Milwaukee Public Schools Curriculum Pacing Guide for Discovering Algebra Semester One (Summer School 2009) Time Lesson/Activity MPS Learning Targets Benchmarks Embedded in District Suggested Chapter Lessons Model CABS vocabulary Chapter 2: CHAPTER 2 CHAPTER 2 Jacki’s Ratio Proportional LT 2: Use a variety of mathematical and 2.2 Measure lengths using a Homework technological tools to determine metric/English ruler (to the appropriate Reasoning and measurements directly (ruler, protractor, degree of tenths of cm and sixteenths of Proportion Variation compass) and to check reasonableness of an inch). answers. When students apply technology, 2.4 Justify reasons to interpret Variable Day 1 2.1 Proportions e.g. computers and graphing calculators, they reasonableness of answers to will interpret results appropriately. mathematical and real-world applications. Constant Day 2 2.2 Capture/ LT 5: Compare, perform, explain and 5.3 Solve problems with ratios and Recapture evaluate mathematical operations (+, -, *, /, proportions. Direct Variation exponents, roots) and properties on real 5.4 Solve real-world application problems Day 3 2.3 Proportions numbers, emphasizing negative and positive using scale factors and scale drawings. Equation and numbers; ratios, proportions and percents; 5.10 Translate verbal expressions into Measurement and exponents and roots in mathematical and algebraic expressions. real-world applications. Systems LT 7: Create and use tables, graphs, 7.2 Create graphs, including real- Day 4 2.4 Direct equations and formulas to describe world data, using equations and Variation relationships between variables. tables. 7.5 Interpret the meaning of tables, Day 5 graphs and equations using data 2.5 Inverse from real-world applications. Variation 7.10 Describe patterns of change from a table of ordered pairs. Day 6 2.7 Evaluating 7.12 Write a linear equation to Expressions represent a pattern in which there is a constant rate of change between variables. Day 7 2.8 Undoing 7.13 Identify the difference between Operations direct and inverse variation in tables, graphs, and equations. Day 8 Assessment and/or Activity LT 9: Model and solve mathematical and 9.1 Solve one-step equations using real-world applications that can be inverse operations. represented by linear equations and systems 9.2 Solve two-step equations using of equations, linear inequalities, and inverse operations and explain the quadratic equations. meaning of the solution in context. 9.3 Solve multi-step equations using inverse operations and explain the meaning of the solution in context. Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. 05/19/09 Milwaukee Public Schools Curriculum Pacing Guide for Discovering Algebra Semester One (Summer School 2009) Time Lesson/Activity MPS Learning Targets Benchmarks Embedded in District Suggested Chapter Lessons Model CABS vocabulary Chapter 3: CHAPTER 3 CHAPTER 3 Toothpick Recursion Linear LT 7: Create and use tables, graphs, 7.1 Create tables, including real- Hexagons equations and formulas to describe world data, using equations and Equations relationships between variables. graphs. Term Day 9 7.2 Create graphs, including real- 3.1 Recursive world data, using equations and Linear Sequences tables. Day 10 7.5 Interpret the meaning of tables, Intercept Form 3.2 Linear Plots graphs and equations using data from (start early if real-world applications. 7.6 Find and describe intercepts on a Y-intercept possible) graph. Day 11 7.7 Find and describe slopes as constant Coefficient 3.4 Linear rates of change. Equations and 7.9 Write an equation from tables Rate of Change the Intercept and graphs using real-world data. 7.10 Describe patterns of change Form from a table of ordered pairs. Day 12 7.12 Write a linear equation to 3.5 Linear represent a pattern in which there Equations and is a constant rate of change Rate of Change between variables. Day 13 LT 9: Model and solve mathematical 9.1 Solve one-step equations using 3.6 Solving and real-world applications that can inverse operations. Equations be represented by linear equations 9.2 Solve two-step equations using Using the and systems of equations, linear inverse operations and explain the Balancing inequalities, and quadratic equations. meaning of the solution in context. Method 9.8 Solve linear equations, inequalities, Day 14 quadratic equations and systems of linear equations related to real-world 3.7 Activity Day: applications Modeling Data 9.9 Model real-world situations (this activity using linear equations, systems of could be skipped equations and inequalities. Day 15 if behind)

Assessment and/or Activity Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. 05/19/09 Milwaukee Public Schools Curriculum Pacing Guide for Discovering Algebra Semester One (Summer School 2009) Time Lesson/Activity MPS Learning Targets Benchmarks Embedded in District Suggested Chapter Lessons Model CABS vocabulary Chapter 4: CHAPTER 4 CHAPTER 4 Equations Slope Fitting a Line to LT 3: Use data in a variety of formats to 3.9 Use the line of best fit to make summarize, predict, and analyze real-world predictions from data on a graph. Data applications. Line of Fit

Day 16 4.1 A Formula LT 5: Compare, perform, explain and 5.7 Identify the properties of real Slope- for Slope evaluate mathematical operations (+, -, *, /, numbers. intercept Form exponents, roots) and properties on real 5.8 Use the order of operations to Day 17 4.2 Writing a numbers, emphasizing negative and positive evaluate and simplify expressions. Point-slope Form Linear Equation numbers; ratios, proportions and percents; 5.9 Simplify expressions using the and exponents and roots in mathematical and commutative, associative, and distributive to Fit Data real-world applications. properties. Equivalent Equations Day 18 4.3 Point-Slope LT 7: Create and use tables, graphs, 7.5 Interpret the meaning of tables, Form of a equations and formulas to describe graphs and equations using data Distributive Linear Equation relationships between variables. from real-world applications. 7.7 Find and describe slopes as constant Property rates of change. Day 19 4.4 Equivalent 7.9 Write an equation from tables Algebraic and graphs using real-world data. Equations 7.11 Use formulas to calculate slope and intercepts from a set of ordered pairs. Day 20 4.5 Writing 7.12 Write a linear equation to Point-Slope represent a pattern in which there Equations to Fit is a constant rate of change Data between variables. LT 9: Solve mathematical 9.2 Solve two-step equations using Day 21 Assessment and real-world applications represented by inverse operations and explain the and/or Activity linear and systems of equations, linear meaning of the solution in context. inequalities and quadratic equations. 9.3 Solve multi-step equations using inverse operations and explain the meaning of the solution in context. Days Review and LT 2, 3, 5, 7, 9 and LT 1 (Process) 22-25 Exam

Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. 05/19/09