Prentice Hall Connected Mathematics, Grade 7 Unit 2004 Correlated to New York State Learning Standards for Mathematics (Intermediate Level)

Transcription

1 New York State Learning Standards for Mathematics (Intermediate Level) Standard 1 Analysis, Inquiry, and Design Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions. Intermediate Mathematical Analysis 1. Abstraction and symbolic representation are used to communicate mathematically. SE/TE: Investigation 4: Comparing by Finding Rates, SE/TE: Investigation 3: Subtracting Integers, 34 52; Investigation 4: Multiplying and Dividing Integers, 53-66; Investigation 5: Coordinate Grids, SE/TE: Investigation 1: Variables and Coordinate Graphs 5-17; Investigation 2: Graphing Change, 18-35; Investigation 3: Analyzing Graphs and Tables, 36-48; Investigation 4: Patterns and Rules, 49-60; Investigation 5: Using a Graphic Calculator, SE/TE: Investigation 1: Predicting From Patterns, 5-14; Investigation 2: Walking Rates, 15-34; Investigation 3: Exploring Lines with Graphic Calculators, 35-52; Investigation 5: Exploring Slope, 64-79; Investigation 6: Writing an Equation for a Line, Students extend mathematical notation and symbolism to include variables and algebraic expressions in order to describe and compare quantities and express mathematical relationships. SE/TE: Investigation 4: Comparing by Finding Rates, SE/TE: Investigation 3: Subtracting Integers, 34 52; Investigation 4: Multiplying and Dividing Integers, 53-66; Investigation 5: Coordinate Grids,

2 extend mathematical notation and symbolism to include variables and algebraic expressions in order to describe and compare quantities and express mathematical relationships. SE/TE: Investigation 1: Variables and Coordinate Graphs 5-17; Investigation 2: Graphing Change, 18-35; Investigation 3: Analyzing Graphs and Tables, 36-48; Investigation 4: Patterns and Rules, 49-60; Investigation 5: Using a Graphic Calculator, SE/TE: Investigation 1: Predicting From Patterns, 5-14; Investigation 2: Walking Rates, 15-34; Investigation 3: Exploring Lines with Graphic Calculators, 35-52; Investigation 5: Exploring Slope, 64-79; Investigation 6: Writing an Equation for a Line, Deductive and inductive reasoning are used to reach mathematical conclusions. Students use inductive reasoning to construct, evaluate, and validate conjectures and arguments, recognizing that patterns and relationships can assist in explaining and extending mathematical phenomena. Through Investigations in Connected Mathematics, students use deductive reasoning and logic to develop and apply a variety of problem-solving strategies. Finding and describing patterns of change and solving problems involving change. Using unit rates, proportional reasoning, and equivalent ratios Filling and Wrapping Finding and applying surface area and volume of geometric and irregular solids Counting outcomes, analyzing situations, and making predictions involving uncertainty. Measuring and comparing, assessing accuracy and reliability of data, and read, write, and use large numbers in measurement. This is evident, for example, when students predict the next triangular number by examining the pattern 1, 3, 6, 10, r. SE/TE: Investigation 1: Extending the Number Line, 5-17; Investigation 2: Adding Integers, 18-33; Investigation 3: Subtracting Integers, 34-52; Investigation 4: Multiplying and Dividing Integers, 53-66; Investigation 5: Coordinate Grids,

3 3. Critical thinking skills are used in the solution of mathematical problems. Students apply mathematical knowledge to solve realworld problems and problems that arise from the investigation of mathematical ideas, using representations such as pictures, charts, and tables. Scientific Inquiry 1. The central purpose of scientific inquiry is to develop explanations of natural phenomena in a continuing, creative process. Students formulate questions independently with the aid of references appropriate for guiding the search for explanations of everyday observations. SE/TE: Investigation 4: Comparing by Finding Rates, SE/TE: Investigation 5: Coordinate Grids, SE/TE: Investigation 3: Analyzing Graphs and Tables, 36-48; Investigation 4: Patterns and Rules, SE/TE: Investigation 1: Predicting From Patterns, 5-14; Investigation 2: Walking Rates, 15-34; Investigation 3: Exploring Lines with Graphic Calculators, 35-52; Investigation 5: Exploring Slope, 64-79; Investigation 6: Writing an Equation for a Line, SE/TE: Investigation 5: Coordinate Grids, SE/TE: Investigation 3: Analyzing Graphs and Tables, 36-48; Investigation 4: Patterns and Rules, SE/TE: Investigation 1: Predicting From Patterns, 5-14; Investigation 2: Walking Rates, 15-34; Investigation 3: Exploring Lines with Graphic Calculators, 35-52; Investigation 5: Exploring Slope, 64-79; Investigation 6: Writing an Equation for a Line, SE/TE: Investigation 1: Evaluating games of Chance, 5-21; Investigation 2: Analyzing Number- Cube Games, 22-31; Investigation 3: Probability and Area, 32-40; Investigation 4: Analyzing Two-Step Games; Investigation 5: Expected Value, 50-58; Investigation 6: Carnival Games, 59-68; Investigation 7: Analyzing Sequences of Outcomes,

