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APS District Curriculum Map 8 ESSENTIAL COMPONENTS 1. Performance Standards Grade Level: Month: August 7th Course /Subject: Math Covering and Surrounding Strand: GEOMETRY 5-8 Benchmark G.1: 7.G.1.2 Understand the concept of a constant (e.g., pi) and use the formulas for the circumference and area of a circle. 7.G.1.4 Determine the radius, diameter, and circumference of a circle and explain their relationship. 5-8 Benchmark G.3: 5-8 Benchmark G.4: 7.G.4.1 Compute the perimeter and area of common geometric shapes and use the results to find measures of less common objects. 7.G.4.2 Identify and describe the properties of two-dimensional figures: a. identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms b. use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle c. draw quadrilaterals and triangles from given information Strand: MEASUREMENT 5-8 Benchmark M.1: 7.M.1.3 Compare masses, weights, capacities, geometric measures, times, and temperatures within measurement systems. 5-8 Benchmark M.2: 7.M.2.1 Apply strategies and formulas to find missing angle measurements in triangles and quadrilaterals. 7.M.2.2 Select and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles. How do you develop formulas for area and perimeter of polygons and circles? 2. Essential Questions Questions that lead students to Big Ideas. You can use the relationships between polygons to develop formulas for area and perimeter of polygons and circles. 3. Big Ideas Student answers to EQs that lead them to the Big Ideas 4. Cognitive Level Webb’s/Bloom’s Taxonomy Link MONTHLY TEMPLATE Problem Solving Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and other contexts Apply and adapt a variety of appropriate strategies to solve problems, and Monitor and reflect on the process of problem solving. Reasoning and Proof Recognize reasoning and proof as fundamental aspects of mathematics, Make and investigate mathematical conjectures, Develop and evaluate mathematical arguments and proofs, and Select and use various types of reasoning and methods of proof. Communication Organize and consolidate their thinking through communication, Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, Analyze and evaluate the mathematical thinking and strategies of others, Use the language of mathematics to express mathematical ideas precisely, and 1 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map Grade Level: 7th Course /Subject: Math MONTHLY TEMPLATE Describe mathematical concepts using developmentally appropriate definitions. Connections Recognize and use connections among mathematical ideas, Understand how mathematical ideas interconnect and build on one another to produce a coherent whole, and Recognize and apply mathematics in contexts outside of mathematics. Representation Create and use representations to organize, record, and communicate mathematical ideas, Select, apply, and translate among mathematical representations to solve problems, and 5. Content What students need to know (nouns) Use representations to model and interpret physical, social, and mathematical phenomena. 7.G.1.2: constant, pi, formula, cirrcumference, area, circle 7.G.1.4: radius, diameter, circumference, circle, relationship 7.G.3.1: perimeter, area, change of scale 7.G.4.1: perimeter, area, shapes 7.G.4.2: properties, two-dimensional figures, vertical angles, adjacent angles, complementary angles, supplementary angles, triangles, quadrilaterals 7.M.1.3: geometric measures 7.M.2.1: strategies, formulas, triangles, quadrilaterals 7.M.2.2: formulas, circumference, circles, area, triangles, parallelograms Area, base, circumference, diameter, height, length, perimeter, pi, radius, width, congruent, dimension, irrational number Vocabulary List Words students need to know to understand concept 6. Skills What students need to be able to do (verbs) Learning Activities / Lesson Plan Links Essential Experiences or Guided Practice 7. Assessments: 7.G.1.2: understand, use formulas 7.G.1.4: determine, explain 7.G.3.1: determine 7.G.4.1: compute, use results 7.G.4.2: identify, describe, use properties, draw 7.M.1.3: compare 7.M.2.1: apply 7.M.2.2:select, use formulas Review complementary, supplementary, vertical, adjacent angles, and angle sums of polygons (CM2 Shapes and Designs) Estimate the areas and perimeter of triangles. (CM2 Covering and Surrounding, 3.1) Discover how base, height, and side length relate to a triangle. (CM2 Covering and Surrounding, 3.2) Derive the formula for the area of triangle. (CM2 Covering and Surrounding, 3.3) Solve problems involving area and perimeters of rectangles and triangles. (CM2 Covering and Surrounding, 3.4) Estimate the areas and perimeter of parallelograms. (CM2 Covering and Surrounding, 4.1) Develop a rule for finding the area of a parallelogram. (CM2 Covering and Surrounding, 4.2) Solve problems involving area and perimeters of parallelogram. (CM2 Covering and Surrounding, 4.3, 4.4) Estimate the area and perimeter of irregular shapes. (CM2 Covering and Surrounding, 5.1) Developing the formula for the circumference of a circle. (CM2 Covering and Surrounding, 5.2) Estimate the area of a circle using real life contexts. (CM2 Covering and Surrounding, 5.3) Derive the formula for the area of a circle. (CM2 Covering and Surrounding, 5.4) Check for understanding: area and perimeter of triangles (CM2 Covering and Surrounding, Multiple Choice Items #1, 7, 8, &9) Check for understanding: area and perimeter of polygons (CM2 Covering and Surrounding, Partner Quiz) Essay: Describe an efficient way to find the area and perimeter of triangles. (CM2 Covering and Surrounding, Mathematical Reflections 3) Essay: Describe an efficient way to find the area and perimeter of parallelograms. (CM2 Covering and Surrounding, Mathematical Reflections 4) Essay: Describe how you can find the circumference and area of a circle by measuring its radius or diameter. (CM2 Covering and Surrounding, Mathematical Reflections 5) Formative Assessments How will students and teacher know what students 2 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map Grade Level: 7th Course /Subject: Math MONTHLY TEMPLATE have learned so far? Differentiated Rubric Links / Attached Summative Assessments How will students show that they have mastered the standard? Differentiated Rubric Links / Attached 8. Resources Links, Curriculum Frameworks, Other Websites Quiz: area and perimeter of triangles (CM2 Covering and Surrounding, Multiple Choice Items #1, 7, 8, &9) Quiz: area and perimeter of polygons (CM2 Covering and Surrounding, Partner Quiz) Unit Test: area and perimeter of geometric shapes (CM2 Covering and Surrounding, Unit Test) Performance Assessment: Plan a park (CM2 Covering and Surrounding, Unit Project) Unit Review: Use understanding of perimeter and area (CM2 Covering and Surrounding, Looking Back and Looking Ahead) Fall Middle School Short Cycle Assessment (MSSCA) = 37 Questions Key= NM State Math Standard (number of items on the MSSCA) Strand: Number and Operations = 15 questions 6.N.2.4(1); 6.N.2.5 (2); 6.N.2.6 (1); 6.N.3.7 (1); 7.N.2.1 (1); 7.N.2.3 (2); 7.N.2.6 (1); 7.N.2.8 (1); 7.N.3.2 (5) Strand: Algebra = 8 questions 6.A.1.5 (2); 6.A.2.3 (1); 6.A.2.4 (1); 7.A.1.1 (2); 7.A.2.1 (1); 7.A.2.3 (1) Strand: Geometry = 4 questions 6.G.1.1 (1); 6.G.1.2 (1); 6.G.1.7 (1); 7.G.4.2 (1) Strand: Measurement = 3 questions 6.M.2.1 (1); 6.M.2.2 (2) Strand: Data and Probability = 7 questions 6.D.1.3 (4); 6.D.2.2 (1); 7.D.3.2 (2) 7th Grade Teacher CD, http://www.phschool.com, http://connectedmath.msu.edu APS/LEI/TLS/JAN08 3 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map 8 ESSENTIAL COMPONENTS 1. Performance Standards 2. Essential Questions Questions that lead students to Big Ideas. Grade Level: 7th Course /Subject: Math Month: September MONTHLY TEMPLATE Variables and Patterns Strand: NUMBER AND OPERATIONS 5-8 Benchmark N.1: 7.N.1.3 Use properties of the real-number system to explain reasoning and to formulate and solve real-world problems. Strand: ALGEBRA 5-8 Benchmark A.1: 7.A.1.1 Identify and continue patterns presented in a variety of formats. 7.A.1.2 Represent a variety of relationships using tables, graphs, verbal rules, and possible symbolic notation, and recognize the same general pattern presented in different representations. 7.A.1.5 Graph and interpret linear functions. 7.A.1.6 Solve problems involving rate, average speed, distance, and time. 5-8 Benchmark A.2: 7.A.2.1 Write verbal expressions and sentences as algebraic expressions and equations: a. evaluate algebraic expressions b. solve simple linear equations c. graph and interpret results 7.A.2.5 Graph linear functions and identify slope as positive or negative. 7.A.2.6 Use letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes. 5-8 Benchmark A.3: 7.A.3.2 Understand and use the coordinate plane to graph ordered pairs and linear equations. 7.A.3.3 Select and use an appropriate model for a particular situation. 5-8 Benchmark A.4: 7.A.4.3 Graph and interpret linear functions as they are used to solve problems. Strand: DATA ANALYSIS AND PROBABILITY 5-8 Benchmark D.1: 7.D.1.6 Identify ordered pairs of data from a graph and interpret the data in terms of the situation depicted by the graph. 5-8 Benchmark D.2: 7.D.2.4 Use appropriate technology to gather and display data sets and identify the relationships that exist among variables within the data set. How can the relationship between two variables be represented? Relationships between variables can be represented by using tables, graphs, equations, and written rules. All four ways have advantages and disadvantages. 