Lesson plan

Subtraction Detectives: Missing Numbers

In this lesson, students must become detectives to solve for the missing number in each subtraction problem. They will develop and use their powers of mathematical reasoning using number bonds to find differences.
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Students will be able to determine the missing numbers in a subtraction problems (minuends and subtrahends).

(5 minutes)
  • Draw a number bond on the board with the number 5 in the large circle and number 2 in one of the smaller circles.
  • Ask students to turn and talk to a neighbor about what number they think goes in the other circle.
  • Take responses from the students. Ask them to share their reasoning. Record strategies on a piece of chart paper.
  • Now do the same process with 12 in the large circle and 10 in one of the smaller circles, giving time to discuss, share, and explain their thinking. Add any new strategies to chart paper.
  • Explain that the thinking they are using now will come in handy as the learn to find missing numbers in a subtraction problem.
(10 minutes)
  • Pass out individual student whiteboards or have students work in math notebooks.
  • Do another example like the ones you just did with the number 40 in the large circle and 25 in the smaller circle. Discuss and share.
  • It is important that students see that the same logic and strategies can be applied even as the numbers get bigger.
  • Generate more two digit examples if students additional more practice.
(10 minutes)
  • Now provide a three-digit example with the number 156 in the larger circle and 45 in the smaller circle. Have students do this three-digit example with a partner if they are unsure. Share and discuss reasoning and strategies as a class, noting that the same strategies can be applied as were used with simpler problems.
  • Demonstrate that these number bond problems can be represented more traditionally as a subtraction problem with the larger number on top and the smaller number below it.
  • They can also be represented as a missing number problem such as 156 - ? = 45. In this kind of problem, students can use the strategies above to find the missing number.
  • One last kind of missing number subtraction problem would be starting with a mystery number, such as ? - 125 = 215. Students can also employ the same strategies to solve this problem.
(15 minutes)
  • Distribute the Solve for Missing Numbers worksheet.
  • Instruct students to work through these problems, solving for the missing number using the strategies that you have noted on the chart paper or whiteboard.


  • Do two to three problems as a class, modeling different strategies for the class.
  • Look at some of the problems prior to starting the worksheet and discuss which strategies might be used for the different problems.


  • Provide problems with larger numbers for students to solve.
  • Have students do bonus problems on the worksheet.
  • Provide multiplication and division problems with missing factors to see if they can use the same process to develop strategies to solve.
(5 minutes)
  • Write the problems 276 - ? = 50 and ? - 37 = 113 on the board. Have students solve on scratch paper and then collect or spot check.
(5 minutes)
  • Have students think back to the first problem you posed in the lesson: A number bond with 5, 2, and ?, where they needed to determine the missing number. Then the problems got harder. How can the process of using a simpler problem help us figure out strategies to solve harder problems?

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