Utah Core Curriculum for Mathematics

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1 Core Curriculum for Mathematics correlated to

2 correlated to 2005 Chapter 1 (pp. 2 57) Variables, Expressions, and Integers Lesson 1.1 (pp. 5 9) Expressions and Variables Evaluate algebraic expressions when given values for the variable(s). Lesson 1.2 (pp ) Powers and Exponents Describe simple patterns using a mathematical rule or algebraic expression Create and extend simple numeric and visual patterns, including those that have a recursive nature (e g., Fibonacci numbers, triangular and square numbers) Evaluate algebraic expressions when given values for the variable(s) Measure angles, perimeter, area, and volume using the correct size and type of units. 1

3 , correlated to 2005 Lesson 1.3 (pp ) Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Describe simple patterns using a mathematical rule or algebraic expression Create and extend simple numeric and visual patterns, including those that have a recursive nature (e g., Fibonacci numbers, triangular and square numbers) Evaluate algebraic expressions when given values for the variable(s). Lesson 1.4 (pp ) Comparing and Ordering Integers Find an approximate location of a rational number on a number line Compare and order rational numbers Recognize absolute value of a rational number as the value of its distance from zero Evaluate numerical and algebraic expressions containing absolute value Evaluate algebraic expressions when given values for the variable(s) Represent and explain numerical and algebraic relationships using geometric models, e.g., rectangular models for multiplication. 2

4 , correlated to 2005 Lesson 1.5 (pp ) Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Add, subtract, multiply, and divide integers Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Identify the effects of arithmetic operations among fractions, decimals, percents, and integers; e g., multiplying or dividing by a number larger or smaller than Recognize absolute value of a rational number as the value of its distance from zero Evaluate numerical and algebraic expressions containing absolute value Evaluate algebraic expressions when given values for the variable(s) Represent and explain numerical and algebraic relationships using geometric models, e.g., rectangular models for multiplication. 3

5 , correlated to 2005 Lesson 1.6 (pp ) Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Add, subtract, multiply, and divide integers Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Identify the effects of arithmetic operations among fractions, decimals, percents, and integers; e g., multiplying or dividing by a number larger or smaller than Evaluate algebraic expressions when given values for the variable(s) Calculate the mean, median, mode, and range for a data set Choose a measure of central tendency most appropriate to analyze a particular set of data Describe how an individual data point may affect the measures of central tendency Interpret and describe the spread of a set of data, e g., range, box plot (box and whisker). 4

6 , correlated to 2005 Lesson 1.7 (pp ) Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Add, subtract, multiply, and divide integers Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Compare and order rational numbers Identify the effects of arithmetic operations among fractions, decimals, percents, and integers; e g., multiplying or dividing by a number larger or smaller than Recognize and use the special multiplication properties of zero Recognize that division by zero is not defined Evaluate algebraic expressions when given values for the variable(s) Calculate the mean, median, mode, and range for a data set Choose a measure of central tendency most appropriate to analyze a particular set of data. 5

7 , correlated to 2005 Lesson 1.8 (pp ) Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Add, subtract, multiply, and divide integers Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Identify the effects of arithmetic operations among fractions, decimals, percents, and integers; e g., multiplying or dividing by a number larger or smaller than Graph ordered pairs of rational numbers on a rectangular coordinate system Identify approximate rational coordinates when given the graph of a point on a rectangular coordinate system Organize and display data using graphical representations such as line plots, bar graphs, stem and leaf plots, histograms, scatter plots, circle graphs, box plots (box and whisker plots), and pictographs Make conjectures from a graphical representation. 6

