Solving Linear Equation-Algebra Tiles

Multiplication by 10

Key Understandings

• Multiplication by 10 is like skip counting

by 10.

• Multiplication by 10 results in a zero in

the ones place.

• The product is 10 times as large as the

factor.

• The order of factors does not change the

product.

Keep it or Toss it game

• We will practice the 10 facts using the Keep It, Toss It game
•• Directions for Keep It, Toss It: Online Spinner •• This is a partner game. Spin a spinner and multiply the

result by 10. The student must decide if they will keep their
product or toss it. Products are recorded in the appropriate
column of the score sheet. Players may only spin a total of
10 spins. After 5 products are recorded in the Keep It
column, the products are added to find the player’s total
score. The player with the highest score wins.

SOLVING
LINEAR
EQUATIONS &
INEQUALITIES

ALGEBRA 1

LEARNING INTENTION

We are learning how to solve linear equations and

inequalities to solve mathematical and real-world problems.

CONTENT SUCCESS CRITERIA

• I can simplify an expression using the distributive

property.

• I can solve one-variable, one-step equations.

LANGUAGE SUCCESS CRITERIA

I can identify words and phrases heard in a discussion about solving linear equations
(listening).

I will share in cooperative groups how to solve linear equations and inequalities.
(speaking)

Add

+

Subtract

-

Multiply

𝑥

Divide

÷

Square

𝑥2

Square
Root

𝑥2

Write this in your
notebook.

In middle school, you learned that an integer addition sentence has an equivalent integer subtraction sentence and vice versa.  Let’s review this learning.

What is the equivalent integer sentences for the following expressions?

We will apply this learning to modeling expressions and solving equations. 

3 + (-4) is equivalent to 3 – 4

8 – 6 is equivalent to  8 + (-6)

-5 – (-3) is equivalent to -5 + 3

​Equivalent

3x + 2 = 7

2 + 3x = 7

7 = 3x + 2

7 = 2 + 3x

Terms in the equation

+ 3x

+ 2

+ 7

Equivalent Equations

Teacher Model

It is extremely important for us to
know how to identify equivalent
equations when the terms are in
different positions. For example,
the equation 3x + 2 = 7 can be
written in 3 different ways.

Before we review the different
ways to write this equation, we
must identify the terms in the
equation and their sign values. The
terms 3x, 2, and 7 are in this
equation all numbers are positive.

Equivalent Equations

-x – 2 = -10

-10 = -x – 2

-2 + (-x) = -10 is the same as -2 – x = -10

-10 = -2 + (-x) is the same as -10 = -2 – x

Terms in the equation

-x + (-2) = -10

- 1x

- 2

- 10

Teacher Model

The Distributive Property of Multiplication

2(3 + 4) = (2 ● 3) + (2 ● 4)

2(x + 2)

Algebraic Method

Polypad – Virtual
Manipulatives (amplify.com)

Algebraic Method

Your Turn

2(x – 5)
2(x + -5)

SOLVING LINEAR EQUATIONS
GUIDED PRACTICE (PRIOR KNOWLEDGE)

SOLVING EQUATIONS

THE GOAL

You find the solution by isolating the variable.

The coefficient of the variable must be a positive one.

Equation Solved

Equation NOT Solved
2x = 3

𝑥 = 3

​2𝑥 = 3

Algebraic Method

𝑥 + 3 = 5

Algebraic Method

𝑥 − 2 = −3

Algebraic Method

4 = 𝑥 − 2

Algebraic Method

−𝑥 = 3

Algebraic Method

−2𝑥 = 6