Topics
6. Equations & Inequalities
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United States of America
Grade 6

Investigation: Solve equations with algebra tiles

Lesson
Practice
Overview
Activity 1
Activity 2
Reflection

Investigate how equations can be solved by using algebra tiles.

Objectives
  • To connect algebra tiles with equations.
  • To solve equations.
  • To understand properties of equality.
Materials
  • None

Solving equations with subtraction

Algebra tiles
We can use algebra tiles to solve equations with integers. Let's look at some examples, and then try a few of our own.
Use algebra tiles in the applet below to model and solve the following equations. Check your solutions with a partner, or by substituting the answer back into the equation.
Equations to solve
  • x+2=10
  • x+3=5
  • 7=x+4
  • 14=7+x

Use the following applet to solve the equations.

Loading interactive...
Investigate
Consider the following questions once you have completed the above procedure.
1.
Explain why it is important to subtract the same amount of +1 tiles to each side and not just one side of the equation.
2.
Explain in your own words what the subtraction property allows you to do.

Solving equations with division

Use algebra tiles in the applet below to model and solve the following equations. Check your solutions with a partner, or by substituting the answer back into the equation.
Equations to solve
  • 2x=4
  • 5x=15
  • 3x=18
  • 12=4x

Use the following applet to solve the equations.

Loading interactive...
Investigate
Consider the following questions once you have completed the above procedure.
1.
To solve the above equations we use a property called the division property of equality. Explain in your own words what this property allows you to do.

Discuss your responses to the previous questions with a classmate, then answer the questions below.

Discussion
1.
There are two more properties of equality - the addition property of equality and the multiplication property of equality. See if you can demonstrate them using algebra tiles.
2.
Algebra tiles are a nice tool for visualizing how to solve an equation, but we can't use Algebra tiles to solve every equation. Write an example of an equation that cannot be solved using Algebra tiles. Explain why it cannot be solved that way. Then, explain how you think it might be solved algebraically.
3.
Explain how you could use algebra tiles to solve an equation like 3x+2=4.

Outcomes

6.EE.A.4

Identify when two expressions are equivalent (i.e., When the two expressions name the same number regardless of which value is substituted into them).

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