4 construct explanations independently for natural phenomena, especially by proposing preliminary visual models of phenomena. represent, present, and defend their proposed explanations of everyday observations so that they can be understood and assessed by others. SE/TE: Investigation 5: Coordinate Grids, SE/TE: Investigation 3: Analyzing Graphs and Tables, 36-48; Investigation 4: Patterns and Rules, SE/TE: Investigation 1: Predicting From Patterns, 5-14; Investigation 2: Walking Rates, 15-34; Investigation 3: Exploring Lines with Graphic Calculators, 35-52; Investigation 5: Exploring Slope, 64-79; Investigation 6: Writing an Equation for a Line, SE/TE: Investigation 1: Evaluating games of Chance, 5-21; Investigation 2: Analyzing Number- Cube Games, 22-31; Investigation 3: Probability and Area, 32-40; Investigation 4: Analyzing Two-Step Games; Investigation 5: Expected Value, 50-58; Investigation 6: Carnival Games, 59-68; Investigation 7: Analyzing Sequences of Outcomes, SE/TE: Investigation 5: Coordinate Grids, SE/TE: Investigation 3: Analyzing Graphs and Tables, 36-48; Investigation 4: Patterns and Rules, SE/TE: Investigation 1: Predicting From Patterns, 5-14; Investigation 2: Walking Rates, 15-34; Investigation 3: Exploring Lines with Graphic Calculators, 35-52; Investigation 5: Exploring Slope, 64-79; Investigation 6: Writing an Equation for a Line, SE/TE: Investigation 1: Evaluating games of Chance, 5-21; Investigation 2: Analyzing Number- Cube Games, 22-31; Investigation 3: Probability and Area, 32-40; Investigation 4: Analyzing Two-Step Games; Investigation 5: Expected Value, 50-58; Investigation 6: Carnival Games, 59-68; Investigation 7: Analyzing Sequences of Outcomes,

5 seek to clarify, to assess critically, and to reconcile with their own thinking the ideas presented by others, including peers, teachers, authors, and scientists. SE/TE: Investigation 5: Coordinate Grids, SE/TE: Investigation 3: Analyzing Graphs and Tables, 36-48; Investigation 4: Patterns and Rules, SE/TE: Investigation 1: Predicting From Patterns, 5-14; Investigation 2: Walking Rates, 15-34; Investigation 3: Exploring Lines with Graphic Calculators, 35-52; Investigation 5: Exploring Slope, 64-79; Investigation 6: Writing an Equation for a Line, SE/TE: Investigation 1: Evaluating games of Chance, 5-21; Investigation 2: Analyzing Number- Cube Games, 22-31; Investigation 3: Probability and Area, 32-40; Investigation 4: Analyzing Two-Step Games; Investigation 5: Expected Value, 50-58; Investigation 6: Carnival Games, 59-68; Investigation 7: Analyzing Sequences of Outcomes, This is evident, for example, when students After being shown the disparity between the amount of solid waste which is recycled and which could be recycled, students working in small groups are asked to explain why this disparity exists. They develop a set of possible explanations and to select one for intensive study. After their explanation is critiqued by other groups, it is refined and submitted for assessment. The explanation is rated on clarity, plausibility, and appropriateness for intensive study using research methods. 2. Beyond the use of reasoning and consensus, scientific inquiry involves the testing of proposed explanations involving the use of conventional techniques and procedures and usually requiring considerable ingenuity. Through Investigations in Connected Mathematics, students use deductive reasoning and logic to develop and apply a variety of problem-solving strategies. Finding and describing patterns of change and solving problems involving change. Using unit rates, proportional reasoning, and equivalent ratios Counting outcomes, analyzing situations, and making predictions involving uncertainty. : Measuring and comparing, assessing accuracy and reliability of data, and read, write, and use large numbers in measurement. Through Investigations in Connected Mathematics, students use deductive reasoning and logic to develop and apply a variety of problem-solving strategies. Finding and describing patterns of change and solving problems involving change. Using unit rates, proportional reasoning, and equivalent ratios 5

6 2. Beyond the use of reasoning and consensus, scientific inquiry involves the testing of proposed explanations involving the use of conventional techniques and procedures and usually requiring considerable ingenuity. Using unit rates, proportional reasoning, and equivalent ratios Counting outcomes, analyzing situations, and making predictions involving uncertainty. Measuring and comparing, assessing accuracy and reliability of data, and read, write, and use large numbers in measurement. Students use conventional techniques and those of their own design to make further observations and refine their explanations, guided by a need for more information. develop, present, and defend formal research proposals for testing their own explanations of common phenomena, including ways of obtaining needed observations and ways of conducting simple controlled experiments. carry out their research proposals, recording observations and measurements (e.g., lab notes, audio tape, computer disk, video tape) to help assess the explanation. is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an Through Investigations in Connected Mathematics, students use deductive reasoning and logic to develop and apply a variety of problem-solving strategies. Finding and describing patterns of change and solving problems involving change. Using unit rates, proportional reasoning, and equivalent ratios Counting outcomes, analyzing situations, and making predictions involving uncertainty. Measuring and comparing, assessing accuracy and reliability of data, and read, write, and use large numbers in measurement. 6

7 This is evident, for example, when students develop a research plan for studying the accuracy of their explanation of the disparity between the amount of solid waste that is recycled and that could be recycled. After their tentative plan is critiqued, they refine it and submit it for assessment. The research proposal is rated on clarity, feasibility and soundness as a method of studying the explanations accuracy. They carry out the plan, with teacher suggested modifications. This work is rated by the teacher while it is in progress. 3. The observations made while testing proposed explanations, when analyzed using conventional and invented methods, provide new insights into phenomena. Students design charts, tables, graphs and other representations of observations in conventional and creative ways to help them address their research question or hypothesis. interpret the organized data to answer the research question or hypothesis and to gain insight into the problem. modify their personal understanding of phenomena based on evaluation of their hypothesis. is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an 7

8 This is evident, for example, when students carry out their plan making appropriate observations and measurements. They analyze the data, reach conclusions regarding their explanation of the disparity between the amount of solid waste which is recycled and which could be recycled., and prepare a tentative report which is critiqued by other groups, refined, and submitted for assessment. The report is rated on clarity, quality of presentation of data and analyses, and soundness of conclusions. is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an Engineering Design 1. Engineering design is an iterative process involving modeling and optimization finding the best solution within given constraints which is used to develop technological solutions to problems within given constraints. is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an Students engage in the following steps in a design process identify needs and opportunities for technical solutions from an investigation of situations of general or social interest. locate and utilize a range of printed, electronic, and human information resources to obtain ideas. is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an 8