8 , correlated to 2005 Chapter 2 (pp ) Solving Equations Lesson 2.1 (pp ) Properties and Operations Add or multiply numbers using the Commutative and Associative Properties of Addition or Multiplication Evaluate algebraic expressions when given values for the variable(s) Graph ordered pairs of rational numbers on a rectangular coordinate system Convert from one unit of measure to an equivalent unit of measure using a given conversion factor, e.g., 60 miles/hour 1 hour/3600 sec 5280 ft/1mile = 88 ft/sec Measure angles, perimeter, area, and volume using the correct size and type of units Develop formulas for calculating the circumference of circles and the areas of triangles, parallelograms, and trapezoids Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas. 7

9 , correlated to 2005 Lesson 2.2 (pp ) The Distributive Property Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Add, subtract, multiply, and divide integers Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Add or multiply numbers using the Commutative and Associative Properties of Addition or Multiplication Convert from one unit of measure to an equivalent unit of measure using a given conversion factor, e.g., 60 miles/hour 1 hour/3600 sec 5280 ft/1mile = 88 ft/sec Measure angles, perimeter, area, and volume using the correct size and type of units Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet. Lesson 2.3 (pp ) Simplifying Variable Expressions Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas Add or multiply numbers using the Commutative and Associative Properties of Addition or Multiplication. 8

10 , correlated to 2005 Lesson 2.4 (pp ) Variables and Equations Add, subtract, multiply, and divide integers Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Add or multiply numbers using the Commutative and Associative Properties of Addition or Multiplication Evaluate algebraic expressions when given values for the variable(s) Solve one and two step single variable equations and inequalities Convert from one unit of measure to an equivalent unit of measure using a given conversion factor, e.g., 60 miles/hour 1 hour/3600 sec 5280 ft/1mile = 88 ft/sec. 9

11 , correlated to 2005 Lesson 2.5 (pp ) Solving Equations Using Addition or Subtraction Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Recognize absolute value of a rational number as the value of its distance from zero Evaluate numerical and algebraic expressions containing absolute value Evaluate algebraic expressions when given values for the variable(s) Solve one and two step single variable equations and inequalities. Lesson 2.6 (pp ) Solving Equations Using Multiplication or Division Convert from one unit of measure to an equivalent unit of measure using a given conversion factor, e.g., 60 miles/hour 1 hour/3600 sec 5280 ft/1mile = 88 ft/sec Add, subtract, multiply, and divide integers Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Solve one and two step single variable equations and inequalities Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas. 10

12 , correlated to 2005 Lesson 2.7 (pp ) Decimal Operations and Equations with Decimals Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Identify the effects of arithmetic operations among fractions, decimals, percents, and integers; e g., multiplying or dividing by a number larger or smaller than Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Add or multiply numbers using the Commutative and Associative Properties of Addition or Multiplication Solve one and two step single variable equations and inequalities Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas. 11

13 , correlated to 2005 Chapter 3 (pp ) Lesson 3.1 (pp ) Solving Two-Step Equations Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Solve one and two step single variable equations and inequalities. Lesson 3.2 (pp ) Solving Equations Having Like Terms and Parentheses Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Solve one and two step single variable equations and inequalities Graph ordered pairs of rational numbers on a rectangular coordinate system. Lesson 3.3 (pp ) Solving Equations with Variables on Both Sides Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Solve one and two step single variable equations and inequalities. Lesson 3.4 (pp ) Solve one and two step single variable equations and inequalities. Lesson 3.5 (pp ) Solving Inequalities Using Multiplication or Division Solve one and two step single variable equations and inequalities. 12

14 , correlated to 2005 Lesson 3.6 (pp ) Solving Multi-Step Inequalities Solve one and two step single variable equations and inequalities Identify approximate rational coordinates when given the graph of a point on a rectangular coordinate system. 13

