(8) Inquiry Lab - Equations with Variables on Each Side

1. HOW do you use the
Properties of Equality
when solving an
equation using algebra
tiles?
Course 3, Inquiry Lab before Lesson 2-4
Expressions and Equations

2. • 8.EE.7
Solve linear equations in one variable.
• 8.EE.7a
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).
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
5 Use appropriate tools strategically.
Course 3, Inquiry Lab before Lesson 2-4 Common Core State Standards © Copyright 2010. National Governors Association Center for
Best Practices and Council of Chief State School Officers. All rights reserved.
Expressions and Equations

3. Course 3, Inquiry Lab before Lesson 2-4
Activity 1
continued

Expressions and Equations
Leah bought 4 pens and a bottle of nail color. Her sister bought 2 of
the same pens and 4 bottles of nail color, and spent the same
amount as Leah. The nail color cost $2. Use algebra tiles to find the
cost of each pen.
The equation 4x + 2 = 2x + 8 represents the real-world situation
above. Use algebra tiles to model and solve the equation.
Model the equation.

4. Course 3, Inquiry Lab before Lesson 2-4
Activity 1
continued

Expressions and Equations
Leah bought 4 pens and a bottle of nail color. Her sister bought 2
of the same pens and 4 bottles of nail color, and spent the same
amount as Leah. The nail color cost $2. Use algebra tiles to find
the cost of each pen.
Remove x-tiles from each side of the mat until
there are x-tiles on only one side.

5. Course 3, Inquiry Lab before Lesson 2-4
Activity 1
continued

Expressions and Equations
Leah bought 4 pens and a bottle of nail color. Her sister bought 2 of
the same pens and 4 bottles of nail color, and spent the same
amount as Leah. The nail color cost $2. Use algebra tiles to find the
cost of each pen.
Remove 1-tiles form each side of the mat until the x-tiles
are by themselves on one side.

6. Course 3, Inquiry Lab before Lesson 2-4
Expressions and Equations
Leah bought 4 pens and a bottle of nail color. Her sister bought
2 of the same pens and 4 bottles of nail color, and spent the
same amount as Leah. The nail color cost $2. Use algebra tiles
to find the cost of each pen.
Separate the tiles in equal groups.
Check 4 • + 2 = 2 • + 8
So, each pen costs $ .

7. Course 3, Inquiry Lab before Lesson 2-4
Activity 2
continued

Expressions and Equations
Use algebra tiles to model and solve 3x + 3 = 2x – 3. Draw the
tiles in the blank mats shown. The first step is done for you.
Model the equation.

8. Course 3, Inquiry Lab before Lesson 2-4
Activity 2
continued

Expressions and Equations
Use algebra tiles to model and solve 3x + 3 = 2x – 3. Draw the
tiles in the blank mats shown. The first step is done for you.
Remove 2 x-tiles from each side of the mat in Step 1 so that
there is an x-tile by itself on the left side. Draw the tiles that
remain.

9. Course 3, Inquiry Lab before Lesson 2-4
Activity 2
continued

Expressions and Equations
Use algebra tiles to model and solve 3x + 3 = 2x – 3. Draw the
tiles in the blank mats shown. The first step is done for you.
To isolate the x-tile, it is not possible to remove the same
number of 1-tiles form each side of the mat. Add three 1-tiles
to each side of the mat. Draw the tiles.

10. Course 3, Inquiry Lab before Lesson 2-4
Expressions and Equations
Use algebra tiles to model and solve 3x + 3 = 2x – 3. Draw the
tiles in the blank mats shown. The first step is done for you.
Remove the zero pairs form the left side. There are six 1-
tiles on the right side of the mat. The x-tile is isolated on
the left side of the mat. Draw the tiles that remain.
So, x =
Check 3( ) + 3 = 2( ) – 3
–15 = –15 ✓

11. Course 3, Inquiry Lab before Lesson 2-4
HOW do you use the
Properties of Equality
when solving an
equation using algebra
tiles?
Expressions and Equations