3. Big Ideas Student answers to EQs that lead them to the Big Ideas 4. Cognitive Level Webb’s/Bloom’s Taxonomy Link Problem Solving Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and other contexts Apply and adapt a variety of appropriate strategies to solve problems, and Monitor and reflect on the process of problem solving. Reasoning and Proof Recognize reasoning and proof as fundamental aspects of mathematics, Make and investigate mathematical conjectures, 4 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map 5. Content What students need to know (nouns) Vocabulary List Words students need to know to understand concept 6. Skills What students need to be able to do (verbs) Grade Level: 7th Course /Subject: Math MONTHLY TEMPLATE Develop and evaluate mathematical arguments and proofs, and Select and use various types of reasoning and methods of proof. Communication Organize and consolidate their thinking through communication, Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, Analyze and evaluate the mathematical thinking and strategies of others, Use the language of mathematics to express mathematical ideas precisely, and Describe mathematical concepts using developmentally appropriate definitions. Connections Recognize and use connections among mathematical ideas, Understand how mathematical ideas interconnect and build on one another to produce a coherent whole, and Recognize and apply mathematics in contexts outside of mathematics. Representation Create and use representations to organize, record, and communicate mathematical ideas, Select, apply, and translate among mathematical representations to solve problems, and Use representations to model and interpret physical, social, and mathematical phenomena. 7.N.1.3: properties, real-number system, reasoning, real-world problems 7.A.1.1: patterns, variety of formats 7.A.1.2: relationships, tables, graphs, verbal rules, symbolic notation, patterns 7.A.1.5: linear functions 7.A.1.6: problems, rate, average speed, distance, time 7.A.2.1: verbal expressions, algebraic expressions, equations, linear equations, results 7.A.2.5: linear functions, slope 7.A.2.6: letters, variables, mathematical expressions, changes 7.A.3.2: coordinate plane, ordered pairs, linear equations 7.A.3.3: model 7.A.4.3: linear functions, problems 7.D.1.6: ordered pairs, graph, data 7.D.2.4: technology, data sets, relationships, variables Change, coordinate graph, coordinate pair, dependent variable distance/time/rate of speed, income/cost/profit/, independent variable, pattern, relationship, scale, table, variable, x-axis, y-axis, x-coordinate, y-coordinate, plot, point, range of values 7.N.1.3: use properties, explain, formulate, solve 7.A.1.1: identify, continue 7.A.1.2: represent, recognize 7.A.1.5: graph, interpret 7.A.1.6: solve 7.A.2.1: write, evaluate, solve, graph, interpret 7.A.2.5: graph, identify 7.A.2.6: use letters, describe 7.A.3.2: understand, use coordinate plane 7.A.3.3: select, use model 7.A.4.3: graph, interpret, solve 7.D.1.6: identify, interpret 7.D.2.4: use technology, gather, display, identify 5 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map Learning Activities / Lesson Plan Links Essential Experiences or Guided Practice 7. Assessments: Formative Assessments How will students and teacher know what students have learned so far? Differentiated Rubric Links / Attached Summative Assessments How will students show that they have mastered the standard? Differentiated Rubric Links / Attached 8. Resources Links, Curriculum Frameworks, Other Websites Grade Level: 7th Course /Subject: Math MONTHLY TEMPLATE Perform an experiment, collect data in a table, and interpret the pattern of change (CM2, Variables and Patterns, 1.1) Graph data from previous problem, introduce variables (CM2, Variables and Patterns, 1.2) Graph data in a table and consider values between plotted points (CM2 Variables and Patterns, 1.3) Interpret a graph, make a table based on the graph, compare the usefulness of each (CM2, Variables and Patterns, 1.4) Create a table and a graph from a narrative (CM2, Variables and Patterns, 1.5) Compare a graph and a table of bike-rental costs for two companies (CM2, Variables and Patterns, 2.1) Graph and analyze information from a survey (CM2, Variables and Patterns, 2.2) Match descriptions of variables with the graph that tells the best “story” (CM2, Variables, and Patterns, 2.3) Check for understanding: Analyze table and put information into graph (CM2, Variables and Patterns, Check Up 1) Check for understanding: Create a table and graph of information, analyze both (CM2, Variables and Patterns, Check Up 2) Essay: Explain how to make a graph to show the relationship between two variables. What are the advantages/disadvantages of using a table, graph, written explanation? (CM2, Variables and Patterns, Mathematical Reflections) Essay: Explain what variable means and what it means for two variables to be related. (CM2, Variables and Patterns, Mathematical Reflections) Summative Assessment for Variables and Patterns will be done in October Quiz: Analyze table and put information into graph (CM2, Variables and Patterns, Check Up 1) Quiz: Create a table and graph of information, analyze both (CM2, Variables and Patterns, Check Up 2) 7th Grade Teacher CD, http://www.phschool.com, http://connectedmath.msu.edu 6 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map 8 ESSENTIAL COMPONENTS 1. Performance Standards 2. Essential Questions Questions that lead students to Grade Level: 7th Month: October Course /Subject: Math Variables and Patterns MONTHLY TEMPLATE Stretching and Shrinking Strand: NUMBER AND OPERATIONS 5-8 Benchmark N.1: 7.N.1.3 Use properties of the real-number system to explain reasoning and to formulate and solve real-world problems. 5-8 Benchmark N.2: Strand: ALGEBRA 5-8 Benchmark A.1: 7.A.1.1 Identify and continue patterns presented in a variety of formats. 7.A.1.2 Represent a variety of relationships using tables, graphs, verbal rules, and possible symbolic notation, and recognize the same general pattern presented in different representations. 7.A.1.5 Graph and interpret linear functions. 7.A.1.6 Solve problems involving rate, average speed, distance, and time. 5-8 Benchmark A.2: 7.A.2.1 Write verbal expressions and sentences as algebraic expressions and equations: d. evaluate algebraic expressions e. solve simple linear equations f. graph and interpret results 7.A.2.2 Use variables and appropriate operations to write an expression, an equation, or an inequality that represents a verbal description. 7.A.2.5 Graph linear functions and identify slope as positive or negative. 7.A.2.6 Use letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes. 5-8 Benchmark A.3: 7.A.3.1 Create scale models and use them for dimensional drawings. 7.A.3.2 Understand and use the coordinate plane to graph ordered pairs and linear equations. 7.A.3.3 Select and use an appropriate model for a particular situation. 5-8 Benchmark A.4: 7.A.4.1 Use variables and appropriate operations to write an expression, an equation, and/or an inequality that represents a verbal description involving change. 7.A.4.3 Graph and interpret linear functions as they are used to solve problems. 7.A.4.4 Solve two-step equations and inequalities with one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results. Strand: GEOMETRY 5-8 Benchmark G.1: 7.G.1.1 Classify geometric figures as similar or congruent. 5-8 Benchmark G.3: 7.G.3.1 Determine how perimeter and area are affected by changes of scale. Strand: MEASUREMENT 5-8 Benchmark M.2: 7.M.2.3 Solve problems involving scale factors, ratios, and proportions. Strand: DATA ANALYSIS AND PROBABILITY 5-8 Benchmark D.1: 7.D.1.6 Identify ordered pairs of data from a graph and interpret the data in terms of the situation depicted by the graph. 5-8 Benchmark D.2: 7.D.2.4 Use appropriate technology to gather and display data sets and identify the relationships that exist among variables within the data set. How can the relationship between two variables be represented? Explain the advantages and disadvantages of each representation. 7 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map Big Ideas. Grade Level: 7th Course /Subject: Math MONTHLY TEMPLATE How would you recognize similarity between two figures? Relationships between variables can be represented by using tables, graphs, equations, and written rules. All four ways have advantages and disadvantages. 3. Big Ideas Student answers to EQs that lead them to the Big Ideas 4. Cognitive Level Webb’s/Bloom’s Taxonomy Link 5. Content What students need to know (nouns) Comparing corresponding parts, and shape, identifies similar figures. Scale factors and ratios can be used to describe relationships among the side lengths of similar figures. Problem Solving Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and other contexts Apply and adapt a variety of appropriate strategies to solve problems, and Monitor and reflect on the process of problem solving. Reasoning and Proof Recognize reasoning and proof as fundamental aspects of mathematics, Make and investigate mathematical conjectures, Develop and evaluate mathematical arguments and proofs, and Select and use various types of reasoning and methods of proof. Communication Organize and consolidate their thinking through communication, Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, Analyze and evaluate the mathematical thinking and strategies of others, Use the language of mathematics to express mathematical ideas precisely, and Describe mathematical concepts using developmentally appropriate definitions. Connections Recognize and use connections among mathematical ideas, Understand how mathematical ideas interconnect and build on one another to produce a coherent whole, and Recognize and apply mathematics in contexts outside of mathematics. Representation Create and use representations to organize, record, and communicate mathematical ideas, Select, apply, and translate among mathematical representations to solve problems, and Use representations to model and interpret physical, social, and mathematical phenomena. 