Pre-Algebra Curriculum Map – 8th
Grade – Unit 1 – Integers, Equations, and Inequalities
Unit 1 – Integers, Equations, and Inequalities
Chapter 1 – Variables, Expressions, and Integers – 12 days Key Skills
and Concepts
Add, subtract, multiply, and divide integers. Make a scatter plot.
Common Core Math Standards
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 Each day includes 30-40 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.
Essential Vocabulary
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
Program Review
Activities
Writing Arts and Humanities PCLS
Resources Needed For Unit
Student Notes Homework Checks Integer Game Cards Number Lines
Order of Operations Activity
Coordinate Plane Graphing Characters
Integers – Football, Golf
Pre-Algebra Curriculum Map – 8th
Grade – Unit 1 – Integers, Equations, and Inequalities
Dates Content Learning Target Essential Questions
HOTQs
Connections to Common
Core Lesson Plan Assignment
8/10 Lesson 1.1
Expressions and Variables
I am learning to 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
Bellringer 5
p. 7 #12-40 EVENS
Homework Check 10
Vocabulary 5
Evaluating a Variable Expression 5
Writing Variable Expressions 5
Note Card Activity 10
Review 5
Exit Slip/Homework 5
8/11 Lesson 1.2 Powers and Exponents
I am learning to use powers to describe
repeated multiplications.
1. If x = 22, what is the value of x2?
2. Does anyone have the same answer but a different way of explaining it/completing it?
6.EE.1
Bellringer 5
p. 12 #14-36 EVENS
Homework Check 10
Vocabulary 5
Using Exponents 5
Evaluating Powers with Variables 5
Using Powers in Formulas 10
Review 5
Exit Slip/Homework 5
8/12 Lesson 1.3
Order of Operations
I am learning to 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
Bellringer 5
Program Review Activity
Homework Check 10
Vocabulary 5
Program Review Activity 30
Exit Slip 5
8/13 Lesson 1.3
Order of Operations
I am learning to 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
Bellringer 5
p. 19 #10-36 EVENS
Homework Check 10
Vocabulary 5
Using Order of Operations 5
Pre-Algebra Curriculum Map – 8th
Grade – Unit 1 – Integers, Equations, and Inequalities
Using Grouping Symbols 5
Evaluating Variable Expressions 10
Order of Operations Puzzle 5
Exit Slip/Homework 5
8/14 Lesson 1.4
Comparing and Ordering Integers
I am learning to compare and order
integers.
1. Why is this definition needed? What can we do with
this concept?
2. How can you use visual information (diagrams or pictures or graphs) of the concept to understand its
definition?
3. Does anyone have the same answer, but a different way of
explaining it?
6.NS.7
Bellringer 5
p. 24 #18-50 EVENS
Homework Check 10
Vocabulary 5
Graphing and Ordering Integers 5
Finding Absolute Value 5
Finding Opposites 5
Evaluating Algebraic Expressions 10
Exit Slip/Homework 5
Lesson 1.5
Adding Integers I am learning to 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
Bellringer 5
p. 32 #14-40 EVENS
Homework Check 10
Vocabulary 5
Adding Integers Using a Number Line
5
Adding Integers 5
Evaluating Variable Expressions 5
Integer Game/Review 10
Exit Slip/Homework 5
Lesson 1.6 Subtracting
Integers
I am learning to 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
Bellringer 5
p. 36 #12-38 EVENS
Homework Check 10
Vocabulary 5
Subtracting Integers 5
Evaluating Variable Expressions 5
Evaluating Change 5
Integer Game/Review 10
Pre-Algebra Curriculum Map – 8th
Grade – Unit 1 – Integers, Equations, and Inequalities
Exit Slip/Homework 5
Lesson 1.7
Multiplying and Dividing Integers
I am learning to 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
Bellringer 5
p. 45 #12-34 EVENS
Homework Check 10
Vocabulary 5
Multiplying Integers 5
Dividing Integers 5
Finding a Mean 5
Integer Game/Review 10
Exit Slip/Homework 5
Lesson 1.8
The Coordinate Plane
I am learning to 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
Bellringer 5
Program Review Activity:
Coordinate Graphing Cartoon
Characters
Homework Check 10
Vocabulary 5
Naming Points in a Coordinate Plane
5
Plotting Points in a Coordinate Plane
5
Program Review Activity 15
Review 5
Exit Slip/Homework 5
Lesson 1.8
The Coordinate Plane
I am learning to 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
Bellringer 5
Finish Coordinate Graphing Activity p. 49
#27-28
Homework Check 10
Review coordinate graphing 5
Finish Program Review Activity 25
Students can create their own coordinate graphing activity
5
Exit Slip/Homework 5
Lesson 1.8
Scatter Plots
I am learning to 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
Bellringer 5
Worksheet
Homework Check 10
Vocabulary 5
Making a Scatter Plot 5
Extended Response 5
Program Review Activity (Coordinate Graphing Activity)
15
Pre-Algebra Curriculum Map – 8th
Grade – Unit 1 – Integers, Equations, and Inequalities
3. Does anyone have the same answer, but a different way of
explaining it?
