Unit 4 – Linear Equations, Inequalities and Functions

Standards addressed in this unit:

1. Solve equations and inequalities arising from a context2. Solve equations and inequalities using algebraic manipulations

(More to come!)

General MathUnit 4 – Day 1

Learning Targets

I can solve equations arising from a context by first drawing a model and then writing an equation to represent the context.

Mathematical Practices

Make sense of problems and persevere in solving themModel with mathematics

Warm UpU4D1

32

4

3

y

xSimplify

Concept Review U4D1

Concept Review U4D1

Concept Review U4D1

Draw a model and solve

Stella has $11 more than Roland. Together they have $159. How much money does Stella have? How much money does Roland have?

ModelingU4D1

Draw a model and solve

Modeling

Jared has twice as many DVDs as Eric. Together they have 51 DVDs. How many DVDs does Jared have? How many DVDs does Eric have?

U4D1

Draw a model and solve

Modeling

The sum of three consecutive integers is 405. What are the three numbers?

U4D1

Draw a model and solve

Modeling

For your birthday you received ten collectable Unicorns from a set of 100. If you use your allowance you can buy 2 more Unicorns every week.

How many weeks until you have collected all 100?

U4D1

YOU TRY!Draw a model and solve

Modeling

A corn plant was 4 inches tall. It grew 1.5 inches a day and is now 22 inches tall. How many days did it take?

U4D1

U4D1 – ICP

Do all BASIC PRACTICE

The odd problems in FURTHER PRACTICE

Pick two from MATH WORK

Pick one from BRAIN WORKS

Independent PracticeU4D1

General MathUnit 4 – Day 2

Learning Targets

I can solve equations using algebraic manipulation

Mathematical Practices

Make sense of problems and persevere in solving themModel with mathematics

U4D2

Bell Work

Get out U4D1 – ICP, make sure it is complete. Circle any problems you want to go over.

U4D2

Warm Up

Kylie is addressing invitations to her party. She has already addressed 17 of them. She finishes the rest of them in 4

hours. If she addressed a total of 81 invitations, how many invitations did she address per hour?

U4D2

Warm UpU4D2

Solving Equations Using Algebra

When we solve an equation using algebra, we want to undo the

operations on the unknown in order to find out what it is.

Remember! Keep the equation balanced by doing the same thing on both sides!!!

Example:

Solve

U4D2

483 x

Explain the opposite of multiplication is division, etc…

Solving Equations Using Algebra

Solve each equation

1.

2.

3.

U4D2

682 y

2039 w

232

p

Do first problem with class, have students do 2 & 3.

Solving Two-Step Equations

What’s the first step in solving this equation? Why?

How about this one? Why?

U4D2

102

8

p

Solving Two-Step Equations

Solve each equation

1.

2.

3.

U4D2

33096 y

863

p

43

10

a

Do first problem with class, have students do 2 & 3.

Solving Multi-Step Equations

Let’s discuss the Distributive Property for a moment…

The Distributive Property says

Simplify

U4D2

)( cba

)3(2 x

Solving Equations with the Distributive Property

What should we do first to solve this equation? Why?

U4D2

15)12(5 x

Explain we need both sides of equation as simplified as possible to make solving easier…

Solving Equations with the Distributive Property

Solve each equation

1.

2.

3.

U4D2

21)4(7 x

15)4(3 x

10)42(55 xx

Independent Practice

U4D2 - ICP

U4D2

General MathU4D3

• Learning Targets: Solve Equations arising from a context.

Solve equations using algebraic manipulation.

Warm Up

Do these problems on your participation page:

1. Simplify 2𝑥3 − 4𝑥𝑦2 + 17𝑥2 − 2𝑥2𝑦

2. Simplify −2𝑝4

−8𝑞2

2

3. Draw a model and solve: You and your friend have $29 for movies and snacks this weekend. You have $7 less than your friend. How much money do you each have?

U4D3

Solving Equations

Follow these steps:

Step 1: Simplify both sides of the equation

This means getting rid of parentheses and combining like terms

Step 2: Get your variable “alone” using the reverse of PEMDAS

U4D3

U4D3

U4D3

Solving Equations

Follow these steps:

Step 1: Simplify both sides of the equation.

This means getting rid of parentheses and combining like terms

IF YOU HAVE VARIABLES ON BOTH SIDES, NEXT:

Step 2: Get all variables to one side of equation.

Step 3: Get your variable alone.

U4D3

U4D3

U4D3

Next Up!

• Writing equations arising from a context!

• Whoopee!

U4D3

WORDS THAT MEAN ADDITION

SUMMORE THAN

PLUSADDED TO

INCREASED BY IN ALLTOTAL

U4D3

WORDS THAT MEAN

SUBTRACTION

MINUS LESS THAN

DECREASED BYDIFFERENCE BETWEEN

HOW MANY FEWER

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WORDS THAT MEAN MULTIPLICATION

TIMESOF

TWICEPRODUCT OF

IN EACHFOR EVERY

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WORDS THAT MEAN

DIVISION

QUOTIENTRATIO OF

HOW MANY TIMESINTO HOW MANY

HOW MUCH DID EACH

U4D3

WORDS THAT MEAN

EQUAL

ISTHE SAME ASEQUIVALENT

U4D3

Write an equation and solve. Draw a model if necessary.

Two more than twice a number is 77.

Find the number.

U4D3

Write an equation and solve. Draw a model if necessary.

The length of a rectangle is 50 meters. This is 6 meters more than twice the width. Find the

width of the rectangle.

U4D3

Write an equation and solve. Draw a model if necessary.

Nine less than one-fourth of a number is 6. Find the number

U4D3

You Try!

Write an equation and solve. Draw a model if necessary.

Twelve decreased by 8 times a number is 36. Find the number.

U4D3

Independent Practice

U4D3 – ICP

U4D3