15 , correlated to 2005 Chapter 4 (pp ) Lesson 4.1 (pp ) Factors and Prime Factorization Lesson 4.2 (pp ) Greatest Common Factor Lesson 4.3 (pp ) Equivalent Fractions Make predictions and describe the limitations of the predictions when using data samples Make conjectures from a graphical representation Recognize and create equivalent forms of a rational number Find an approximate location of a rational number on a number line Recognize absolute value of a rational number as the value of its distance from zero Evaluate numerical and algebraic expressions containing absolute value. Lesson 4.4 (pp ) Least Common Multiple Evaluate algebraic expressions when given values for the variable(s) Describe simple patterns using a mathematical rule or algebraic expression Create and extend simple numeric and visual patterns, including those that have a recursive nature (e g., Fibonacci numbers, triangular and square numbers). Lesson 4.5 (pp ) Rules of Exponents Evaluate algebraic expressions when given values for the variable(s) Recognize and create equivalent forms of a rational number Create and extend simple numeric and visual patterns, including those that have a recursive nature (e g., Fibonacci numbers, triangular and square numbers). 14

16 , correlated to 2005 Lesson 4.6 (pp ) Negative and Zero Exponents Recognize and create equivalent forms of a rational number Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Create and extend simple numeric and visual patterns, including those that have a recursive nature (e g., Fibonacci numbers, triangular and square numbers). Lesson 4.7 (pp ) Scientific Notation Solve one and two step single variable equations and inequalities Recognize and create equivalent forms of a rational number Represent very large and very small numbers using scientific notation Identify the effects of arithmetic operations among fractions, decimals, percents, and integers; e g., multiplying or dividing by a number larger or smaller than Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Solve one and two step single variable equations and inequalities. 15

17 , correlated to 2005 Chapter 5 (pp ) Lesson 5.1 (pp ) Rational Numbers Recognize and create equivalent forms of a rational number Find an approximate location of a rational number on a number line Find a rational number between any two rational numbers. Lesson 5.2 (pp ) Adding and Subtracting Like Fractions Compare and order rational numbers Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares. Lesson 5.3 (pp ) Adding and Subtracting Unlike Fractions Solve one and two step single variable equations and inequalities Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Check the reasonableness of results using estimation Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Represent and explain numerical and algebraic relationships using geometric models, e.g., rectangular models for multiplication. 16

18 , correlated to 2005 Lesson 5.4 (pp ) Multiplying Fractions Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Represent very large and very small numbers using scientific notation Identify the effects of arithmetic operations among fractions, decimals, percents, and integers; e g., multiplying or dividing by a number larger or smaller than Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares. Lesson 5.5 (pp ) Dividing Fractions Solve one and two step single variable equations and inequalities Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Compare and order rational numbers Identify the effects of arithmetic operations among fractions, decimals, percents, and integers; e g., multiplying or dividing by a number larger or smaller than Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Solve one and two step single variable equations and inequalities. 17

19 , correlated to 2005 Lesson 5.6 (pp ) Using Multiplicative Inverses to Solve Equations Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Compare and order rational numbers Identify the effects of arithmetic operations among fractions, decimals, percents, and integers; e g., multiplying or dividing by a number larger or smaller than Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Solve one and two step single variable equations and inequalities. Lesson 5.7 (pp ) Equations and Inequalities with Rational Numbers Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares Solve one and two step single variable equations and inequalities. 18

20 , correlated to 2005 Chapter 6 (pp ) Lesson 6.1 (pp ) Ratios and Rates Lesson 6.2 (pp ) Writing and Solving Proportions Lesson 6.3 (pp ) Solving Proportions Using Cross Products Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet Solve problems using simple proportions Recognize and create equivalent forms of a rational number Represent very large and very small numbers using scientific notation Solve problems using simple proportions. Lesson 6.4 (pp ) Similar and Congruent Figures Classify two and three dimensional objects according to the defining characteristics Recognize and create equivalent forms of a rational number Solve problems using simple proportions Identify congruent and similar shapes Find missing lengths of similar plane figures using proportions Identify relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects Measure angles, perimeter, area, and volume using the correct size and type of units Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet. 19

