Math Background

Lesson: Using Inverse Operations to Solve Equations
Developing the Concept

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Now that students understand how to use inverse operations to solve an equation, they are ready to write and solve equations to find the answer to a word problem.

Materials: An overhead transparency with the following problem written on it: Kayla has two pet snakes, a king snake, and a bull snake. The bull snake is 4 times as long as the king snake. If the king snake is 16 inches long, how long is the bull snake?; chart paper; copies of Pet Problems (PDF file) Worksheet for each student.

Preparation: On chart paper, create a large version of the problem-solving chart shown on the students' Pet Problems worksheet. Write the word problem given above on an overhead transparency.

Prerequisite Skills and Concepts: Children should know how to write and evaluate algebraic expressions and how to write and solve addition, subtraction, multiplication and division equations using inverse operations. They should also know basic multiplication and division facts.

Begin by reviewing how to use inverse operations to solve y x 6 = 54.

  • Say: Now that we have learned how to use inverse operations to solve equations, we are going to use equations to solve word problems about pets. Let's figure out what kind of equation to write for this problem.
    On the overhead, place the overhead transparency with the word problem about snakes. Read the problem aloud.
  • Ask: What is the question that we need to answer?
    Students may say that the question is “How long is the bull snake?”
  • Say: We are going to use this chart to help us solve this equation. Let's write the question here.
    Tape the chart paper Problem Solving Chart to the chalkboard. Write “How long is the bull snake?” next to the word “Question.”
  • Ask: Now let's add what we already know to the chart. What information is given in the problem?
    Students should say that the problem tells us that Kayla's king snake is 16 inches long, and that the bull snake is 4 times as long as the king snake. Add this information to the first column of the chart.
  • Ask: Remember, the variable stands for the unknown value, or the value that you are trying to find. So, what does the variable stand for in this problem?
    The students should say the variable stands for the length of the bull snake.
  • Ask: Since the variable stands for the length of the longer snake, and we already know the length of the shorter snake, what operation will we need to perform on the variable?
    Students may say division.
  • Ask: If we let b stand for the length of the bull snake, or the longer snake, who can tell me what division equation we should write to solve this problem?
    A volunteer may say b x 4 = 16. If not, tell the students that this is the equation they need to use. Write this in the second column of the chart.
  • Ask: What inverse operation do we use to solve a division equation?
    Students may say multiplication.
  • Say: We can solve for b by multiplying both sides of the equation by 4.
    In the space below where you wrote the equation, solve it as shown below:
(b × 4) x 4   =   16 x 4
b   =   64
  • Say: Now that we have solved the problem, we need to check our work. To check, we can substitute 64 for b in the original equation, simplify, and then check that both sides are equal.
    Rewrite the original equation in the third column of the chart and then simplify:
b × 4   =   16
64 × 4   =   16
16   =   16

Wrap-Up and Assessment
To see if the students understand how to use inverse operations to solve problems, have them solve the problems on the worksheet. Remind them to analyze each problem by writing the question first, finding the given information, and then writing an equation. Emphasize the need to check each answer. Here are the equations and answers:

  1. 7x − 2.00 = 7.73; x = $1.39
  2. x + 2x = 16.05; x = $5.35, 2x = $10.70
  3. 3(3.95) = x; x = $11.85
    or x ÷ 3 = 3.95; x = $11.85
  4. 4x + 5.90 = 14.66; x = $2.19
  5. x × 4 = 8; x = 32 in.

Houghton Mifflin Math Grade 5