Samples to Estimate the Size of a Population Display and interpret data in a variety of ways, including circle graphs and histograms Use reasoning with proportions to Samples and Populations, Making display and interpret data in circle graphs (pie Comparisons and Predictions charts) and histograms. Choose the 3.3 Five Chocolate Chips in Every Cookie, Using appropriate data display and know how to Sampling in a Simulation create the display using a spreadsheet or other graphing technology. Calculate probabilities and reason about probabilities using proportions to solve real-world and mathematical problems Use random numbers generated by a What Do You Expect? Probability and calculator or a spreadsheet or taken from a Expected Value table to simulate situations involving 1.1 Choosing Cereal, Tossing a Coin to Find randomness, make a histogram to display the Probabilities results, and compare the results to known 1.3 One More Try, Finding Experimental probabilities. Probabilities For example: Use a spreadsheet function such 3.1 Designing a Spinner to Find Probabilities as RANDBETWEEN(1, 10) to generate random 3.2 Making Decisions, Analyzing Fairness whole numbers from 1 to 10, and display the 3.3 Roller Derby, Analyzing Fairness results in a histogram. 3.4 Scratching Spots, Designing and Using a Simulation 4.2 Making Purple, Area Models and Probability 4.3 One-and-One Free Throws, Simulating a Probability Simulation 15

18 to the 2007 (Continued) Use random numbers generated by a calculator or a spreadsheet or taken from a table to simulate situations involving randomness, make a histogram to display the results, and compare the results to known probabilities. For example: Use a spreadsheet function such as RANDBETWEEN(1, 10) to generate random whole numbers from 1 to 10, and display the results in a histogram Calculate probability as a fraction of sample space or as a fraction of area. Express probabilities as percents, decimals and fractions. For example: Determine probabilities for different outcomes in game spinners by finding fractions of the area of the spinner. 5.1 Guessing Answers, Finding More Expected Values 5 Unit Project, The Carnival Game Samples and Populations, Making Comparisons and Predictions 2.2 Selecting a Sample, Different Kinds of Samples 2.3 Choosing Random Samples, Comparing Samples Using Center and Spread 3.3 Five Chocolate Chips in Every Cookie, Using Sampling in a Simulation 3.4 Estimating a Deer Population, Using Samples to Estimate the Size of a Population What Do You Expect? Probability and Expected Value 1.1 Choosing Cereal, Tossing a Coin to Find Probabilities 1.2 Tossing Paper Cups, Finding More Probabilities 1.3 One More Try, Finding Experimental Probabilities 1.4 Analyzing Events, Understanding Equally Likely 2.1 Predicting to Win, Finding Theoretical Probabilities 2.2 Choosing Marbles, Developing Probability Models 2.3 Designing a Fair Game, Pondering Possible and Probable 2.4 Winning the Bonus Prize, Using Strategies to Find Theoretical Probabilities 3.1 Designing a Spinner to Find Probabilities 3.2 Making Decisions, Analyzing Fairness 3.3 Roller Derby, Analyzing Fairness 3.4 Scratching Spots, Designing and Using a Simulation 4.1 Drawing Area Models to Find the Sample Space 4.2 Making Purple, Area Models and Probability 4.3 One-and-One Free Throws, Simulating a Probability Simulation 4.4 Finding Expected Value 5.1 Guessing Answers, Finding More Expected Values 5.2 Ortonville, Binomial Probability 5.3 A Baseball Series, Expanding Binomial Probability 5 Unit Project, The Carnival Game 16

19 to the Use proportional reasoning to draw conclusions about and predict relative frequencies of outcomes based on probabilities. For example: When rolling a number cube 600 times, one would predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. What Do You Expect? Probability and Expected Value 2.1 Predicting to Win, Finding Theoretical Probabilities 2.2 Choosing Marbles, Developing Probability Models 2.3 Designing a Fair Game, Pondering Possible and Probable 2.4 Winning the Bonus Prize, Using Strategies to Find Theoretical Probabilities 3.1 Designing a Spinner to Find Probabilities 3.2 Making Decisions, Analyzing Fairness 3.3 Roller Derby, Analyzing Fairness 4.1 Drawing Area Models to Find the Sample Space 4.2 Making Purple, Area Models and Probability 4.3 One-and-One Free Throws, Simulating a Probability Simulation 5.1 Guessing Answers, Finding More Expected Values 5.2 Ortonville, Binomial Probability 5.3 A Baseball Series, Expanding Binomial Probability 5 Unit Project, The Carnival Game Samples and Populations, Making Comparisons and Predictions 1.3 Pick Your Preference, Distinguishing Categorical Data From Numerical Data 17