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September – June Milwaukee Public Schools Curriculum Guide for Glencoe, Gr. 7 Throughout The Year Glencoe Grade 7 2007–2008 Mathematics Curriculum Guides Wisconsin Mathematics Standard MPS Learning Target A. Mathematical Processes Note: Mathematical processes need to be embedded in all mathematical strands throughout the school year. Math processes are assessed on the WKCE-CRT and reported as a separate proficiency area. For example, students are asked to provide written justifications and explanations, pose problems, and represent concepts. Wisconsin Assessment Descriptors for Mathematics Curriculum 1) Reasoning: Use reasoning and logic to: • Perceive patterns • Identify relationships • Formulate questions • Pose problems • Make conjectures • Justify strategies • Test reasonableness of results 2) Communication: Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways (e.g., using words, numbers, symbols, pictures, charts, tables, diagrams, graphs, and models). 3) Connections: Connect mathematics to the real world as well as within mathematics. 4) Representations: Create and use representations to organize, record, and communicate mathematical ideas. 5) Problem Solving: Solve and analyze routine and non-routine problems. Lessons are aligned with MPS Learning Targets and Wisconsin State Framework Descriptor as indicated by (5.2) = Lesson 5.2. V.2 Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. updated 11/07 September – June Milwaukee Public Schools Curriculum Guide for Glencoe, Gr. 7 Time September Chapter MPS Learning Targets Chapter 1: Decimals Patterns and Algebra Number Operations and Relationships: Learning Target # 1 Represent, rename, compare, and identify equivalent forms of fractions, decimals, and percents using place value and number theory concepts. (1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9) Number Operations and Relationships: Learning Target #2 Estimate and justify solutions to problems with and without context involving whole numbers, integers, and rational numbers, including applications of proportional reasoning. (1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9) Algebraic Relationships: Learning Target #9 Describe functional relationships in words, tables, graphs, and symbolic rules, extend and justify sequences, and describe graphs of real-world situations. (1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9) Lessons are aligned with MPS Learning Targets and Wisconsin State Framework Descriptor as indicated by (5.2) = Lesson 5.2. Wisconsin State Framework Assessment Descriptors District Model CABS Mathematical Processes: Mathematical Processes are embedded throughout all lessons when, for example, students are asked to provide written justifications and explanations, pose problems, and represent concepts We hope these district CABS will be used to continue and expand the formative assessment (i.e. assessment for learning vs. assessment of learning) initiatives promoted by the MMP. Number Operations and Relationships: B.a.1 Recognize and apply place-value concepts to numbers less than 100,000,000 with decimals to the thousandths place. (1.7, 1.8, 1.9) B.a.2 Read, write, and represent numbers using words, numerals, number lines, arrays, and expanded form (12.09 = 10 + 2 + 0.09) and symbolic renaming (12.09 = 13 – 0.91). (1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9) B.a.3 Compare and order a set of fractions or decimals (to the hundredths place) and use symbols (<, >, =,). (1.5) B.b.8 Use all operations in everyday situations to solve single or multi-step word problems. (1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9) B.b.14 Determine reasonableness of answers. (1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9) Algebraic Relationships: Algebraic Relationships: #2, 12 F.a.3 Extend an increasing or decreasing arithmetic or geometric pattern. (1.1, 1.2, 1.4, 1.5, 1.7) F.a.6 Describe real-world phenomena represented by a graph. Describe real-world phenomena that a given graph might represent. (1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9) F.a.7 Justify the accuracy of the chosen item in a sequence. (1.7) F.c.15 Identify a pair of equivalent numerical or onevariable expressions when using commutative or associative properties with addition and multiplication. Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. V.2 updated 11/07 September – June Milwaukee Public Schools Curriculum Guide for Glencoe, Gr. 7 (1.6) F.c.16 Demonstrate understanding of up to four-step order of operations expressions using parentheses, exponents, and fraction symbol. (1.3, 1.4, 1.5, 1.6, 1.7) F.c.17 Demonstrate understanding of distributive property without variables. (1.6) F.c.18 Solve order of operations problems with one variable to demonstrate understanding of commutatively and associatively. (1.4, 1.5, 1.6) September / October Chapter 2: Statistics: Analyzing Data Statistics and Probability: Learning Target #7 Interpret and analyze data sets and displays using measures of central tendency and variation, and compare data sets to evaluate hypotheses and multiple representations. (2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8) October / November Chapter 3: Algebra: Integers Lessons are aligned with MPS Learning Targets and Wisconsin State Framework Descriptor as indicated by (5.2) = Lesson 5.2. Mathematical Processes: Mathematical processes are embedded through out all lessons when, for example, students are asked to provide written justifications and explanations, pose problems, and represent concepts. We hope these district CABS will be used to continue and expand the formative assessment (i.e. assessment for learning vs. assessment of learning) initiatives promoted by the MMP. Statistics and Probability: E.a.1 Compare two sets of data to generate or confirm/deny hypotheses. (2.2, 2.7, 2.8) E.a.2 