7.N.1.3: properties, real-number system, reasoning, real-world problems 7.N.2.3: percentage, quantities, discounts, interest, markups, commission, profit, simple interest 7.A.1.1: patterns, variety of formats 7.A.1.2: relationships, tables, graphs, verbal rules, symbolic notation, patterns 7.A.1.5: linear functions (informally addressed) 7.A.1.6: problems, rate, average speed, distance, time 7.A.2.1: verbal expressions, algebraic expressions, equations, linear equations, results 7.A.2.5: linear functions (informally addressed), slope (informally addressed) 7.A.2.6: letters, variables, mathematical expressions, changes 7.A.3.1: scale model, dimensional drawing 7.A.3.2: coordinate plane, ordered pairs, linear equations 7.A.3.3: model 7.A.4.1: variables, operations, expression, equation, inequality, verbal description, change 7.A.4.3: linear functions (informally addressed), problems 7.A.4.4: two-step equations, two-step inequalities, variable, rational numbers, solutions, reasonableness, results 7.G.1.1: similar figures, congruent figures 8 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map Vocabulary List Words students need to know to understand concept 6. Skills What students need to be able to do (verbs) Learning Activities / Lesson Plan Links Essential Experiences or Guided Practice 7. Assessments: Formative Assessments How will students and teacher know what students have learned so far? Differentiated Rubric Links / Attached Grade Level: 7th Course /Subject: Math MONTHLY TEMPLATE 7.G.3.3: perimeter, area, changes of scale 7.M.2.3: scale factors, ratios, proportions 7.D.1.6: ordered pairs, graph, data 7.D.2.4: technology, data sets, relationships, variables Change, coordinate graph, coordinate pair, dependent variable distance/time/rate of speed, equation (formula), income/cost/profit/, independent variable, pattern, relationship, rule, scale, table, variable, x-axis, y-axis, x-coordinate, y-coordinate, plot, point, range of values Complementary angles, corresponding angles, corresponding sides, equivalent ratios, image, ratio, rep-tile, scale factor, similar, supplementary angles, 7.N.1.3: use properties, explain, formulate, solve 7.N.2.3: calculate, solve 7.A.1.1: identify, continue 7.A.1.2: represent, recognize 7.A.1.5: graph, interpret 7.A.1.6: solve 7.A.2.1: write, evaluate, solve, graph, interpret 7.A.2.5: graph, identify 7.A.2.6: use letters, describe 7.A.3.1: create 7.A.3.2: understand, use coordinate plane 7.A.3.3: select, use model 7.A.4.1: use variables, write expressions 7.A.4.3: graph, interpret, solve 7.G.1.1: classify 7.G.3.3: determine 7.M.2.3: solve 7.D.1.6: identify, interpret 7.D.2.4: use technology, gather, display, identify Write one-step equations representing relationships between variables (CM2, Variables and Patterns, 3.1) Write rules and equations involving two-steps, and explore pattern of change reflected in an equation, table, and graph (CM2, Variables and Patterns, 3.2) Write rules and equations for revenue, expenses, and profit (CM2, Variables and Patterns, 3.3) Use the known size of a small object to estimate the unknown size of a larger object (CM2, Stretching and Shrinking, 1.1) Make similar figures and compare approximate measurements of corresponding parts in similar figures (CM2, Stretching and Shrinking, 1.2) Use percents as a way to describe change and make accurate comparisons of measurements of similar figures (CM2, Stretching and Shrinking, 1.3) Use algebraic rules to produce similar figures, contrast similar figures with non-similar figures (CM2, Stretching and Shrinking, 2.1) Understand the role of multiplication in similarity and understand the effect on the image if a number is added to the x- and y-coordinates (CM2, Stretching and Shrinking, 2.2) Investigate side lengths, angles, perimeters, and areas of similar triangles and rectangles, introduce Scale Factor (CM2, Stretching and Shrinking, 2.3) Check for understanding: Create table and graph for two sets of information, write a rule/equation to show the relationship between variables (CM2, Variables and Patterns, Partner Quiz) Essay: Explain what decisions need to be made to write an equation to represent a relationship between variables. (CM2, Variables and Patterns, Mathematical Reflections) Unit Review: Use understanding of variables and patterns. Looking Back and Looking Ahead (CM2, Variables and Patterns) Essay: When you enlarge or reduce a figure, what features stay the same, what features change? (CM2, Stretching and Shrinking, Mathematical Reflections) Check for understanding: Determine if two figures are similar. Find scale factor between two figures and use the scale factor to find corresponding side lengths. (CM2, Stretching and Shrinking, Check-UP 2) Essay: When a figure is transformed to make a similar figure, what does the scale factor tell you about how the figure changes? (CM2, Stretching, and Shrinking, Mathematical Reflections) 9 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map Summative Assessments How will students show that they have mastered the standard? Differentiated Rubric Links / Attached 8. Resources Links, Curriculum Frameworks, Other Websites Grade Level: 7th Course /Subject: Math MONTHLY TEMPLATE Quiz: Create table and graph for two sets of information, write a rule/equation to show the relationship between variables (CM2, Variables and Patterns, Partner Quiz) Quiz: Determine if two figures are similar. Find scale factor between two figures and use the scale factor to find corresponding side lengths. (CM2, Stretching and Shrinking, Check-UP 2) Looking back and ahead: Use understanding of variables and patterns. Looking Back and Looking Ahead (CM2, Variables and Patterns) Self Assessment: Explain what ideas you learned about variables and patterns and site evidence. (CM2, Variables and Patterns, Self Assessment) Unit Test: Create tables, graphs, and equations based on data. Analyze information in tables, graphs, and equations. (CM2, Variables and Patterns, Unit Test) Looking back and ahead: Use understanding of variables and patterns. Looking Back and Looking Ahead (CM2, Variables and Patterns) Unit Project: Enlarge or shrink a picture using coordinate graphing system and identify scale factor, compare a pair of corresponding angles, and compare two corresponding areas within the drawings. Write a report of findings. (CM2, Stretching and Shrinking, Unit Project) 7th Grade Teacher CD, http://www.phschool.com, http://connectedmath.msu.edu 10 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map 8 ESSENTIAL COMPONENTS 7.N.2.2 Convert terminating decimals into reduced fractions. 7.N.2.3 Calculate given 1. Performance Standards Grade Level: 7th Course /Subject: Math Month: November MONTHLY TEMPLATE Comparing and Scaling Strand: NUMBER AND OPERATIONS 5-8 Benchmark N.2: 7.N.2.3 Calculate given percentages of quantities and use them to solve problems (e.g., discounts of sales, interest earned, tips, markups, commission, profit, simple interest). 5-8 Benchmark N.3: 7.N.3.2 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications. 7.N.3.4 Calculate the percentage of increases and decreases of a quantity Strand: MEASUREMENT 5-8 Benchmark M.7: 7.M.1.1 Choose appropriate units of measure and ratios to recognize new equivalencies to solve problems. 7.M.1.5 Use measures expressed as rates and measures expressed as products to solve problems, check the units of solutions, and analyze the reasonableness of answers. 5-8 Benchmark M.2: 7.M.2.3 Solve problems involving scale factors, ratios, and proportions. How can quantities with different measurements be compared? 2. Essential Questions Questions that lead students to Big Ideas. Quantities with different measurements can be compared by using ratios, proportions, and percents. 3. Big Ideas Student answers to EQs that lead them to the Big Ideas 4. Cognitive Level Webb’s/Bloom’s Taxonomy Link Problem Solving Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and other contexts Apply and adapt a variety of appropriate strategies to solve problems, and Monitor and reflect on the process of problem solving. Reasoning and Proof Recognize reasoning and proof as fundamental aspects of mathematics, Make and investigate mathematical conjectures, Develop and evaluate mathematical arguments and proofs, and Select and use various types of reasoning and methods of proof. Communication Organize and consolidate their thinking through communication, Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, Analyze and evaluate the mathematical thinking and strategies of others, Use the language of mathematics to express mathematical ideas precisely, and Describe mathematical concepts using developmentally appropriate definitions. Connections Recognize and use connections among mathematical ideas, Understand how mathematical ideas interconnect and build on one another to produce a coherent whole, and Recognize and apply mathematics in contexts outside of mathematics. 11 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map 5. Content What students need to know (nouns) Grade Level: 7th Course /Subject: Math MONTHLY TEMPLATE Representation Create and use representations to organize, record, and communicate mathematical ideas, Select, apply, and translate among mathematical representations to solve problems, and Use representations to model and interpret physical, social, and mathematical phenomena. 