9 consider constraints and generate several ideas for alternative solutions, using group and individual ideation techniques (group discussion, brainstorming, forced connections, role play); defer judgment until a number of ideas have been generated; evaluate (critique) ideas; and explain why the chosen solution is optimal. develop plans, including drawings with measurements and details of construction, and construct a model of the solution, exhibiting a degree of craftsmanship. in a group setting, test their solution against design specifications, present and evaluate results, describe how the solution might have been modified for different or better results, and discuss tradeoffs that might have to be made. is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an This is evident, for example, when students reflect on the need for alternative growing systems in desert environments and design and model a hydroponic greenhouse for growing vegetables without soil. brainstorm and evaluate alternative ideas for an adaptive device that will make life easier for a person with a disability, such as a device to pick up objects from the floor. is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an 9

10 design a model vehicle (with a safety belt restraint system and crush zones to absorb impact) to carry a raw egg as a passenger down a ramp and into a barrier without damage to the egg. assess the performance of a solution against various design criteria, enter the scores on a spreadsheet, and see how varying the solution might have affected total score. is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an Standard 2 Information Systems Students will access, generate, process, and transfer information using appropriate technologies. Intermediate Information Systems 1. Information technology is used to retrieve, process, and communicate information and as a tool to enhance learning. Students use a range of equipment and software to integrate several forms of information in order to create good quality audio, video, graphic, and text-based presentations. is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an SE/TE: Investigation 5: Coordinate Grids,

11 use a range of equipment and software to integrate several forms of information in order to create good quality audio, video, graphic, and text-based presentations. use spreadsheets and database software to collect, process, display, and analyze information. Students access needed information from electronic databases and online telecommunication services. SE/TE: Investigation 3: Analyzing Graphs and Tables, 36-48; Investigation 4: Patterns and Rules, SE/TE: Investigation 1: Predicting From Patterns, 5-14; Investigation 2: Walking Rates, 15-34; Investigation 3: Exploring Lines with Graphic Calculators, 35-52; Investigation 5: Exploring Slope, 64-79; Investigation 6: Writing an Equation for a Line, What Do You Expect SE/TE: Investigation 1: Evaluating games of Chance, 5-21; Investigation 2: Analyzing Number- Cube Games, 22-31; Investigation 3: Probability and Area, 32-40; Investigation 4: Analyzing Two-Step Games; Investigation 5: Expected Value, 50-58; Investigation 6: Carnival Games, 59-68; Investigation 7: Analyzing Sequences of Outcomes, is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an SE/TE: Investigation 5: Coordinate Grids, SE/TE: Investigation 3: Analyzing Graphs and Tables, 36-48; Investigation 4: Patterns and Rules, SE/TE: Investigation 1: Predicting From Patterns, 5-14; Investigation 2: Walking Rates, 15-34; Investigation 3: Exploring Lines with Graphic Calculators, 35-52; Investigation 5: Exploring Slope, 64-79; Investigation 6: Writing an Equation for a Line,

12 use spreadsheets and database software to collect, process, display, and analyze information. Students access needed information from electronic databases and online telecommunication services. systematically obtain accurate and relevant information pertaining to a particular topic from a range of sources, including local and national media, libraries, museums, governmental agencies, industries, and individuals. collect data from probes to measure events and phenomena. What Do You Expect SE/TE: Investigation 1: Evaluating games of Chance, 5-21; Investigation 2: Analyzing Number- Cube Games, 22-31; Investigation 3: Probability and Area, 32-40; Investigation 4: Analyzing Two-Step Games; Investigation 5: Expected Value, 50-58; Investigation 6: Carnival Games, 59-68; Investigation 7: Analyzing Sequences of Outcomes, is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an SE/TE: Investigation 5: Coordinate Grids, SE/TE: Investigation 3: Analyzing Graphs and Tables, 36-48; Investigation 4: Patterns and Rules, SE/TE: Investigation 1: Predicting From Patterns, 5-14; Investigation 2: Walking Rates, 15-34; Investigation 3: Exploring Lines with Graphic Calculators, 35-52; Investigation 5: Exploring Slope, 64-79; Investigation 6: Writing an Equation for a Line, What Do You Expect SE/TE: Investigation 1: Evaluating games of Chance, 5-21; Investigation 2: Analyzing Number- Cube Games, 22-31; Investigation 3: Probability and Area, 32-40; Investigation 4: Analyzing Two-Step Games; Investigation 5: Expected Value, 50-58; Investigation 6: Carnival Games, 59-68; Investigation 7: Analyzing Sequences of Outcomes, is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an 12

13 collect data from probes to measure events and phenomena. use simple modeling programs to make predictions. SE/TE: Investigation 5: Coordinate Grids, SE/TE: Investigation 3: Analyzing Graphs and Tables, 36-48; Investigation 4: Patterns and Rules, SE/TE: Investigation 1: Predicting From Patterns, 5-14; Investigation 2: Walking Rates, 15-34; Investigation 3: Exploring Lines with Graphic Calculators, 35-52; Investigation 5: Exploring Slope, 64-79; Investigation 6: Writing an Equation for a Line, What Do You Expect SE/TE: Investigation 1: Evaluating games of Chance, 5-21; Investigation 2: Analyzing Number- Cube Games, 22-31; Investigation 3: Probability and Area, 32-40; Investigation 4: Analyzing Two-Step Games; Investigation 5: Expected Value, 50-58; Investigation 6: Carnival Games, 59-68; Investigation 7: Analyzing Sequences of Outcomes, is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an SE/TE: Investigation 5: Coordinate Grids, SE/TE: Investigation 3: Analyzing Graphs and Tables, 36-48; Investigation 4: Patterns and Rules, SE/TE: Investigation 1: Predicting From Patterns, 5-14; Investigation 2: Walking Rates, 15-34; Investigation 3: Exploring Lines with Graphic Calculators, 35-52; Investigation 5: Exploring Slope, 64-79; Investigation 6: Writing an Equation for a Line,

