Process and Content Standards for Mathematics (Grades 6-8) MATHEMATICS PROCESS STANDARDS Grade 6-8 Process Standard 1: Problem Solving integrated response 1. Develop and test strategies to solve practical, everyday problems which may have single or multiple answers. 2. Use technology to generate and analyze data to solve problems. 3. Formulate problems from situations within and outside of mathematics and generalize solutions and strategies to new problem situations. 4. Evaluate results to determine their reasonableness. 5. Apply a variety of strategies (e.g., restate the problem, look for a pattern, diagrams, solve a simpler problem, work backwards, trial and error) to solve problems, with emphasis on multistep and nonroutine problems. 6. Use oral, written, concrete, pictorial, graphical, and/or algebraic methods to model mathematical situations. Connected Mathematics units are divided into investigations that present problems for students to solve. The entire curriculum is built around these problems, which are set in contexts students find interesting. Many problems address the real world; others use fantasy or mathematics itself as a context. The investigations guide and support students in their development of appropriate strategies and methods in problem solving. The availability of a range of tools manipulative and graphing materials, calculators, and computers gives students more ways to approach problems and allows them to organize, demonstrate, and explain their solutions. See indicated Teacher s Guide pages for recommended technology, manipulatives, and materials for each investigation: Develop a variety of strategies for finding and describing patterns of change and solving problems involving quantities that change. SE/TE: Problem Situations, 6, 9, 19, 20, 23, 24, 25, 37, 39, 40, 41, 51, 52, 53, 62, 63 TE: 1h, 4b, 17f, 35l, 48n, 60j Develop a variety of strategies for recognizing and comparing similar geometric figures, applying the concept of scale, and solving problems involving similarity. SE/TE: Problem Situations, 7, 16, 19, 21, 28, 31, 32, 42, 43, 44, 46, 60, 62, 63, 78, 79 TE: 1g-h, 4b, 13f, 27n, 40l, 58j, 74l Develop a variety of strategies such as unit rates, proportional reasoning, and equivalent ratios for solving problems involving ratio, proportion and percent. SE/TE: Problem Situations, 6, 7, 9, 17, 19, 28, 29, 30, 39, 41, 42, 43, 53, 54, 56, 57, 58, 66, 67, 70 TE: 1g, 4b, 15f, 25f, 36h, 51j, 64l 1
Process Standard 1: Problem Solving integrated response (continued) 1. Develop and test strategies to solve practical, everyday problems which may have single or multiple answers. 2. Use technology to generate and analyze data to solve problems. 3. Formulate problems from situations within and outside of mathematics and generalize solutions and strategies to new problem situations. 4. Evaluate results to determine their reasonableness. 5. Apply a variety of strategies (e.g., restate the problem, look for a pattern, diagrams, solve a simpler problem, work backwards, trial and error) to solve problems, with emphasis on multistep and nonroutine problems. 