7.N.2.3: percentage, quantities, discounts, interest, markups, commission, profit, simple interest 7.N.3.2: fractions, decimals, percents, representations, estimations, computation, application 7.N.3.4: percentage, increase, decrease, quantity 7.M.1.1: units of measure, equivalencies 7.M.1.5: measures, rates, products, units, reasonableness of answers 7.M.2.3: scale factors, ratios, proportions Rate, ratio, proportion, unit rate, scale/scaling factor/scale factor Vocabulary List Words students need to know to understand concept 6. Skills What students need to be able to do (verbs) Learning Activities / Lesson Plan Links Essential Experiences or Guided Practice 7. Assessments: Formative Assessments How will students and teacher know what students have learned so far? Differentiated Rubric Links / Attached Summative Assessments How will students show that they have mastered the standard? Differentiated Rubric Links / Attached 7.N.2.3: calculate, solve 7.N.3.2: convert, use representations 7.N.3.4: calculate percentage 7.M.1.1: choose unit, recognize equivalencies 7.M.1.5: use measures, check solution, analyze 7.M.2.3: solve Explore various strategies for presenting quantitative comparisons (CM2, Comparing and Scaling, 1.1) Analyze given comparative statements about quantities (CM2, Comparing and Scaling, 1.2) Analyze and create comparison statements from given data (CM2. Comparing and Scaling, 1.3) Make comparisons using the part-to-whole relationship in the form of fractions, decimals, and percents and informally explore, rates, ratios, and proportional reasoning (CM2, Comparing and Scaling, 2.1) Continue to work with ratio comparisons (CM2, Comparing and Scaling, 2.2) Find equivalent ratios and develop strategies for comparing ratios (CM2. Comparing and Scaling, 2.3) Examine and connect the idea of unit rates with ratios and linear relationships (CM2, Comparing and Scaling, 3.1) Further develop understanding of unit rates and how to compute and interpret them (CM2, Comparing and Scaling, 3.2) Relate unit rate to slope of a line and formalize the meaning of unit rate including strategies for computing unit rate (CM2. Comparing and Scaling, 3.3) Explore how division determines the label of the unit rate (miles per gallon/gallons per mile). (CM2, Comparing and Scaling, 3.4) Essay: Explain what you think each word means when it is used to make a comparison: ratio, percent, fraction, difference (CM2, Comparing and Scaling, Mathematical Reflections) Check for understanding: Use survey data to write mathematical comparison statements using ratios and percents, write equivalent ratios (CM2, Comparing and Scaling, Check-Up) Check for understanding: Use real-world data to solve problems involving unit rates (CM2, Comparing and Scaling, Partner Quiz) Essay: Describe the process for finding a unit rate and how to use unit rates to make comparisons (CM2, Comparing and Scaling, Mathematical Reflections) Summative Assessments will be done in December (CM2, Comparing and Scaling) Quiz: Use survey data to write mathematical comparison statements using ratios and percents, write equivalent ratios (CM2, Comparing and Scaling, CheckUp) Quiz: Use real-world data to solve problems involving unit rates (CM2, Comparing and Scaling, Partner Quiz) Chapter, section and unit tests (PH) Winter Middle School Short Cycle Assessment (MSSCA) = 39 Questions Key= NM State Math Standard (number of items on the MSSCA) Strand: Number and Operations = 12 questions 12 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map 8. Resources Links, Curriculum Frameworks, Other Websites Grade Level: 7th Course /Subject: Math 7.N.1.3 (2); 7.N.2.3 (3); 7.N.3.2 (5); 7.N.3.3 (1); 7.N.3.4 (1) Strand: Algebra = 7 questions 7.A.1.6 (1); 7.A.2.1 (5); 7.A 2.2 (1) Strand: Geometry = 12 questions 7.G.1.1 (4); 7.G.1.2 (1); 7.G.2.1 (1); 7.G. 3.1 (3); 7.G.4.1 (3) Strand: Measurement = 7 questions 7.M.1.1 (1); 7.M.2.2 (1); 7.M.2.3 (5) Strand: Data and Probability = 1 questions 7.D.1.13 (1) 7th Grade Teacher CD, http://www.phschool.com, http://connectedmath.msu.edu 13 – APS/Math 7 Curriculum Map/May 2008 DRAFT MONTHLY TEMPLATE APS District Curriculum Map 8 ESSENTIAL COMPONENTS 1. Performance Standards Grade Level: 7th Course /Subject: Math MONTHLY TEMPLATE Month: December Comparing and Scaling & Stretching and Shrinking Strand: NUMBER AND OPERATIONS 5-8 Benchmark N.2: 7.N.2.2 Convert terminating decimals into reduced fractions. 7.N.2.3 Calculate given percentages of quantities and use them to solve problems (e.g., discounts of sales, interest earned, tips, markups, commission, profit, simple interest). 5-8 Benchmark N.3: 7.N.3.2 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications. 7.N.3.4 Calculate the percentage of increases and decreases of a quantity. Strand: GEOMETRY 5-8 Benchmark G.1: 7.G.1.1 Classify geometric figures as similar or congruent. 7.G.1.5 Use properties to classify solids including pyramids, cones, prisms, and cylinders. 5-8 Benchmark G.2: 7.G.2.1 Construct and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine the image under translations and reflections. Strand: MEASUREMENT 5-8 Benchmark M.1: 7.M.1.1 Choose appropriate units of measure and ratios to recognize new equivalencies to solve problems. 7.M.1.2 Select and use appropriate size and type of unit for a given measurement situation. 7.M.1.3 Compare masses, weights, capacities, geometric measures, times, and temperatures within measurement systems. 7.M.1.4 Approximate the relationship between standard and metric measurement systems (e.g. inches and centimeters, pounds and kilograms, quarts and liters) 7.M.1.5 Use measures expressed as rates and measures expressed as products to solve problems, check the units of solutions, and analyze the reasonableness of answers. 5-8 Benchmark M.2: 7.M.2.3 Solve problems involving scale factors, ratios, and proportions. How can proportions help us solve problems? (Comparing and Scaling) 2. Essential Questions Questions that lead students to Big Ideas. 3. Big Ideas Student answers to EQs that lead them to the Big Ideas 4. Cognitive Level Webb’s/Bloom’s Taxonomy Link How can we use geometric similarity to solve problems? (Stretching and Shrinking) You can use proportions to set up equations and solve for missing values. (C and S) You can also use proportions for indirect measurements, estimating, predicting and probability. You can use similar triangles, rectangles and their corresponding angles to find missing measurements to solve problems. (S and S) Problem Solving Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and other contexts Apply and adapt a variety of appropriate strategies to solve problems, and Monitor and reflect on the process of problem solving. Reasoning and Proof Recognize reasoning and proof as fundamental aspects of mathematics, Make and investigate mathematical conjectures, Develop and evaluate mathematical arguments and proofs, and 14 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map 5. Content What students need to know (nouns) Vocabulary List Words students need to know to understand concept 6. Skills What students need to be able to do (verbs) Grade Level: 7th Course /Subject: Math MONTHLY TEMPLATE Select and use various types of reasoning and methods of proof. Communication Organize and consolidate their thinking through communication, Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, Analyze and evaluate the mathematical thinking and strategies of others, Use the language of mathematics to express mathematical ideas precisely, and Describe mathematical concepts using developmentally appropriate definitions. Connections Recognize and use connections among mathematical ideas, Understand how mathematical ideas interconnect and build on one another to produce a coherent whole, and Recognize and apply mathematics in contexts outside of mathematics. Representation Create and use representations to organize, record, and communicate mathematical ideas, Select, apply, and translate among mathematical representations to solve problems, and Use representations to model and interpret physical, social, and mathematical phenomena. 7.N.2.2: terminating decimal, reduced fraction 7.N.2.3: percentage, quantities, discounts, interest, tips, markups, commission, profit, simple interest 7.N.3.2: fractions, decimals, percents, representations, estimations, computations, applications 7.N.3.4: percentage, increase, decrease, quantity 7.G.1.1: similar figures, congruent figures 7.G.1.5: properties, solids, pyramids, cones, prisms, cylinders 7.G.2.1: coordinate graph, figures, length, image, translations, reflections 7.M.1.1: units of measure, ratios, equivalencies 7.M.1.2: appropriate unit 7.M.1.3: masses, weights, capacities, geometric measures, times, temperatures, measurement system 7.M.1.4: standard measurement system, metric measurement system 7.M.1.5: measures, rates, products, units of solution, reasonableness of answer 7.M.2.3: scale factors, ratios, proportions Rate, ratio, proportion, unit rate, scale/scaling factor/scale factor (C and S) Complementary angles, corresponding angles, corresponding sides, equivalent ratios, image, ratio, scale factor, similar supplementary angles (S and S) Three-dimensional figures, face, edge, base, pyramid, cylinder, cone, sphere, translation, reflection (Prentice Hall Supplemental Activities) 7.N.2.2: convert 7.N.2.3: calculate, solve 7.N.3.2: convert, use representations 7.N.3.4: calculate 7.G.1.1: classify 7.G.1.5: use properties 7.G.2.1: construct, use coordinate graph 7.M.1.1: choose unit, recognize equivalencies 7.M.1.2: select, use appropriate unit 7.M.1.3: compare 7.M.1.4: approximate 7.M.1.5: use measures 7.M.2.3: solve 15 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map Learning Activities / Lesson Plan Links Essential Experiences or Guided Practice Grade Level: 7th Course /Subject: Math MONTHLY TEMPLATE Set up and solve proportions that arise in applications (CM2, Comparing & Scaling, 4.1, 4.2) Choose strategies in solving problems that require proportional reasoning (CM2, Comparing & Scaling, 4.3) Apply knowledge of similar triangles and develop a technique for indirect measurement (CM2, Stretching & Shrinking, 5.1, 5.2) Apply knowledge of similar triangles and similar quadrilaterals and develop a technique for indirect measurement (CM2, Stretching & Shrinking, 5.3) Graph and write rules for translations (Prentice Hall Course 2, 10-5) * Identify