14 use simple modeling programs to make predictions. What Do You Expect SE/TE: Investigation 1: Evaluating games of Chance, 5-21; Investigation 2: Analyzing Number- Cube Games, 22-31; Investigation 3: Probability and Area, 32-40; Investigation 4: Analyzing Two-Step Games; Investigation 5: Expected Value, 50-58; Investigation 6: Carnival Games, 59-68; Investigation 7: Analyzing Sequences of Outcomes, This is evident, for example, when students compose letters on a word processor and send them to representatives of industry, governmental agencies, museums, or laboratories seeking information pertaining to a student project. acquire data from weather stations. use a software package, such as Science Tool Kit, to monitor the acceleration of a model car traveling down a given distance on a ramp. is a Million? 38-50; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an 12-22; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an Average Day, ; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an Average Day, What Do You Expect SE/TE: Investigation 1: Evaluating games of Chance, 5-21; Investigation 2: Analyzing Number- Cube Games, 22-31; Investigation 3: Probability and Area, 32-40; Investigation 4: Analyzing Two-Step Games; Investigation 5: Expected Value, 50-58; Investigation 6: Carnival Games, 59-68; Investigation 7: Analyzing Sequences of Outcomes,

15 use computer software to model how plants grow plants under different conditions ; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an Average Day, What Do You Expect SE/TE: Investigation 1: Evaluating games of Chance, 5-21; Investigation 2: Analyzing Number- Cube Games, 22-31; Investigation 3: Probability and Area, 32-40; Investigation 4: Analyzing Two-Step Games; Investigation 5: Expected Value, 50-58; Investigation 6: Carnival Games, 59-68; Investigation 7: Analyzing Sequences of Outcomes, Knowledge of the impacts and limitations of information systems is essential to its effective and ethical use. Students understand the need to question the accuracy of information displayed on a computer because the results produced by a computer may be affected by incorrect data entry. identify advantages and limitations of datahandling programs and graphics programs ; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an Average Day, What Do You Expect SE/TE: Investigation 7: Analyzing Sequences of Outcomes, ; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an Average Day, What Do You Expect SE/TE: Investigation 7: Analyzing Sequences of Outcomes,

16 understand why electronically stored personal information has greater potential for misuse than records kept in conventional form. 3. Information technology can have positive and negative impacts on society, depending upon how it is used ; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an Average Day, What Do You Expect SE/TE: Investigation 7: Analyzing Sequences of Outcomes, Students use graphical, statistical, and presentation software to presents project to fellow classmates. describe applications of information technology in mathematics, science, and other technologies that address needs and solve problems in the community. explain the impact of the use and abuse of electronically generated information on individuals and families. : 12-22; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an Average Day, What Do You Expect SE/TE: Investigation 7: Analyzing Sequences of Outcomes, ; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an Average Day, What Do You Expect SE/TE: Investigation 7: Analyzing Sequences of Outcomes, : 12-22; Investigation 5: Every Little Bit Hurts, 51-60; Investigation 6: On an Average Day, What Do You Expect SE/TE: Investigation 7: Analyzing Sequences of Outcomes,

17 Standard 3 Mathematics Students will: understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry. Intermediate Mathematical Reasoning 1. Students use MATHEMATICAL REASONING to analyze mathematical situations, make conjectures, gather evidence, and construct an argument. Students apply a variety of reasoning strategies make and evaluate conjectures and arguments using appropriate language make conclusions based on inductive reasoning justify conclusions involving simple and compound (i.e., and/or) statements Through discussion of the problems and their solutions throughout Connected Math, students learn to reason about mathematics. By engaging in problem situations that involve real but accessible challenges, they learn to collect and organize information; to assemble evidence to support their conjectures, and to reason mathematically in ways that lead to logical deductions. (Introducing Algebra) Problem Situations SE/TE: 6, 9, 19, 20, 23, 24, 25, 37, 39, 40, 41, 51, 52, 53, 62, 63 (Similarity) Problem Situations SE/TE: 7, 16, 19, 21, 28, 31, 32, 42, 43, 44, 46, 60, 62, 63, 78, 79 (Ratio, Proportion, and Percent) Problem Situations SE/TE: 6, 7, 9, 17, 19, 28, 29, 30, 39, 41, 42, 43, 53, 54, 56, 57, 58, 66, 67, 70 (Integers) Problem Situations SE/TE: 7, 8, 10, 20, 24, 37, 42, 43, 44, 54, 56, 57, 59, 69, 71, 72, 74, 76 (Linear Relationships) Problem Situations SE/TE: 6, 8, 17, 18, 20, 21, 22, 36, 39, 40, 42, 53, 56, 57, 65, 68, 69, 60, 81, 83 Filling and Wrapping (Three-Dimensional Measurement) Problem Situations SE/TE: 6, 7, 8, 9, 16, 17, 24, 26, 28, 38, 39, 40, 48, 49, 50, 58, 59, 60, 69 17