Extract, interpret, and analyze data including multiple representations of the same data from tables, double back-to-back stem-and-leaf plots, double bar graphs, simple circle graphs, line plots, line graphs, charts and diagrams with and without context. (2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8) E.a.3 Create graph with one-variable data sets using backto-back stem-and-leaf plots, double bar graphs, circle graphs, and line plots and line graphs; discuss appropriateness of graph selected. (2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8) E.a.4 Find mean, median (with odd or even number of data), mode and range of a set of data with and without context. (2.3, 2.4, 2.5, 2.6, 2.7, 2.8) E.a.5 Evaluate sources of data in context and multiple representations of a given data set. (2.8) Statistics and Probability: #1a, 1b, 1c, 2, 3 ‘ We hope these district CABS Mathematical Processes: Mathematical processes are embedded through out all will be used to continue and lessons when, for example, students are asked to provide expand the formative written justifications and explanations, pose problems, and assessment (i.e. assessment Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. V.2 updated 11/07 Milwaukee Public Schools Curriculum Guide for Glencoe, Gr. 7 represent concepts. November Number Operations and Relationships: Learning Target #2 Estimate and justify solutions to problems with and without context involving whole numbers, integers, and rational numbers, including applications of proportional reasoning. (3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7) Number Operations and Relationships: B.a.2 Read, write, and represent numbers using words, numerals, number lines, arrays, and expanded form (12.09 = 10 + 2 + 0.09) and symbolic renaming (12.09 = 13 – 0.91). (3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7) B.b.10 Add and subtract decimals including thousandths with and without text. Multiply decimals and integers (100 to 100) including thousandths with and without context. (Ex. Interest rates). Divide decimals and integers in problems with and without context. (3.4, 3.5, 3.6, 3.7) B.b.14 Determine reasonableness of answers. (3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7) Algebraic Relationships: Learning Target #9 Describe functional relationships in words, tables, graphs, and symbolic rules, extend and justify sequences, and describe graphs of real-world situations. (3.1, 3.2, 3.4, 3.5, 3.6, 3.7) Algebraic Relationships: F.b.8 Solve single-variable inequalities using symbols. (3.2) F.b.9 Solve single-variable one-and two-step equations with whole number, whole number integer, or rational, coefficients with and without context. (3.4, 3.5, 3.6, 3.7) F.b.11 Solve two-step multi-operation equations with letter variables and whole number or integer coefficients with and without context. Ex: -3 + 1 = 7. (3.1, 3.4, 3.5, 3.6, 3.7) F.b.13 Create a corresponding algebraic expression when given an arithmetic operation/relationship expressed in words. (3.4, 3.5, 3.6, 3.7) Geometry: Learning Target #4 Design and classify symmetrical figures, transform points and figures using the coordinate plane, and apply properties of similarity in problem solving situations. (3.3) Geometry: C.c.12 Identify, locate, plot coordinates in all four quadrants; draw or identify the reflection of a point across the x- or y-axis or the translations of a point at integer coordinates in any of the four quadrants. (3.3) Chapter 4: Algebra: Linear Equations and Lessons are aligned with MPS Learning Targets and Wisconsin State Framework Descriptor as indicated by (5.2) = Lesson 5.2. September – June for learning vs. assessment of learning) initiatives promoted by the MMP. Algebraic Relationships: #6a, 7, 12 We hope these district CABS Mathematical Processes: Mathematical processes are embedded through out all will be used to continue and lessons when, for example, students are asked to provide expand the formative written justifications and explanations, pose problems, and assessment (i.e. assessment Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. V.2 updated 11/07 Milwaukee Public Schools Curriculum Guide for Glencoe, Gr. 7 represent concepts. Functions Algebraic Relationships: Learning Target #9 Describe functional relationships in words, tables, graphs, and symbolic rules, extend and justify sequences, and describe graphs of real-world situations. (4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7) Lessons are aligned with MPS Learning Targets and Wisconsin State Framework Descriptor as indicated by (5.2) = Lesson 5.2. September – June for learning vs. assessment of learning) initiatives promoted by the MMP. Algebraic Relationships: Algebraic Relationships: F.a.1 Use two concurrent numeric patterns to describe and #1a, 1b, 3a, 3b, 3c, 3d, 3e, analyze functional relationships between two variables. 4a, 4b, 4c, 5, 6a, 6b, 6c, 6d, 7, 8, 10, 10a, 10b, 10c, (4.6, 4.7) F.a.3 Extend an increasing or decreasing arithmetic or geometric pattern. (4.6, 4.7) F.a.4 Describe and interpret linear patterns in tables and graphs. (4.6, 4.7) F.a.5 Identify the rule to complete or extend a function table or any combination of the two using one or two operations (+, -, x,) and numbers (-100 through 100) in the function table. (4.6, 4.7) F.a.6 Describe real-world phenomena represented by a graph. Describe real-world phenomena that a given graph might represent. (4.2, 4.3, 4.4, 4.5, 4.6, 4.7) F.a.7 Justify the accuracy of the chosen item in a sequence. (4.6, 4.7) F.b.8 Solve single-variable inequalities using symbols. (4.5, 4.6, 4.7) F.b.9 Solve single-variable one-and two-step equations with whole number, whole number integer, or rational, coefficients with and without context. (4.2, 4.3, 4.4, 4.5, 4.6, 4.7) F.b.10 Find values of expressions with one variable and up to two operations including basic operations and