21 , correlated to 2005 Lesson 6.5 (pp ) Similarity and Measurement Compare and order rational numbers Solve problems using simple proportions Identify congruent and similar shapes Find missing lengths of similar plane figures using proportions Identify relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects Solve problems involving scale factors using ratios and proportions. Lesson 6.6 (pp ) Scale Drawings Measure inaccessible heights or distances using similar triangles Solve problems using simple proportions Describe simple patterns using a mathematical rule or algebraic expression Identify congruent and similar shapes Find missing lengths of similar plane figures using proportions Identify relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects Create and interpret scale drawings Determine an approximate distance between two points using map scales Solve problems involving scale factors using ratios and proportions. 20

22 , correlated to 2005 Lesson 6.7 (pp ) Probability and Odds Compare and order rational numbers Solve problems using simple proportions Identify congruent and similar shapes Find missing lengths of similar plane figures using proportions Identify relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects Solve problems involving scale factors using ratios and proportions Measure inaccessible heights or distances using similar triangles Conduct a survey or experiment to collect data Make predictions and describe the limitations of the predictions when using data samples Conduct experiments to approximate the probability of simple events Conduct experiments to approximate the probability of simple events Recognize that results of an experiment more closely approximate the actual or theoretical probability of an event as the number of trials increases Derive the probability of an event mathematically, e g., building a table or tree diagram, creating an area model, making a list, or using the basic counting principle. Lesson 6.8 (pp ) Represent the probability of an event as a fraction, percent, ratio, or decimal Derive the probability of an event mathematically, e g., building a table or tree diagram, creating an area model, making a list, or using the basic counting principle Represent the probability of an event as a fraction, percent, ratio, or decimal. 21

23 , correlated to 2005 Chapter 7 (pp ) Lesson 7.1 (pp ) Percents and Fractions Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Recognize and create equivalent forms of a rational number Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Compute with percents, including those greater than 100% and less than 1% Solve problems using simple proportions Represent and explain numerical and algebraic relationships using geometric models, e.g., rectangular models for multiplication. Lesson 7.2 (pp ) Percents and Proportions Make conjectures from a graphical representation Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Check the reasonableness of results using estimation Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Compute with percents, including those greater than 100% and less than 1% Solve problems using simple proportions Represent and explain numerical and algebraic relationships using geometric models, e.g., rectangular models for multiplication Make predictions and describe the limitations of the predictions when using data samples. 22

24 , correlated to 2005 Lesson 7.3 (pp ) Percents and Decimals Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator Check the reasonableness of results using estimation Recognize and create equivalent forms of a rational number Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions Identify the effects of arithmetic operations among fractions, decimals, percents, and integers; e g., multiplying or dividing by a number larger or smaller than Compute with percents, including those greater than 100% and less than 1% Solve problems using simple proportions Create and extend simple numeric and visual patterns, including those that have a recursive nature (e g., Fibonacci numbers, triangular and square numbers) Make conjectures from a graphical representation Make predictions and describe the limitations of the predictions when using data samples. Lesson 7.4 (pp ) The Percent Equation Lesson 7.5 (pp ) Percent of Change Represent the probability of an event as a fraction, percent, ratio, or decimal Recognize and create equivalent forms of a rational number Compute with percents, including those greater than 100% and less than 1% Check the reasonableness of results using estimation Compute with percents, including those greater than 100% and less than 1% Represent and explain numerical and algebraic relationships using geometric models, e.g., rectangular models for multiplication. 23

25 , correlated to 2005 Lesson 7.6 (pp ) Percent Applications Check the reasonableness of results using estimation Recognize and create equivalent forms of a rational number Compute with percents, including those greater than 100% and less than 1%. Lesson 7.7 (pp ) Simple and Compound Interest Evaluate algebraic expressions when given values for the variable(s) Compute with percents, including those greater than 100% and less than 1% Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet. 24

