Unit 2 – 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!)

Math 8CUnit 2 – 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 Up U2D1

32

4

3

y

xSimplify

U2D1Concept Review

Concept Review U2D1

U2D1Concept Review

Must do:• The sum of two integers is -42. One integer is 12.

Find the other integer.

• Say the sum of 4 consecutive positive integers is 38. What are the digits?

Challenge:• Carlos begins with twice as much money as

David. After Carlos gives $12 to David, Carlos still has $10 more than David. How much money did they have combined at the start?

U2D1

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?

Modeling

U2D1

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?

U2D1

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?

U2D1

Draw a model and solve

Modeling

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

U2D1

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?

U2D1

U2D1 – ICP

Independent Practice

Math 8CUnit 2 – Day 2

Learning Targets

I can solve equations using algebraic manipulation

Mathematical Practices

Make sense of problems and persevere in solving themModel with mathematics

U2D2

Bell Work

Get out U2D1 – ICP, make sure it is complete. Circle any problems you want to go over.

U2D2

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?

U2D2

Warm Up U2D2

Must do: Draw a model and solve.• 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?• 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?

Challenge:• One kind of candy (jelly) sells for $5 a pound and another

(chocolate) for $10 a pound. How many pounds of each should be used to make a mixture of 10 pounds of candy (both kinds) that sells for $80?

Solving Equations using Algebra

• Steps:1. Optional: Make a dotted line down the middle of

the equal sign2. Get all variables to one side, all constants to the

other.3. Get variable alone by multiplying or dividing.

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

U2D2

483 x

Explain the opposite of multiplication is division, etc…

Solving Equations Using Algebra

Solve each equation

1. 3.

2.

U2D2

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?

U2D2

102

8

p

Solving Two-Step Equations

Solve each equation

1.

2.

3.

U2D2

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

U2D2

)( cba

)3(2 x

Solving Equations with the Distributive Property

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

U2D2

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.

U2D2

21)4(7 x

15)4(3 x

10)42(55 xx

Independent Practice

U2D2 - ICP

U2D2