exponents. (4.4, 4.6, 4.7) F.b.11 Solve two-step multi-operation equations with letter variables and whole number or integer coefficients with and without context. Ex: -3 + 1 = 7. (4.2, 4.3, 4.4, 4.6, 4.7) F.b.12 Write an algebraic expression (with one or two operations) which generalizes a linear pattern. (4.6, 4.7) F.b.13 Create a corresponding algebraic expression when given an arithmetic operation expressed in words. (4.1, 4.2, 4.3, 4.4) F.b.14 Evaluate formulas with and without context by solving for a specified variable. (4.5, 4.6) F.c.15 Identify a pair of equivalent numerical or oneDeveloped by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. V.2 updated 11/07 September – June Milwaukee Public Schools Curriculum Guide for Glencoe, Gr. 7 variable expressions when using commutative or associative properties with addition and multiplication. (4.2, 4.3, 4.4,) F.c.18 Solve order of operations problems with one variable to demonstrate understanding of commutatively and associatively. (4.2, 4.3, 4.4, 4.6, 4.7) Geometry: Learning Target #4 Design and classify symmetrical figures, transform points and figures using the coordinate plane, and apply properties of similarity in problem solving situations. (4.6, 4.7) Geometry: C.c.12 Identify, locate, plot coordinates in all four quadrants; draw or identify the reflection of a point across the x- or y-axis or the translation of a point at integer coordinates in any of the four quadrants. (4.6, 4.7) Number Operations and Relationships: Learning Target #1 Represent, rename, compare, and identify equivalent forms of fractions, decimals, and percents using place value and number theory concepts. (4.6, 4.7) Number Operations and Relationships: B.a.2 Read, write, and represent numbers using words, numerals, number lines, arrays, and expanded form (12.09 = 10 + 2 + 0.09) and symbolic renaming (12.09 = 13 – 0.91). (4.6, 4.7) Number Operations and Relationships: #5 Mathematical Processes: Mathematical processes are embedded through out all lessons when, for example, students are asked to provide written justifications and explanations, pose problems, and represent concepts. We hope these district CABS will be used to continue and expand the formative assessment (i.e. assessment for learning vs. assessment of learning) initiatives promoted by the MMP. Number Operations and Relationships: Learning Target #2 Estimate and justify solutions to problems with and without context involving whole numbers, integers, and rational numbers, including applications of proportional reasoning. (4.6, 4.7) November / December Chapter 5: Fractions, Decimals and Percents Number Operations and Relationships: Lessons are aligned with MPS Learning Targets and Wisconsin State Framework Descriptor as indicated by (5.2) = Lesson 5.2. Number Operations and Relationships: Number Operations and B.a.1 Recognize and apply place-value concepts to Relationships: Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. V.2 updated 11/07 Milwaukee Public Schools Curriculum Guide for Glencoe, Gr. 7 Learning Target #1 Represent, rename, compare, and identify equivalent forms of fractions, decimals, and percents using place value and number theory concepts. (5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8) numbers less than 100,000,000 with decimals to the thousandths place. (5.4, 5.5, 5.6, 5.8) B.a.2 Read, write, and represent numbers using words, numerals, number lines, arrays, and expanded form (12.09 = 10 + 2 + 0.09) and symbolic renaming (12.09 = 13 – 0.91). 5.4, 5.5, 5.6) B.a.3 Compare and order a set of fractions or decimals (to the hundredths place) and use symbols (<, >, =,). (5.8) Number Operations and Relationships: Learning Target #2 Estimate and justify solutions to problems with and without context involving whole numbers, integers, and rational numbers, including applications of proportional reasoning. (5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8) B.a.4 Identify and use number theory concepts: Prime and composite numbers Divisibility potential of numbers (divisors of 1-10, 25, and multiples of 10). Least common multiples Greatest common factor of two numbers (5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8) B.a.5 Demonstrate understanding of fractions and percents with and without contexts (e.g., sales tax and discounts, 40 is 25 percent of what number?; What number is 25 percent of 160?) (5.5, 5.6, 5.8) B.a.6 Apply proportional reasoning to a variety of problem situations (e.g., comparisons, rates, and similarities). (5.5, 5.6, 5.8) B.a.7 Identify equivalent forms of fractions, decimals, and percents. (5.3, 5.4, 5.5, 5.6, 5.8) B.b.8 Use all operations in everyday situations to solve single or multi-step word problems. (5.3, 5.4, 5.5, 5.6, 5.8) B.b.9 Solve problems involving percents with and without context. (5.5, 5.6, 5.8) B.b.11 Demonstrate understanding of the concept of division of fractions in a contextual setting. (5.3) B.b.14 Determine reasonableness of answers. (5.1, 5.2, 5.3, 5.4, 5.4, 5.6, 5.7, 5.8) Lessons are aligned with MPS Learning Targets and Wisconsin State Framework Descriptor as indicated by (5.2) = Lesson 5.2. V.2 September – June #1, 7a, 7b, 7c, 7d Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. updated 11/07 Milwaukee Public Schools Curriculum Guide for Glencoe, Gr. 7 December / January Chapter 6: Applying Fractions Mathematical Processes: Mathematical processes are embedded through out all lessons when, for example, students are asked to provide written justifications and explanations, pose problems, and represent concepts. Number Operations and Relationships: Learning Target #1 Represent, rename, compare, and identify equivalent forms of fractions, decimals, and percents using place value and number theory concepts. (6.3, 6.4, 6.6) Number Operations and Relationships: Learning Target #2 Estimate and justify solutions to problems with and without context