# Equal and Equivalent

Warmup

Find a solution to each equation mentally.

Activity #1

Solve Linear Equations.

You are going to solve two-steps linear equations in the applet below. There are 4 difficulty levels here (see slider at bottom.) Just follow the instructions below and do as many problem as time allows you. Activity #2

Exploring Equal and Equivalent Expressions.

You are going to solve two-steps linear equations in the applet below. Just follow the instructions below and do as many problem as time allows you. • Solve the problem on a sheet of paper or your notebook.
• Then, click .
• If your answer isn’t correct, then it is recommended that you give it another try before you click on .

Activity #3

Draw Diagrams to Represent Expressions.

In this activity, you are going to use geometric tools to draw diagrams of mathematics expressions. See the example below.

Here is a diagram of  x + 2 and 3x , when x = 4. Notice that the unknown, x, are lined up on their left.  • Follow the example above to do the problems below.

Using the Pen and Text tools, draw a diagram of x+2, and a separate diagram of 3x, when x is 3.

Draw a diagram of x+2, and a separate diagram of 3x, when x is 2.

Draw a diagram of x+2, and a separate diagram of 3x, when x is 1

Draw a diagram of x+2, and a separate diagram of 3x, when x is 0.

Challenge #1

When are x + 2 and 3x equal? When are they not equal? Explain.

Challenge #2

Here is a list of expressions. Find any pairs of expressions that are equivalent. If you get stuck, try reasoning with diagrams.

Challenge #3

Below are four questions about equivalent expressions. For each one:

• Decide whether you think the expressions are equivalent.
• Test your guess by choosing numbers for (and if needed).