Download 8th Grade Pre-Algebra Curriculum Map

th
Pre-Algebra Curriculum Map – 8 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.
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.
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.
1
7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
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
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.
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
Order of Operations
Activity
Program
Review
Activities
Arts and Humanities
Coordinate Plane
Graphing Characters
PCLS
Integers – Football,
Golf
Resources
Needed For
Unit
Student Notes
Homework Checks
Integer Game Cards
Number Lines
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Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities
Dates
8/10
Content
Lesson 1.1
Expressions and
Variables
Learning Target
I am learning to
evaluate and write
variable expressions.
Essential Questions
HOTQs
Connections
to Common
Core
1. How is a variable useful in
writing a numerical pattern?
2. Compare and Contrast:
Numerical Expressions and
Variable Expressions
8/11
I am learning to use
powers to describe
repeated
multiplications.
1. If x = 2 , what is the value of
x2 ?
2. Does anyone have the same
answer but a different way of
explaining it/completing it?
Assignment
Bellringer
5
Homework Check
10
Vocabulary
5
Evaluating a Variable Expression
5
Writing Variable Expressions
5
Note Card Activity
10
Review
5
Exit Slip/Homework
5
Bellringer
5
Homework Check
10
Vocabulary
5
Using Exponents
5
Evaluating Powers with Variables
5
Using Powers in Formulas
10
Review
5
Exit Slip/Homework
5
Bellringer
5
Homework Check
10
Vocabulary
5
Program Review Activity
30
Exit Slip
5
Bellringer
5
Homework Check
10
Vocabulary
5
Using Order of Operations
5
6.EE.2
2
Lesson 1.2
Powers and
Exponents
Lesson Plan
6.EE.1
p. 7
#12-40 EVENS
p. 12
#14-36 EVENS
1. Program Review Activity
8/12
Lesson 1.3
Order of
Operations
I am learning to use
the order of operations
to evaluate
expressions.
2. What is the purpose of the
order of operations? What
would happen if we did not use
them?
6.EE.3
1. Program Review Activity
8/13
Lesson 1.3
Order of
Operations
I am learning to use
the order of operations
to evaluate
expressions.
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
p. 19
#10-36 EVENS
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Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities
1. Why is this definition
needed? What can we do with
this concept?
8/14
Lesson 1.4
Comparing and
Ordering Integers
I am learning to
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
3. Does anyone have the same
answer, but a different way of
explaining it?
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?
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.1b
7.NS.3
7.NS.1
7.NS.1a
7.NS.1c
Using Grouping Symbols
5
Evaluating Variable Expressions
10
Order of Operations Puzzle
5
Exit Slip/Homework
5
Bellringer
5
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
Bellringer
5
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
Bellringer
5
Homework Check
10
Vocabulary
5
Subtracting Integers
5
Evaluating Variable Expressions
5
Evaluating Change
5
Integer Game/Review
10
p. 24
#18-50 EVENS
p. 32
#14-40 EVENS
p. 36
#12-38 EVENS
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Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities
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?
Lesson 1.8
The Coordinate
Plane
Lesson 1.8
The Coordinate
Plane
Lesson 1.8
Scatter Plots
I am learning to
identify and plot points
in a coordinate plane.
I am learning to
identify and plot points
in a coordinate plane.
I am learning to create
and make
interpretations from
scatter plots.
7.NS.2
7.NS.2a
7.NS.2b
7.NS.3
1. Do you see a
pattern? Explain.
2. Why is this definition
needed? What can we do with
this concept?
8.SP.1
1. Do you see a
pattern? Explain.
2. Why is this definition
needed? What can we do with
this concept?
5
Bellringer
5
Homework Check
10
Vocabulary
5
Multiplying Integers
5
Dividing Integers
5
Finding a Mean
5
Integer Game/Review
10
Exit Slip/Homework
5
Bellringer
5
Homework Check
10
Vocabulary
5
Naming Points in a Coordinate
Plane
Plotting Points in a Coordinate
Plane
5
5
Program Review Activity
15
Review
5
Exit Slip/Homework
5
Bellringer
5
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
Bellringer
5
Homework Check
10
Vocabulary
5
Making a Scatter Plot
5
Extended Response
5
Program Review Activity
(Coordinate Graphing Activity)
15
8.SP.1
1. Do you see a
pattern? Explain.
