Prentice Hall Connected Mathematics, Grade 7 Unit 2004 Correlated to: Maine Learning Results for Mathematics (Grades 5-8)

Transcription

1 : Maine Learning Results for Mathematics (Grades 5-8) A. NUMBERS AND NUMBER SENSE Students will understand and demonstrate a sense of what numbers mean and how they are used. Students will be able to: 1. Use numbers in a variety of equivalent and interchangeable forms (e.g., integer, fraction, decimal, percent, exponential, and scientific notation) in problem-solving. 2. Demonstrate understanding of the relationships among the basic arithmetic operations on different types of numbers. SE/TE: Investigation 1-Making Comparisons, 5-14; Investigation 2- Comparing by Finding Percents, 16-24; Investigation 3-Comparing by Using Ratios, 26-35; Investigation 6- Choosing Strategies, SE/TE: Investigation 1-Extending the Number Line, 7-16; Investigation 2-Adding Integers18-32; Investigation 3-Subtracting Integers, 34-35, 43, 46-51; Investigation 4-Multiplying and Dividing Integers, 53-65; Investigation 5- Coordinate Grids, 77-81; SE/TE: Investigation 3-Comparing Large Numbers, 23; Investigation 4-How Many Is a Million, SE/TE: Investigation 1-Making Comparisons, 5-14; Investigation 2- Comparing by Finding Percents, 16-24; Investigation 3-Comparing by Using Ratios, 26-35; Investigation 6- Choosing Strategies, SE/TE: Investigation 1-Extending the Number Line, 7-16; Investigation 2-Adding Integers18-32; Investigation 3-Subtracting Integers, 34-51; Investigation 4-Multiplying and Dividing Integers, 53-65; Investigation 5-Coordinate Grids, 77-81; SE/TE: Investigation 1-Interpreting disaster Reports, 5-8; Investigation 3-Comparing Large Numbers, 23-30; Investigation 4-How Many Is a Million, 38-43; Investigation 5-Every Little Bit Hurts, 51-54; Investigation 6-On an Average Day,

2 3. Apply concepts of ratios, proportions, percents, and number theory (e.g., primes, factors, and multiples) in practical and other mathematical situations. 4. Represent numerical relationships in graphs, tables, and charts. SE/TE: Investigation 2-Similar Figures, 18-20; Investigation 4-Using Similarity, 44; SE/TE: Investigation 1-Making Comparisons, 5-14; Investigation 2-Comparing by Finding Percents, 16-24; Investigation 3-Comparing by using Ratios, 26-35; Investigation 4- Comparing by Finding rates, 38; Investigation 5-Estimating Populations and Population Densities, 55-63; Investigation 6-Choosing Strategies, 65-80; Data About Us SE/TE: Investigation 4-How Many Is a Million?, 45; Graphs, 5-17; Investigation 2-Graphing Graphs and Tables, 36-47; Investigation 4- Patterns and Rules, 49-59; Investigation 5- Using a Graphing Calculator, 61-67; SE/TE: Investigation 4-Comparing by Finding Rates, 48-49; Investigation 6-Choosing Strategies, 77-78; SE/TE: Investigation 5-Coordinate Grids, 67-81; SE/TE: Investigation 1-Predicting from Patterns, 5-8; Investigation 2-Walking Rates, 16-23; Graphing Calculator, 39-40; Investigation 5- Exploring Slope, 69 B. COMPUTATION Students will understand and demonstrate computation skills. Students will be able to: 1. Compute and model all four operations with whole numbers, fractions, decimals, sets of numbers, and percents, applying the proper order of operations. SE/TE: Investigation 1-Making Comparisons, 5-14; Investigation 2- Comparing by Finding Percents, 16-24; Investigation 3-Comparing by Using Ratios,