6. Use oral, written, concrete, pictorial, graphical, and/or algebraic methods to model mathematical situations. Develop a variety of strategies for comparing, graphing, adding, subtracting, multiplying and dividing integers and exploring the use of integers in real-world applications. SE/TE: Problem Situations, 7, 8, 10, 20, 24, 37, 42, 43, 44, 54, 56, 57, 59, 69, 71, 72, 74, 76 TE: 1h, 4b, 17h, 33n, 52p, 66l Moving Straight Ahead: Linear Relationships Develop a variety of strategies for recognizing and describing relationships among variables and applying various representations of linear equations to realworld situations. SE/TE: Problem Situations, 6, 8, 17, 18, 20, 21, 22, 36, 39, 40, 42, 53, 56, 57, 65, 68, 69, 60, 81, 83 TE: 1k, 4b, 14f, 34r, 52r, 63j, 79n Filling and Wrapping: 3-Dimensional Measurement Develop a variety of strategies for finding and applying surface area and volume of geometric and irregular solids. SE/TE: Problem Situations, 6, 7, 8, 9, 16, 17, 24, 26, 28, 38, 39, 40, 48, 49, 50, 58, 59, 60, 69 TE: 1k, 4b, 14j, 23h, 36h, 45j, 56h, 67h Develop a variety of strategies for counting outcomes, analyzing situations, and making predictions involving uncertainty. SE/TE: Problem Situations, 6, 7, 9, 11, 22, 23, 34, 35, 42, 44, 51, 52, 60, 61, 63, 70, 72 TE: 1j, 4b, 21n, 31j, 40d, 49n, 58l, 68n Choose sensible units and benchmarks for measuring and comparing, assess accuracy and reliability of data, and read, write, and use large numbers in measurement. SE/TE: Problem Situations, 6, 8, 13, 14, 17, 24, 26, 28, 30, 38, 40, 43, 52, 53, 54, 61, 62, 63 TE: 1f, 4b, 11f, 22f, 37j, 50h, 60h 2
Process Standard 2: Communication integrated response 1. Discuss, interpret, translate (from one to another) and evaluate mathematical ideas (e.g., oral, written, pictorial, concrete, graphical, algebraic). 2. Reflect on and justify reasoning in mathematical problem solving (e.g., convince, demonstrate, formulate). 3. Select and use appropriate terminology when discussing mathematical concepts and ideas. In Connected Mathematics, emphasis is placed on students carefully reading and analyzing problem situations and given information, discussing the problems in class, talking through their solutions, and learning ways to communicate their solutions to a more general audience. They learn to communicate ideas by using such representations as graphs, tables, diagrams, and written or mathematical explanations and arguments, and to reflect upon their understanding. SE/TE: Problem Situations and Follow-Up, 6, 9, 19, 20, 23, 24, 25, 37, 39, 40, 41, 51, 52, 53, 62, 63; Mathematical Reflections, 13, 27, 40, 58, 74, 84; Descriptive Glossary Entries, 7, 8, 21, 39, 49, 52, 148-152 SE/TE: Problem Situations and Follow-Up, 7, 16, 19, 21, 28, 31, 32, 42, 43, 44, 46, 60, 62, 63, 78, 79; Mathematical Reflections, 13, 27, 40, 58, 74, 84; Descriptive Glossary Entries, 6, 7, 18, 20, 27a, 27d, 185-189 SE/TE: Problem Situations and Follow-Up, 6, 7, 9, 17, 19, 28, 29, 30, 39, 41, 42, 43, 53, 54, 56, 57, 58, 66, 67, 70; Mathematical Reflections, 15, 25, 36, 51, 64, 81; Descriptive Glossary Entries, 26, 37, 38, 40, 56, 69, 164-166 SE/TE: Problem Situations and Follow-Up, 7, 8, 10, 20, 24, 37, 42, 43, 44, 54, 56, 57, 59, 69, 71, 72, 74, 76; Mathematical Reflections, 17, 33, 52, 66, 82; Descriptive Glossary Entries, 5, 10, 18, 19, 21, 39, 40, 59, 68, 156-159 Moving Straight Ahead: Linear Relationships SE/TE: Problem Situations and Follow-Up, 6, 8, 17, 18, 20, 21, 22, 36, 39, 40, 42, 53, 56, 57, 65, 68, 69, 60, 81, 83; Mathematical Reflections, 14, 34, 52, 63, 79, 91; Descriptive Glossary Entries, 15, 16, 37, 39, 41, 52i, 64, 65, 178-182 3
