Working Backwards Toward Answers

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Mathematics, Data Analysis and Probability, Operations (+, -, x, /, etc.), Problem Solving

Grade 3- 5


Students learn to work backwards in order to solve a problem.


Facts to Know
To solve some problems, you may need to undo the key actions in the problem. This strategy is called working backwards. But before you start these problems, keep in mind that you need to ask yourself these four important questions:

  • What does the problem ask you to find?
  • What information is needed to solve the problem?
  • How can you show the problem with numbers?
  • What is your answer?

Sample A
The bakers at Slice o' Pie Restaurant ate 4 pies that were left over from work on Thursday night. 12 pies were sold at the restaurant that night. The manager took 2 home with her after work. How many pies were at the restaurant Thursday night?
First, find out the total number of pies sold or taken home.
12 pies sold + 2 pies taken home = 14 pies
Next, add back the 4 pies that the bakers ate.
14 pies sold or taken home + 4 pies eaten by the bakers = 18 pies
Therefore, there were 18 pies at Slice o' Pie Restaurant Thursday night.
Sample B
Marta likes to borrow books from the library. She borrowed 18 books over a 3-month period of time (January-March). If Marta borrowed 8 books in January and 6 books in February, how many books did she borrow in March?
Subtract the number of books Marta borrowed in January and February from the total number of books to determine how many she borrowed in March.
18 books - 8 books - 6 books = 4 books
Marta borrowed 4 books in March.
Distribute the activity sheets and have students use what they have learned to solve the problems.


  • Working Backwards activity sheets
  • pencils

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