lines of symmetry and graph reflections (PH C2, 10-6) * Choose appropriate units to measure different objects (PH C2, 3-7a Activity Lab) * Estimate equivalent measures in the metric system and the customary system (PH C2, 3-7b Activity Lab) * Classify and draw 3-dimensional figures (PH C2, 8-8) * 7. Assessments: Essay: Write a problem that can be solved using proportions and explain problem-solving procedures. (CM2, Comparing & Scaling, Mathematical Reflections 4) Check for understandings Formative Assessments How will students and teacher know what students have learned so far? Differentiated Rubric Links / Attached Summative Assessments How will students show that they have mastered the standard? Differentiated Rubric Links / Attached 8. Resources Links, Curriculum Frameworks, Other Websites Unit Test: Use ratios and proportions to solve problems. (CM2, Comparing & Scaling, Unit Test) Self-Assessment: Explain what you have learned about ratios and proportions and cite evidence; include what you have struggled with. (CM2, Comparing & Scaling, Self-Assessment) Performance Assessment: Unit project was assigned in October to be completed in December (Stretching & Shrinking, CM2, Unit Project) Chapter, section and unit tests (PH) PBA 7th Grade Teacher CD, http://www.phschool.com, http://connectedmath.msu.edu 16 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map 8 ESSENTIAL COMPONENTS 1. Performance Standards Grade Level: 7th Course /Subject: Math Month: January MONTHLY TEMPLATE Data Distributions Strand: DATA ANALYSIS AND PROBABILITY 5-8 Benchmark D.1: 7.D.1.1 Describe how data representations influences interpretation. 7.D.1.2 Select and use appropriate representation for presenting collected data and justify the selection. 7.D.1.3 Use measures of central tendency and spread to describe a set of data. 7.D.1.4 Choose between median and mode to describe a set of data and justify the choice for a particular situation. 7.D.1.5 Determine the quartiles of a data set. 7.D.1.7 Use various scales and formats to display the same data set. 7.D.1.8 Identify and explain the misleading representations of data. 7.D.1.10 Compute the minimum, lower quartile, median, upper quartile, and maximum of a data set. 7.D.1.11 Identify and explain the effects of scale and/or interval changes on graphs of whole number data sets. 7.D.1.12 Use and explain sampling techniques (e.g., observations, surveys, and random sampling) for gathering data. 7.D.1.13 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, and selecting, collecting, and displaying appropriate data to address the problem. 5-8 Benchmark D.2: 7.D.2.1 Choose and justify appropriate measures of central tendencies (e.g., mean, median, mode, range) to describe given or derived data. 7.D.2.2 Know various ways to display data sets (e.g., stem and leaf plot, box and whisker plot, scatter plots) and use these forms to display a single set of data or to compare two sets of data. 7.D.2.3 Use the analysis of data to make convincing arguments. 7.D.2.5 Use data samples of population and describe the characteristics and limitations of the sample. 7.D.2.6 Identify data that represent sampling errors and explain why the sample and the display might be biased. 7.D.2.7 Identify claims based on statistical data and evaluate the validity of the claims. 5-8 Benchmark D.3: 7.D.3.1 Formulate and justify mathematical conjectures based on data and a general description of the mathematical question or problem posed. 7.D.3.2 Analyze data to make accurate inferences, predictions, and to develop convincing arguments from data displayed in a variety of forms. 7.D.3.3 Approximate a line of best fit for a data set in a scatter plot form and make predictions using the simple equation of that line. 2. Essential Questions Questions that lead students to Big Ideas. 3. Big Ideas Student answers to EQs that lead them to the Big Ideas How would you analyze and interpret data? How would you use data to formulate conjectures and predict future situations? How would you identify appropriate displays for data sets? You would analyze and interpret data by considering several factors, including: Measures of center (mean, median, mode, range,) Upper and lower quartiles Sampling techniques (variability, bias, and randomness) Distribution of data Scale and interval changes Relevancy of data You can use statistical investigations to generate questions which help determine strategies for analyzing, justifying, and predicting situations. Measures of Central Tendency are used to analyze different graphical representations. You can consider the measure of central tendency and the type of data to determine the appropriate display model (line plots, scatter plots, histograms, bar graphs, and line graphs). 17 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map 4. Cognitive Level Webb’s/Bloom’s Taxonomy Link 5. Content What students need to know (nouns) Grade Level: 7th Course /Subject: Math MONTHLY TEMPLATE Problem Solving Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and other contexts Apply and adapt a variety of appropriate strategies to solve problems, and Monitor and reflect on the process of problem solving. Reasoning and Proof Recognize reasoning and proof as fundamental aspects of mathematics, Make and investigate mathematical conjectures, Develop and evaluate mathematical arguments and proofs, and Select and use various types of reasoning and methods of proof. Communication Organize and consolidate their thinking through communication, Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, Analyze and evaluate the mathematical thinking and strategies of others, Use the language of mathematics to express mathematical ideas precisely, and Describe mathematical concepts using developmentally appropriate definitions. Connections Recognize and use connections among mathematical ideas, Understand how mathematical ideas interconnect and build on one another to produce a coherent whole, and Recognize and apply mathematics in contexts outside of mathematics. Representation Create and use representations to organize, record, and communicate mathematical ideas, Select, apply, and translate among mathematical representations to solve problems, and Use representations to model and interpret physical, social, and mathematical phenomena. 7.D.1.1: data representations, interpretation 7.D.1.2: representations, collected data 7.D.1.3: measures of central tendency, spread 7.D.1.4: median, mode, set of data 7.D.1.5: quartiles 7.D.1.7: scales, formats, data set 7.D.1.8: misleading representation, data 7.D.1.10: minimum, lower quartile, median, upper quartile, maximum, data set 7.D.1.11: effect of scale, interval change, graphs 7.D.1.12: sampling techniques, observations, surveys, random sampling, data 7.D.1.13: relationships, relevant information, irrelevant information, missing information 7.D.2.1: measures of central tendency, mean, median, mode, range, derived data, given data 7.D.2.2: data sets, stem-and-leaf plots, box-and-whisker plots, scatter plots 7.D.2.3: analysis, data, arguments 7.D.2.5: data samples of populations, characteristics, limitations 7.D.2.6: sampling errors sample, bias 7.D.2.7: claims, statistical data, validity of claims 7.D.3.1: mathematical conjectures, general description, mathematical question, mathematical problem 7.D.3.2: inference, prediction, argument 7.D.3.3: line of best fit, scatter plot, predictions, simple equation 18 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map Vocabulary List Words students need to know to understand concept 6. Skills What students need to be able to do (verbs) Grade Level: 7th Course /Subject: Math 7.D.1.1: describe 7.D.1.2: select, use representations 7.D.1.3: use measure of central tendency, present data, justify 7.D.1.4: choose, describe, justify 7.D.1.5: determine 7.D.1.7: scales, formats, data set 7.D.1.8: misleading representation, data 7.D.1.10: compute 7.D.1.11: identify, explain 7.D.1.12: use sampling techniques, explain 7.D.1.13: analyze, distinguish, identify, select, collect, display 7.D.2.1: choose, justify, describe 7.D.2.2: know, use displays 7.D.2.3: use analysis of data, make arguments 7.D.2.5: use data samples of populations, describe 7.D.2.6: identify, represent, explain 7.D.2.7: identify claims, evaluate 7.D.3.1: formulate, justify 7.D.3.2: analyze data, make inferences, make predictions, develop arguments Learning Activities / Lesson Plan Links Essential Experiences or Guided Practice MONTHLY TEMPLATE Attribute, counts, distribution, measures, measures of center, ordered value bar graph, range, outlier, value of an attribute, variability of a set of numerical data, box –and-whisker-plot, quartiles, line of best fit, quartile, stem-and-leaf-plot, histogram, scatter plot, random sample, biased question, population 7.D.3.3: approximate line of best fit, make predictions Examine data to describe variability and make predictions (CM2, Data Distributions, 1.1) Represent data as counts and percents (CM2, Data Distributions, 1.2) Use measurements to describe variability in data (CM2, Data Distributions, 1.3) Analyzing two types of variability (CM2, Data Distributions, 1.4) Use line of best fit in a scatter plot to make predictions (CM2, Data Distributions, Investigation 1 Ace question 22) Explore mean in terms of equal shares (CM2, Data Distributions, 2.1) Explore mean in terms as a balance point (CM2, Data Distributions, 2.2) Explore displays in terms of the measures of central tendencies (CM2, Data Distributions, 2.3) Explore how change effects the measures of central of tendencies (CM2, Data Distributions, 2.4) Use box and whisker plots to show data (Prentice Hall Course 2, 1-10b) Represent data using frequency tables, line plots, and histograms (Prentice Hall Course 2, 11-1) Interpret bar and line graphs (PH C2, 11-2) Represent and interpret data using stem and leaf plots (PH C2, 11-3) Choose