18 apply a variety of reasoning strategies make and evaluate conjectures and arguments using appropriate language make conclusions based on inductive reasoning justify conclusions involving simple and compound (i.e., and/or) statements (Probability and Expected Value) Problem Situations SE/TE: 6, 7, 9, 11, 22, 23, 34, 35, 42, 44, 51, 52, 60, 61, 63, 70, 72 (Number Sense) Problem Situations SE/TE: 6, 8, 13, 14, 17, 24, 26, 28, 30, 38, 40, 43, 52, 53, 54, 61, 62, 63 This is evident, for example, when students use trial and error and work backwards to solve a problem. SE/TE: Investigation 4: Comparing by Finding Rates, SE/TE: Investigation 3: Subtracting Integers, 34-52; Investigation 4: Multiplying and Dividing Integers, 53-66; Investigation 5: Coordinate Grids, SE/TE: Investigation 1: Variables and Coordinate Graphs 5-17; Investigation 2: Graphing Change, 18-35; Investigation 3: Analyzing Graphs and Tables, 36-48; Investigation 4: Patterns and Rules, 49-60; Investigation 5: Using a Graphic Calculator, SE/TE: Investigation 1: Predicting From Patterns, 5-14; Investigation 2: Walking Rates, 15-34; Investigation 3: Exploring Lines with Graphic Calculators, 35-52; Investigation 5: Exploring Slope, 64-79; Investigation 6: Writing an Equation for a Line, identify patterns in a number sequence. are asked to find numbers that satisfy two conditions, such as n > -4 and n < 6. SE/TE: Investigation 1: Predicting From Patterns, 5-14; Investigation 2: Walking Rates, 15-34; Investigation 3: Exploring Lines with Graphic Calculators, 35-52; Investigation 5: Exploring Slope, 64-79; Investigation 6: Writing an Equation for a Line, SE/TE: Investigation 4: Comparing by Finding Rates, SE/TE: Investigation 3: Subtracting Integers, 34-52; Investigation 4: Multiplying and Dividing Integers, 53-66; Investigation 5: Coordinate Grids,

19 are asked to find numbers that satisfy two conditions, such as n > -4 and n < 6. Number Sense & Numeration 2. Students use NUMBER SENSE AND NUMERATION to develop an understanding of multiple uses of numbers in the real world, use of numbers to communicate mathematically, and use of numbers in the development of mathematical ideas. SE/TE: Investigation 1: Variables and Coordinate Graphs 5-17; Investigation 2: Graphing Change, 18-35; Investigation 3: Analyzing Graphs and Tables, 36-48; Investigation 4: Patterns and Rules, 49-60; Investigation 5: Using a Graphic Calculator, SE/TE: Investigation 1: Predicting From Patterns, 5-14; Investigation 2: Walking Rates, 15-34; Investigation 3: Exploring Lines with Graphic Calculators, 35-52; Investigation 5: Exploring Slope, 64-79; Investigation 6: Writing an Equation for a Line, Students understand, represent, and use numbers in a variety of equivalent forms (integer, fraction, decimal, percent, exponential, expanded and scientific notation) SE/TE: Investigation 1: Making Comparisons, 5-15; Investigation 2: Comparing by Finding Percents, 16-25; Investigation 3: Comparing by Using Ratios, 26-36; Investigation 4: Comparing by Finding Rates, 37-51; Investigation 5: Estimating Populations and Population Densities, SE/TE: Investigation 1: Extending the Number Line, 5-17 SE/TE: Investigation 2: Analyzing Number-Cube Games, 22-31; Investigation 3: Probability and Area, SE/TE: Investigation 2: Measuring Oil Spills,

20 understand and apply ratios, proportions, and percents through a wide variety of hands-on explorations develop an understanding of numbered theory (primes, factors, and multiples) recognize order relations for decimals, integers, and rational numbers SE/TE: Investigation 1: Making Comparisons, 5-15; Investigation 2: Comparing by Finding Percents, 16-25; Investigation 3: Comparing by Using Ratios, 26-36; Investigation 4: Comparing by Finding Rates, 37-51; Investigation 5: Estimating Populations and Population Densities, 52-64; Investigation 6: Choosing Strategies, SE/TE: Investigation 1: Evaluating Games of Chance, 5-21 SE/TE: Investigation 3: Comparing Large Numbers, SE/TE: Investigation 1: Enlarging Figures, 5-13; Investigation 2: Similar Figures, 14-27; Investigation 3: Patterns of Similar Figures, 28-40; Investigation 4: Using Similarity, 41-58; Investigation 5: Similar Triangles, 59-74; Investigation 6: with a Computer, SE/TE: Investigation 1: Making Comparisons, 5-15; Investigation 2: Comparing by Finding Percents, 16-25; Investigation 3: Comparing by Using Ratios, 26-36; Investigation 4: Comparing by Finding Rates, 37-51; Investigation 5: Estimating Populations and Population Densities, 52-64; Investigation 6: Choosing Strategies, SE/TE: Investigation 5: Exploring Slope, 64-79; Investigation 6: Writing an Equation for a Line, SE/TE: Investigation 1: Making Comparisons, 5-15; Investigation 2: Comparing by Finding Percents, 16-25; Investigation 3: Comparing by Using Ratios, 26-36; Investigation 4: Comparing by Finding Rates, SE/TE: Investigation 1: Extending the Number Line, 5-17 SE/TE: Investigation 3: Comparing Large Numbers,

21 This is evident, for example, when students use prime factors of a group of denominators to determine the least common denominator. select two pairs from a number of ratios and prove that they are in proportion. demonstrate the concept that a number can be symbolized by many different numerals as in: = = = 0.25 = 25% Can be developed with the following Investigation SE/TE: Investigation 4: Multiplying and Dividing Integers, SE/TE: Investigation 5: Every Little Bit Hurts, SE/TE: Investigation 1: Making Comparisons, 5-15; Investigation 2: Comparing by Finding Percents, 16-25; Investigation 3: Comparing by Using Rates, 26-36; Investigation 4: Comparing by Finding Rates, 37-51; Investigation 5: Estimating Population and Population Densities, 52-64; Investigation 6: Choosing Strategies, SE/TE: Investigation 5: Every Little Bit Hurts, SE/TE: Investigation 1: Making Comparisons, 5-15; Investigation 2: Comparing by Finding Percents, 16-25; Investigation 3: Comparing by Using Rates, 26-36; Investigation 4: Comparing by Finding Rates, 37-51; Investigation 5: Estimating Population and Population Densities, 52-64; Investigation 6: Choosing Strategies, Operations 3. Students use MATHEMATICAL OPERATIONS and RELATIONSHIPS among them to understand mathematics. add, subtract, multiply, and divide fractions, decimals, and integers SE/TE: Investigation 1: Making Comparisons, 5-15 SE/TE: Investigation 2: Adding Integers, 18-33; Investigation 3: Subtracting Integers, 34-52; Investigation 4: Multiplying and Dividing Integers, SE/TE: Investigation 2: Measuring Oil Spills,

