Time Lesson/Activity MPS Learning Targets Benchmarks … · 2013-03-05 · Chapter Lessons District...

Milwaukee Public Schools Suggested Curriculum Pacing Guide for Discovering Algebra (Block and Regular schools)

Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. Draft 08/25/08

Time Lesson/Activity MPS Learning Targets Benchmarks Embedded in

Chapter Lessons District Model CABS

Suggested vocabulary

Chapter 0: Fractions and Fractals 0.1 The Same

Yet Smaller

CHAPTER 0

LT 5: Compare, perform, explain and evaluate mathematical operations (+, -, *, /, exponents, roots) and properties on real numbers, emphasizing negative and positive numbers; ratios, proportions and percents; and exponents and roots in mathematical and real-world applications.

CHAPTER 0 5.2 Solve problems with fractions, decimals and percents.

integer, ratio, proportion, expression

Reflections/ Feedback



Time Lesson/Activity MPS Learning Targets Benchmarks Embedded in Chapter Lessons

District Model CABS


Chapter 0, continued 0.2 More and More 0.3 Shorter Yet Longer 0.4 Going Somewhere? 0.5 Out of Chaos

LT 2:Use a variety of mathematical and technological tools to determine measurements directly (ruler, protractor, compass) and to check reasonableness of answers. When students apply technology, e.g. computers and graphing calculators, they will interpret results appropriately. LT 5: Compare, perform, explain and evaluate mathematical operations (+, -, *, /, exponents, roots) and properties on real numbers, emphasizing negative and positive numbers; ratios, proportions and percents; and exponents and roots in mathematical and real-world applications.

2.1 Estimate measurements with precision, using appropriate units. 2.2 Measure lengths using a metric/English ruler (to the appropriate degree of tenths of cm and sixteenths of an inch). 5.1 Solve problems using integers and absolute values. 5.2 Solve problems with fractions, decimals and percents. 5.5 Solve problems involving exponents and roots. 5.8 Use the order of operations to evaluate and simplify expressions.

Fractals and Fractions

estimate, length, centimeter, metric unit, meter, exponent, power





District Model CABS


Chapter 0, continued Review Assessment Chapter 1 Data Analysis 1.1 Bar Graphs and Dot Plots 1.2 Summarizing Data with Measures of Center

CHAPTER 1 LT 3*: Use data in a variety of formats to summarize, predict, and analyze real-world applications. LT7*: Create and use tables, graphs, equations and formulas to describe relationships between variables.

CHAPTER 1

3.3 Create and interpret bar graphs and circle graphs. 3.4 Determine the means, median and mode of a set of data. 3.6 Use measures of center and measures of variation to interpret, analyze and make predictions from the data. 7.5 Interpret the meaning of tables, graphs and equations using data from real-world applications.

mean, median, mode, graph, range, data, outliers





District Model CABS


Chapter 1, continued 1.3 Five-Number Summaries and Box Plots 1.4 Histograms and Stem-and-Leaf Plots Assessment 1.5 Activity Day: Exploring a Conjecture

LT 3: Use data in a variety of formats to summarize, predict, and analyze real-world applications.

3.1 Organize information into tables and stem-and-leaf plots. 3.2 Create histograms and describe the distribution. 3.5 Calculate the 5 number summary (quartiles) and create a box and whisker plot. 3.10 Compare and contrast two sets of data using measures of central tendency from a box and whisker plot and a stem and leaf plot. 3.11 Choose a graph given a set of data and justify its appropriateness.

Bob’s Blocks data, box and whisker plot, histogram, quartiles, stem and leaf, inter-quartile range





District Model CABS


Chapter 1, continued 1.6 Two-Variable Data 1.7 Estimating 1.8 Using Matrices to Organize and Combine Data

LT 3: Use data in a variety of formats to summarize, predict, and analyze real-world applications. LT7*: Create and use tables, graphs, equations and formulas to describe relationships between variables.

3.7 Display and interpret data using line graphs and scatter plots. 3.8 Use the line of best fit to make predictions from data on a graph. 3.9 Compare and contrast two sets of data using measures of central tendency from a box and whisker plot and a stem and leaf plot. 7.2 Create graphs, including real- world data, using equations and tables. 7.5 Interpret the meaning of tables, graphs and equations using data from real-world applications.

graph, scatter plot, line of best fit, matrices





District Model CABS


Chapter 1, continued Review Assessment Chapter 2: Proportional Reasoning and Variation 2.1 Proportions 2.2 Capture/ Recapture 2.3 Proportions and Measurement Systems

CHAPTER 2 LT 2: Use a variety of mathematical and technological tools to determine measurements directly (ruler, protractor, compass) and to check reasonableness of answers. When students apply technology, e.g. computers and graphing calculators, they will interpret results appropriately. LT 5: Compare, perform, explain and evaluate mathematical operations (+, -, *, /, exponents, roots) and properties on real numbers, emphasizing negative and positive numbers; ratios, proportions and percents; and exponents and roots in mathematical and real-world applications.