Process Standard 2: Communication integrated response (continued) 1. Discuss, interpret, translate (from one to another) and evaluate mathematical ideas (e.g., oral, written, pictorial, concrete, graphical, algebraic). 2. Reflect on and justify reasoning in mathematical problem solving (e.g., convince, demonstrate, formulate). 3. Select and use appropriate terminology when discussing mathematical concepts and ideas. Filling and Wrapping: 3-Dimensional Measurement SE/TE: Problem Situations and Follow-Up, 6, 7, 8, 9, 16, 17, 24, 26, 28, 38, 39, 40, 48, 49, 50, 58, 59, 60, 69; Mathematical Reflections, 14, 23, 36, 45, 56, 67, 72; Descriptive Glossary Entries, 5, 14e, 15, 26, 37, 46, 153-158 SE/TE: Problem Situations and Follow-Up, 6, 7, 9, 11, 22, 23, 34, 35, 42, 44, 51, 52, 60, 61, 63, 70, 72; Mathematical Reflections, 21, 31, 40, 49, 58, 68, 78; Descriptive Glossary Entries, 5, 6, 7, 10, 11, 13, 21b, 33, 52, 175-179 SE/TE: Problem Situations and Follow-Up, 6, 8, 13, 14, 17, 24, 26, 28, 30, 38, 40, 43, 52, 53, 54, 61, 62, 63; Mathematical Reflections, 11, 22, 37, 50, 60, 69; Descriptive Glossary Entries, 14, 39, 42, 43, 137-140 Process Standard 3: Reasoning integrated response 1. Identify and extend patterns and use experiences and observations to make suppositions. 2. Use counter examples to disprove suppositions (e.g., all squares are rectangles, but are all rectangles squares?). 3. Develop and evaluate mathematical arguments (e.g., agree or disagree with the reasoning of other classmates and explain why). 4. Select and use various types of reasoning (e.g., recursive [loops], inductive [specific to general], deductive [general to specific], spatial, and proportional). Through discussion of the problems and their solutions, students learn to reason about mathematics. By engaging in problem situations that involve real but accessible challenges, students learn to collect and organize information and evidence to support their conjectures and to reason mathematically in ways that lead to logical deductions. Students discover that mathematics is created by humans in an attempt to explain the world around them, and that mathematics is a field in which they can be involved in a real way. SE/TE: Problem Situations and Follow-Up, 6, 9, 19, 20, 23, 24, 25, 37, 39, 40, 41, 51, 52, 53, 62, 63; Mathematical Reflections, 13, 27, 40, 58, 74, 84 SE/TE: Problem Situations and Follow-Up, 7, 16, 19, 21, 28, 31, 32, 42, 43, 44, 46, 60, 62, 63, 78, 79; Mathematical Reflections, 13, 27, 40, 58, 74, 84 SE/TE: Problem Situations and Follow-Up, 6, 7, 9, 17, 19, 28, 29, 30, 39, 41, 42, 43, 53, 54, 56, 57, 58, 66, 67, 70; Mathematical Reflections, 15, 25, 36, 51, 64, 81 4
Process Standard 3: Reasoning integrated response (continued) 1. Identify and extend patterns and use experiences and observations to make suppositions. 2. Use counter examples to disprove suppositions (e.g., all squares are rectangles, but are all rectangles squares?). 3. Develop and evaluate mathematical arguments (e.g., agree or disagree with the reasoning of other classmates and explain why). 4. Select and use various types of reasoning (e.g., recursive [loops], inductive [specific to general], deductive [general to specific], spatial, and proportional). SE/TE: Problem Situations and Follow-Up, 7, 8, 10, 20, 24, 37, 42, 43, 44, 54, 56, 57, 59, 69, 71, 72, 74, 76; Mathematical Reflections, 17, 33, 52, 66, 82 Moving Straight Ahead: Linear Relationships SE/TE: Problem Situations and Follow-Up, 6, 8, 17, 18, 20, 21, 22, 36, 39, 40, 42, 53, 56, 57, 65, 68, 69, 60, 81, 83; Mathematical Reflections, 14, 34, 52, 63, 79, 91 Filling and Wrapping: 3-Dimensional Measurement SE/TE: Problem Situations and Follow-Up, 6, 7, 8, 9, 16, 17, 24, 26, 28, 38, 39, 40, 48, 49, 50, 58, 59, 60, 69; Mathematical Reflections, 14, 23, 36, 45, 56, 67, 72 SE/TE: Problem Situations and Follow-Up, 6, 7, 9, 11, 22, 23, 34, 35, 42, 44, 51, 52, 60, 61, 63, 70, 72; Mathematical Reflections, 21, 31, 40, 49, 58, 68, 78 SE/TE: Problem Situations and Follow-Up, 6, 8, 13, 14, 17, 24, 26, 28, 30, 38, 40, 43, 52, 53, 54, 61, 62, 63; Mathematical Reflections, 11, 22, 37, 50, 60, 69 Process Standard 4: Connections integrated response 1. Apply mathematical strategies to solve problems that arise from other disciplines and the real world. 