involving whole numbers, integers, and rational numbers, including applications of proportional reasoning. (6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.9) Measurement: Learning Target #5 Make estimates, measures, and conversions, determine distances using scales and formulas, and apply proportional reasoning to enlarge and shrink figures. (6.2, 6.7) September – June We hope these district CABS will be used to continue and expand the formative assessment (i.e. assessment for learning vs. assessment of learning) initiatives promoted by the MMP. Number Operations and Relationships: B.a.3 Compare and order a set of fractions or decimals (to the hundredths place) and use symbols (<, >, =,). (6.1, 6.2, 6.3, 6.4, 6.5, 6.6) B.a.4 Identify and use number theory concepts: Prime and composite numbers Divisibility potential of numbers (divisors of 1-10, 25, and multiples of 10). Least common multiples Greatest common factor of two numbers (6.1, 6.2, 6.3, 6.4, 6.5, 6.6) B.a.7 Identify equivalent forms of fractions, decimals, and percents. (6.1, 6.2, 6.3, 6.4, 6.5, 6.6) B.b.8 Use all operations in everyday situations to solve single or multi-step word problems. (6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9) B.b.11 Demonstrate understanding of the concept of division of fractions in a contextual setting. (6.6) B.b.12 Add and subtract mixed numbers and fractions with unlike denominators, multiply mixed numbers. (6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9) B.b.14 Determine reasonableness of answers. (6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9) Number Operations and Relationships: #10a, 10b, 10c Measurement: D.a.2 Convert units within a system e.g., feet to yards; ounces to pounds; inches to feet; pints to quarts. Approximate conversions of units between metric and U.S. customary systems using a model or in context (quart/liter, yard/meter). (6.2, 6.7) D.c.6 Estimate area given a reference. (6.8) D.c.7 Determine perimeter/circumference and area of polygons and circles with and without context. (6.8, 6.9) Measurement: #1a, 1b Lessons are aligned with MPS Learning Targets and Wisconsin State Framework Descriptor as indicated by (5.2) = Lesson 5.2. V.2 Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. updated 11/07 September – June Milwaukee Public Schools Curriculum Guide for Glencoe, Gr. 7 Measurement: Learning Target #6 Estimate and determine the perimeter/circumference and area of polygons and circles and the volume and surface area of cylinders, prisms, and pyramids. (6.8, 6.9) Algebraic Relationships: Learning Target #9 Describe functional relationships in words, tables, graphs, and symbolic rules, extend and justify sequences, and describe graphs of real-world situations. (6.2, 6.3, 6.4, 6.5, 6.7, 6.8, 6.9) January Algebraic Relationships: F.a.6 Describe real-world phenomena represented by a graph. Describe real-world phenomena that a given graph might represent. (6.2, 6.3, 6.4, 6.5, 6.7, 6.8) Mathematical Processes: Mathematical processes are embedded through out all lessons when, for example, students are asked to provide written justifications and explanations, pose problems, and represent concepts. Chapter 7: Ratios and Proportions Number Operations and Relationships: Learning Target #1 Represent, rename, compare, and identify equivalent forms of fractions, decimals, and percents using place value and number theory concepts. (7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8) Number Operations and Relationships: Learning Target #2 Estimate and justify solutions to problems with and without context involving whole numbers, integers, and rational numbers, including applications of proportional reasoning. (7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8) Number Operations and Relationships: B.a.3 Compare and order a set of fractions or decimals (to the hundredths place) and use symbols (<, >, =,). (7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8) B.a.4 Identify and use number theory concepts: Prime and composite numbers Divisibility potential of numbers (divisors of 1-10, 25, and multiples of 10). Least common multiples Greatest common factor of two numbers (7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8) B.a.6 Apply proportional reasoning to a variety of problem situations (e.g., comparisons, rates, and similarities). (7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8) B.a.7 Identify equivalent forms of fractions, decimals, and percents. (7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8) B.b.8 Use all operations in everyday situations to solve single or multi-step word problems. (7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8) Lessons are aligned with MPS Learning Targets and Wisconsin State Framework Descriptor as indicated by (5.2) = Lesson 5.2. V.2 We hope these district CABS will be used to continue and expand the formative assessment (i.e. assessment for learning vs. assessment of learning) initiatives promoted by the MMP. Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. updated 11/07 September – June Milwaukee Public Schools Curriculum Guide for Glencoe, Gr. 7 B.b.9 Solve problems involving percents with and without context. (7.5, 7.6, 7.7, 7.8) B.b.14 Determine reasonableness of answers. (7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8) Measurement: Learning Target #5 Make estimates, measures, and conversions, determine distances using scales and formulas, and apply proportional reasoning to enlarge and shrink figures. (7.1, 7.2, 7.3, 7.4, 7.7, 7.8) Measurement: D.c.6 Estimate area given a reference. (7.4) D.c.7 Determine perimeter/circumference and area of polygons and circles with and without context. (7.4) D.c.8 Determine the distance between points using a scale. (7.4) D.c.11 Use ratio and proportion in context. (7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8) Measurement: #4, 5 Algebraic