the best data display (PH C2, 11-3b) Identify random samples and write survey questions (PH C2, 11-4) Identify misleading graphs and statistics (PH C2, 11-6) Draw and interpret scatter plots (PH C2, 11-7) Collecting two-variable data (PH C2, 11-7a) 19 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map 7. Assessments: Formative Assessments How will students and teacher know what students have learned so far? Differentiated Rubric Links / Attached Grade Level: 7th Course /Subject: Math Check for Understanding: Create graphs to display data (PH C2, Check for Understanding 1 11-1 through 11-3, p. 549) Quiz: Central tendencies are used to analyze data sets (CM2, Data Distributions, Check-up 1) Summative Assessments How will students show that they have mastered the standard? Differentiated Rubric Links / Attached 8. Resources Links, Curriculum Frameworks, Other Websites MONTHLY TEMPLATE Essay: Explain how to interpret central tendencies to summarize data (CM2, Data Distributions, Mathematical Reflection #2 questions 1,2,3,) Check For Understanding: Central tendencies are used to analyze data sets (CM2, Data Distributions, Check-up 1) Quiz: Create graphs to display data (PH C2, Check for Understanding 1 11-1 through 11-3, p. 549) Quiz: Create graphs to display data (PH C2, Checkpoint Quiz 1 11-1 through 11-3, p. 549) Creating multiple displays of data, determine measures of center, (PH C2, Chapter 11 Test (Teacher Resource) PBA for different models 6th Grade Teacher CD, http://www.phschool.com, http://connectedmath.msu.edu 20 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map 8 ESSENTIAL COMPONENTS 1. Performance Standards Grade Level: 7th Course /Subject: Math Month: February MONTHLY TEMPLATE What do you Expect? Strand: DATA ANALYSIS AND PROBABILITY 5-8 Benchmark D.1: 7.D.1.9 Collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set. 5-8 Benchmark D.2: 7.D.2.7 Identify claims based on statistical data and evaluate the validity of the claims. 5-8 Benchmark D.4: 7.D.4.1 Determine the probability of a compound event composed of two independent events. 7.D.4.2 Identify examples of events having the probability of one or zero. 7.D.4.3 Describe the probability of events using fractions, decimals, and percents. 7.D.4.4 Express probability as a fraction, zero, or one. 7.D.4.5 Use probability to generate convincing arguments, draw conclusions, and make decisions in a variety of situations. 7.D.4.6 Make predictions based on theoretical probabilities of compound events. 7.D.4.7 Determine the probability of a simple event or a compound event composed of a simple, independent events. Strand: NUMBER AND OPERATIONS 5-8 Benchmark N.2: 7.N.2.7 Find square roots of perfect whole number squares 7.N.2.8 Simplify and evaluate positive rational numbers raised to positive whole number powers. 5-8 Benchmark N.3: 7.N.3.3 Read, write, and compare rational numbers in scientific notation (e.g., positive and negative powers of 10) with approximate numbers using scientific notation. 7.N.3.6 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer. Strand: ALGEBRA 5-8 Benchmark A.4: 7.A.4.2 Interpret and evaluate expressions involving integer powers and simple roots as they relate to change. Strand: GEOMETRY 5-8 Benchmark G.1: 7.G.1.3 Explain and use the Pythagorean Theorem. How and when would you use probability to make predictions? 2. Essential Questions Questions that lead students to Big Ideas. How can you use solve problems using the Pythagorean Theorem? Gathering, analyzing and displaying data helps predict future events. You can use experimental and/or theoretical probability to make predictions. 3. Big Ideas Student answers to EQs that lead them to the Big Ideas 4. Cognitive Level Webb’s/Bloom’s Taxonomy Link The Pythagorean Theorem is used to find side lengths of right triangles. Problem Solving Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and other contexts Apply and adapt a variety of appropriate strategies to solve problems, and Monitor and reflect on the process of problem solving. Reasoning and Proof 21 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map 5. Content What students need to know (nouns) Grade Level: 7th Course /Subject: Math Probability, equally likely, theoretical probability, experimental probability, fair game, outcomes, random events Vocabulary List Words students need to know to understand concept 6. Skills What students need to be able to do (verbs) MONTHLY TEMPLATE Recognize reasoning and proof as fundamental aspects of mathematics, Make and investigate mathematical conjectures, Develop and evaluate mathematical arguments and proofs, and Select and use various types of reasoning and methods of proof. Communication Organize and consolidate their thinking through communication, Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, Analyze and evaluate the mathematical thinking and strategies of others, Use the language of mathematics to express mathematical ideas precisely, and Describe mathematical concepts using developmentally appropriate definitions. Connections Recognize and use connections among mathematical ideas, Understand how mathematical ideas interconnect and build on one another to produce a coherent whole, and Recognize and apply mathematics in contexts outside of mathematics. Representation Create and use representations to organize, record, and communicate mathematical ideas, Select, apply, and translate among mathematical representations to solve problems, and Use representations to model and interpret physical, social, and mathematical phenomena. 7.D.1.9: data sets, variable, relationships 7.D.2.7: claims, statistical data, validity of claims 7.D.4.1: probability, compound event, independent events 7.D.4.2: examples, probability of one, probability of zero 7.D.4.3: probability, fractions, decimals, percents 7.D.4.5: probability, argument, conclusions, decision 7.D.4.6: prediction, threoretical probability, compound event 7.D.4.7: probability, simple event, compound event, simple, independent events 7.N.2.1: rational numbers, integers, fractions, terminating decimals, positive rational numbers, whole-number powers 7.N.2.7: square roots, perfect whole number squares 7.N.2.8: positive rational numbers, positive whole-number powers 7.N.3.6: relationship, power, root, perfect square integer 7.A.1.4: expressions, integer powers, simple roots 7.A.4.2: expressions, powers, simple roots, change 7.G.1.3: Pythagorean theorem scientific notation, perfect square, square root, right triangle, hypotenuse, legs, Pythagorean Theorem 7.D.1.9: collect, organize, represent, identify 7.D.2.7: identify, evaluate 7.D.4.1: determine probability 7.D.4.2: identify 7.D.4.3: describe 7.D.4.5: use probability, generate arguments, draw conclusions, make decisions 7.D.4.6: make predictions 7.D.4.7: determine probability 7.N.2.1: add, subtract, multiply, divide, take to powers 7.N.2.7: find square roots 22 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map Learning Activities / Lesson Plan Links Essential Experiences or Guided Practice Grade Level: 7th Course /Subject: Math MONTHLY TEMPLATE 7.N.2.8: simplify 7.N.3.6: use relationships, extract roots 7.A.1.4: interpret, evaluate 7.A.4.2: interpret, evaluate 7.G.1.3: explain, use Pythagorean theorem Playing spinner game and decide on fairness (CM2, What Do you Expect 1.1) Playing bucket- block game and determine long term average results (CM2, What Do You Expect 1.2) Playing dice game and make predictions ( CM2, What Do You Expect 1.3) Analyzing probabilities using area models( CM2, What Do You Expect 2.1) Design simulations to determine experimental probabilities( CM2, What Do You Expect 2.2) Use area models to find theoretical probabilities in a novel context( CM2, What Do You Expect 2.3) Find the probability and the complement of an event (Prentice Hall Course 2, 12-1) Write integers in scientific notation and standard form (Prentice Hall, Mathematics Course 2, 2-8 and extension) Find and estimate square roots (Prentice Hall, Mathematics Course 2, 8-6) Discovering relationship between side lengths of right triangles (Prentice Hall, Mathematics Course 2, 8-7a) Use the Pythagorean Theorem to solve real-world problems. (Prentice Hall, Mathematics Course 2, 8-7) 7. Assessments: Formative Assessments How will students and teacher know what students have learned so far? Differentiated Rubric Links / Attached Summative Assessments How will students show that they have mastered the standard? Differentiated Rubric Links / Attached 8. Resources Links, Curriculum Frameworks, Other Websites Check for understanding :Use Theoretical probability to draw conclusions- tree diagram(CM2What Do You Expect: Check-Up 1) Check for understanding : Use Theoretical Probability to draw conclusions- tree diagram and area model ( CM2 What Do You Expect: Partner Quiz) Essay: Compare Experimental and Theoretical Probabilities ( CM2 Mathematical Reflection 1a) Self Assessment: Understanding of Experimental/ Theoretical Probability to draw conclusions ( CM2 What Do You Expect Self Assessment) Unit Test: Analyzing Theoretical Probability to draw conclusions (CM2, What Do You Expect, Unit Test questions 1-4) Performance Assessment: Design a Carnival Game (CM2, What Do You Expect, Unit Project) Quiz :Use Theoretical probability to draw conclusions- tree diagram(CM2What Do You Expect: Check-Up 1) Quiz : Use Theoretical Probability to draw conclusions- tree diagram and area model ( CM2 What Do You Expect: Partner Quiz) PBA for different models Mini-Unit Test: scientific notation, perfect squares, square roots, solve problems with Pythagorean Theorem (Prentice Hall, Mathematics Course 2, Chapter 8 Test, 9-16, 22-26, Chapter 2 Test, 51 & 52) 7th Grade Teacher CD, http://www.phschool.com, http://connectedmath.msu.edu 23 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map 8 ESSENTIAL COMPONENTS 1. Performance Standards Grade Level: Month: March 7th Course /Subject: Math MONTHLY TEMPLATE Accentuate the Negative Strand: NUMBER AND OPERATIONS 5-8 Benchmark N.2: 7.N.1.2 Illustrate the relationships among natural (i.e., counting) numbers, whole numbers, integers, rational and irrational numbers. 