3 1. Compute and model all four operations with whole numbers, fractions, decimals, sets of numbers, and percents, applying the proper order of operations. 2. Create, solve, and justify the solution for multistep, real-life problems including those with ratio and proportion. SE/TE: Investigation 6-Choosing Strategies, SE/TE: Investigation 1-Extending the Number Line, 7-16; Investigation 2-Adding Integers18-32; Investigation 3-Subtracting Integers, 34-51; Investigation 4-Multiplying and Dividing Integers, 53-65; Investigation 5-Coordinate Grids, 77-81; SE/TE: Investigation 1-Interpreting Disaster Reports, 5-10; Investigation 3-Comparing Large Numbers, 25-27; Investigation 4-How Many Is a Million, 41-43; Investigation 5-Every Little Bit Hurts, 51-59; Investigation 6-On an Average Day, SE/TE: Investigation 2-Similar Figures, 18-20; SE/TE: Investigation 1-Making Comparisons, 5-14; Investigation 3-Comparing by Using Ratios, 26-35; Investigation 5-Estimating Populations and Population Densities, 55-63; Investigation 6-Choosing Strategies, 65-80; SE/TE: Investigation 1-Building Boxes, 5-13; Investigation 2-Designing Packages, 15-22; Investigation 3-Finding Volume of Boxes, 24-35; Investigation 4-Cylinders, 37-44; Investigation 5-Cones and Spheres, 46-55; Investigation 6-Scaling Boxes, 57-66; Investigation 7-Finding Volume of Irregular Objects, C. DATA ANALYSIS AND STATISTICS Students will understand and apply concepts of data analysis. Students will be able to: 1. Organize and analyze data using mean, median, mode, and range. Graphs, 8; SE/TE: Graphing Calculator,

4 2. Assemble data and use matrices to formulate and solve problems. 3. Construct inferences and convincing arguments based on data. Graphs, 7-17; Investigation 2-Graphing Graphs and Tables, 36-47; Investigation 4- Patterns and Rules, 49-59; Investigation 5- Using a Graphing Calculator, 61-67; SE/TE: Investigation 4-Comparing and Finding Rates, 48-49; Investigation 6-Choosing Strategies, 77-78; SE/TE: Investigation 5-Coordinate Grids, 67-81; SE/TE: Investigation 1-Predicting from Patterns, 9-13; Investigation 2-Walking Rates, 15-33; Graphing Calculator, 44-51; Investigation 6- Writing an Equation for a Line, 80-90; SE/TE: Investigation 1-Interpreting Disaster Reports, 5-11; Investigation 2-Measuring Oil Spills, 12-21; Investigation 6-On an Average Day, SE/TE: Investigation 1-Applications-Connections- Extensions, 10-16; Investigation 2- Applications-Connections-Extensions, 26-34; Investigation 3-Applications-Connections- Extensions, 42-47; Investigation 4- Applications-Connections-Extensions, 54-59; Investigation 5-Applications-Connections- Extensions, 64-67; SE/TE: Investigation 2-Applications-Connections- Extensions, 22-26; Investigation 4- Applications-Connections-Extensions, 47-57; Investigation 6-Applications-Connections- Extensions, 81-83; SE/TE: Investigation 1-Applications-Connections- Extensions, 9-13; Investigation 2- Applications-Connections-Extensions, 24-33; Investigation 3-Applications-Connections- Extensions, 44-51; Investigation 6- Applications-Connections-Extensions, 84-90; 4

5 3. Construct inferences and convincing arguments based on data. SE/TE: investigation 5-Applications-Connections- Extensions, 77-81; SE/TE: Investigation 1-Applications-Connections- Extensions, 9-10; Investigation 2- Applications-Connections-Extensions, 19-21; Investigation 6-Applications-Connections- Extensions, D. PROBABILITY Students will understand and apply concepts of probability. Students will be able to: 1. Find the probability of simple events and make predictions by applying the theories of probability. 2. Explain the idea that probability can be represented as a fraction between and including zero and one. What Do You Expect? SE/TE: Investigation 1-Evaluating Games of Chance, 5-9, 14, 18-20; Investigation 2-Analyzing Number-Cube Games, 22-30; Investigation 3- Probability and Area, 32-39; Investigation 4- Analyzing Two-Stage Games, 41-48; Investigation 5-Expected Value, 50-52; Investigation 7-Analyzing Sequences of Outcomes, What Do You Expect? SE/TE: Investigation 1-Evaluating Games of Chance, 6-9, 15, 19-20; Investigation 2-Analyzing number-cube Games, 22-23, 26; Investigation 6-Carnival Games, 59-60; Investigation 7- Analyzing Sequences of Outcomes, Use simulations to estimate probabilities. What Do You Expect? SE/TE: Investigation 4-Analyzing Two-Stage Games, 42; Investigation 5-Expected Value, 51; Data About Us SE/TE: Investigation 1-Interpreting Disaster Reports, 5-11; Investigation 2-Measuring Oil Spills, 16-21; Investigation 5-Every Litter Bit Hurts, 51-59; Investigation 6-On an Average Day,