26 , correlated to 2005 Chapter 8 (pp ) Lesson 8.1 (pp ) Relations and Functions Compute with percents, including those greater than 100% and less than 1% Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules Create a table, graph, or algebraic expression to represent the relationship between two variables Graph ordered pairs of rational numbers on a rectangular coordinate system. Lesson 8.2 (pp ) Linear Equations in Two Variables Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet Compute with percents, including those greater than 100% and less than 1% Solve problems using simple proportions Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules Describe simple patterns using a mathematical rule or algebraic expression Describe simple patterns using a mathematical rule or algebraic expression Evaluate algebraic expressions when given values for the variable(s) Create a table, graph, or algebraic expression to represent the relationship between two variables Graph ordered pairs of rational numbers on a rectangular coordinate system. 25

27 , correlated to 2005 Lesson 8.3 (pp ) Using Intercepts Compute with percents, including those greater than 100% and less than 1% Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules Describe simple patterns using a mathematical rule or algebraic expression Evaluate algebraic expressions when given values for the variable(s) Identify the horizontal and vertical intercepts of a linear relation from a graph or table Create a table, graph, or algebraic expression to represent the relationship between two variables Graph ordered pairs of rational numbers on a rectangular coordinate system. 26

28 , correlated to 2005 Lesson 8.4 (pp ) The Slope of a Line Recognize that division by zero is not defined Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules Describe simple patterns using a mathematical rule or algebraic expression Identify the horizontal and vertical intercepts of a linear relation from a graph or table Determine the slope of a linear relation from a graph or ordered pairs Create a table, graph, or algebraic expression to represent the relationship between two variables Identify approximate rational coordinates when given the graph of a point on a rectangular coordinate system Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet. 27

29 , correlated to 2005 Lesson 8.5 (pp ) Slope-Intercept Form Compute with percents, including those greater than 100% and less than 1% Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules Describe simple patterns using a mathematical rule or algebraic expression Identify the horizontal and vertical intercepts of a linear relation from a graph or table Determine the slope of a linear relation from a graph or ordered pairs Create a table, graph, or algebraic expression to represent the relationship between two variables Graph ordered pairs of rational numbers on a rectangular coordinate system Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet. 28

30 , correlated to 2005 Lesson 8.6 (pp ) Writing Linear Equations Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules Describe simple patterns using a mathematical rule or algebraic expression Identify the horizontal and vertical intercepts of a linear relation from a graph or table Determine the slope of a linear relation from a graph or ordered pairs Create a table, graph, or algebraic expression to represent the relationship between two variables Graph ordered pairs of rational numbers on a rectangular coordinate system Identify approximate rational coordinates when given the graph of a point on a rectangular coordinate system Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet Make predictions and describe the limitations of the predictions when using data samples. 29

31 , correlated to 2005 Lesson 8.7 (pp ) Function Notation Compute with percents, including those greater than 100% and less than 1% Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules Describe simple patterns using a mathematical rule or algebraic expression Create and extend simple numeric and visual patterns, including those that have a recursive nature (e g., Fibonacci numbers, triangular and square numbers) Evaluate algebraic expressions when given values for the variable(s) Evaluate algebraic expressions when given values for the variable(s) Identify the horizontal and vertical intercepts of a linear relation from a graph or table Determine the slope of a linear relation from a graph or ordered pairs Create a table, graph, or algebraic expression to represent the relationship between two variables Graph ordered pairs of rational numbers on a rectangular coordinate system. 30

32 , correlated to 2005 Lesson 8.8 (pp ) Systems of Linear Equations Represent very large and very small numbers using scientific notation Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules Describe simple patterns using a mathematical rule or algebraic expression Create and extend simple numeric and visual patterns, including those that have a recursive nature (e g., Fibonacci numbers, triangular and square numbers) Determine the slope of a linear relation from a graph or ordered pairs Create a table, graph, or algebraic expression to represent the relationship between two variables Graph ordered pairs of rational numbers on a rectangular coordinate system Identify approximate rational coordinates when given the graph of a point on a rectangular coordinate system. 31