2. Why is this definition
needed? What can we do with
this concept?
Exit Slip/Homework
8.SP.1
p. 45
#12-34 EVENS
Program
Review Activity:
Coordinate
Graphing
Cartoon
Characters
Finish
Coordinate
Graphing
Activity
p. 49
#27-28
Worksheet
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Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities
3. Does anyone have the same
answer, but a different way of
explaining it?
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
Review
5
Exit Slip/Homework
5
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.
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
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 Additive identity, multiplicative identity, equivalent numerical expressions, equivalent variable expressions, term, coefficient, constant term, like
Vocabulary terms, equation, solution of an equation, solving an equation, inverse operations, equivalent equations, inverse operations, absolute value
Resources
Writing
Arts and Humanities
PCLS
Student Notes
Program
th
Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities
Word problems
involving sports
Review
Activities
Needed For
Unit
Homework Checks
Create own word
problem
Dates
Content
Lesson 2.1
Properties and
Operations
Lesson 2.2
The Distributive
Property
Lesson 2.3
Simplifying
Variable
Expressions
Learning Target
I am learning to use
properties of addition
and multiplication.
I am learning to use
the distributive
property.
I am learning to
simplify variable
expressions.
Essential Questions
HOTQs
1. Why is this definition
needed? What can we do with
this concept?
Connections
to Common
Core
Review of
5.NBT.7
2. Why do we not learn
properties dealing with
subtraction and division?
1. Explain how to use the
distributive property to write an
equivalent variable expression
for 4(10 + x).
1. How do you simplify an
expression that has several
terms?
Review
6.NS.4
Lesson Plan
Bellringer
5
Homework Check
10
Vocabulary
5
Properties Flip Chart
5
Using Properties to Simplify
Expressions
5
Conversion Factors
15
Review
5
Exit Slip/Homework
5
Bellringer
5
Homework Check
10
Vocabulary
5
The Distributive Property
5
Using the Distributive Property
5
Writing Equivalent Variable
Expressions
Finding Areas of Geometric
Figures
7.EE.1
Assignment
p. 66
#16-36 EVENS
p. 76
#12-40 EVENS
15
5
Exit Slip/Homework
5
Bellringer
5
Homework Check
10
Vocabulary
5
Identifying Parts of an Expression
10
Simplifying an Expression
5
p. 81
#10-36 EVENS
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Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities
Simplifying Expressions with
Parentheses
Writing and Simplifying an
Expression
Lesson 2.4
Variables and
Equations
Lesson 2.5
Solving
Equations Using
Addition or
Subtraction
Lesson 2.6
Solving
Equations Using
Multiplication or
Division
Lesson 2.7
I am learning to solve
equations with
variables.
I am learning to solve
equations using
addition or subtraction.
I am learning to solve
equations using
multiplication or
division.
I am learning to solve
1. How is the addition property
of equality used to solve an
equation?
7.EE.4
2. Solve. Explain the steps and
why you could use them to
solve.
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.
1. Explain how the property is
used to find the solution.
2. Solve. Justify your steps.
1. How does absolute value help
7.EE.4
8.EE.7
8.EE.7b
7.EE.4
8.EE.7
8.EE.7b
8.SP.1
7.EE.4
10
5
Exit Slip/Homework
5
Bellringer
5
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
Bellringer
5
Homework Check
10
Vocabulary
5
Solving an Equation Using
Subtraction
Solving an Equation Using
Addition
10
5
Writing and Solving an Equation
10
Review
5
Exit Slip/Homework
5
Bellringer
5
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
Bellringer
5
p. 87
#8-32 EVENS
p. 93
#12-28 EVENS
p. 99
#8-26 EVENS
p. 105
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Pre-Algebra Curriculum Map – 8 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?
8.EE.7
8.EE.7b
2. Solve. Justify your steps.
Lesson 2.7
Decimal
Operations and
Equations with
Decimals
Review and
Chapter 2 Test
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?