6 4. Find all possible combinations and arrangements involving a limited number of variables. Graphs, 7-17; Investigation 2-Graphing Change, 18-25; Investigation 3-Analyzing Graphs and Tables, 36-47; Investigation 4- Patterns and Rules, 49-59; SE/TE: Investigation 2, 15; What Do You Expect? SE/TE: Investigation 4-Analyzing Two-Stage Games, 43-44; E. GEOMETRY Students will understand and apply concepts from geometry. Students will be able to: 1. Compare, classify, and draw two dimensional shapes and three dimensional figures. 2. Apply geometric properties to represent and solve real-life problems involving regular and irregular shapes. Can be developed using the following SE/TE: Investigation 1-Enlarging Figures, 5-12; Investigation 2-Similar Figures, 14-26; Investigation 3-Patterns of Similar Figures, 28-39; Investigation 4-Using Similarity, 41-57; Investigation 5-Similar Triangles, 59-73; Investigation 6- with a Computer, 75-83; SE/TE: Investigation 1-Building Boxes, 5-13; Investigation 2-Designing Packages, 16-22; Investigation 3-Finding Volume of Boxes, 24-35; Investigation 4-Cylinders, 37-44; Investigation 5-Cones and Spheres, 46-55; Investigation 6-Scaling Boxes, 57-66; Investigation 7-Finding Volumes of Irregular Objects, SE/TE: Investigation 1-Applications-Connections- Extensions, 9-12; Investigation 2- Applications-Connections-Extensions, 22-26; Investigation 3-Applications-Connections- Extensions, 33-39; Investigation 4- Applications-Connections-Extensions, 47-57; Investigation 5-Applications-Connections- Extensions, 64-73; Investigation 6- Applications-Connections-Extensions,

7 2. Apply geometric properties to represent and solve real-life problems involving regular and irregular shapes. 3. Use a coordinate system to define and locate position. 4. Use the appropriate geometric tools and measurements to draw and construct two and three dimensional figures. SE/TE: Investigation 1-Applications-Connections- Extensions10-13; Investigation 2- Applications-Connections-Extensions, 19-22; Investigation 3-Applications-Connections- Extensions, 29-35; Investigation 4- Applications-Connections-Extensions, 41-44; Investigation 5-Applications-Connections- Extensions, 51-55; Investigation 6- Applications-Connections-Extensions, 61-66; Investigation 7-Applications-Connections- Extensions, Variable and Patterns Graphs, 7-8; Investigation 2-Graphing Graphs and Tables, 36-47; SE/TE: Investigation 5-Coordinate Grids, Can be developed using the following SE/TE: Investigation 1-Enlarging Figures, 5-12; Investigation 2-Similar Figures, 14-26; Investigation 3-Patterns of Similar Figures, 28-39; Investigation 4-Using Similarity, 41-57; Investigation 5-Similar Triangles, 59-73; Investigation 6- with a Computer, 75-83; SE/TE: Investigation 1-Building Boxes, 5-13; Investigation 2-Designing Packages, 16-22; Investigation 3-Finding Volume of Boxes, 24-35; Investigation 4-Cylinders, 37-44; Investigation 5-Cones and Spheres, 46-55; Investigation 6-Scaling Boxes, 57-66; Investigation 7-Finding Volumes of Irregular Objects,

8 F. MEASUREMENT Students will understand and demonstrate measurement skills. Students will be able to: 1. Demonstrate the structure and use of systems of measurement. 2. Develop and use concepts that can be measured directly, or indirectly (e.g., the concept of rate). 3. Demonstrate an understanding of length, area, volume, and the corresponding units, square units, and cubic units of measure. Stretching and Shrinking and Shrinking SE/TE: Investigation 4-Using Similarity, 41; Investigation 5-Similar Triangles, 59-63; Investigation 2-Measuring Oil Spills, 14; SE/TE: Investigation 2-Measuring Oil Spills, 14 SE/TE: Investigation 3-Comparing Large Numbers, 29-36; Investigation 5-Every Litter Bit Hurts, 51-59; Investigation 6-On an Average Day, SE/TE: Investigation 1-Enlarging Figures, 7; Investigation 3-Patterns of Similar Figures, 28-32; SE/TE: Investigation 2-Designing Packages, 15-22; Investigation 3-Finding Volumes of Boxes, 24-35; Investigation 4-Cylinders, 41-44; Investigation 5-Cones and Spheres, 47-55; Investigation 6-Scaling Boxes, 58-66; Investigation 7-Finding Volumes of Irregular Objects, 68-71; Data About us SE/TE: Investigation 2-Measuring Oil Spills, G. PATTERNS, RELATIONS, FUNCTIONS Students will understand that mathematics is the science of patterns, relationships, and functions. Students will be able to: 1. Describe and represent relationships with tables, graphs, and equations. Graphs, 5-17; Investigation 2-Graphing Graphs and Tables, 36-47; Investigation 4- Patterns and Rules, 49-59; Investigation 5- Using a Graphing Calculator, 61-67; 8

