# Pre-Algebra Curriculum Map 8 th Grade Unit 1 Integers, Equations, and Inequalities

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1 Key Skills and Concepts Common Core Math Standards Unit 1 Integers, Equations, and Inequalities Chapter 1 Variables, Expressions, and Integers 12 days Add, subtract, multiply, and divide integers. Make a scatter plot. 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. b. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. c. Understand subtraction of rational numbers as adding the additive inverse, p q = p + ( q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. d. Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.2 Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers. a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. b. Understand that integers can be divided provided that the divisor is not zero and every quotient of integers (with nonzero divisor) is a rational number. If p and q are integers, then (p/q) = -p/q = p/-q. Interpret quotients of rational numbers by describing real-world contexts. c. Apply properties of operations as strategies to multiply and divide rational numbers. d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in zeroes or eventually repeats. 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. 1 1 Computations with rational numbers extend the rules for manipulating fractions to complex fractions. 8.SP.1. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. RTI Essential Vocabulary Program Review Activities Each day includes of individualized RTI Instruction including small group instruction, one-on-one tutoring, and computer program. Teacher will utilize MAP and classroom data to determine tiers and subject of instruction. Numerical expression, variable, variable expression, evaluate, verbal model, power, base, exponent, order of operations, integer, negative integer, positive integer, absolute value, opposite, additive inverse, opposite, difference, mean, coordinate plane, ordered pair, scatter plot Writing Arts and Humanities PCLS Order of Operations Activity Coordinate Plane Graphing Characters Integers Football, Golf Resources Needed For Unit Student Notes Homework Checks Integer Game Cards Number Lines

2 Dates Content Learning Target Essential Questions HOTQs Connections to Common Core Lesson Plan Assignment 8/10 Lesson 1.1 Expressions and Variables evaluate and write variable expressions. 1. How is a variable useful in writing a numerical pattern? 2. Compare and Contrast: Numerical Expressions and Variable Expressions 6.EE.2 Evaluating a Variable Expression Writing Variable Expressions Note Card Activity 10 p. 7 #12-40 EVENS Review 8/11 Lesson 1.2 Powers and Exponents use powers to describe repeated multiplications. 1. If x = 2 2, what is the value of x 2? 2. Does anyone have the same explaining it/completing it? 6.EE.1 Using Exponents Evaluating Powers with Variables Using Powers in Formulas 10 p. 12 #14-36 EVENS Review 8/12 Lesson 1.3 Order of Operations use the order of operations to evaluate expressions. 1. Program Review Activity 2. What is the purpose of the order of operations? What would happen if we did not use them? 6.EE.3 Program Review Activity 30 Exit Slip Program Review Activity 8/13 Lesson 1.3 Order of Operations use the order of operations to evaluate expressions. 1. Program Review Activity 2. What is the purpose of the order of operations? What would happen if we did not use them? 6.EE.3 Using Order of Operations p. 19 #10-36 EVENS

3 Using Grouping Symbols Evaluating Variable Expressions 10 Order of Operations Puzzle 1. Why is this definition needed? What can we do with this concept? 8/14 Lesson 1.4 Comparing and Ordering Integers compare and order integers. 2. How can you use visual information (diagrams or pictures or graphs) of the concept to understand its definition? 6.NS.7 Graphing and Ordering Integers Finding Absolute Value Finding Opposites p. 24 #18-0 EVENS 3. Does anyone have the same answer, but a different way of explaining it? Evaluating Algebraic Expressions 10 Lesson 1. Adding Integers add integers. 1. How can you use visual information (diagrams or pictures or graphs) of the concept to understand its definition? 2. Does anyone have the same answer, but a different way of explaining it? 7.NS.1 7.NS.1a 7.NS.1b 7.NS.3 Adding Integers Using a Number Line Adding Integers Evaluating Variable Expressions Integer Game/Review 10 p. 32 #14-40 EVENS Lesson 1.6 Subtracting Integers subtract integers. 1. How can you use visual information (diagrams or pictures or graphs) of the concept to understand its definition? 2. Does anyone have the same answer, but a different way of explaining it? 7.NS.1 7.NS.1a 7.NS.1c Subtracting Integers Evaluating Variable Expressions Evaluating Change Integer Game/Review 10 p. 36 #12-38 EVENS

