Lesson Plan:

Breaking Apart to Put Back Together

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October 13, 2015
by Angela Fiorille

Learning Objectives

Students will be able to apply the breaking apart strategy to solve multiplication problems involving up to four-digit numbers. Students will be able to use their understanding of place value when breaking apart a larger multiplication problem and putting the answers together to find a solution.


Introduction (10 minutes)

  • Tell your students that they will need to apply their understanding of place value throughout today's lesson.
  • Spend a few minutes reviewing place value before getting into the actual lesson. Great examples of questions you could ask are: What is place value? How is understanding place value helpful when completing math problems?
  • Write a two-digit number on the board, such as 64. Ask your students how they could break this number down by place value or expanded notation. Remind students that expanded notation means writing a number to show the value of each digit.
  • Write the two-digit number in expanded form. For example: 64 = 60 + 4. Make sure your students understand that these numbers came from identifying the total of tens and ones in the number.
  • Do this same process for a few more increasingly larger numbers, such as: 79, 234, 1456.

Explicit Instruction/Teacher Modeling (5 minutes)

  • Explain that the focus of today's lesson is on solving multiplication problems involving a one-digit an up to four-digit number.
  • Tell students that while these types of larger multiplication problems can seem scary, this lesson will teach them a very helpful strategy for solving them.
  • Write breaking apart on the board. Ask your students what breaking apart means. After some discussion, remind them that it means to split up or separate.
  • Explain that the strategy they'll be using to solve multiplication problems today will be breaking apart by place value.

Guided Practice/Interactive Modeling (15 minutes)

  • Start this section by modeling this strategy for your class.
  • Write a two-digit by one-digit multiplication problem on the board. For example: 23 x 4
  • Model breaking apart the problem. For example:
    20 x 4 =
    3 x 4 =
  • Explain that you broke the two-digit number up by tens and ones, so 23 became 20 and 3.
  • Solve both of the multiplication problems. Describe the equation 20 x 4 as 2 tens times 4. If necessary, use base-ten blocks to illustrate this.
  • Explain that once the original problem has been broken apart into two separate equations, and those equations have been solved, the final step is adding the products together to find your final answer.
  • Model this for the class by writing out each step on the board. For example:
    20 x 4 = 80
    3 x 4 = 12
    80 + 12 = 92
    So, 23 x 4 = 92
  • Model this process for three-digit and four-digit by one-digit multiplication problems such as: 356 x 3 and 1,278 x 6. Make sure to show breaking apart by place value (base-ten blocks are good for to use for modeling how to find the solutions) and then adding the answers together to find the solution for the original problem.

Independent Working Time (25 minutes)

  • Tell students they will now solve equations using the breaking apart strategy independently. If you feel your students need extra support, split your class into pairs of students so each person has a partner to work with.
  • Hand a copy of the Breaking Apart and Putting Back Together worksheet to each student.
  • Remind your students to use base-ten blocks to help them if they get stuck.
  • As students work, walk around to make sure they are breaking apart correctly. Provide assistance to those who need extra support.
  • Once students finish, give them the Breaking Apart Word Problems worksheet to work on.



  • Enrichment: Challenge advanced students to try multiplication problems with five-digit and six-digit numbers.
  • Support: Gather students who need additional support together in a small group. Work with them on practicing the breaking apart strategy by multiplying one-digit numbers by two-digit numbers. Vocalizing the problem again, step-by-step, and scaffolding it with examples will help your students better understand how its done.


Assessment (10 minutes)

  • Formative assessment: Keep track of student participation during the whole group part of the lesson and modify instruction as needed.
  • Summative assessment: Assess the Breaking Apart and Putting Back Together worksheet and the Breaking Apart Word Problems worksheet to gauge your students' understanding of this strategy.

Review and Closing (5 minutes)

  • Five minutes before the end of the lesson, pull students back together to review breaking apart. Call on student volunteers to explain each step of the strategy.
  • Write a sample problem on the board, featuring a four-digit number being multiplied with a one-digit number. For example: 1,678 x 5
  • Encourage your class to break apart the problem to find the solution.

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