22 explore and use the operations dealing with roots and powers use grouping symbols (parentheses) to clarify the intended order of operations apply the associative, commutative, distributive, inverse, and identity properties demonstrate an understanding of operational algorithms (procedures for adding, subtracting, etc.) SE/TE: Investigation 4: Patterns and Rules, 49-60; Investigation 5: Using a Graphing Calculator, Filling and Wrapping SE/TE: Investigation 4: Cylinders, 37-45; Investigation 5: Cones and Spheres, SE/TE: Investigation 4: Patterns and Rules, 49-60; Investigation 5: Using a Graphing Calculator, SE/TE: Investigation 5: Similar Triangles, SE/TE: Investigation 4: Comparing by Finding Rates, SE/TE: Investigation 2: Adding Integers, 18-33; Investigation 3: Subtracting Integers, 34-52; Investigation 4: Multiplying and Dividing Integers, SE/TE: Investigation 2: Walking Rates, 15-34; Investigation 4: Solving Equations, 53-63; Investigation 5: Exploring Slope, 64-79; Investigation 6: Writing an Equation for a Line, Filling and Wrapping SE/TE: Investigation 4: Cylinders, SE/TE: Investigation 1: Evaluating Games of Chance, 5-21; Investigation 4: Analyzing Two-Stage Games, SE/TE: Investigation 1: Making Comparisons, 5-15 SE/TE: Investigation 2: Adding Integers, 18-33; Investigation 3: Subtracting Integers, 34-52; Investigation 4: Multiplying and Dividing Integers, SE/TE: Investigation 2: Measuring Oil Spills,

23 develop appropriate proficiency with facts and algorithms apply concepts of ratio and proportion to solve problems SE/TE: Investigation 1: Making Comparisons, 5-15 SE/TE: Investigation 2: Adding Integers, 18-33; Investigation 3: Subtracting Integers, 34-52; Investigation 4: Multiplying and Dividing Integers, SE/TE: Investigation 2: Measuring Oil Spills, SE/TE: Investigation 1: Enlarging Figures, 5-13; Investigation 4: Using Similarity, 41-58; Investigation 5: Similar Triangles, SE/TE: Investigation 3: Comparing by Using Ratios, 26-36; Investigation 4: Comparing by Finding Rates, 37-51; Investigation 5: Estimating Populations and Population Densities, 52-64; Investigation 6: Choosing Strategies, SE/TE: Investigation 5: Exploring Slope, Filling and Wrapping SE/TE: Investigation 6: Scaling Boxes, SE/TE: Investigation 4: How Many is a Million?, This is evident, for example, when students create area models to help in understanding fractions, decimals, and percents. find the missing number in a proportion in which three of the numbers are known, and letters are used as place holders. arrange a set of fractions in order, from the smallest to the largest: ,,,, SE/TE: Investigation 5: Every Little Bit Hurts, SE/TE: Investigation 1: Making Comparisons, 5-15; Investigation 2: Comparing by Finding Percents, 16-25; Investigation 3: Comparing by Using Rates, 26-36; Investigation 4: Comparing by Finding Rates, 37-51; Investigation 5: Estimating Population and Population Densities, 52-64; Investigation 6: Choosing Strategies, SE/TE: Investigation 2: Comparing by Finding Percents, 16-25; Investigation 3: Comparing by Using Rates,

24 illustrate the distributive property for multiplication over addition, such as 2(a + 3) = 2a + 6. SE/TE: Investigation 4: Multiplying and Dividing Integers, Modeling/Multiple Representation 4. Students use MATHEMATICAL MODELING/MULTIPLE REPRESENTATION to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships. Students visualize, represent, and transform two- and three-dimensional shapes use maps and scale drawings to represent real objects or places SE/TE: Investigation 1: Enlarging Figures, 5-13; Investigation 2: Similar Figures, 14-27; Investigation 3: Patterns of Similar Figures, 28-40; Investigation 4: Using Similarity, 41-58; Investigation 5: Similar Triangles, 59-74; Investigation 6: with a Computer, Filling and Wrapping SE/TE: Investigation 1: Building Boxes, 5-14; Investigation 2: Designing Packages, 15-23; Investigation 3: Finding Volumes of Boxes, 24-36; Investigation 4: Cylinders, 37-45; Investigation 5: Cones and Spheres, 46-56; Investigation 6: Scaling Boxes, SE/TE: Investigation 1: Enlarging Figures, 5-13; Investigation 2: Similar Figures, 14-27; Investigation 3: Patterns of Similar Figures, 28-40; Investigation 4: Using Similarity, 41-58; Investigation 5: Similar Triangles, 59-74; Investigation 6: with a Computer, Filling and Wrapping SE/TE: Investigation 1: Building Boxes, 5-14; Investigation 2: Designing Packages, 15-23; Investigation 3: Finding Volumes of Boxes, 24-36; Investigation 4: Cylinders, 37-45; Investigation 5: Cones and Spheres, 46-56; Investigation 6: Scaling Boxes,

