Student Exploration: Modeling and Solving Two-Step Equations

Vocabulary: equation, unit, substituting, multiply, subtract, add, divide

Prior Knowledge:

Variable = ______

Substitution =______

Simplify = ______

What is the Order of operation? ______

Gizmo Warm-up:

At the top of the Gizmotm, you will see an equation displayed. Beneath the equation are two blue spaces, separated by an equal sign. You will use these spaces to model the two sides of the equation. Once you have a correct model, you will use the model to solve the equation.

  1. The first equation is 2x + 2 = 6. (If you see a different equation, restart the Gizmo by refreshing your browser window.)
  2. The left side of the equation is 2x + 2. How many x-cups will you need to model this? ______
  3. How many unit counters will you need to model this? ______
  4. Drag the correct number of cups and counters to the left side of the equal sign.
  5. The right side of the equation is the number ______.
  6. How many x-cups and unit counters will you need to model this? ______
  7. Drag the correct number of cups and counters to the right side of the equal sign.
  8. Click the Check button to make sure that your model is correct.

To solve the equation:

  1. You first need to subtract the unit counters from the left side. You will also need to subtract an equal number from the right side. Click the counters to remove them.
  2. How many unit counters should be subtracted from each side of the equation? ______
  3. Then click the Check button to see if you are correct.
  4. Next you need to divide the remaining unit counters so that there are an equal number in each of the x-cups.
  5. Drag an equal number of unit counters to each x-cup. How many unit counters will be in each cup? ______
  6. Then click the Check button to see if you are correct.
  7. What is the solution to the equation 2x + 2 = 6?
  8. Check your solution by substituting the number you think is the solution into the equation 2x + 2 = 6.

Activity
Two Step Equation / Get the Gizmo ready:
  • Click NEW and on a separate sheet of paper, try ______more examples.
  • Write down the algebraic expressions and phrases that the Gizmo gives you, and write down your answer for each one.

  1. What equation were you given?
  1. How many x-cups and how many unit counters did you use to model each side of the equation?
  1. What steps did you use to solve the equation?
  1. What is the solution to the equation that you were given?
  1. Check your solution by substituting it into the original equation.