7.EE.4
8.EE.7
8.EE.7b
2. Solve. Justify your steps.
I am demonstrating
my knowledge of
solving equations on
my Chapter 2 Test.
Chapter 2 Test
See Above
Homework Check
10
Vocabulary
5
Adding / Subtracting Decimals
5
Multiplying Decimals
5
Dividing Decimals
15
Review
5
Exit Slip/Homework
5
Bellringer
5
Homework Check
10
Vocabulary
5
Solving Addition and Subtraction
Equations
Solving Multiplication and Division
Equations
5
5
Writing and Solving an Equation
10
Review
5
Exit Slip/Homework
5
Chapter 2 Test and Extended
Response
50
#12-23 ALL
p. 105
#24-38 EVENS
Chapter 3
Vocabulary
th
Pre-Algebra Curriculum Map – 8 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.
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.
Common
Core Math
Standards
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 Inequality, solution of an inequality, equivalent inequalities
Vocabulary
Writing
Create own word
problem
Program
Review
Activities
Arts and Humanities
PCLS
Word problems
involving sports
Resources
Needed For
Unit
Student Notes
Homework Checks
th
Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities
Dates
Content
Learning Target
Essential Questions
HOTQs
1. Solve. Justify your steps.
9/22
9/23
9/24
9/25
Lesson 3.1
Solving Two-Step
Equations
Lesson 3.2
Solving
Equations Having
Like Terms and
Parentheses
I am learning to solve
two-step equations.
2. Does someone have the same
answer but a different way of
explaining it/solving it?
Connections
to Common
Core
7.EE.3
7.EE.4
8.EE.7
8.SP.1
1. Solve. Justify your steps.
I am learning to solve
equations using the
distributive property.
2. Does someone have the same
answer but a different way of
explaining it/solving it?
7.EE.4
8.EE.7
9/30
Common
Assessment
10/1
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
10/2
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
Lesson Plan
Assignment
Bellringer
5
Homework Check
10
Vocabulary
5
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
5
5
Puzzle
5
10
Exit Slip/Homework
5
Bellringer
5
Homework Check
10
Vocabulary
5
Writing and Solving an Equation
5
Solving Equations Using the
Distributive Property
Combing Like Terms After
Distributing
p. 123
#8-32 EVENS
5
p. 127
#10-36 EVENS
Puzzle
10
Review
5
Exit Slip/Homework
5
Bellringer
5
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
Bellringer
Homework Check
Review
Quiz
5
10
5
20
p. 134
#12-30 EVENS
No Homework 
FALL BREAK!
th
Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities
1. Solve. Justify your steps.
10/14
Lesson 3.4
Solving
Inequalities Using
Addition or
Subtraction
I am learning to solve
inequalities using
addition or subtraction.
2. Does someone have the same
answer but a different way of
explaining it/solving it?
3. Compare and contrast:
Inequality Symbols
10/15
I am learning to solve
inequalities using
multiplication or
division.
2. Does someone have the same
answer but a different way of
explaining it/solving it?
5
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
Bellringer
5
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
Bellringer
5
Homework Check
10
Vocabulary
5
Writing and Solving a Multi-Step
Inequality
5
7.EE.4
1. Solve. Justify your steps.
Lesson 3.5
Solving
Inequalities Using
Multiplication or
Division
Bellringer
7.EE.4
3. Justify that your answer was
right.
p. 143
#12-38 EVENS
p. 148
#12-36 EVENS
10/16 Teen Talk
1. Solve. Justify your steps.
10/17
Lesson 3.6
Solving MultiStep Inequalities
I am learning to solve
multi-step inequalities.
2. Does someone have the same
answer but a different way of
explaining it/solving it?
7.EE.4
8.SP.1
3. Compare and contrast:
Inequality Symbols
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
Solving a Multi-Step Inequality
5
Combining Like Terms in a MultiStep Inequality
10
Review
5
Exit Slip/Homework
5
Chapter 3 Test and Extended
Response
50
p. 153
#10-30 EVENS
Unit 1 Review
th
Pre-Algebra Curriculum Map – 8 Grade – Unit 1 – Integers, Equations, and Inequalities
Chapter 3 Test.