9 1. Describe and represent relationships with tables, graphs, and equations. 2. Analyze relationships to explain how a change in one quantity can result in a change in another. 3. Use patterns and multiple representations to solve problems. SE/TE: Investigation 4-Comparing by Finding Rates, 48-49; Investigation 6-Choosing Strategies, 77-78; SE/TE: Investigation 5-Coordinate Grids, 67-81; SE/TE: Investigation 1-Predicting from Patterns, 5-8; Investigation 2-Walking Rates, 15-23; Graphing Calculator, 35-51; Investigation 4- Solving Equations, 53-58, 60-62; Investigation 5-Exploring Slope, 69-78; Investigation 6-Writing an Equation for a Line, 80-90; Graphs, 7-8; Investigation 2-Graphing Graphs and Tables, 36-47; SE/TE: Investigation 5-Coordinate Grids, Graphs, 7; Investigation 3-Analyzing Graphs and Tables, 38, 41-47; Investigation 4- Patterns and Rules, 49-59; SE/TE: Investigation 3-Patterns of Similar Figures, 28-32; SE/TE: Investigation 3-Subtracting Integers, 43; Investigation 4-Multiplying and Dividing Integers, 56-57; SE/TE: Investigation 1-Building Boxes, 5-13; Investigation 3-Finding Volumes of Boxes, 27-28; Investigation 4-Cylinders,

10 H. ALGEBRA CONCEPTS Students will understand and apply algebraic concepts. Students will be able to: 1. Use the concepts of variables and expressions. Graphs, 7-17; Investigation 2-Graphing Change, 18-25; Investigation 3-Analyzing graphs and Tables, 36-47; Investigation 4- Patterns and Rules, SE/TE: Investigation 2-Walking Rates, Solve linear equations using concrete, informal, and formal methods which apply the order of operations. 3. Analyze tables and graphs to identify properties and relationships in a practical context. SE/TE: Investigation 5-Coordinate Grids, 71-76; SE/TE: Investigation 1-Predicting from Patterns, 9-13; Investigation 2-Walking Rates, 15-33; Graphing Calculator, 35-51; Investigation 4- Solving Equations, 53-58, 60-62; Investigation 5-Exploring Slope, 70-78; Investigation 6-Writing an Equation for a Line, Graphs, 5-17; Investigation 2-Graphing Graphs and Tables, 36-47; Investigation 4- Patterns and Rules, 49-59; Investigation 5- Using a Graphing Calculator, 61-67; SE/TE: Investigation 4-Comparing by Finding Rates, 48-49; Investigation 6-Choosing Strategies, 77-78; SE/TE: Investigation 5-Coordinate Grids, 67-81; SE/TE: Investigation 1-Predicting from Patterns, 5-8; Investigation 2-Walking Rates, 16-23; Graphing Calculator, 39-40; Investigation 5- Exploring Slope, 69 10