33 , correlated to 2005 Lesson 8.9 (pp ) Graphs of Linear Inequalities Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules Describe simple patterns using a mathematical rule or algebraic expression Create a table, graph, or algebraic expression to represent the relationship between two variables Graph ordered pairs of rational numbers on a rectangular coordinate system Identify approximate rational coordinates when given the graph of a point on a rectangular coordinate system. 32

34 , correlated to 2005 Chapter 9 (pp ) Lesson 9.1 (pp ) Square Roots Lesson 9.2 (pp ) Simplifying Square Roots Lesson 9.3 (pp ) The Pythagorean Theorem Lesson 9.4 (pp ) Real Numbers Recognize and create equivalent forms of a rational number Compute with percents, including those greater than 100% and less than 1% Recognize and create equivalent forms of a rational number Evaluate algebraic expressions when given values for the variable(s) Represent and explain numerical and algebraic relationships using geometric models, e.g., rectangular models for multiplication Find an approximate location of a rational number on a number line Compare and order rational numbers Evaluate algebraic expressions when given values for the variable(s) Determine the slope of a linear relation from a graph or ordered pairs. Lesson 9.5 (pp ) The Distance and Midpoint Formulas Lesson 9.6 (pp ) Special Right Triangles Lesson 9.7 (pp ) The Tangent Ratio Lesson 9.8 (pp ) The Sine and Cosine Ratios Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet Compare and order rational numbers Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet Solve problems using simple proportions Measure angles, perimeter, area, and volume using the correct size and type of units Measure inaccessible heights or distances using similar triangles Measure angles, perimeter, area, and volume using the correct size and type of units. 33

35 , correlated to 2005 Chapter 10 (pp ) Measurement, Area, and Volume Lesson 10.1 (pp ) Triangles Lesson 10.2 (pp ) Polygons and Quadrilaterals Classify two and three dimensional objects according to the defining characteristics Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules Describe simple patterns using a mathematical rule or algebraic expression Create a table, graph, or algebraic expression to represent the relationship between two variables Identify approximate rational coordinates when given the graph of a point on a rectangular coordinate system. Lesson 10.3 (pp ) Areas of Parallelograms and Trapezoids Classify two and three dimensional objects according to the defining characteristics Classify two and three dimensional objects according to the defining characteristics Measure angles, perimeter, area, and volume using the correct size and type of units Develop formulas for calculating the circumference of circles and the areas of triangles, parallelograms, and trapezoids. Lesson 10.4 (pp ) Circumference and Area of a Circle Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas Classify two and three dimensional objects according to the defining characteristics Measure angles, perimeter, area, and volume using the correct size and type of units Develop formulas for calculating the circumference of circles and the areas of triangles, parallelograms, and trapezoids Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas. 34

36 , correlated to 2005 Lesson 10.5 (pp ) Surface Areas of Prisms and Cylinders Classify two and three dimensional objects according to the defining characteristics Calculate surface area and volume of right prisms and cylinders using appropriate units. Lesson 10.6 (pp ) Surface Areas of Pyramids and Cones Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas Classify two and three dimensional objects according to the defining characteristics Measure inaccessible heights or distances using similar triangles Calculate surface area and volume of right prisms and cylinders using appropriate units Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas. 35

37 , correlated to 2005 Lesson 10.7 (pp ) Volumes of Prisms and Cylinders Determine the slope of a linear relation from a graph or ordered pairs Classify two and three dimensional objects according to the defining characteristics Identify relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects Estimate measurable quantities in both standard and metric units, e.g., a vase holds a little less than a quart or about a liter; a 10K run is about 6 miles Convert from one unit of measure to an equivalent unit of measure using a given conversion factor, e.g., 60 miles/hour 1 hour/3600 sec 5280 ft/1mile = 88 ft/sec Measure angles, perimeter, area, and volume using the correct size and type of units Calculate surface area and volume of right prisms and cylinders using appropriate units. Lesson 10.8 (pp ) Volumes of Pyramids and Cones Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas Find missing lengths of similar plane figures using proportions Classify two and three dimensional objects according to the defining characteristics Identify relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects Measure angles, perimeter, area, and volume using the correct size and type of units Calculate surface area and volume of right prisms and cylinders using appropriate units Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas. 36

