This activity will help us further our understanding of the role/meaning of equality sign by utilizing the balance scale with expressions to solve an algebraic equation and revisit the meaning of “solution of an equation.”

Part A

1) Go to the following link: Pan Balance – Expressions (Open in new window)

Follow the instructions to get familiar with the app, then complete the exploration. Provide your answers to the exploration questions #2-6 below :

2)

3)

4)

5)

6)

Try another equation and solve it using this app. Write your equation and solution below and explain how you used the app to solve it .

Part B

Review the following model (from Mathematics for Elementary Teachers by Sybilla Beckman), showing how to solve equations algebraically and using a pan balance.  Consider the following questions:

(1) What did you learn about solving an equation?

(2) What similarities and differences do you see with this activity and the previous scale activities?

(3) How might an elementary school teacher use the Pan Balance to explain the process of solving an equation algebraically?

With a Pan Balance and Equations

[latex]4x+2+x=5+3x+3[/latex]

Change to equivalent expressions.

[latex]\begin{align*} 5x+2 &= 3x+8 \\ -2 &= -2 \\ \end{align*}[/latex]

Take 2 away from both sides.

[latex]\begin{align*} 5x &= 3x+6 \\ -3x &= -3x \\ \end{align*}[/latex]

Take 3x away from both sides.

[latex]2x=6[/latex]

Divide both sides by 2.

[latex]x=3[/latex]

For extra explanation and examples watch the following videos:

Part C

Solve [latex]5x + 1 = 2x + 7[/latex] in two ways, (1) with equations and (2) with pictures of a pan balance. Relate the two methods with common explanations as done in Part B.

With equations:

[latex]5x + 1 = 2x + 7[/latex]

With a pan balance:

Part D

Write an equation involving variable x. Solve your equation in two ways: (1) with equations and (2) with the pictures of a pan balance. Relate the two methods with common explanations as done in Part B.