11 4. Use graphs to represent two-variable equations. Graphs, 10-17; Investigation 2-Graphing Change, 26-34; Investigation 3-Analyzing Graphs and Tables, 42-47; Investigation 4- Patterns and Rules, 54-59; Investigation 5- Using a Graphing Calculator, 61-67; SE/TE: Investigation 4-Comparing by Finding Rates, 48-49; Investigation 6-Choosing Strategies, 77-78; SE/TE: Investigation 5-Coordinate Grids, Demonstrate an understanding of inequalities and non-linear equations. 6. Find solutions for unknown quantities in linear equations and in simple equations and inequalities. SE/TE: Investigation 2-Walking Rates, 15-33; graphing Calculator, 35-51; Investigation 4- Solving Equations, 53-58, 60-62; Investigation 5-Exploring Slope, 70-78; Investigation 6-Writing an Equation for a Line, I. DISCRETE MATHEMATICS Students will understand and apply concepts in discrete mathematics. Students will be able to: 1. Create and use networks to explain practical situations or solve problems. SE/TE: Investigation 1-Applications-Connections- Extensions, 9-10; Investigation 2- Applications-Connections-Extensions, 19-21; Investigation 3-Applications-Connections- Extensions, 31-36; Investigation 4- Applications-Connections-Extensions, 44-49; Investigation 5-Applications-Connections- Extensions, 55-59; Investigation 6- Applications-Connections-Extensions,

12 2. Identify patterns in the world and express these patterns with rules. Graphs, 7; Investigation 3-Analyzing Graphs and Tables, 38, 41-47; Investigation 4- Patterns and Rules, 49-59; SE/TE: Investigation 3-Patterns of Similar Figures, 28-32; SE/TE: Investigation 3-Subtracting Integers, 43; Investigation 4-Multiplying and Dividing Integers, 56-57; SE/TE: Investigation 1-Building Boxes, 5-13; Investigation 3-Finding Volumes of Boxes, 27-28; Investigation 4-Cylinders, J. MATHEMATICAL REASONING Students will understand and apply concepts of mathematical reasoning. Students will be able to: 1. Support reasoning by using models, known facts, properties, and relationships. 2. Demonstrate that multiple paths to a conclusion may exist. SE/TE: Investigation 1-Building Boxes, 5-13; Investigation 2-Designing Packages, 15-22; Investigation 3-Finding Volumes of Boxes, 24-35; Investigation 4-Cylinders, 37-44; Investigation 5-Cones and Spheres, 46-55; Investigation 6-Scaling Boxes, 57-66; Investigation 7-Finding Volumes of Irregular Objects, Graphs, 5-17; Investigation 2-Graphing Graphs and Tables, 36-47; Investigation 4- Patterns and Rules, 49-59; Investigation 5- Using a Graphing Calculator, 61-67; SE/TE: Investigation 4-Comparing by Finding Rates, 48-49; Investigation 6-Choosing Strategies, 77-78; SE/TE: Investigation 5-Coordinate Grids, 67-81; 12

13 2. Demonstrate that multiple paths to a conclusion may exist. SE/TE: Investigation 1-Predicting from Patterns, 5-8; Investigation 2-Walking Rates, 15-23; Graphing Calculator, 35-51; Investigation 4- Solving Equations, 53-58, 60-62; Investigation 5-Exploring Slope, 69-78; Investigation 6-Writing an Equation for a Line, 80-90; SE/TE: Investigation 1-Building Boxes, 5-13; Investigation 2-Designing Packages, 15-22; Investigation 3-Finding Volumes of Boxes, 24-35; Investigation 4-Cylinders, 37-44; Investigation 5-Cones and Spheres, 46-55; Investigation 6-Scaling Boxes, 57-66; Investigation 7-Finding Volumes of Irregular Objects, K. MATHEMATICAL COMMUNICATION Students will reflect upon and clarify their understanding of mathematical ideas and relationships. Students will be able to: 1. Translate relationships into algebraic notation. SE/TE: Investigation 3-Comparing large Numbers, 23; Investigation 4-How Many Is a Million?, Use statistics, tables, and graphs to communicate ideas and information in convincing presentations and analyze presentations of others for bias or deceptive presentation. Graphs, 5-17; Investigation 2-Graphing Graphs and Tables, 36-47; Investigation 4- Patterns and Rules, 49-59; Investigation 5- Using a Graphing Calculator, 61-67; SE/TE: Investigation 4-Comparing by Finding Rates, 48-49; Investigation 6-Choosing Strategies, 77-78; SE/TE: Investigation 5-Coordinate Grids, 67-81; 13

14 2. Use statistics, tables, and graphs to communicate ideas and information in convincing presentations and analyze presentations of others for bias or deceptive presentation. SE/TE: Investigation 1-Predicting from Patterns, 5-8; Investigation 2-Walking Rates, 16-23; Graphing Calculator, 39-40; Investigation 5- Exploring Slope, 69 Reference: 14