2. Connect one area or idea of mathematics to another (e.g., relate equivalent number representations to each other, relate experiences with geometric shapes to understanding ratio and proportion). The name Connected Mathematics conveys the program s commitment to connecting mathematical ideas to other areas of mathematics, to other subject areas, and to real-world applications. The investigation problems are set in interesting everyday, scientific, or technological contexts, and the application, connection, and extension questions in each investigation provide opportunities for students to explore and reflect on these connections. SE/TE: Problem Situations, 6, 9, 19, 20, 23, 24, 25, 37, 39, 40, 41, 51, 52, 53, 62, 63; Applications, 9-10, 22-24, 33-35, 47-53, 64-68, 81; Connections, 10, 24-25, 36-37, 54-57, 68-69, 82; Extensions, 11-12, 26, 37-39, 57, 69-73, 83 5
Process Standard 4: Connections integrated response (continued) 1. Apply mathematical strategies to solve problems that arise from other disciplines and the real world. 2. Connect one area or idea of mathematics to another (e.g., relate equivalent number representations to each other, relate experiences with geometric shapes to understanding ratio and proportion). SE/TE: Problem Situations, 7, 16, 19, 21, 28, 31, 32, 42, 43, 44, 46, 60, 62, 63, 78, 79; Applications, 9-10, 22-24, 33-35, 47-53, 64-68, 81; Connections, 10, 24-25, 36-37, 54-57, 68-69, 82; Extensions, 11-12, 26, 37-39, 57, 69-73, 83 SE/TE: Problem Situations, 6, 7, 9, 17, 19, 28, 29, 30, 39, 41, 42, 43, 53, 54, 56, 57, 58, 66, 67, 70; Applications, 10-11, 20-21, 31-33, 44-47, 59-61, 73-74; Connections, 11-12, 22-23, 33-34, 47-49, 61-62, 75; Extensions, 12-14, 23-24, 34-35, 49-50, 63, 76-80 SE/TE: Problem Situations, 7, 8, 10, 20, 24, 37, 42, 43, 44, 54, 56, 57, 59, 69, 71, 72, 74, 76; Applications, 12-14, 26-29, 46-49, 60-61, 77-79; Connections, 14-15, 29-30, 50, 61-64, 80-81; Extensions, 15-16, 31-32, 51, 64-65, 81 Moving Straight Ahead: Linear Relationships SE/TE: Problem Situations, 6, 8, 17, 18, 20, 21, 22, 36, 39, 40, 42, 53, 56, 57, 65, 68, 69, 60, 81, 83; Applications, 9, 24-29, 44-48, 59-61, 70-74, 84-87; Connections, 10-11, 29-31, 48-49, 61-62, 74-75, 87-89; Extensions, 12-13, 32-33, 50-51, 62, 76-78, 90 Filling and Wrapping: 3-Dimensional Measurement SE/TE: Problem Situations, 6, 7, 8, 9, 16, 17, 24, 26, 28, 38, 39, 40, 48, 49, 50, 58, 59, 60, 69; Applications, 10-11, 19, 29-32, 41-42, 51-52, 61-62, 70; Connections, 11-12, 20-21, 32-34, 43, 53, 63-64; Extensions, 13, 22, 35, 44, 53-55, 65-66, 71 SE/TE: Problem Situations, 6, 7, 9, 11, 22, 23, 34, 35, 42, 44, 51, 52, 60, 61, 63, 70, 72; Applications, 13-18, 24-27, 36-38, 45-46, 53-55, 64-65, 74-75; Connections, 18-19, 28-30, 38-39, 46-47, 55-57, 65-66, 75-76; Extensions, 19-20, 30, 39, 48, 57, 66-67, 76-77 6
