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.
- Read the problem.
- Solve the problem on a sheet of paper or your notebook.
- Enter your answer in the yellow input box, and press the Enter key on your keyboard. If your answer is correct, you’ll see a confirmation.
- 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).