Review 5
Exit Slip/Homework 5
Review and
Chapter 1 Test
I am demonstrating my knowledge of
variables, expressions and integers on my
Chapter 1 Test.
Chapter 1 Test See Above Chapter 1 Test and Extended
Response 50
Chapter 2 Vocabulary
Chapter 2 – Solving Equations – 10 days Key Skills
and Concepts
Understand properties and simplify expressions. Construct and solve linear equations in one variable to solve problems.
Common Core Math Standards
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.
7.EE.4 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 54 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 $50 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.
8.EE.7 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
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
Pre-Algebra Curriculum Map – 8th
Grade – Unit 1 – Integers, Equations, and Inequalities
Review Activities
Create own word problem
Word problems involving sports
Needed For Unit
Homework Checks
Dates Content Learning Target Essential Questions
HOTQs
Connections to Common
Core Lesson Plan Assignment
Lesson 2.1
Properties and Operations
I am learning to 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 5.NBT.7
Bellringer 5
p. 66 #16-36 EVENS
Homework Check 10
Vocabulary 5
Properties Flip Chart 5
Using Properties to Simplify Expressions
5
Conversion Factors 15
Review 5
Exit Slip/Homework 5
Lesson 2.2
The Distributive Property
I am learning to 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
Bellringer 5
p. 76 #12-40 EVENS
Homework Check 10
Vocabulary 5
The Distributive Property 5
Using the Distributive Property 5
Writing Equivalent Variable Expressions
15
Finding Areas of Geometric Figures
5
Exit Slip/Homework 5
Lesson 2.3 Simplifying
Variable Expressions
I am learning to simplify variable
expressions.
1. How do you simplify an expression that has several terms?
7.EE.1
Bellringer 5
p. 81 #10-36 EVENS
Homework Check 10
Vocabulary 5
Identifying Parts of an Expression 10
Simplifying an Expression 5
Pre-Algebra Curriculum Map – 8th
Grade – Unit 1 – Integers, Equations, and Inequalities
Simplifying Expressions with Parentheses
10
Writing and Simplifying an Expression
5
Exit Slip/Homework 5
Lesson 2.4
Variables and Equations
I am learning to solve 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.
7.EE.4
Bellringer 5
p. 87 #8-32 EVENS
Homework Check 10
Vocabulary 5
Writing Verbal Sentences as Equations
5
Checking Possible Solutions 5
Solving Equations Using Mental Math
5
Writing and Solving an Equation 10
Exit Slip/Homework 5
Lesson 2.5 Solving
Equations Using Addition or Subtraction
I am learning to solve 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.
7.EE.4 8.EE.7
8.EE.7b
Bellringer 5
p. 93 #12-28 EVENS
Homework Check 10
Vocabulary 5
Solving an Equation Using Subtraction
10
Solving an Equation Using Addition
5
Writing and Solving an Equation 10
Review 5
Exit Slip/Homework 5
Lesson 2.6 Solving
Equations Using Multiplication or
Division
I am learning to solve equations using multiplication or
division.
1. Explain how the property is used to find the solution. 2. Solve. Justify your steps.
7.EE.4 8.EE.7
8.EE.7b 8.SP.1
Bellringer 5
p. 99 #8-26 EVENS
Homework Check 10
Vocabulary 5
Solving an Equation Using Division 10
Solving an Equation Using Multiplication
5
Writing and Solving an Equation 10
Review 5
Exit Slip/Homework 5
Lesson 2.7 I am learning to solve 1. How does absolute value help 7.EE.4 Bellringer 5 p. 105
Pre-Algebra Curriculum Map – 8th
Grade – Unit 1 – Integers, Equations, and Inequalities
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.
8.EE.7 8.EE.7b
Homework Check 10 #12-23 ALL
Vocabulary 5
Adding / Subtracting Decimals 5
Multiplying Decimals 5
Dividing Decimals 15
Review 5
Exit Slip/Homework 5
Lesson 2.7 Decimal
Operations and Equations with
Decimals
I am learning to solve 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.
7.EE.4 8.EE.7
8.EE.7b
Bellringer 5
p. 105 #24-38 EVENS
Homework Check 10
Vocabulary 5
Solving Addition and Subtraction Equations
5
Solving Multiplication and Division Equations
5
Writing and Solving an Equation 10
Review 5
Exit Slip/Homework 5
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 50
Chapter 3 Vocabulary
Pre-Algebra Curriculum Map – 8th
Grade – Unit 1 – Integers, Equations, and Inequalities
Chapter 3 – Multi-Step Equations and Inequalities – 10 days Key Skills
and Concepts
Construct and solve multi-step linear equations and inequalities in one variable to solve problems.