Process Standard 4: Connections integrated response (continued) 1. Apply mathematical strategies to solve problems that arise from other disciplines and the real world. 2. Connect one area or idea of mathematics to another (e.g., relate equivalent number representations to each other, relate experiences with geometric shapes to understanding ratio and proportion). Process Standard 5: Representation integrated response 1. Use a variety of representations to organize and record data (e.g., use concrete, pictorial, and symbolic representations). 2. Use representations to promote the communication of mathematical ideas (e.g., number lines, rectangular coordinate systems, scales to illustrate the balance of equations). 3. Develop a variety of mathematical representations that can be used flexibly and appropriately (e.g., base-10 blocks to represent fractions and decimals, appropriate graphs to represent data). 4. Use a variety of representations to model and solve physical, social, and mathematical problems (e.g., geometric objects, pictures, charts, tables, graphs). SE/TE: Problem Situations, 6, 8, 13, 14, 17, 24, 26, 28, 30, 38, 40, 43, 52, 53, 54, 61, 62, 63; Applications, 9, 19-20, 31-32, 44-45, 55, 64-65; Connections, 10, 20-21, 32-35, 45-47, 56-58, 65-66; Extensions, 10, 21, 36, 47-49, 58-59, 67-68 Throughout Connected Mathematics, students explore methods of mathematical representation of real-world problem situations, discover the relative effectiveness and interchangeability of those representations, and transform and select among words, numbers, symbols, charts, graphs, tables, diagrams, and models as appropriate. SE/TE: Problem Situations, 6, 9, 19, 20, 23, 24, 25, 37, 39, 40, 41, 51, 52, 53, 62, 63 SE/TE: Problem Situations, 7, 16, 19, 21, 28, 31, 32, 42, 43, 44, 46, 60, 62, 63, 78, 79 SE/TE: Problem Situations, 6, 7, 9, 17, 19, 28, 29, 30, 39, 41, 42, 43, 53, 54, 56, 57, 58, 66, 67, 70 SE/TE: Problem Situations, 7, 8, 10, 20, 24, 37, 42, 43, 44, 54, 56, 57, 59, 69, 71, 72, 74, 76 7
Process Standard 5: Representation integrated response (continued) 1. Use a variety of representations to organize and record data (e.g., use concrete, pictorial, and symbolic representations). 2. Use representations to promote the communication of mathematical ideas (e.g., number lines, rectangular coordinate systems, scales to illustrate the balance of equations). 3. Develop a variety of mathematical representations that can be used flexibly and appropriately (e.g., base-10 blocks to represent fractions and decimals, appropriate graphs to represent data). Moving Straight Ahead: Linear Relationships SE/TE: Problem Situations, 6, 8, 17, 18, 20, 21, 22, 36, 39, 40, 42, 53, 56, 57, 65, 68, 69, 60, 81, 83 Filling and Wrapping: 3-Dimensional Measurement SE/TE: Problem Situations, 6, 7, 8, 9, 16, 17, 24, 26, 28, 38, 39, 40, 48, 49, 50, 58, 59, 60, 69 SE/TE: Problem Situations, 6, 7, 9, 11, 22, 23, 34, 35, 42, 44, 51, 52, 60, 61, 63, 70, 72 SE/TE: Problem Situations, 6, 8, 13, 14, 17, 24, 26, 28, 30, 38, 40, 43, 52, 53, 54, 61, 62, 63 4. Use a variety of representations to model and solve physical, social, and mathematical problems (e.g., geometric objects, pictures, charts, tables, graphs). MATHEMATICS CONTENT STANDARDS Grade 7 Standard 1: Algebraic Reasoning - The student will use number properties to simplify and solve simple linear equations. 1. Identify and apply the commutative, associative, distributive, inverse and identity properties (e.g., n + 0 = n, 2 (x + 3) = 2 x + 6). SE/TE: Patterns and Rules, 49-60 TE: 48n, 60a-60i TR: Transparencies 4.1A to 4.3B SE/TE: Adding Integers, 18-33; Subtracting Integers, 34-52; Multiplying and Dividing Integers, 53-66 TE: 17h, 33a-33l, 33n, 52a-52o, 52p, 66a-66j TR: Labsheets 4.3; Transparencies 2.1 to 2.2, 3.1A to 3.4, 4.1A to 4.4 see also Grade 8 unit: Say It With Symbols: Algebra 8
