Math Background

Using Inverse Operations to Solve Equations: Tips and Tricks

  • Have students play “Expression Concentration.” Create a set of cards with word phrases such as “3 more than 4 times a number” and a second set of cards with the corresponding algebraic expressions. Students must match the phrases to the expressions.
  • Provide students with a double-pan balance for hands-on practice with multiplication and division equations. Use similarly sized and weighted manipulatives, such as unit cubes, counting tiles, coins, or blocks. To practice multiplication equations, have students place multiple envelopes containing the same number of objects on one side of the balance. Have them add more of that object to the other side until the pans balance. Students then record the equation, solve using the inverse operation (division), and then open the envelopes to check. To practice division equations, tell students the number of objects to place on one side of the balance. Then have them place multiple envelopes—each containing the same number of objects—on the other side, until the pans balance. Have students record the equation and solve using multiplication.
  • Use a pan balance to demonstrate the Commutative Property and Distributive Properties. For example, to show that 6 x 3 = 3 x 6, place 6 cube trains that are 3 cubes long on one side of the scale. On the other side, place 3 cube trains that are 6 cubes long. To show that 4(3 + 2) = (4 x 3) + (4 x 2), place 4 cube trains that are 5 cubes long on one side of a pan balance. On the other side place, 4 cube trains that are 3 cubes long and 4 cube trains that are 2 cubes long.
  • Write the following phrases on the chalkboard and have students use them to write word problems involving multiplication and division. Have partners exchange problems and then write the appropriate equation to solve.
    • multiplied by
    • same amount
    • twice as often
    • half as many
    • cost the same amount
    • separated into equal groups
    • fives times as much
    • shared equally
    • same amount each week
    • earns the same amount
    • cost per item
    • divided by
    • equal amount
    • gave each friend the same number

Houghton Mifflin Math Grade 5