4 Lesson 1.7 Multiplying and Dividing Integers multiply and divide integers. 1. How can you use visual information (diagrams or pictures or graphs) of the concept to understand its definition? 2. Does anyone have the same answer, but a different way of explaining it? 7.NS.2 7.NS.2a 7.NS.2b 7.NS.3 Multiplying Integers Dividing Integers Finding a Mean Integer Game/Review 10 p. 4 #12-34 EVENS Lesson 1.8 The Coordinate Plane identify and plot points in a coordinate plane. 1. Do you see a pattern? Explain. 2. Why is this definition needed? What can we do with this concept? 8.SP.1 Naming Points in a Coordinate Plane Plotting Points in a Coordinate Plane Program Review Activity 1 Program Review Activity: Coordinate Graphing Cartoon Characters Review Lesson 1.8 The Coordinate Plane identify and plot points in a coordinate plane. 1. Do you see a pattern? Explain. 2. Why is this definition needed? What can we do with this concept? 8.SP.1 Review coordinate graphing Finish Program Review Activity 2 Students can create their own coordinate graphing activity Finish Coordinate Graphing Activity p. 49 #27-28 Lesson 1.8 Scatter Plots create and make interpretations from scatter plots. 1. Do you see a pattern? Explain. 2. Why is this definition needed? What can we do with this concept? 8.SP.1 Making a Scatter Plot Extended Response Program Review Activity (Coordinate Graphing Activity) 1 Worksheet

5 Key Skills and Concepts Review and Chapter 1 Test I am demonstrating my knowledge of variables, expressions and integers on my Chapter 1 Test. 3. Does anyone have the same answer, but a different way of explaining it? Chapter 1 Test See Above Review Chapter 1 Test and Extended Response Chapter 2 Solving Equations 10 days Understand properties and simplify expressions. Construct and solve linear equations in one variable to solve problems. 0 Chapter 2 Vocabulary 7.NS.2 Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers. a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. b. Understand that integers can be divided provided that the divisor is not zero and every quotient of integers (with nonzero divisor) is a rational number. If p and q are integers, then (p/q) = -p/q = p/-q. Interpret quotients of rational numbers by describing real-world contexts. c. Apply properties of operations as strategies to multiply and divide rational numbers. d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in zeroes or eventually repeats. 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Common Core Math Standards Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. a. Solve word problems leading to equations of the form px+q=r and p(x+q)=r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 4 cm. Its length is 6 cm. What is its width? b. Solve word problems leading to inequalities of the form px+q>r or px+q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid \$0 per week plus \$3 per sale. This week you want your pay to be at least \$100. Write an inequality for the number of sales you need to make, and describe the solutions. Essential Vocabulary Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Additive identity, multiplicative identity, equivalent numerical expressions, equivalent variable expressions, term, coefficient, constant term, like terms, equation, solution of an equation, solving an equation, inverse operations, equivalent equations, inverse operations, absolute value Program Writing Arts and Humanities PCLS Resources Student Notes

6 Review Activities Word problems involving sports Needed For Unit Homework Checks Create own word problem Dates Content Learning Target Essential Questions HOTQs Connections to Common Core Lesson Plan Assignment Lesson 2.1 Properties and Operations use properties of addition and multiplication. 1. Why is this definition needed? What can we do with this concept? 2. Why do we not learn properties dealing with subtraction and division? Review of.nbt.7 Properties Flip Chart Using Properties to Simplify Expressions Conversion Factors 1 Review p. 66 #16-36 EVENS Lesson 2.2 The Distributive Property use the distributive property. 1. Explain how to use the distributive property to write an equivalent variable expression for 4(10 + x). Review 6.NS.4 The Distributive Property Using the Distributive Property Writing Equivalent Variable Expressions Finding Areas of Geometric Figures 1 p. 76 #12-40 EVENS Lesson 2.3 Simplifying Variable Expressions simplify variable expressions. 1. How do you simplify an expression that has several terms? 7.EE.1 Identifying Parts of an Expression 10 p. 81 #10-36 EVENS Simplifying an Expression

7 Simplifying Expressions with Parentheses Writing and Simplifying an Expression 10 Lesson 2.4 Variables and Equations equations with variables. 1. How is the addition property of equality used to solve an equation? 2. Solve. Explain the steps and why you could use them to solve. Writing Verbal Sentences as Equations Checking Possible Solutions Solving Equations Using Mental Math Writing and Solving an Equation 10 p. 87 #8-32 EVENS Lesson 2. Solving Equations Using Addition or Subtraction equations using addition or subtraction. 1. How is the addition property of equality used to solve an equation? 2. Solve. Explain the steps and why you could use them to solve. b Solving an Equation Using Subtraction Solving an Equation Using Addition 10 Writing and Solving an Equation 10 Review p. 93 #12-28 EVENS Lesson 2.6 Solving Equations Using Multiplication or Division equations using multiplication or division. 1. Explain how the property is used to find the solution. 2. Solve. Justify your steps. b 8.SP.1 Solving an Equation Using Division 10 Solving an Equation Using Multiplication Writing and Solving an Equation 10 p. 99 #8-26 EVENS Review Lesson How does absolute value help p. 10