CHAPTER 2 2.2 Measure lengths using a metric/English ruler (to the appropriate degree of tenths of cm and sixteenths of an inch). 2.4 Justify reasons to interpret reasonableness of answers to mathematical and real-world applications. 5.3 Solve problems with ratios and proportions. 5.4 Solve real-world application problems using scale factors and scale drawings.

dimension, conversion, centimeter, kilometer, inch, foot, yard, mile, percent





District Model CABS


Chapter 2, continued 2.4 Direct Variation Assessment 2.5 Inverse Variation 2.6 Activity Day: Variation with a Bicycle

LT 7*: Create and use tables, graphs, equations and formulas to describe relationships between variables.

7.2 Create graphs, including real- world data, using equations and tables. 7.5 Interpret the meaning of tables, graphs and equations using data from real-world applications. 7.10 Describe patterns of change from a table of ordered pairs. 7.12 Write a linear equation to represent a pattern in which there is a constant rate of change between variables. 7.13 Identify the difference between direct and inverse variation in tables, graphs, and equations.

equation, table, coordinates, coordinate system, rate of change, variable





District Model CABS


Chapter 2, continued 2.7 Evaluating Expressions 2.8 Undoing Operations Review Assessment

LT5. Compare, perform, explain and evaluate mathematical operations (+, -, *, /, exponents, roots) and properties on real numbers, emphasizing negative and positive numbers; ratios, proportions and percents; and exponents and roots in mathematical and real-world applications. LT 9: Model and solve mathematical and real-world applications that can be represented by linear equations and systems of equations, linear inequalities, and quadratic equations.

5.10 Translate verbal expressions into algebraic expressions. 9.1 Solve one-step equations using inverse operations. 9.2 Solve two-step equations using inverse operations and explain the meaning of the solution in context. 9.3 Solve multi-step equations using inverse operations and explain the meaning of the solution in context.

inverse properties, inverse





District Model CABS


Chapter 3: Linear Equations 3.1 Recursive Sequences 3.2 Linear Plots

CHAPTER 3 LT 7: Create and use tables, graphs, equations and formulas to describe relationships between variables.

CHAPTER 3 7.2 Create graphs, including real- world data, using equations and tables. 7.5 Interpret the meaning of tables, graphs and equations using data from real-world applications. 7.10 Describe patterns of change from a table of ordered pairs.





District Model CABS


Chapter 3, continued 3.3 Time-Distance Relationships Assessment 3.4 Linear Equations and the Intercept Form 3.5 Linear Equations and Rate of Change

LT 7: Create and use tables, graphs, equations and formulas to describe relationships between variables.

7.1 Create tables, including real- world data, using equations and graphs. 7.2 Create graphs, including real- world data, using equations and tables. 7.5 Interpret the meaning of tables, graphs and equations using data from real-world applications. 7.6 Find and describe intercepts on a graph. 7.7 Find and describe slopes as constant rates of change, 7.9 Write an equation from tables and graphs using real-world data. 7.12 Write a linear equation to represent a pattern in which there is a constant rate of change between variables.

slope-intercept, pattern, model, perimeter, area





District Model CABS


Chapter 3, continued 3.6 Solving Equations Using the Balancing Method 3.7 Activity Day: Modeling Data Review Assessment

LT 9: Model and solve mathematical and real-world applications that can be represented by linear equations and systems of equations, linear inequalities, and quadratic equations.

9.1 Solve one-step equations using inverse operations. 9.2 Solve two-step equations using inverse operations and explain the meaning of the solution in context. 9.8 Solve linear equations, inequalities, quadratic equations and systems of linear equations related to real-world applications 9.9 Model real-world situations using linear equations, systems of equations and inequalities.

Toothpick Hexagons

substitution, formula




Chapter 4: Fitting a Line to Data 4.1 A Formula for Slope 4.2 Writing a Linear Equation to Fit Data 4.3 Point-Slope Form of a Linear Equation

CHAPTER 4 LT 7: Create and use tables, graphs, equations and formulas to describe relationships between variables.