2. Use a variety of methods to model and solve onestep linear equations (e.g., use properties of equality, graph ordered pairs with paper and pencil, use graphing calculators). 2. Use a variety of methods to model and solve onestep linear equations (e.g., use properties of equality, graph ordered pairs with paper and pencil, use graphing calculators). SE/TE: Patterns and Rules, 49-60; Using a Graphing Calculator, 61-68 TE: 48n, 60a-60i, 60j, 68a-68e TR: Transparencies 4.1A to 4.3B, 5.1 to 5.2, Graphing Calculators Moving Straight Ahead: Linear Relationships SE/TE: Solving Equations, 53-63; Writing an Equation for a Line, 80-91 TE: 52r, 63a-63i, 79n, 91a-92 TR: Transparencies 4.1 to 4.3, 6.1 to 6.3 TECH: Graphing Calculators, Computers (optional) Standard 2: Number Sense - The student will use numbers and number relationships to acquire basic facts and determine the reasonableness of results. 1. Integers a. Compare and order positive and negative integers and describe their use in real-life situations (e.g., temperature, sea level, stock market fluctuations, football yardage). b. Use the basic operations on integers to solve problems. SE/TE: Extending the Number Line, 5-17 TE: 4b, 17a-17f TR: Transparencies 1.1A to 1.3 SE/TE: Adding Integers, 18-33; Subtracting Integers, 34-52; Multiplying and Dividing Integers, 53-66 TE: 17h, 33a-33l, 33n, 52a-52o, 52p, 66a-66j TR: Labsheets 4.3; Transparencies 2.1 to 2.2, 3.1A to 3.4, 4.1A to 4.4 2. Ratio, Proportion and Percents 9
*a. Demonstrate the concept of ratio and proportion with models (e.g., similar geometric shapes, scale models). SE/TE: Using Similarity, 41-58; Similar Triangles, 59-74; Stretching and Shrinking with a Computer, 75-84 TE: TR: 40l, 58a-58h, 58j, 74a-74k, 74l, 84a-84h Transparencies 4.1 to 4.4, 5.1 to 5.3, 6.1A to 6.2, Computers (optional), Turtle Math Software (optional) SE/TE: Comparing by Using Ratios, 26-36; Comparing by Finding Rates, 37-51; Estimating Populations and Population Densities, 52-64; Choosing Strategies, 65-81 TE: 25f, 36a-36g, 36h, 51a-51h, 51j, 64a-64k, 64l, 81a-81g TR: Labsheets 6.3A to 6.ACE; Transparencies 3.1 to 3.3, 4.1 to 4.4, 5.1 to 5.5, 6.1 to 6.3B *a. Demonstrate the concept of ratio and proportion with models (e.g., similar geometric shapes, scale models). b. Set up equivalent ratios, estimate and solve problems using ratio, proportions, and percents including percents greater than 100 and less than 1 (e.g., determine missing sides of similar figures, heart rate per minute, cost per pound, pay to hours worked overtime). c. Solve percent application problems (e.g., discounts, tax, finding the missing value of percent/part/whole). Moving Straight Ahead: Linear Relationships SE/TE: Walking Rates, 15-34; Exploring Slope, 64-79 TE: 14f, 34a-34q. 63j, 79a-79m TR: Transparencies 2.1 to 2.5, 5.1 to 5.3 TECH: Graphing Calculators, Computers (optional) SE/TE: Making Comparisons, 5-15; Comparing by Finding Percents, 16-25; Comparing by Using Ratios, 26-36; Comparing by Finding Rates, 37-51; Estimating Populations and Population Densities, 52-64; Choosing Strategies, 65-81 TE: 4b, 15a-15d, 15f, 25a-25d, 25f, 36a-36g, 36h, 51a-51h, 51j, 64a-64k, 64l, 81a-81g TR: Labsheets 6.3A to 6.ACE; Transparencies 1.1 to 1.3, 2.1 to 2.2, 3.1 to 3.3, 4.1 to 4.4, 5.1 to 5.5, 6.1 to 6.3B SE/TE: Making Comparisons, 5-15; Comparing by Finding Percents, 16-25; Choosing Strategies, 65-81 TE: 4b, 15a-15d, 15f, 25a-25d, 64l, 81a-81g TR: Labsheets 6.3A to 6.ACE; Transparencies 1.1 to 1.3, 2.1 to 2.2, 6.1 to 6.3B 10