Relationships: F.a.6 Describe real-world phenomena represented by Algebraic Relationships: #6a, 6b, 6c, 6d Measurement: Learning Target #6 Estimate and determine the perimeter/circumference and area of polygons and circles and the volume and surface area of cylinders, prisms, and pyramids. (7.4) Algebraic Relationships: Learning Target #9 Describe functional relationships in words, tables, graphs, and symbolic rules, extend and justify sequences, and describe graphs of real-world situations. (7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8) February Chapter 8: Applying Percent Lessons are aligned with MPS Learning Targets and Wisconsin State Framework Descriptor as indicated by (5.2) = Lesson 5.2. a graph. Describe real-world phenomena that a given graph might represent. (7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8) F.b.9 Solve single-variable one-and two-step equations with whole number, whole number integer, or rational, coefficients with and without context. (7.2, 7.3, 7.4, 7.5 7.7, 7.8) F.b.10 Find values of expressions with one variable and up to two operations including basic operations and exponents. (7.2, 7.3, 7.4, 7.5 7.7, 7.8) F.b.14 Evaluate formulas with and without context by solving for a specified variable. (7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8) We hope these district CABS will be used to continue and expand the formative assessment (i.e. assessment Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. Mathematical Processes: Mathematical processes are embedded through out all lessons when, for example, students are asked to provide V.2 updated 11/07 Milwaukee Public Schools Curriculum Guide for Glencoe, Gr. 7 written justifications and explanations, pose problems, and represent concepts. Number Operations and Relationships: Learning Target #1 Represent, rename, compare, and identify equivalent forms of fractions, decimals, and percents using place value and number theory concepts. (8.1, 8.2, 8.3, 8.4, 8.5, 8.6) Number Operations and Relationships: Learning Target #2 Estimate and justify solutions to problems with and without context involving whole numbers, integers, and rational numbers, including applications of proportional reasoning. (8.1, 8.2, 8.3, 8.4, 8.5, 8.6) Number Operations and Relationships: B.a.1 Recognize and apply place-value concepts to numbers less than 100,000,000 with decimals to the thousandths place. (8.1, 8.2, 8.3, 8.4, 8.5, 8.6) B.a.2 Read, write, and represent numbers using words, numerals, number lines, arrays, and expanded form (12.09 = 10 + 2 + 0.09) and symbolic renaming (12.09 = 13 – 0.91). (8.1, 8.2, 8.3, 8.4, 8.5, 8.6) B.a.3 Compare and order a set of fractions or decimals (to the hundredths place) and use symbols (<, >, =,). (8.1, 8.2, 8.3, 8.4, 8.5, 8.6) B.a.4 Identify and use number theory concepts: Prime and composite numbers Divisibility potential of numbers (divisors of 1-10, 25, and multiples of 10). Least common multiples Greatest common factor of two numbers (8.1) B.a.5 Demonstrate understanding of fractions and percents with and without contexts (e.g., sales tax and discounts, 40 is 25 percent of what number?; What number is 25 percent of 160?) (8.1, 8.2, 8.3, 8.4, 8.5, 8.6) B.a.6 Apply proportional reasoning to a variety of problem situations (e.g., comparisons, rates, and similarities). (8.1, 8.2, 8.3, 8.4, 8.5, 8.6) B.a.7 Identify equivalent forms of fractions, decimals, and percents. (8.1, 8.2, 8.3, 8.4, 8.5, 8.6) B.b.8 Use all operations in everyday situations to solve single or multi-step word problems. (8.1, 8.2, 8.3, 8.4, 8.5, 8.6) B.b.9 Solve problems involving percents with and without context. (8.1, 8.2, 8.3, 8.4, 8.5, 8.6) B.b.13 Estimate the sum, difference, and product of whole numbers, common fractions, mixed numbers, and decimals to thousandths. (8.1, 8.2, 8.3) B.b.14 Determine reasonableness of answers. (8.1, 8.2, 8.3, 8.4, 8.5, 8.6) Lessons are aligned with MPS Learning Targets and Wisconsin State Framework Descriptor as indicated by (5.2) = Lesson 5.2. V.2 September – June for learning vs. assessment of learning) initiatives promoted by the MMP. Number Operations and Relationships: #4, 6a, 6b, 6c Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. updated 11/07 September – June Milwaukee Public Schools Curriculum Guide for Glencoe, Gr. 7 Statistics and Probability: Learning Target #7 Interpret and analyze data sets and displays using measures of central tendency and variation, and compare data sets to evaluate hypotheses and multiple representations. (8.1, 8.2, 8.3, 8.4, 8.5, 8.6) February / March Statistics and Probability: Learning Target #8 Design and conduct simulations to solve problems, determine likelihood and fairness of events, and make predictions and analyze outcomes based on theoretical and experimental probability. (8.1, 8.2, 8.3, 8.4, 8.5, 8.6) Statistics and Probability: E.a.2 Extract, interpret, and analyze data including multiple representations of the same data from tables, double back-to-back stem-and-leaf plots, double bar graphs, simple circle graphs, line plots, line graphs, charts and diagrams with and without context. (8.1, 8.2, 8.3, 8.4, 8.5, 8.6) E.a.3 Create graph with one-variable data sets using backto-back stem-and-leaf plots, double bar graphs, circle graphs, and line plots and line graphs; discuss appropriateness of graph selected. (8.1, 8.2, 8.3, 8.4, 8.5, 8.6) E.a.5 Evaluate sources of data in context and multiple representations of a given data set. (8.1, 8.2, 8.3, 8.4, 8.5, 8.6) E.b.7 Use probabilities to estimate outcomes and evaluate fair and unfair simple events. (8.3) Algebraic Relationships: Learning Target #9 Describe functional relationships in words, tables, graphs, and symbolic rules, extend and justify sequences, and describe graphs of real-world situations. (8.1, 8.2, 8.3, 8.4, 8.5, 8.6) Algebraic Relationships: F.a.6 Describe real-world phenomena represented by