Keeping the Equation Balanced


Represent an Equation with Models.

  • Drag the x’s and dots (units) in and out of the blue bins below to match the given equation. ​
  • Then click the button to continue.


Balance a System of Hangers.

(A). This picture represents a hanger that is balanced because the weight on both sides is the same.

(1). Elena removes two triangles from the left side and three triangles from the right side. Will the hanger still be in balance, or will it tip to one side? Which side?

(2). Use the applet below to see if your answer to the questions above were correct. (Unlock the hanger before reducing/adding weights.)

(3). Explain how you know.

(4). Can you find another way to make the hanger balance?

(5). After you make a prediction, use the applet to see if you were right. If a triangle weighs 1 gram, how much does a square weigh?

Try your own Hanger Balances!

(6). Can you find another pair of values that makes the hanger balance?

(B). In the applet below, a triangle weighs 3 grams, and a circle weighs 6 grams.

(1). Use this applet below to help find the weight of a square. (Remember to unlock the hanger.)

(2). Write an equation to represent the hanger.

(3). Find the weight of a pentagon in the applet below.

(4). Write an equation to represent this hanger.

(5). Try your own!


Equation Balance Model.

Your goal in this activity is to isolate x.

  • Subtract an equal amount from both sides of the scale so that x is the only term left on the left hand side.​
  • Enter the number in the boxes below the scales.
  • Press the Enter key on your keyboard. A guide to the right answer is when the scale is horizontal after entering your values.
  • Click to verify your answer.
  • Click to solve another problem.


What is the weight of a square if a triangle weighs 4 grams?

Explain your reasoning.


Andre came up with the following puzzle. “I am three years younger than my brother, and I am 2 years older than my sister. My mom’s age is one less than three times my brother’s age. When you add all our ages, you get 87. What are our ages?” To solve the puzzle, Jada writes this equation for the sum of the ages as:

() + (+ 3) + (– 2) + 3(+ 3) – 1 = 87

(1). Explain the meaning of the variable and each term of the equation.

(2). Write the equation with fewer terms.

(3). Solve the puzzle if you haven’t already.