38 , correlated to 2005 Chapter 11 (pp ) Data Analysis and Probability Lesson 11.1 (pp ) Stem-and-Leaf Plots and Histograms Determine the slope of a linear relation from a graph or ordered pairs Organize and display data using graphical representations such as line plots, bar graphs, stem and leaf plots, histograms, scatter plots, circle graphs, box plots (box and whisker plots), and pictographs Make conjectures from a graphical representation Calculate the mean, median, mode, and range for a data set Choose a measure of central tendency most appropriate to analyze a particular set of data. Lesson 11.2 (pp ) Box-and-Whisker Plots Interpret and describe the spread of a set of data, e g., range, box plot (box and whisker) Measure angles, perimeter, area, and volume using the correct size and type of units Calculate surface area and volume of right prisms and cylinders using appropriate units Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas Organize and display data using graphical representations such as line plots, bar graphs, stem and leaf plots, histograms, scatter plots, circle graphs, box plots (box and whisker plots), and pictographs Make conjectures from a graphical representation Calculate the mean, median, mode, and range for a data set Choose a measure of central tendency most appropriate to analyze a particular set of data Interpret and describe the spread of a set of data, e g., range, box plot (box and whisker). 37

39 , correlated to 2005 Lesson 11.3 (pp ) Using Data Displays Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas Organize and display data using graphical representations such as line plots, bar graphs, stem and leaf plots, histograms, scatter plots, circle graphs, box plots (box and whisker plots), and pictographs Make conjectures from a graphical representation Calculate the mean, median, mode, and range for a data set Choose a measure of central tendency most appropriate to analyze a particular set of data. Lesson 11.4 (pp ) Collecting Data Interpret and describe the spread of a set of data, e g., range, box plot (box and whisker) Conduct a survey or experiment to collect data Organize and display data using graphical representations such as line plots, bar graphs, stem and leaf plots, histograms, scatter plots, circle graphs, box plots (box and whisker plots), and pictographs Calculate the mean, median, mode, and range for a data set. Lesson 11.5 (pp ) Interpreting Data Evaluate reported inferences or predictions based on a data set Make conjectures from a graphical representation Make predictions and describe the limitations of the predictions when using data samples Evaluate reported inferences or predictions based on a data set. 38

40 , correlated to 2005 Lesson 11.6 (pp ) Permutations Organize and display data using graphical representations such as line plots, bar graphs, stem and leaf plots, histograms, scatter plots, circle graphs, box plots (box and whisker plots), and pictographs Interpret and describe the spread of a set of data, e g., range, box plot (box and whisker) Derive the probability of an event mathematically, e g., building a table or tree diagram, creating an area model, making a list, or using the basic counting principle. Lesson 11.7 (pp ) Combinations Represent the probability of an event as a fraction, percent, ratio, or decimal Organize and display data using graphical representations such as line plots, bar graphs, stem and leaf plots, histograms, scatter plots, circle graphs, box plots (box and whisker plots), and pictographs Interpret and describe the spread of a set of data, e g., range, box plot (box and whisker). Lesson 11.8 (pp ) Probabilities of Disjoint and Overlapping Events Derive the probability of an event mathematically, e g., building a table or tree diagram, creating an area model, making a list, or using the basic counting principle Conduct a survey or experiment to collect data Conduct experiments to approximate the probability of simple events Derive the probability of an event mathematically, e g., building a table or tree diagram, creating an area model, making a list, or using the basic counting principle Represent the probability of an event as a fraction, percent, ratio, or decimal Identify mutually exclusive events Recognize that the sum of the probability of an event and the probability of its complement is equal to one Determine whether a game or process is fair. 39