a graph. Describe real-world phenomena that a given graph might represent. (8.1, 8.2, 8.3, 8.4, 8.5, 8.6) F.b.14 Evaluate formulas with and without context by solving for a specified variable. (8.1, 8.2, 8.3, 8.4, 8.5, 8.6) Chapter 9: Probability Mathematical Processes: Mathematical processes are embedded through out all lessons when, for example, students are asked to provide written justifications and explanations, pose problems, and represent concepts. Number Operations and Relationships: Learning Target #1 Represent, rename, compare, and identify equivalent forms of fractions, Lessons are aligned with MPS Learning Targets and Wisconsin State Framework Descriptor as indicated by (5.2) = Lesson 5.2. We hope these district CABS will be used to continue and expand the formative assessment (i.e. assessment for learning vs. assessment of learning) initiatives promoted by the MMP. Number Operations and Relationships: B.a.4 Identify and use number theory concepts: Prime and composite numbers Divisibility potential of numbers (divisors of 1-10, 25, and multiples of 10). Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. V.2 updated 11/07 Milwaukee Public Schools Curriculum Guide for Glencoe, Gr. 7 decimals, and percents using place value and number theory concepts. (9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) Number Operations and Relationships: Learning Target #2 Estimate and justify solutions to problems with and without context involving whole numbers, integers, and rational numbers, including applications of proportional reasoning. (9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) Statistics and Probability: Learning Target #7 Interpret and analyze data sets and displays using measures of central tendency and variation, and compare data sets to evaluate hypotheses and multiple representations. ( 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) Statistics and Probability: Learning Target #8 Design and conduct simulations to solve problems, determine likelihood and fairness of events, and make predictions and analyze outcomes based on theoretical and experimental probability. (9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) Lessons are aligned with MPS Learning Targets and Wisconsin State Framework Descriptor as indicated by (5.2) = Lesson 5.2. September – June Least common multiples Greatest common factor of two numbers (9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) B.a.5 Demonstrate understanding of fractions and percents with and without contexts (e.g., sales tax and discounts, 40 is 25 percent of what number?; What number is 25 percent of 160?) (9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) B.a.6 Apply proportional reasoning to a variety of problem situations (e.g., comparisons, rates, and similarities). (9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) B.a.7 Identify equivalent forms of fractions, decimals, and percents. (9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) B.b.8 Use all operations in everyday situations to solve single or multi-step word problems. (9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) B.b.9 Solve problems involving percents with and without context. (9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) B.b.14 Determine reasonableness of answers. (9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) Statistics and Probability: Statistics and Probability: #4, 5, 6 E.a.2 Extract, interpret, and analyze data including multiple representations of the same data from tables, double back-to-back stem-and-leaf plots, double bar graphs, simple circle graphs, line plots, line graphs, charts and diagrams with and without context. ( 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) E.a.3 Create graph with one-variable data sets using backto-back stem-and-leaf plots, double bar graphs, circle graphs, and line plots and line graphs; discuss appropriateness of graph selected. ( 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) E.a.5 Evaluate sources of data in context and multiple representations of a given data set. ( 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) E.b.6 Determine the likelihood of an event and probability based on one or two dependent independent events. ( 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) E.b.7 Use probabilities to estimate outcomes and evaluate fair and unfair simple events. ( 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) E.b.8 Use data from simultaneous provided in Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. V.2 updated 11/07 September – June Milwaukee Public Schools Curriculum Guide for Glencoe, Gr. 7 charts/tables to solve and interpret probability problems. ( 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) E.b.9 Determine the number of arrangements from a set of 5 or less. Es: How many different ways could 5 students stand in line? (9.4, 9.5) E.b.10 Solve problems involving sample spaces or diagrams. ( 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) E.b.11 Analyze outcomes based on an understanding of theoretical and experimental probability. ( 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) Algebraic Relationships: Learning Target #9 Describe functional relationships in words, tables, graphs, and symbolic rules, extend and justify sequences, and describe graphs of real-world situations. (9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) March / April Chapter 10: Geometry Number Operations and Relationships: Learning Target #1 Represent, rename, compare, and identify equivalent forms of fractions, decimals, and percents using place value and number theory concepts. (10.2) Number Operations and Relationships: Learning Target #2 Estimate and justify solutions to problems with and without context involving whole numbers, integers, and Lessons are aligned with MPS Learning Targets and Wisconsin State Framework Descriptor as