7.N.2.1 Add, subtract, multiply, and divide rational numbers (e.g., integers, fractions, terminating decimals) and take positive rational numbers to wholenumber powers. 7.N.2.9 Solve addition, subtraction, multiplication, and division problems that use positive and negative integers and combinations of these operations. What strategies or models can be used to develop an algorithm for adding or subtracting integers? 2. Essential Questions Questions that lead students to Big Ideas. You can use chip models and number line models to develop an algorithm to add and subtract integers. 3. Big Ideas Student answers to EQs that lead them to the Big Ideas 4. Cognitive Level Webb’s/Bloom’s Taxonomy Link Problem Solving Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and other contexts Apply and adapt a variety of appropriate strategies to solve problems, and Monitor and reflect on the process of problem solving. Reasoning and Proof Recognize reasoning and proof as fundamental aspects of mathematics, Make and investigate mathematical conjectures, Develop and evaluate mathematical arguments and proofs, and Select and use various types of reasoning and methods of proof. Communication Organize and consolidate their thinking through communication, Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, Analyze and evaluate the mathematical thinking and strategies of others, Use the language of mathematics to express mathematical ideas precisely, and Describe mathematical concepts using developmentally appropriate definitions. Connections Recognize and use connections among mathematical ideas, Understand how mathematical ideas interconnect and build on one another to produce a coherent whole, and Recognize and apply mathematics in contexts outside of mathematics. Representation Create and use representations to organize, record, and communicate mathematical ideas, Select, apply, and translate among mathematical representations to solve problems, and Use representations to model and interpret physical, social, and mathematical phenomena. 24 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map 5. Content What students need to know (nouns) Grade Level: 7th Course /Subject: Math MONTHLY TEMPLATE 7.N.1.2: relationship, natural (counting) number, whole number, integer, rational numbers 7.N.2.1: integers 7.N.2.9: addition, subtraction, positive integer, negative integer Negative numbers, positive numbers, opposites, integer, rational numbers, absolute value Vocabulary List Words students need to know to understand concept 6. Skills What students need to be able to do (verbs) Learning Activities / Lesson Plan Links Essential Experiences or Guided Practice 7.N.1.2: illustrate 7.N.2.1: add, subtract 7.N.2.9: solve Interpret and write mathematical sentences involving integers (CM2, Accentuate the Negative, 1.1) Locate and compare integers on a number line; find opposites (additive inverses) (CM2, Accentuate the Negative, 1.2) Develop and use number line model for adding and subtracting integers (CM2, Accentuate the Negative, 1.3) Develop and use chip model for adding and subtracting integers (CM2, Accentuate the Negative, 1.4) Essay: What does comparing locations of numbers on a number line tell you about the numbers? (CM2, Accentuate the Negative, Mathematical Reflections 1) 7. Assessments: Formative Assessments How will students and teacher know what students have learned so far? Differentiated Rubric Links / Attached NO Summative Assessment at this time. Summative Assessments How will students show that they have mastered the standard? Differentiated Rubric Links / Attached 8. Resources Links, Curriculum Frameworks, Other Websites 6th Grade Teacher CD, http://www.phschool.com, http://connectedmath.msu.edu 25 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map 8 ESSENTIAL COMPONENTS 1. Performance Standards Grade Level: 7th Course /Subject: Math Month: April MONTHLY TEMPLATE Accentuate the Negative Strand: NUMBER AND OPERATIONS 5-8 Benchmark N.1: 7.N.1.1 Determine the absolute value of rational numbers. 7.N.1.2 Illustrate the relationships among natural (i.e., counting) numbers, whole numbers, integers, rational and irrational numbers. 7.N.1.3 Use properties of the real-number system to explain reasoning and to formulate and solve real-world problems. 7.N.1.5 Simplify numerical expressions using order of operations. 5-8 Benchmark N.2: 7.N.2.1 Add, subtract, multiply, and divide rational numbers (e.g., integers, fractions, terminating decimals) and take positive rational numbers to wholenumber powers. 7.N.2.3 Calculate given percentages of quantities and use them to solve problems (e.g., discounts of sales, interest earned, tips, markups, commission, profit, simple interest). 7.N.2.4 Add or subtract fractions with unlike denominators. 7.N.2.6 Understand the meaning of the absolute value of a number: a. interpret the absolute value as the distance of the number from zero on a number line b. determine the absolute value of real numbers 7.N.2.9 Solve addition, subtraction, multiplication, and division problems that use positive and negative integers and combinations of these operations. 5-8 Benchmark N.3: 7.N.3.1 Use estimation to check reasonableness of results, and use this information to make predictions in situations involving rational numbers, pi, and simple algebraic equations. 7.N.3.2 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications. 7.N.3.5 Add or subtract fractions with unlike denominators. Strand: ALGEBRA 5-8 Benchmark A.1: 7.A.1.3 Simplify numerical expressions by applying properties of rational numbers, and justify the process used. 5-8 Benchmark A.2: 7.A.2.3 Use the order of operations to evaluate algebraic expressions. 7.A.2.4 Simplify numerical expressions by applying properties of rational numbers. What strategies or models can be used to develop an algorithm for adding, subtracting, multiplying and dividing integers 2. Essential Questions Questions that lead students to Big Ideas. 3. Big Ideas Student answers to EQs that lead them to the Big Ideas 4. Cognitive Level Webb’s/Bloom’s Taxonomy Link You can use models (chips, coordinate graphs), patterns, relationships between operations, properties, number lines to develop algorithms to add, subtract, multiply, or divide integers. Problem Solving Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and other contexts Apply and adapt a variety of appropriate strategies to solve problems, and Monitor and reflect on the process of problem solving. 26 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map 5. Content What students need to know (nouns) Vocabulary List Words students need to know to understand concept 6. Skills What students need to be able to do (verbs) Grade Level: 7th Course /Subject: Math MONTHLY TEMPLATE Reasoning and Proof Recognize reasoning and proof as fundamental aspects of mathematics, Make and investigate mathematical conjectures, Develop and evaluate mathematical arguments and proofs, and Select and use various types of reasoning and methods of proof. Communication Organize and consolidate their thinking through communication, Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, Analyze and evaluate the mathematical thinking and strategies of others, Use the language of mathematics to express mathematical ideas precisely, and Describe mathematical concepts using developmentally appropriate definitions. Connections Recognize and use connections among mathematical ideas, Understand how mathematical ideas interconnect and build on one another to produce a coherent whole, and Recognize and apply mathematics in contexts outside of mathematics. Representation Create and use representations to organize, record, and communicate mathematical ideas, Select, apply, and translate among mathematical representations to solve problems, and Use representations to model and interpret physical, social, and mathematical phenomena. 7.N.1.1: absolute value, rational number 7.N.1.2: relationship, natural (counting) numbers, whole numbers, integers, rational numbers, irrational numbers 7.N.1.3: properties, real-number system, reasoning, real-world problems 7.N.1.5: numerical expressions, order of operations 7.N.2.1: rational numbers, integers, fractions, terminating decimals, positive rational numbers, whole-number powers 7.N.2.3: percentages, quantities, discounts, interest, tips, markups, commission, profit, simple interest 7.N.2.4; 7.N.3.5: fractions, unlike denominators 7.N.2.6: absolute value, distance, number line, real numbers 7.N.2 9: addition, subtraction, multiplication, division, integers, combinations of operations 7.N.3.1: estimation, reasonableness of results, predictions, rational numbers, simple algebraic equations 7.N.3.2: fractions, decimals, percents, representations, estimations, computations, applications 7.A.1.3: numerical expressions, properties, rational numbers, process 7.A.2.3: order of operations, algebraic expressions 7.A.2.4: numerical expressions, properties, rational numbers Commutative property, integer, negative number, positive number, opposites, rational number, absolute value, additive inverse, associative property, expanding, factoring, quadrants I, II, III, IV 7.N.1.1: determine 7.N.1.2: illustrate 7.N.1.3: use properties, explain, solve 7.N.1.5: simplify 7.N.2.1: add, subtract, multiply, divide 7.N.2.3: calculate percentages 7.N.2.4; 7.N.3.5: add, subtract fractions 7.N.2.6: understand, interpret, determine 7.N.2 9: solve 7.N.3.1: use estimation, make predictions, 7.N.3.2: convert, use representations 27 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map Learning Activities / Lesson Plan Links Essential