Pan Balance -- Shapes

  • Pan Balance – Shapes

    Grade: 3rd to 5th, 6th to 8th

    Build up to algebraic thinking by exploring this balance tool using shapes of unknown weight. Challenge yourself to find the weight of each shape in one of six built-in sets or a random set.

    Two other tools, Pan Balance - Numbers and Pan Balance - Expressions, are natural extensions.

    This interactive is optimized for your desktop and tablet.



    • Begin by choosing a set from the top menu. Random creates a new set every time you choose it.
    • Each shape is assigned a certain weight.
      • Try to find equivalent sets of shapes by places shapes on each side of the balance.
      • To grab a shape, mouse over the shape you want, move your cursor to the desired pan, and click to drop it.
      • To remove a shape, click it.
      • The pans move according to which side is heavier and which is lighter.
      • When both sides of the pan balance, the equivalent relationship is added to the right-hand table.
    • When you think you know any of the weights, you can check your guess.
      • Click Guess Weights at the bottom when the pans are balanced. This brings up the Guess Weights screen.
      • Enter your guess beside your desired shape, and then click Check. Correct values get a green check. Incorrect values get a red X.
      • Click Close to return to the balance screen. Note: All shapes always have positive whole number weights.
    • There are four additional buttons at the bottom to manipulate the tool:
      • Reset Table: Removes all entries from the table.
      • Count Items/Show Array: Toggles between what is shown on the pans, either counts of how many there are of a shape or each shape separately.
      • Reset Balance: Removes all shapes from the pans.
      • New Weights: Changes the weights of the shapes when you are in Random mode only.
      • When you are finished with a set, select another one from the top menu to changes the weights of the shapes.


      Place one red square on the left pan and one blue circle on the right pan. Are they equal in weight? If not, which weighs more? Try to make the pans balance by adding another shape to one pan. Which pan should get another weight? Why?

      Continue adding either red squares or blue circles to the pans. When the balance, an entry will be added to the table. Do you think you know the weight of the blue circle? Check by clicking the Guess Weights button and entering your guess.

      Is there another combination of red squares and blue circles that will make the pans balance? Try to find at least one more.

      Conduct similar investigations to find out how red squares and blue circles are related to pink triangles and yellow diamonds.

      Objectives and Standards

      NCTM Standards and Expectations
      • Algebra
      • 3-5
      • 6-8
      • Algebra