indicated by (5.2) = Lesson 5.2. Algebraic Relationships: F.a.6 Describe real-world phenomena represented by a graph. Describe real-world phenomena that a given graph might represent. (9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7) Mathematical Processes: Mathematical processes are embedded through out all lessons when, for example, students are asked to provide written justifications and explanations, pose problems, and represent concepts. We hope these district CABS will be used to continue and expand the formative assessment (i.e. assessment for learning vs. assessment of learning) initiatives promoted by the MMP. Number Operations and Relationships: B.a.2 Read, write, and represent numbers using words, numerals, number lines, arrays, and expanded form (12.09 = 10 + 2 + 0.09) and symbolic renaming (12.09 = 13 – 0.91). (10.1, 10.2, 10.3, 10.4, 10.5, 10.6, 10.7, 10.8, 10.9) B.a.6 Apply proportional reasoning to a variety of problem situations (e.g., comparisons, rates, and similarities). (10.2, 10.6) B.a.7 Identify equivalent forms of fractions, decimals, and percents. (10.2) B.b.8 Use all operations in everyday situations to solve single or multi-step word problems. (10.1, 10.2, 10.3, 10.4, 10.5, 10.6, 10.7, 10.8, 10.9) Number Operations and Relationships: #9a, 9b, 9c V.2 Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. updated 11/07 Milwaukee Public Schools Curriculum Guide for Glencoe, Gr. 7 rational numbers, including applications of proportional reasoning. (10.1, 10.2, 10.3, 10.4, 10.5, 10.6, 10.7, 10.8, 10.9) Geometry: Learning Target #3 Identify and describe polyhedra from multiple perspectives and determine the measure of angles and angle pairs in polygons.. (10.3, 10.4, 10.5, 10.6, 10.7, 10.8, 10.9) Geometry: Learning Target #4 Design and classify symmetrical figures, transform points and figures using the coordinate plane, and apply properties of similarity in problem solving situations. (10.8, 10.9) Measurement: Learning Target #5 Make estimates, measures, and conversions, determine distances using scales and formulas, and apply Lessons are aligned with MPS Learning Targets and Wisconsin State Framework Descriptor as indicated by (5.2) = Lesson 5.2. September – June B.b.9 Solve problems involving percents with and without context. (10.2) B.b.14 Determine reasonableness of answers. (10.1, 10.2, 10.3, 10.4, 10.5, 10.6, 10.7, 10.8, 10.9) Geometry: C.a.2 Find the measure of the third angle of a triangle when given the measures of two interior or exterior angles. (10.4, 10.6) C.a.4 Determine the measure of an angle in a drawing of an adjacent and supplementary or adjacent and complementary pair of angles when given the measure of the other angle. (10.3) C.b.5 Draw and/or describe a similar figure when given a polygon drawn on graph paper with vertices at lattice points. (10.9) C.b.6 Identify figures that are congruent and/or similar. (10.6, 10.9) C.b.7 Demonstrate understanding of similarity by finding the relationship between the sides of two figures. (10.6, 10.9) C.b.8 Draw or identify the image of a figure based on one or more transformations (reflection, rotation, and/or translation). (10.9) C.b.9 Design symmetrical shapes. Draw or identify lines of symmetry. (10.9) C.b.10 Classify figures possessing line symmetry only; line and rotation symmetry; rotational symmetry only; no symmetry. (10.9) C.c.12 Identify, locate, plot coordinates in all four quadrants; draw or identify the reflection of a point across the x- or y-axis or the translation of a point at integer coordinates in any of the four quadrants. (10.8, 10.9) C.c.13 Locate or plot coordinates in any of the four quadrants using a geometric figure (e.g., transformations). (10.8, 10.9) Geometry: #1, 2, 4, 5, 8, 9, 10a, 10b, 11a, 11b, 12 Measurement: D.b.5 Measure and/or draw angles up to 360 degrees. (10.1, 10.2, 10.3, 10.4, 10.6) Measurement: #1, 3 V.2 Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. updated 11/07 September – June Milwaukee Public Schools Curriculum Guide for Glencoe, Gr. 7 proportional reasoning to enlarge and shrink figures. (10.1, 10.2, 10.3, 10.4, 10.6) April Statistics and Probability: Learning Target #7 Interpret and analyze data sets and displays using measures of central tendency and variation, and compare data sets to evaluate hypotheses and multiple representations. (10.2, 10.3) Statistics and Probability: E.a.2 Extract, interpret, and analyze data including multiple representations of the same data from tables, double back-to-back stem-and-leaf plots, double bar graphs, simple circle graphs, line plots, line graphs, charts and diagrams with and without context. (10.2, 10.3) E.a.3 Create graph with one-variable data sets using backto-back stem-and-leaf plots, double bar graphs, circle graphs, and line plots and line graphs; discuss appropriateness of graph selected. (10.2) Algebraic Relationships: Learning Target #9 Describe functional relationships in words, tables, graphs, and symbolic rules, extend and justify sequences, and describe graphs of real-world situations. (10.2, 10.3, 10.7) Algebraic Relationships: F.a.6 Describe real-world phenomena represented by a graph. Describe real-world phenomena that a given graph might represent. (10.2, 10.3, 10.7) Chapter 11: Geometry: Measuring TwoDimensional Figures Mathematical Processes: Mathematical processes are embedded through out all lessons when, for example, students are asked to provide written justifications and explanations, pose problems, and represent concepts. Number Operations and Relationships: Learning Target #1 Represent, rename, compare, and identify equivalent forms of fractions, decimals, and percents using place value and number theory concepts. (11.8) Number Operations and Relationships: Learning Target #2 Estimate and justify solutions to Lessons are aligned with MPS Learning Targets and Wisconsin State Framework Descriptor as indicated by (5.2) = Lesson 5.2. We hope these district CABS will be used to continue and expand the formative assessment (i.e. assessment for learning vs. assessment of learning) initiatives promoted by the MMP. Number Operations and Relationships: B.a.2 Read, write, and represent numbers using words, numerals, number lines, arrays, and expanded form (12.09 = 10 + 2 + 0.09) and symbolic renaming (12.09 = 13 – 0.91). (11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7, 11.8) B.a.7 Identify equivalent forms of fractions, decimals, and percents. (11.8) B.b.8 Use all operations in everyday situations to solve single or multi-step word problems. (11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7, 11.8) B.b.14 Determine reasonableness of answers. (11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7, 11.8) Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. V.2 updated 11/07 September – June Milwaukee Public Schools Curriculum Guide for Glencoe, Gr. 7 problems with and without context involving whole numbers, integers, and rational numbers, including applications of proportional reasoning. (11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7, 11.8) May Measurement: Learning Target #6 Estimate and determine the perimeter/circumference and area of polygons and circles and the volume and surface area of cylinders, prisms, and pyramids. (11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7, 11.8) Measurement: D.c.6 Estimate area given a reference. (11.4, 11.5) D.c.7 Determine perimeter/circumference and area of polygons and circles with and without context. (11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7, 11.8) Statistics and Probability: Learning Target #8 Design and conduct simulations to solve problems, determine likelihood and fairness of events, and make predictions and analyze outcomes based on theoretical and experimental probability. (11.8) Statistics and Probability: E.b.6 Determine the likelihood of an event and probability based on one or two dependent independent events. ( 11.8) E.b.7 Use probabilities to estimate outcomes and evaluate fair and unfair simple events. (11.8) Algebraic Relationships: Learning Target #9 Describe functional relationships in words, tables, graphs, and symbolic rules, extend and justify sequences, and describe graphs of real-world situations. (11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7, 11.8) Algebraic Relationships: F.a.6 Describe real-world phenomena represented by a graph. Describe real-world phenomena that a given graph might represent. (11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7, 11.8) F.b.14 Evaluate formulas with and without context by solving for a specified variable. (11.3, 11.4, 11.5, 11.6, 11.7, 11.8) Chapter 12: Geometry: Measuring ThreeDimensional Figures Mathematical Processes: Mathematical processes are embedded through out all lessons when, for example, students are asked to provide written justifications and explanations, pose problems, and represent concepts. Lessons are aligned with MPS Learning Targets and Wisconsin State Framework Descriptor as indicated by (5.2) = Lesson 5.2. V.2 Measurement: #1b, 7 We hope these district CABS will be used to continue and expand the formative assessment (i.e. assessment for learning vs. assessment of learning) initiatives promoted by the MMP. Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. updated 11/07 September – June Milwaukee Public Schools Curriculum Guide for Glencoe, Gr. 7 Number Operations and Relationships: Learning Target #2 Estimate and justify solutions to problems with and without context involving whole numbers, integers, and rational numbers, including applications of proportional reasoning. (12,1, 12.2, 12.3, 12.4, 12.5, 12.6) Number Operations and Relationships: B.b.8 Use all operations in everyday situations to solve single or multi-step word problems. (12.1, 12.2, 12.3, 12.4, 12.5, 12.6) B.b.14 Determine reasonableness of answers. (12.1, 12.2, 12.3, 12.4, 12.5, 12.6) Geometry: Learning Target #4 Design and classify symmetrical figures, transform points and figures using the coordinate plane, and apply properties of similarity in problem solving situations. (12.1, 12.2, 12.3, 12.4, 12.5, 12.6) Geometry: C.a.1 Name 3-dimensional figures (e.g., rectangular prisms, square pyramids, cones, cylinders, and spheres). (12.1, 12.2, 12.3, 12.4, 12.5) C.b.5 Draw and/or describe a similar figure when given a polygon drawn on graph paper with vertices at lattice points. (12.1, 12.4,) C.b.11 Identify and describe 3-dimensional figures from multiple perspectives. (12.1, 12.2, 12.3, 12.4, 12.5) Geometry: #3,7, 9 Measurement: Learning Target #5 Make estimates, measures, and conversions, determine distances using scales and formulas, and apply proportional reasoning to enlarge and shrink figures. (12.6) Measurement: D.a.1 Select the appropriate unit of measure (U.S. customary and metric) to estimate the length, liquid capacity, volume, time, and weight/mass of everyday objects. (12.2, 12.3, 12.4, 12.5, 12.6) D.b.3 Apply appropriate tools techniques to measure down to the nearest 1/4-, 1/8- or 1/16-inch or nearest centimeter or millimeter. (12.6) D.c.7 Determine perimeter/circumference and area of polygons and circles with and without context. (12.4, 12.5) D.c.9 Determine volume and surface area of cylinders, rectangular prisms and pyramids with base shapes of triangle, square, regular pentagon, and regular hexagon in real-world context. (12.2, 12.3, 12.4, 12.5) Measurement: 11, 11a Measurement: Learning Target #6 Estimate and determine the perimeter/circumference and area of polygons and circles and the volume and surface area of cylinders, prisms, and pyramids. (12.2, 12.3, 12.4, 12.5) Lessons are aligned with MPS Learning Targets and Wisconsin State Framework Descriptor as indicated by (5.2) = Lesson 5.2. V.2 Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. updated 11/07