7th Grade Mathematics - Orange Board Of Education

7th Grade MathematicsExpressions & Equations: Generate equivalent expressionsand solve real-life problems using expressions & equationsUnit 2 Pacing Calendar:ORANGE PUBLIC SCHOOLSOFFICE OF CURRICULUM AND INSTRUCTIONOFFICE OF MATHEMATICS

From the Common Core State Standards:In Grade 7, instructional time should focus on four critical areas: (1) developing understanding of andapplying proportional relationships; (2) developing understanding of operations with rational numbers andworking with expressions and linear equations; (3) solving problems involving scale drawings and informalgeometric constructions, and working with two- and three-dimensional shapes to solve problems involvingarea, surface area, and volume; and (4) drawing inferences about populations based on samples.1. Students extend their understanding of ratios and develop understanding of proportionality to solvesingle- and multi-step problems. Students use their understanding of ratios and proportionality to solve awide variety of percent problems, including those involving discounts, interest, taxes, tips, and percentincrease or decrease. Students solve problems about scale drawings by relating corresponding lengthsbetween the objects or by using the fact that relationships of lengths within an object are preserved insimilar objects. Students graph proportional relationships and understand the unit rate informally as ameasure of the steepness of the related line, called the slope. They distinguish proportional relationshipsfrom other relationships.2. Students develop a unified understanding of number, recognizing fractions, decimals (that have a finite ora repeating decimal representation), and percents as different representations of rational numbers.Students extend addition, subtraction, multiplication, and division to all rational numbers, maintaining theproperties of operations and the relationships between addition and subtraction, and multiplication anddivision. By applying these properties, and by viewing negative numbers in terms of everyday contexts (e.g.,amounts owed or temperatures below zero), students explain and interpret the rules for adding,subtracting, multiplying, and dividing with negative numbers. They use the arithmetic of rational numbers asthey formulate expressions and equations in one variable and use these equations to solve problems.3. Students continue their work with area from Grade 6, solving problems involving the area andcircumference of a circle and surface area of three dimensional objects. In preparation for work oncongruence and similarity in Grade 8 they reason about relationships among two-dimensional figures usingscale drawings and informal geometric constructions, and they gain familiarity with the relationshipsbetween angles formed by intersecting lines. Students work with three-dimensional figures, relating them totwo-dimensional figures by examining cross-sections. They solve real-world and mathematical problemsinvolving area, surface area, and volume of two- and three-dimensional objects composed of triangles,quadrilaterals, polygons, cubes and right prisms.4. Students build on their previous work with single data distributions to compare two data distributionsand address questions about differences between populations. They begin informal work with randomsampling to generate data sets and learn about the importance of representative samples for drawinginferences.

th7 Grade Unit 2: Expressions and EquationsPacing GuideActivityChapter 3 OpenerChapter 3 Pre-Test (MIF)3.1- Adding Algebraic Terms3.2- Subtracting Algebraic Terms3.3- Simplifying Algebraic Expressions3.4- Expanding Algebraic Expressions3.5- Factoring Algebraic Expressions3.6- Writing Algebraic Expressions3.7- Real World Problems: Algebraic ReasoningChapter 3 Wrap Up/ Review LessonChapter 3 Test (MIF) *Optional*Performance Task 1Unit 2 Review LessonUnit 2 Assessment 1Chapter 4 OpenerChapter 4 Pre-Test (MIF)Transition Lesson Skills 23-264.1- Understanding Equivalent Equations4.2- Solving Algebraic Equations4.3- Real-World Problems: Algebraic EquationsPerformance Task 24.4- Solving Algebraic Inequalities4.5- Real-World Problems: Algebraic InequalitiesChapter 4 Wrap Up/ Review LessonChapter 2 Test (MIF) *Optional*Unit 2 Review LessonUnit 2 Assessment 2Solidify Unit 2 Concepts / Project Based LearningNew Jersey StateLearning Standards(NJSLS)7.EE.1; 7.EE.2; 7.EE.37.EE.1; 7.EE.2; EE.1; 7.EE.2; 7.EE.37.EE.1; 7.EE.2; 7.EE.37.EE.17.EE.1; 7.EE.2;7.EE.1; 7.EE.2;7.EE.4; 7.EE.4a; 7.EE.4b7.EE.4; 7.EE.4a; 7.EE.4b7.EE.1; 7.EE.2; 3; 7.EE.4; 7.EE.4a;7.EE.4b7.EE.3; 7.EE.4; 7.EE.4a;7.EE.4b7.EE.3; 7.EE.47.EE.3; 7.EE.47.EE.1; 7.EE.2; 7.EE.3;7.EE.4Total 11311111545 BlocksMajor Work Supporting Content Additional Content1

th7 Grade Unit 2: Expressions and EquationsPacing CalendarPlease complete the pacing calendar based on the suggested pacing (see Pacing Guide on page 1).Chapter 3: Algebraic Expressions: In this chapter, students extend their knowledge to more complex expressions.They learn to simplify, expand, and factor increasingly complex algebraic expressions. Students close the chapter bysolving real-world problems. They create bar models and diagrams to help them visualize algebraic situations.Chapter4: Algebraic Equations and Inequalities: In this chapter, students learn to identify equivalent equations.They solve multi-step equations with variables on both sides, including equations with parentheses, and they learn tosolve real-world problems algebraically. After solving equations, students learn how to solve inequalities, graph thesolution set of an inequality, and use inequalities to solve real-world 2223242526272829302

