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Decompose to Multiply: 6, 7, 8, and 9
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Students will be able to decompose factors to find multiples of six, seven, eight, and nine.
- 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.
- Beginning: Pair learners with another EL with the same home language (L1) or a supportive non-EL.
- Allow students to share drawings of their math strategies.
- Intermediate: Activate prior knowledge by asking students to discuss what strategies they already know for mastering multiplication facts.
- Provide a student friendly definition of the word strategy, including a visual and examples.
Explicit Instruction/Teacher modeling(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.
- Beginning: Put students with another EL with the same L1 or a supportive peer. Have them discuss how to decompose each of the factors in the top portion of the Multiplication Strategies worksheet.
- Intermediate: Engage students in the creation of a physical movement to represent the term decompose.
- Ask students to use their own words to explain the strategies on the top of the worksheet to a peer and then the whole group.
Guided Practice(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.
- Beginning: Invite students to work in a small, teacher-led group. Ask prompting questions, such as, "How should you decompose the number?"
- Intermediate: Group students with supportive peers.
- Provide sentence stems for student discussion, such as: I will decompose this number by...
Independent working time(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.
- Beginning: Have learners work in a small, teacher-led group. Prompt students to discuss the problems and how to decompose the numbers to make the problems easier.
- Allow students to use their L1 when talking about the problems.
- Intermediate: Allow students to discuss their answers with a partner after they have completed the work independently.
- Provide a sentence stem for student discussion as they review answers, such as: I agree/disagree with you because...
- 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.
- 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).
- Beginning: Invite students to play the Race to Multiply game in a small, teacher-led group.
- Allow students to choose whether they wish to play the Race to Multiply game or complete the page of multiplication problems.
- Intermediate: Call on students to explain how to decompose numbers in the multiplication facts.
Review and closing(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.)
- Beginning: Ask students to create a visual to explain how to decompose a number.
- Intermediate: Ask students to turn and talk to a partner as a comprehension check after the video. Allow them to use their L1 or L2 as they discuss.
- Have students review the main idea of the lesson and why the strategy of decomposing numbers is helpful with multiplication.