Lesson plan

Decompose to Multiply: 6, 7, 8, and 9

Teach your students to decompose factors as a strategy to find multiples of 6, 7, 8, and 9. This lesson supports flexible thinking and number sense.
Need extra help for EL students? Try the Decomposing Numbers pre-lesson.
EL Adjustments
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Need extra help for EL students? Try the Decomposing Numbers pre-lesson.

Students will be able to decompose factors to find multiples of six, seven, eight, and nine.

The adjustment to the whole group lesson is a modification to differentiate for children who are English learners.
EL adjustments
(2 minutes)
  • Explain to the students that in third grade they will be working on mastering their multiplication facts. Some facts are tricky or hard to remember. Today's emphasis will be on learning strategies that will help them multiply by six, seven, eight, and nine.
(13 minutes)
  • Introduce the term decompose (break apart). Explain that if we get stuck when we are multiplying, we can break apart a factor, or decompose it, into smaller numbers that are easier to multiply.
  • Write the number six on the board and explain, "For example, if you were trying to multiply by six, and you were stuck, you could break the number six into smaller parts."
  • Model how to decompose six and write 6 = 5 + 1.
  • Explain, "When we decompose, or break apart the number, we aren't changing its value. We are breaking it into chunks that are easier to think about in our head. In this example, 5+1 has the same value as six."
  • Refer back to the example on the board and explain that sometimes it is challenging to count by sixes in our heads, but we can count by fives and ones more easily.
  • Tell students that the strategies they will learn today will help them decompose factors so that they can multiply more easily in their heads.
  • Display the top portion of the Multiplication Strategies worksheet and go over each strategy and example with the students.
(10 minutes)
  • Hand out the Multiplication Strategies worksheet and review the example problem.
  • Instruct students to work with a partner to solve each problem using the decomposition strategies.
  • Go over the worksheet as a class.
(20 minutes)
  • Write four problems on the board (e.g., 6 x 5, 7 x 3, 8 x 6, 9 x 4) and instruct students to use the strategies they’ve learned to solve each problem.
  • Hand out scratch paper for students to show their work for each problem.


  • Have students use flashcards to quiz themselves or friends.
  • Teach additional strategies, like using fingers to multiply by nine (see Related books and/or media).


  • Have students play the multiplication war game with a partner and give the additional instruction that when a card with six, seven, eight, or nine comes up, the winning player for that round gets another turn.
  • Use a digital flashcard application on a tablet to play Race to Multiply or to randomly choose problems for guided practice.
(5 minutes)
  • Using flash cards for factors six through nine only, play Race to Multiply.
  • Beginning with all students standing, display a flashcard and instruct students to raise their hand if they know the answer. Call on the first student who raises his or her hand to give the answer and have them sit down. Continue until all students are seated. (Optional: Stack the deck so that the later cards are easier facts which will boost confidence for struggling students.)
  • Make a note of students who do not raise their hands to answer during the beginning as these are the students to check in with post lesson.
  • As an alternative assessment or additional practice, hand out a page of multiplication problems with facts six through nine and have students solve them. Collect and check for understanding (see resources for printable multiplication problems).
(5 minutes)
  • Show students the Multiplication Mash Up video. (Optional: Jump to the songs for facts six through nine by skipping to minute 2:49.)

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