Common Core Math Standards
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 $25 an hour gets a 10% raise, she will make
an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. 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.
7.EE.4 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 54 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 $50 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.
8.EE.7 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
Program Review
Activities
Writing Arts and Humanities PCLS
Resources Needed For Unit
Student Notes Homework Checks
Create own word problem
Word problems involving sports
Pre-Algebra Curriculum Map – 8th
Grade – Unit 1 – Integers, Equations, and Inequalities
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
I am learning to solve two-step equations.
1. Solve. Justify your steps.
2. Does someone have the same answer but a different way of
explaining it/solving it?
7.EE.3 7.EE.4 8.EE.7 8.SP.1
Bellringer 5
p. 123 #8-32 EVENS
Puzzle
Homework Check 10
Vocabulary 5
Using Subtraction and Division to Solve
5
Using Addition and Multiplication to Solve
5
Solving an Equation with Negative Coefficients
5
Writing and Solving a Two-Step Equation
10
Exit Slip/Homework 5
9/24 9/25
Lesson 3.2 Solving
Equations Having Like Terms and
Parentheses
I am learning to solve equations using the distributive property.
1. Solve. Justify your steps.
2. Does someone have the same answer but a different way of
explaining it/solving it?
7.EE.4 8.EE.7
Bellringer 5
p. 127 #10-36 EVENS
Puzzle
Homework Check 10
Vocabulary 5
Writing and Solving an Equation 5
Solving Equations Using the Distributive Property
5
Combing Like Terms After Distributing
10
Review 5
Exit Slip/Homework 5
9/30
Common Assessment
10/1
10/2
Lesson 3.3 Solve Equations with Variables on
Both Sides
I am learning to solve equations with
variables on both sides.
1. Solve. Justify your steps.
2. Does someone have the same answer but a different way of
explaining it/solving it?
7.EE.3 7.EE.4 8.EE.7
Bellringer 5
p. 134 #12-30 EVENS
Homework Check 10
Vocabulary 5
Solving an Equation with the Variable on Both Sides
5
Writing and Solving an Equation 5
Special Cases 10
Solving an Equation to Find a Perimeter
5
Exit Slip/Homework 5
10/3 Mid-Chapter Quiz I am learning to solve multi-step equations.
Mid-Chapter Quiz 7.EE.3 7.EE.4 8.EE.7
Bellringer 5
No Homework FALL BREAK!
Homework Check 10
Review 5
Quiz 20
Pre-Algebra Curriculum Map – 8th
Grade – Unit 1 – Integers, Equations, and Inequalities
10/14
Lesson 3.4 Solving
Inequalities Using Addition or Subtraction
I am learning to solve inequalities using
addition or subtraction.
1. Solve. Justify your steps.
2. Does someone have the same answer but a different way of
explaining it/solving it?
3. Compare and contrast: Inequality Symbols
7.EE.4
Bellringer 5
p. 143 #12-38 EVENS
Homework Check 10
Vocabulary 5
Writing and Graphing an Inequality 5
Solving One-Step Inequalities 5
Writing and Solving an Inequality 10
Review 5
Exit Slip/Homework 5
10/15
Lesson 3.5 Solving
Inequalities Using Multiplication or
Division
I am learning to solve inequalities using multiplication or
division.
1. Solve. Justify your steps.
2. Does someone have the same answer but a different way of
explaining it/solving it?
3. Justify that your answer was right.
7.EE.4
Bellringer 5
p. 148 #12-36 EVENS
Homework Check 10
Vocabulary 5
Writing and Graphing an Inequality 5
Solving One-Step Inequalities 5
Writing and Solving an Inequality 10
Review 5
Exit Slip/Homework 5
10/16 Teen Talk
10/17 Lesson 3.6
Solving Multi-Step Inequalities
I am learning to solve multi-step inequalities.
1. Solve. Justify your steps.
2. Does someone have the same answer but a different way of
explaining it/solving it?
3. Compare and contrast: Inequality Symbols
7.EE.4 8.SP.1
Bellringer 5
p. 153 #10-30 EVENS
Homework Check 10
Vocabulary 5
Writing and Solving a Multi-Step Inequality
5
Solving a Multi-Step Inequality 5
Combining Like Terms in a Multi-Step Inequality
10
Review 5
Exit Slip/Homework 5
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 50
Unit 1 Review
Pre-Algebra Curriculum Map – 8th
Grade – Unit 1 – Integers, Equations, and Inequalities
Chapter 3 Test.