CHAPTER 4 7.7 Find and describe slopes as

constant rates of change. 7.11 Use formulas to calculate slope and intercepts from a set of ordered pairs 7.12 Write a linear equation to represent a pattern in which there is a constant rate of change between variables.

point – slope




Chapter 4, continued 4.4 Equivalent Algebraic Equations Assessment

LT 5: Compare, perform, explain and evaluate mathematical operations (+, -, *, /, exponents, roots) and properties on real numbers, emphasizing negative and positive numbers; ratios, proportions and percents; and exponents and roots in mathematical and real-world applications. LT 9: Solve mathematical and real-world applications represented by linear and systems of equations, linear inequalities and quadratic equations.

5.7 Identify the properties of real numbers. 5.8 Use the order of operations to evaluate and simplify expressions. 5.9 Simplify expressions using the commutative, associative, and distributive properties. 9.2 Solve two-step equations using inverse operations and explain the meaning of the solution in context. 9.3 Solve multi-step equations using inverse operations and explain the meaning of the solution in context.




Chapter 4, continued 4.5 Writing Point-Slope Equations to Fit Data 4.6 More on Modeling 4.7 Applications of Modeling Assessment

LT 3: Use data in a variety of formats to summarize, predict, and analyze real-world applications. LT 7: Create and use tables, graphs, equations and formulas to describe relationships between variables.

3.9 Use the line of best fit to make predictions from data on a graph.

7.5 Interpret the meaning of tables, graphs and equations using data from real-world applications. 7.9 Write an equation from tables and graphs using real-world data. 7.11 Use formulas to calculate slope and intercepts from a set of ordered pairs 7.12 Write a linear equation to represent a pattern in which there is a constant rate of change between variables.




Chapter 4, continued 4.8 Activity Day: Data Collection and Modeling (OPTIONAL) Review Assessment Chapter 5, Systems of Equations and Inequalities 5.1 Solving Systems of Equations

CHAPTER 5 LT 7: Create and use tables, graphs, equations and formulas to describe relationships between variables. LT 9: Solve mathematical and real-world applications represented by linear and systems of equations, linear inequalities and quadratic equations.

LT 10: Evaluate information, analyze patterns, identify relationships, and represent them using algebraic expressions, functions, and equations, e.g., linear, exponential and quadratic, recognizing that a family of functions can model a variety of real-world applications.

CHAPTER 5 7.2 Create graphs, including real- world data, using equations and tables. 9.6 Solve a system of linear equations and explain the meaning of the solution in context (methods: graphs, table, substitution, elimination, or matrices). 10.5 Identify and interpret the intersection of a system.

systems of equations




Chapter 5, continued 5.2 Solving Systems of Equations Using Substitution 5.3 Solving Systems of Equations Using Elimination Assessment

LT 7: Create and use tables, graphs, equations and formulas to describe relationships between variables. LT 9: Solve mathematical and real-world applications represented by linear and systems of equations, linear inequalities and quadratic equations.

7.5 Interpret the meaning of tables, graphs and equations using data from real-world applications. 9.6 Solve a system of linear equations and explain the meaning of the solution in context (methods: graphs, table, substitution, elimination, or matrices). 9.9 Model real-world situations with linear equations, systems of equations, and inequalities.




Chapter 5, continued 5.4 Solving Systems of Equations Using Matrices Assessment 5.5 Inequalities in One Variable

LT 9: Solve mathematical and real-world applications represented by linear and systems of equations, linear inequalities and quadratic equations.

9.4 Solve linear inequalities in one or two variables and graph the results. 9.6 Solve a system of linear equations and explain the meaning of the solution in context (methods: graphs, table, substitution, elimination, or matrices). 9.8 Solve linear equations, inequalities, quadratic equations and systems of linear equations related to real-world applications

Umbrella Problem

inequality




Chapter 5, continued 5.6 Graphing Inequalities in Two Variables 5.7 Systems of Inequalities ( optional) Review Assessment

LT 9: Solve mathematical and real-world applications represented by linear and systems of equations, linear inequalities and quadratic equations.

LT 10: Evaluate information, analyze patterns, identify relationships, and represent them using algebraic expressions, functions, and equations, e.g., linear, exponential and quadratic, recognizing that a family of functions can model a variety of real-world applications.

9.4 Solve linear inequalities in one or two variables and graph the results. 10.2 Identify the characteristics of an inequality graph.

Reflection and Feedback



[End of First Semester]

Exam Review and Exams

CHAPTERS 0-5 Learning Targets: Semester One (to be assessed) LTs: 2, 3, 5, 7, 9 LT1: Process should be incorporated in constructed response type items. Vocabulary: - MPS Academic Vocabulary for Math covered in this semester should be assessed

Reflection and Feedback: Semester One

Time Lesson/Activity MPS Learning Targets Benchmarks … · 2013-03-05 · Chapter Lessons District...

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