25 use the coordinate plane to explore geometric ideas represent numerical relationships in one- and two-dimensional graphs SE/TE: Investigation 1: Variables and Coordinate Graphs, 5-17; Investigation 5: Using a Graphing Calculator, SE/TE: Investigation 1: Enlarging Figures, 5-13; Investigation 2: Similar Figures, 14-27; Investigation 3: Patterns of Similar Figures, 28-40; Investigation 4: Using Similarity, 41-58; Investigation 5: Similar Triangles, 59-74; Investigation 6: with a Computer, SE/TE: Investigation 5: Coordinate Grids, Filling and Wrapping SE/TE: Investigation 2: Designing Packages, SE/TE: Investigation 1: Variables and Coordinate Graphs, 5-17; Investigation 2: Graphing Change, 18-35; Investigation 3: Analyzing Graphs and Tables, 36-48; Investigation 4: Patterns and Rules, 49-60; Investigation 5: Using a Graphing Calculator, SE/TE: Investigation 1: Extending the Number Line, 5-17; Investigation 5: Coordinate Grids, SE/TE: Investigation 3: Exploring Lines with a Graphing Calculator, 35-52; Investigation 4: Solving Equations, 53-63; Investigation 5: Exploring Slope, 64-79; Investigation 6: Writing an Equation for a Line, use variables to represent relationships SE/TE: Investigation 1: Variables and Coordinate Graphs, 5-17; Investigation 2: Graphing Change, 18-35; Investigation 3: Analyzing Graphs and Tables, 36-48; Investigation 4: Patterns and Rules, 49-60; Investigation 5: Using a Graphing Calculator, SE/TE: Investigation 5: Similar Triangles, 59-74; Investigation 6: with a Computer,

26 use variables to represent relationships use concrete materials and diagrams to describe the operation of real world processes and systems SE/TE: Investigation 2: Comparing by Finding Percents, 16-25; Investigation 3: Comparing by Using Ratios, 26-36; Investigation 4: Comparing by Finding Rates, 37-51; Investigation 5: Estimating Populations and Population Densities, 52-64; Investigation 6: Choosing Strategies, SE/TE: Investigation 1: Predicting from Patterns, 5-14; Investigation 2: Walking Rates, 15-34; Investigation 3: Exploring Lines with a Graphing Calculator, 35-52; Investigation 4: Solving Equations, 53-63; Investigation 5: Exploring Slope, 64-79; Investigation 6: Writing an Equation for a Line, SE/TE: Investigation 2: Graphing Change, SE/TE: Investigation 4: Using Similarity, SE/TE: Investigation 1: Making Comparisons, 5-15; Investigation 2: Comparing by Finding Percents, 16-25; Investigation 3: Comparing by Using Ratios, 26-36; Investigation 4: Comparing by Finding Rates, 37-51; Investigation 5: Estimating Populations and Population Densities, 52-64; Investigation 6: Choosing Strategies, SE/TE: Investigation 2: Walking Rates, Filling and Wrapping SE/TE: Investigation 1: Building Boxes, 5-14; Investigation 2: Designing Packages, 15-23; Investigation 7: Finding Volumes of Irregular Objects, SE/TE: Investigation 6: Carnival Games, 59-68; Investigation 7: Analyzing Sequences of Outcomes, ; Investigation 3: Comparing Large is a Million?, 38-50; Investigation 5: Every Litter Bit Hurts, 51-60; Investigation 6: On an 26

27 develop and explore models that do and do not rely on chance investigate both two- and three-dimensional transformations use appropriate tools to construct and verify geometric relationships SE/TE: Investigation 2: Graphing Change, SE/TE: Investigation 4: Using Similarity, SE/TE: Investigation 5: Estimating Populations and Population Densities, 52-64; Investigation 6: Choosing Strategies, SE/TE: Investigation 2: Walking Rates, Filling and Wrapping SE/TE: Investigation 1: Building Boxes, 5-14; Investigation 2: Designing Packages, SE/TE: Investigation 1: Evaluating Games of Chance, 5-21; Investigation 2: Analyzing Number- Cube Games, 22-31; Investigation 3: Probability and Area, 32-40; Investigation 4: Analyzing Two-Stage Games, 41-49; Investigation 5: Expected Value, 50-58; Investigation 6: Carnival Games, 59-68; Investigation 7: Analyzing Sequences of Outcomes, ; Investigation 3: Comparing Large is a Million?, 38-50; Investigation 5: Every Litter Bit Hurts, 51-60; Investigation 6: On an SE/TE: Investigation 1: Enlarging Figures, 5-13; Investigation 2: Similar Figures, 14-27; Investigation 3: Patterns of Similar Figures, 28-40; Investigation 4: Using Similarity, 41-58; Investigation 5: Similar Triangles, 59-74; Investigation 6: with a Computer, SE/TE: Investigation 1: Enlarging Figures, 5-13; Investigation 2: Similar Figures, 14-27; Investigation 3: Patterns of Similar Figures, 28-40; Investigation 4: Using Similarity, 41-58; Investigation 5: Similar Triangles, 59-74; Investigation 6: with a Computer,

28 use appropriate tools to construct and verify geometric relationships develop procedures for basic geometric constructions Filling and Wrapping SE/TE: Investigation 1: Building Boxes, 5-14; Investigation 2: Designing Packages, 15-23; Investigation 3: Finding Volumes of Boxes, 24-36; Investigation 4: Cylinders, 37-45; Investigation 5: Cones and Spheres, 46-56; Investigation 6: Scaling Boxes, 57-67; Investigation 7: Finding Volumes of Irregular Objects, SE/TE: Investigation 1: Enlarging Figures, 5-13; Investigation 2: Similar Figures, 14-27; Investigation 3: Patterns of Similar Figures, 28-40; Investigation 4: Using Similarity, 41-58; Investigation 5: Similar Triangles, 59-74; Investigation 6: with a Computer, This is evident, for example, when students build a city skyline to demonstrate skill in linear measurements, scale drawing, ratio, fractions, angles, and geometric shapes. bisect an angle using a straight edge and compass. SE/TE: Investigation 1: Enlarging Figures, 5-13; Investigation 2: Similar Figures, 14-27; Investigation 3: Patterns of Similar Figures, 28-40; Investigation 4: Using Similarity, 41-58; Investigation 5: Similar Triangles, 59-74; Investigation 6: with a Computer, Filling and Wrapping SE/TE: Investigation 1: Building Boxes, 5-14; Investigation 2: Designing Packages, 15-23; Investigation 3: Finding Volumes of Boxes, 24-36; Investigation 4: Cylinders, 37-45; Investigation 5: Cones and Spheres, 46-56; Investigation 6: Scaling Boxes, SE/TE: Investigation 1: Enlarging Figures, 5-13; Investigation 2: Similar Figures, 14-27; Investigation 3: Patterns of Similar Figures, 28-40; Investigation 4: Using Similarity, 41-58; Investigation 5: Similar Triangles, 59-74; Investigation 6: with a Computer,

