# 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. You will need a sheet of paper and pencil/pen. • Read the given equation in the applet.
• Solve it on a sheet of paper.
• Enter your answer in the space provided for the value of x.
• Read the second part of the equation and also enter your answer in the space provided.
• Press the Enter key on your keyboard.
• If your first answer isn’t correct, it is recommended that you correct it before proceeding. Otherwise, click .
• Continue to practice, and change difficulty level after mastering a lower level.

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.
• If your answer isn’t correct, then it is recommended that you give it another try before you click on • Then, click .

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 following problems. You can use the Pen or 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).

Quiz Time