th7 Grade Unit 2: Expressions and EquationsPacing CalendarPlease complete the pacing calendar based on the suggested pacing (see Pacing Guide on page 1).Chapter 3: Algebraic Expressions: In this chapter, students extend their knowledge to more complex expressions.They learn to simplify, expand, and factor increasingly complex algebraic expressions. Students close the chapter bysolving real-world problems. They create bar models and diagrams to help them visualize algebraic situations.Chapter4: Algebraic Equations and Inequalities: In this chapter, students learn to identify equivalent equations.They solve multi-step equations with variables on both sides, including equations with parentheses, and they learn tosolve real-world problems algebraically. After solving equations, students learn how to solve inequalities, graph thesolution set of an inequality, and use inequalities to solve real-world 222324252627282930313

th7 Grade Unit 2: Expressions and EquationsPacing CalendarPlease complete the pacing calendar based on the suggested pacing (see Pacing Guide on page 1).Chapter 3: Algebraic Expressions: In this chapter, students extend their knowledge to more complex expressions.They learn to simplify, expand, and factor increasingly complex algebraic expressions. Students close the chapter bysolving real-world problems. They create bar models and diagrams to help them visualize algebraic situations.Chapter4: Algebraic Equations and Inequalities: In this chapter, students learn to identify equivalent equations.They solve multi-step equations with variables on both sides, including equations with parentheses, and they learn tosolve real-world problems algebraically. After solving equations, students learn how to solve inequalities, graph thesolution set of an inequality, and use inequalities to solve real-world 22324252627282930314

th7 Grade Unit 2: Expressions and EquationsPARCC Assessment Evidence StatementsType IType IIType IIINJSLSEvidence StatementClarification7.EE.1Apply properties of operations asstrategies to add, subtract, factor, andexpand linear expressions withrational coefficients.7.EE.27.EE.3Understand that rewriting anexpression in different forms in aproblem context can shed light on theproblem and how the quantities in itare related. For example, a 0.05a 1.05a means that "increase by 5%" isthe same as "multiply by 1.05."Solve multi-step real-life andmathematical problems posed withpositive and negative rationalnumbers in any form (whole numbers,fractions, and decimals), using toolsstrategically. Apply properties ofoperations to calculate with numbersin any form; convert between forms asappropriate; and assess thereasonableness of answers usingmental computation and estimationstrategies. For example: If a womanmaking 25 an hour gets a 10% raise,she will make an additional 1/10 of hersalary an hour, or 2.50, for a newsalary of 27.50. If you want to placea towel bar 9 3/4 inches long in thecenter of a door that is 27 1/2 incheswide, you will need to place the barabout 9 inches from each edge; thisestimate can be used as a check onthe exact computation.MathPracticesCalculator?i) Tasks are not limited tointeger coefficients. ii)Tasks may involve issuesof strategy, e.g., byproviding a factoredexpression such asy(3 x k) and a fullyexpanded expression 3y xy ky, and requiringstudents to produce oridentify a new expressionequivalent to both (such asy(3 x) yk).MP.7No-MP.7No-MP.5Yes5

th7 Grade Unit 2: Expressions and Equations7.EE.4a-17.EE.4a-27.EE.4b7.C.1.27.C.5Use variables to represent quantitiesin a real-world or mathematicalproblem, and construct simpleequations and inequalities to solveproblems by reasoning about thequantities. a. Solve word problemsleading to equations of the form px q r and p(x q) r, where p, q, andr are specific rational numbers.Use variables to represent quantitiesin a real-world or mathematicalproblem, and construct simpleequations and inequalities to solveproblems by reasoning about thequantities. a. Fluently solve equationsof the form px q r and p(x q) r,where p, q, and r are specific rationalnumbers.Use variables to represent quantitiesin a real-world or mathematicalproblem, and construct simpleequations and inequalities to solveproblems by reasoning about thequantities. b. Solve word problemsleading to inequalities of the form px q r or px q r, where p, q and rare specific rational numbers. Graphthe solution set of the inequality andinterpret it in the context of theproblem. For example: As asalesperson, you are paid 50 perweek plus 3 per sale. This week youwant your pay to be at least 100.Write an inequality for the number ofsales you need to make, and describethe solutions.Base explanations/reasoning on theproperties of operations. ContentScope: Knowledge and skillsarticulated in 7.EE.Given an equation, present thesolution steps as a logical argumentthat concludes with the set ofsolutions (if any). Content Scope:Knowledge and skills articulated in7.EE.4ai) Comparison of analgebraic solution to anarithmetic solution is notassessed here; for thisaspect of 7.EE.4a, see7.C.5.MP.1MP.2MP.6MP.7Noi) Each task requiresstudents to solve twoequations (one of each ofthe given two forms). Onlythe answer is required. ii)Comparison of analgebraic solution to anarithmetic solution is notassessed here; for thisaspect of 7.EE.4a, see7.C.5.MP.6MP.7NoMP.1MP.2MP.5MP.6MP.7Noi) Tasks should not requirestudents to identify orname i) Tasks may involve , or .6