8 Decimal Operations and Equations with Decimals equations involving decimals. you determine the sign of the sum when adding numbers with different signs? 2. Solve. Justify your steps. b #12-23 ALL Adding / Subtracting Decimals Multiplying Decimals Dividing Decimals 1 Review Lesson 2.7 Decimal Operations and Equations with Decimals equations involving decimals. 1. How does absolute value help you determine the sign of the sum when adding numbers with different signs? 2. Solve. Justify your steps. b Solving Addition and Subtraction Equations Solving Multiplication and Division Equations Writing and Solving an Equation 10 p. 10 #24-38 EVENS Review Review and Chapter 2 Test I am demonstrating my knowledge of solving equations on my Chapter 2 Test. Chapter 2 Test See Above Chapter 2 Test and Extended Response 0 Chapter 3 Vocabulary

9 Key Skills and Concepts Common Core Math Standards Multi-Step Equations and Inequalities 10 days Construct and solve multi-step linear equations and inequalities in one variable to solve problems. 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making \$2 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or \$2.0, for a new salary of \$27.0. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. a. Solve word problems leading to equations of the form px+q=r and p(x+q)=r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 4 cm. Its length is 6 cm. What is its width? b. Solve word problems leading to inequalities of the form px+q>r or px+q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid \$0 per week plus \$3 per sale. This week you want your pay to be at least \$100. Write an inequality for the number of sales you need to make, and describe the solutions. Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Essential Vocabulary Inequality, solution of an inequality, equivalent inequalities Writing Arts and Humanities PCLS Create own word problem Word problems involving sports Program Review Activities Resources Needed For Unit Student Notes Homework Checks

10 Dates Content Learning Target Essential Questions HOTQs Connections to Common Core Lesson Plan Assignment 9/22 9/23 Lesson 3.1 Solving Two-Step Equations two-step equations. 1. Solve. Justify your steps. 2. Does someone have the same explaining it/solving it? 7.EE.3 8.SP.1 Using Subtraction and Division to Solve Using Addition and Multiplication to Solve Solving an Equation with Negative Coefficients Writing and Solving a Two-Step Equation 10 p. 123 #8-32 EVENS Puzzle 9/24 9/2 Lesson 3.2 Solving Equations Having Like Terms and Parentheses equations using the distributive property. 1. Solve. Justify your steps. 2. Does someone have the same explaining it/solving it? Writing and Solving an Equation Solving Equations Using the Distributive Property Combing Like Terms After Distributing 10 p. 127 #10-36 EVENS Puzzle Review 9/30 Common Assessment 10/1 10/2 Lesson 3.3 Solve Equations with Variables on Both Sides equations with variables on both sides. 1. Solve. Justify your steps. 2. Does someone have the same explaining it/solving it? 7.EE.3 Solving an Equation with the Variable on Both Sides Writing and Solving an Equation Special Cases 10 Solving an Equation to Find a Perimeter p. 134 #12-30 EVENS 10/3 Mid-Chapter Quiz multi-step equations. Mid-Chapter Quiz 7.EE.3 Review Quiz 20 No Homework FALL BREAK!

11 1. Solve. Justify your steps. 10/14 Lesson 3.4 Solving Inequalities Using Addition or Subtraction inequalities using addition or subtraction. 2. Does someone have the same explaining it/solving it? 3. Compare and contrast: Inequality Symbols Writing and Graphing an Inequality Solving One-Step Inequalities Writing and Solving an Inequality 10 Review p. 143 #12-38 EVENS 1. Solve. Justify your steps. 10/1 Lesson 3. Solving Inequalities Using Multiplication or Division inequalities using multiplication or division. 2. Does someone have the same explaining it/solving it? 3. Justify that your answer was right. Writing and Graphing an Inequality Solving One-Step Inequalities Writing and Solving an Inequality 10 Review p. 148 #12-36 EVENS 10/16 Teen Talk 1. Solve. Justify your steps. 10/17 Lesson 3.6 Solving Multi- Step Inequalities multi-step inequalities. 2. Does someone have the same explaining it/solving it? 3. Compare and contrast: Inequality Symbols 8.SP.1 Writing and Solving a Multi-Step Inequality Solving a Multi-Step Inequality Combining Like Terms in a Multi- Step Inequality 10 Review p. 13 #10-30 EVENS 10/20 10/21 Review and Chapter 3 Test I am demonstrating my knowledge of solving multi-step equations and inequalities on my Chapter 3 Test See Above Chapter 3 Test and Extended Response 0 Unit 1 Review

12 Chapter 3 Test.

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