41 , correlated to 2005 Lesson 11.9 (pp ) Independent and Dependent Events Make predictions and describe the limitations of the predictions when using data samples Conduct experiments to approximate the probability of simple events Conduct experiments to approximate the probability of simple events Recognize that results of an experiment more closely approximate the actual or theoretical probability of an event as the number of trials increases Represent the probability of an event as a fraction, percent, ratio, or decimal Recognize that the sum of the probability of an event and the probability of its complement is equal to one Determine whether a game or process is fair. 40

42 , correlated to 2005 Chapter 12 (pp ) Lesson 12.1 (pp ) Polynomials Lesson 12.2 (pp ) Adding and Subtracting Polynomials Lesson 12.3 (pp ) Multiplying Monomials and Polynomials Lesson 12.4 (pp ) Multiplying Binomials Lesson 12.5 (pp ) Other Rules of Exponents Lesson 12.6 (pp ) Quadratic Functions Represent the probability of an event as a fraction, percent, ratio, or decimal Represent and explain numerical and algebraic relationships using geometric models, e.g., rectangular models for multiplication Represent and explain numerical and algebraic relationships using geometric models, e.g., rectangular models for multiplication Recognize and create equivalent forms of a rational number Convert from one unit of measure to an equivalent unit of measure using a given conversion factor, e.g., 60 miles/hour 1 hour/3600 sec 5280 ft/1mile = 88 ft/sec Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules Describe simple patterns using a mathematical rule or algebraic expression Solve one and two step single variable equations and inequalities Create a table, graph, or algebraic expression to represent the relationship between two variables. 41

43 , correlated to 2005 Lesson 12.7 (pp ) Exponential Growth and Decay Recognize and create equivalent forms of a rational number Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules Describe simple patterns using a mathematical rule or algebraic expression Solve one and two step single variable equations and inequalities Create a table, graph, or algebraic expression to represent the relationship between two variables. Lesson 12.8 (pp ) Sequences Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet Describe simple patterns using a mathematical rule or algebraic expression Create and extend simple numeric and visual patterns, including those that have a recursive nature (e g., Fibonacci numbers, triangular and square numbers) Solve one and two step single variable equations and inequalities Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet. 42

44 , correlated to 2005 Chapter 13 (pp ) Lesson 13.1 (pp ) Angle Relationships Lesson 13.2 (pp ) Angles and Parallel Lines Lesson 13.3 (pp ) Angles and Polygons Lesson 13.4 (pp ) Translations Create and extend simple numeric and visual patterns, including those that have a recursive nature (e g., Fibonacci numbers, triangular and square numbers) Classify two and three dimensional objects according to the defining characteristics Graph ordered pairs of rational numbers on a rectangular coordinate system. Lesson 13.5 (pp ) Reflections and Symmetry Translate a geometric shape a given distance on a coordinate plane and identify the vertices Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules Create a table, graph, or algebraic expression to represent the relationship between two variables Graph ordered pairs of rational numbers on a rectangular coordinate system Reflect a geometric shape across a line in a coordinate plane and identify the coordinates of the vertices Translate a geometric shape a given distance on a coordinate plane and identify the vertices. 43

45 , correlated to 2005 Lesson 13.6 (pp ) Graph ordered pairs of rational numbers on a rectangular coordinate system Reflect a geometric shape across a line in a coordinate plane and identify the coordinates of the vertices. Lesson 13.7 (pp ) Dilations Translate a geometric shape a given distance on a coordinate plane and identify the vertices Graph ordered pairs of rational numbers on a rectangular coordinate system Create and interpret scale drawings Solve problems involving scale factors using ratios and proportions. 44

46 UT / CC2

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