Experiences or Guided Practice 7. Assessments: Formative Assessments How will students and teacher know what students have learned so far? Differentiated Rubric Links / Attached Summative Assessments How will students show that they have mastered the standard? Differentiated Rubric Links / Attached 8. Resources Links, Curriculum Frameworks, Other Websites Grade Level: 7th Course /Subject: Math MONTHLY TEMPLATE 7.A.1.3: simplify, apply 7.A.2.3: use order of operations 7.A.2.4: simplify Develop algorithm for adding integers; use models and properties of addition (CM2, Accentuate the Negative, 2.1) – The opportunity to review and practice Adding Fractions Problem B.4b and B.4c and D.2 Develop algorithm for subtracting integers; use models (CM2, Accentuate the Negative, 2.2) – The opportunity to review and practice Subtracting Fractions Problem A.5.b, A.5.c, A.5.d Use addition and subtraction algorithms to solve problems with integers; use relationship between addition and subtraction of integers to solve problems (CM2, Accentuate the Negative, 2.3, 2.4) Graph integers on all four quadrants of the coordinate plane (CM2, Accentuate the Negative, 2.5) Use models to develop relationship between multiplication and repeated addition of integers; develop algorithm for multiplying with integers (CM2, Accentuate the Negative, 3.1) Identify and use number patters to confirm multiplication algorithm (CM2, Accentuate the Negative, 3.2) Use relationship between multiplication and division (fact families) to understand division of integers; solve multiplication and division problems with integers; develop algorithm for division of integers (CM2, Accentuate the Negative, 3.3) Develop skills with multiplication and division of integers (CM2, Accentuate the Negative, 3.4) Check for understanding: locate rational numbers on a number line, add and subtract integers, solve problems, write expressions for addition and subtraction situations, complete table (CM2, Accentuate the Negative, Partner Quiz) Check for understanding: add, subtract, multiply, and divide integers, solve problems, write expressions for addition, subtraction, multiplication, and division situations (CM2, Accentuate the Negative, Check-Up) Essay: Describe a procedure for adding and subtracting integers. (CM2, Accentuate the Negative, Mathematical Reflections 2) Essay: Describe a procedure for multiplying and dividing integers. (CM2, Accentuate the Negative, Mathematical Reflections 3) Quiz: locate rational numbers on a number line, add and subtract integers, solve problems, write expressions for addition and subtraction situations, complete table (CM2, Accentuate the Negative, Partner Quiz) Quiz: add, subtract, multiply, and divide integers, solve problems, write expressions for addition, subtraction, multiplication, and division situations (CM2, Accentuate the Negative, Check-Up) PBA for different models Spring Middle School Short Cycle Assessment (MSSCA) = 41 Questions Key= NM State Math Standard (number of items on the MSSCA) Strand: Number and Operations = 11 questions 7.N1.4 (1); 7.N.2.1 (3); 7.N.2.5 (1); 7.N.2.9 (6) Strand: Algebra = 11 questions 7.A.1.2 (3); 7.A.1.3 (1); 7.A.2.3 (2); 7.A.2.4 (5) Strand: Geometry = 1 questions 7.G.1.3 (1) Strand: Measurement = 0 questions Strand: Data and Probability = 18 questions 7.D.1.2 (1); 7.D.1.3 (2); 7.D.1.4 (2); 7.D.1.6 (1); 7.D.2.1 (3); 7.D.2.3 (1); 7.D.4.6 (4); 7.D.4.7 (2) 7th Grade Teacher CD, http://www.phschool.com, http://connectedmath.msu.edu 28 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map 8 ESSENTIAL COMPONENTS 1. Performance Standards Grade Level: 7th Course /Subject: Math Month: May MONTHLY TEMPLATE Accentuate the Negative Strand: NUMBER AND OPERATIONS 5-8 Benchmark N.1: 7.N.1.1 Determine the absolute value of rational numbers. 7.N.1.2 Illustrate the relationships among natural (i.e., counting) numbers, whole numbers, integers, rational and irrational numbers. 7.N.1.4 Read, write, and compare rational numbers in scientific notation (e.g., positive and negative powers of 10) with approximate numbers using scientific notation. 7.N.1.5 Simplify numerical expressions using order of operations. 5-8 Benchmark N.2: 7.N.2.1 Add, subtract, multiply, and divide rational numbers (e.g., integers, fractions, terminating decimals) and take positive rational numbers to wholenumber powers. 7.N.2.6 Understand the meaning of the absolute value of a number: c. interpret the absolute value as the distance of the number from zero on a number line d. determine the absolute value of real numbers 7.N.2.9 Solve addition, subtraction, multiplication, and division problems that use positive and negative integers and combinations of these operations. Strand: ALGEBRA 5-8 Benchmark A.1: 7.A.1.3 Simplify numerical expressions by applying properties of rational numbers, and justify the process used. 7.A.1.4 Interpret and evaluate expressions involving integer powers and simple roots. 5-8 Benchmark A.2: 7.A.2.3 Use the order of operations to evaluate algebraic expressions. 7.A.2.4 Simplify numerical expressions by applying properties of rational numbers. How would you simplify expressions when solving problems? 2. Essential Questions Questions that lead students to Big Ideas. 3. Big Ideas Student answers to EQs that lead them to the Big Ideas 4. Cognitive Level Webb’s/Bloom’s Taxonomy Link You can apply order of operations and use the commutative and associative properties of addition and multiplication, and distributive property of multiplication to simplify expressions. Problem Solving Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and other contexts Apply and adapt a variety of appropriate strategies to solve problems, and Monitor and reflect on the process of problem solving. Reasoning and Proof Recognize reasoning and proof as fundamental aspects of mathematics, Make and investigate mathematical conjectures, Develop and evaluate mathematical arguments and proofs, and Select and use various types of reasoning and methods of proof. Communication Organize and consolidate their thinking through communication, 29 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map 5. Content What students need to know (nouns) Vocabulary List Words students need to know to understand concept 6. Skills What students need to be able to do (verbs) Learning Activities / Lesson Plan Links Essential Experiences or Guided Practice Grade Level: 7th Course /Subject: Math MONTHLY TEMPLATE Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, Analyze and evaluate the mathematical thinking and strategies of others, Use the language of mathematics to express mathematical ideas precisely, and Describe mathematical concepts using developmentally appropriate definitions. Connections Recognize and use connections among mathematical ideas, Understand how mathematical ideas interconnect and build on one another to produce a coherent whole, and Recognize and apply mathematics in contexts outside of mathematics. Representation Create and use representations to organize, record, and communicate mathematical ideas, Select, apply, and translate among mathematical representations to solve problems, and Use representations to model and interpret physical, social, and mathematical phenomena. 7.N.1.1: absolute value 7.N.1.2: relationship, natural (counting) numbers, whole numbers, integers, rational numbers, irrational number 7.N.1.4; 7.N.3.3: rational numbers, scientific notation 7.N.1.5: numerical expressions, order of operations 7.N.2.6: absolute value, distance, number line, real numbers 7.N.2 9: addition, subtraction, multiplication, division, integers, combination of operations 7.A.1.3: numerical expression, properties of rational numbers, process 7.A.2.3: order of operations, algebraic expressions 7.A.2.4: numerical expressions, properties of rational numbers Commutative property, integer, negative number, positive number, opposites, rational number, absolute value, additive inverse, associative property, expanding, factoring, quadrants I, II, III, IV, distributive property, order of operations 7.N.1.1: determine 7.N.1.2: illustrate 7.N.1.4; 7.N.3.3: read, write, compare 7.N.1.5: simplify 7.N.2.1: add, subtract, multiply, divide, take to powers 7.N.2.6: understand, interpret, determine absolute value 7.N.2.8: simplify 7.N.2 9: solve 7.A.1.3: simplify, apply properties 7.A.1.4: interpret, evaluate 7.A.2.3: use order of operations 7.A.2.4: simplify properties Use order of operations (CM2, Accentuate the Negative, 4.1) Model and use distributive property over addition (CM2, Accentuate the Negative, 4.2) Use distributive property over subtraction (CM2, Accentuate the Negative, 4.3) 30 – APS/Math 7 Curriculum Map/May 2008 DRAFT APS District Curriculum Map 7. Assessments: Grade Level: 7th Course /Subject: Math MONTHLY TEMPLATE Check for understanding: solve problems using order of operations and distributive property (CM2, Accentuate the Negative, Question Bank, 33, 34, 36) Essay: Describe what order of operations means and its importance (CM2, Accentuate the Negative, Mathematical Reflections 4) Formative Assessments How will students and teacher know what students have learned so far? Differentiated Rubric Links / Attached Summative Assessments How will students show that they have mastered the standard? Differentiated Rubric Links / Attached 8. Resources Links, Curriculum Frameworks, Other Websites Unit Test: Add, subtract, multiply and divide integers; plot ordered pairs; solve problems; use order of operations (CM2, Accentuate the Negative, Unit Test) Quiz: solve problems using order of operations and distributive property (CM2, Accentuate the Negative, Question Bank, 33, 34, 36) PBA for different models Performance Assessment: Dealing Down (CM2, Accentuate the Negative, Unit Project) 6th Grade Teacher CD, http://www.phschool.com, http://connectedmath.msu.edu 31 – APS/Math 7 Curriculum Map/May 2008 DRAFT