3. Exponents *a. Analyze and develop generalizations of exponential patterns, including zero as an exponent, using manipulatives and calculators (e.g., model getting paid a penny the first day, 2 cents the second day, 4 cents the third day...). SE/TE: Comparing Large Numbers, 23-37; How Many is a Million?, 38-50 TE: 22f, 37a-37h, 37j, 50a-50g TR: Labsheets 3.1A to 3.2, 4.2; Transparencies 3.1 to 3.4, 4.1 to 4.3 see also Grade 6 unit: Prime Time see also Grade 8 unit: Growing, Growing, Growing b. Build and recognize models of multiples to investigate squares and square roots (e.g., build rectangular arrays for numbers 1 to 100 and note which can be represented as squares). c. Estimate the square root of a number (e.g., between two consecutive integers). see Grade 6 unit: Covering and Surrounding see Grade 8 unit: Looking for Pythagoras see Grade 8 unit: Looking for Pythagoras Standard 3: Geometry - The student will apply the properties and relationships of plane geometry in a variety of contexts. 1. Classifying Geometric Figures a. Classify triangles according to their sides and angles. SE/TE: Similar Triangles, 59-74 TE: 58j, 74a-74k TR: Transparencies 5.1 to 5.3, Computers (optional) see also Grade 6 unit: Shapes and Designs b. Classify quadrilaterals according to their sides and angles (e.g., determine whether all squares are rectangles). SE/TE: Similar Figures, 14-27; Patterns of Similar Figures, 28-40 TE: 13f, 27a-27l, 27n, 40a-40j TR: Labsheets 2.1A to 2.3B, 3.1 to 3.3; Transparencies 2.1A to 2.3B, 3.1A to 3.ACE, Computers (optional) see also Grade 6 unit: Shapes and Designs 11
2. Identify and compare bisectors, interior, exterior, and vertical angles (e.g., using graph paper, software, protractors to measure angles between parallel lines with a transversal). SE/TE: Similar Figures, 14-27; Patterns of Similar Figures, 28-40; Using Similarity, 41-58 TE: 13f, 27a-27l, 27n, 40a-40j, 40l, 58a-58h TR: Labsheets 2.1A to 2.3B, 3.1 to 3.3; Transparencies 2.1A to 2.3B, 3.1A to 3.ACE, 4.1 to 4.4, Computers (optional) see also Grade 6 unit: Shapes and Designs 3. Rectangular Coordinate System a. Locate points on a plane in all four quadrants. SE/TE: Coordinate Grids, 67-82 TE: 66l, 82a-82o TR: Labsheets 5.ACE; Transparencies 5.1A to 5.5 TECH: Graphing Calculators b. Identify geometric transformation of figures (rotations, translations, and reflections). b. Identify geometric transformation of figures (rotations, translations, and reflections). SE/TE: Similar Figures, 14-27; Similar Triangles, 59-74; Stretching and Shrinking with a Computer, 75-84 TE: 13f, 27a-27l, 58j, 74a-74k, 74l, 84a-84h TR: Labsheets 2.1A to 2.3B; Transparencies 2.1A to 2.3B, 4.1 to 4.4, 5.1 to 5.3, 6.1A to 6.2, Computers (optional), Turtle Math Software (optional) see also Grade 8 unit: Kaleidoscopes, Hubcaps, and Mirrors Standard 4: Measurement - The student will use measurement to solve problems in a variety of contexts. 1. Area and Perimeter a. Develop area and perimeter concepts (e.g., use grids to estimate the area of irregular shapes). see Grade 6 unit: Covering and Surrounding 12
