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).