29 bisect an angle using a straight edge and compass. draw a complex of geometric figures to illustrate that the intersection of a plane and a sphere is a circle or point. Filling and Wrapping SE/TE: Investigation 1: Building Boxes, 5-14; Investigation 2: Designing Packages, 15-23; Investigation 3: Finding Volumes of Boxes, 24-36; Investigation 4: Cylinders, 37-45; Investigation 5: Cones and Spheres, 46-56; Investigation 6: Scaling Boxes, SE/TE: Investigation 1: Enlarging Figures, 5-13; Investigation 2: Similar Figures, 14-27; Investigation 3: Patterns of Similar Figures, 28-40; Investigation 4: Using Similarity, 41-58; Investigation 5: Similar Triangles, 59-74; Investigation 6: with a Computer, Filling and Wrapping SE/TE: Investigation 1: Building Boxes, 5-14; Investigation 2: Designing Packages, 15-23; Investigation 3: Finding Volumes of Boxes, 24-36; Investigation 4: Cylinders, 37-45; Investigation 5: Cones and Spheres, 46-56; Investigation 6: Scaling Boxes, Measurement 5. Students use MEASUREMENT in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data. Students estimate, make, and use measurements in realworld situations SE/TE: Investigation 1: Extending the Number Line, 5-17; Investigation 4: Multiplying and Dividing Integers, Filling and Wrapping SE/TE: Investigation 1: Building Boxes, 5-14; Investigation 2: Designing Packages, 15-23; Investigation 3: Finding Volumes of Boxes, 24-36; Investigation 4: Cylinders, 37-45; Investigation 5: Cones and Spheres, 46-56; Investigation 6: Scaling Boxes, 57-67; Investigation 7: Finding Volumes of Irregular Objects,

30 select appropriate standard and nonstandard measurement units and tools to measure to a desired degree of accuracy develop measurement skills and informally derive and apply formula in direct measurement activities SE/TE: Investigation 1: Variables and Coordinate Graphs, 5-17; Investigation 2: Graphing Change, 18-35; Investigation 3: Analyzing Graphs and Tables, 36-48; Investigation 4: Patterns and Rules, 49-60; Investigation 5: Using a Graphing Calculator, SE/TE: Investigation 5: Similar Triangles, SE/TE: Investigation 5: Estimating Populations and Population Densities, SE/TE: Investigation 2: Walking Rates, 15-34; Investigation 4: Solving Equations, 53-63; Investigation 6: Writing an Equation for a Line, Filling and Wrapping SE/TE: Investigation 1: Building Boxes, 5-14; Investigation 2: Designing Packages, 15-23; Investigation 3: Finding Volumes of Boxes, 24-36; Investigation 4: Cylinders, 37-45; Investigation 5: Cones and Spheres, 46-56; Investigation 6: Scaling Boxes, 57-67; Investigation 7: Finding Volumes of Irregular Objects, SE/TE: Investigation 2: Measuring Oil Spills, SE/TE: Investigation 1: Variables and Coordinate Graphs, 5-17; Investigation 2: Graphing Change, 18-35; Investigation 3: Analyzing Graphs and Tables, 36-48; Investigation 4: Patterns and Rules, 49-60; Investigation 5: Using a Graphing Calculator, SE/TE: Investigation 5: Similar Triangles, SE/TE: Investigation 5: Estimating Populations and Population Densities, SE/TE: Investigation 2: Walking Rates, 15-34; Investigation 4: Solving Equations, 53-63; Investigation 6: Writing an Equation for a Line,

31 develop measurement skills and informally derive and apply formula in direct measurement activities use statistical methods and measures of central tendencies to display, describe, and compare data explore and produce graphic representations of data using calculators/ computers Filling and Wrapping SE/TE: Investigation 1: Building Boxes, 5-14; Investigation 2: Designing Packages, 15-23; Investigation 3: Finding Volumes of Boxes, 24-36; Investigation 4: Cylinders, 37-45; Investigation 5: Cones and Spheres, 46-56; Investigation 6: Scaling Boxes, SE/TE: Investigation 2: Measuring Oil Spills, SE/TE: Investigation 1: Variables and Coordinate Graphs, 8-9; Investigation 4: Patterns and Rules, 58 SE/TE: Investigation 1: Making Comparisons, 10; Investigation 6: Choosing Strategies, 75, 77 SE/TE: Investigation 4: Multiplying and Dividing Integers, SE/TE: Investigation 5: Expected Value, SE/TE: Investigation 5: Every Litter Bit Hurts, 51-60; Investigation 6: On an SE/TE: Investigation 1: Variables and Coordinate Graphs, 5-17; Investigation 2: Graphing Change, 18-35; Investigation 3: Analyzing Graphs and Tables, 36-48; Investigation 4: Patterns and Rules, 49-60; Investigation 5: Using a Graphing Calculator, SE/TE: Investigation 3: Patterns of Similar Figures, SE/TE: Investigation 5: Coordinate Grids, SE/TE: Investigation 1: Predicting from Patterns, 5-14; Investigation 2: Walking Rates, 15-34; Investigation 3: Exploring Lines with a Graphing Calculator, SE/TE: Investigation 7: Analyzing Sequences of Outcomes,