b. Apply formulas to solve problems involving perimeter (circumference) and area of polygons and circles. SE/TE: Patterns and Rules, 49-60 TE: 48n, 60a-60i TR: Transparencies 4.1A to 4.3B SE/TE: Enlarging Figures, 5-13; Similar Figures, 14-27; Patterns of Similar Figures, 28-40; Using Similarity, 41-58; Similar Triangles, 59-74; Stretching and Shrinking with a Computer, 75-84 TE: 4b, 13a-13e, 13f, 27a-27l, 27n, 40a-40j, 40l, 58a-58h, 58j, 74a-74k, 74l, 84a-84h TR: Labsheets 1.1A to 1.1B, 2.1A to 2.3B, 3.1 to 3.3; Transparencies 1.1A to 1.1B, 2.1A to 2.3B, 3.1A to 3.ACE, 4.1 to 4.4, 5.1 to 5.3, 6.1A to 6.2, Computers (optional), Turtle Math Software (optional) see also Grade 6 unit: Covering and Surrounding 2. Customary and Metric Measurements a. Select and use appropriate tools for measurements in practical applications and make reasonable estimates of measurements in a particular situation using the appropriate unit. a. Select and use appropriate tools for measurements in practical applications and make reasonable estimates of measurements in a particular situation using the appropriate unit. Filling and Wrapping: 3-Dimensional Measurement SE/TE: Building Boxes, 5-14; Designing Packages, 15-23; Finding Volumes of Boxes, 24-36; Cylinders, 37-45; Cones and Spheres, 46-56; Scaling Boxes, 57-67; Finding Volumes of Irregular Objects, 68-72 TE: 4b, 14a-14i, 14j, 23a-23f, 23h, 36a-36f, 36h, 45a-45h, 45j, 56a-56f, 56h, 67a-67g, 67h, 72a Filling and Wrapping: 3-Dimensional Measurement TR: Labsheets 1.4 to 1.ACE, 4.2; Transparencies 1.1A to 1.4, 2.1 to 2.2, 3.1 to 3.3, 4.1 to 4.3, 5.1 to 5.3, 6.1 to 6.3, 7.1, Computers (optional) SE/TE: Interpreting Disaster Reports, 5-11; Measuring Oil Spills, 12-22 TE: TR: 4b, 11a-11e, 11f, 22a-22e Labsheets 2.1; Transparencies 1.1A to 1.2B, 2.1 to 2.3B 13
b. Use estimates to relate customary and metric measurements to each other. SE/TE: Interpreting Disaster Reports, 5-11; Measuring Oil Spills, 12-22 TE: TR: 4b, 11a-11e, 11f, 22a-22e Labsheets 2.1; Transparencies 1.1A to 1.2B, 2.1 to 2.3B Standard 5: Data Analysis and Probability - The student will use probability to formulate and justify predictions from a set of data. 1. Use data from a sample to predict possible outcomes and compute simple probabilities as fractions, decimals or percents (e.g., use data from lists, tree diagrams, frequency distribution tables, area models). 2. Determine the probability of an event involving or, and, or not (e.g., on a spinner with 1 blue, 2 red and 2 yellow sections, what is the probability of getting a red or a yellow?). 2. Determine the probability of an event involving or, and, or not (e.g., on a spinner with 1 blue, 2 red and 2 yellow sections, what is the probability of getting a red or a yellow?). SE/TE: Evaluating Games of Chance, 5-21; Analyzing Number-Cube Games, 22-31; Probability and Area, 32-40; Carnival Games, 59-68; TE: 4b, 21a-21l, 21n, 31a-31h, 31j, 40a-40c, 58l, 68a-68m TR: Labsheets 1.2 to 1.3, 2.1 to 2.2; Transparencies 1.1 to 1.4, 2.1 to 2.2, 3.1A to 3.2C, 6.1 to 6.3, Computers (optional) SE/TE: Evaluating Games of Chance, 5-21; Analyzing Number-Cube Games, 22-31; Probability and Area, 32-40; Analyzing Two- Stage Games, 41-49; Expected Value, 50-58; Carnival Games, 59-68; Analyzing Sequences of Outcomes, 69-78 TE: 4b, 21a-21l, 21n, 31a-31h, 31j, 40a-40c, 40d, 49a-49l, 49n, 58a-58k, 58l, 68a-68m, 68n, 78a-78i TR: Labsheets 1.2 to 1.3, 2.1 to 2.2, 5.1 to 5.2, 7.2; Transparencies 1.1 to 1.4, 2.1 to 2.2 TR: Transparencies 3.1A to 3.2C, 4.1 to 4.2, 5.1A to 5.2, 6.1 to 6.3, 7.1 to 7.2B, Computers (optional) 14
3. Find all possible combinations and permutations involving a limited number of variables SE/TE: Analyzing Sequences of Outcomes, 69-78 TE: 68n, 78a-78i TR: Labsheets 7.2; Transparencies 7.1 to 7.2B, Computers (optional) 15