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# Subtracting Mixed Numbers Using the Decomposition Strategy

Teach your students to subtract mixed numbers with like denominators using the strategy of decomposition. This strategy helps students to manipulate and break down numbers to help them solve tricky subtraction problems.
Need extra help for EL students? Try the Writing Questions for Word Problems pre-lesson.

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Need extra help for EL students? Try the Writing Questions for Word Problems pre-lesson.

Students will be able to solve subtraction problems with mixed numbers that have like denominators using the decomposition strategy.

The adjustment to the whole group lesson is a modification to differentiate for children who are English learners.
(5 minutes)
• Write on the board: 43 – 17 = ?
• Ask your students to explain how they would solve this problem. (Possible answers: adding on from 17 to 43 or regrouping one ten from the 43 into ten ones and then subtracting.)
• Explain that just like there is more than one strategy for subtracting whole numbers, there is more than one strategy for subtracting mixed numbers (a number that has a part that is a whole and a part that is a fraction).
• Tell students that today you are going to teach them to decompose, or break numbers apart when subtracting mixed numbers.
(8 minutes)
• Write on the board: 3 1/4 − 1 2/4 and show your students three whole pieces of copy paper and 1/4 of a piece of copy paper.
• Point out that you only have one fourth fraction pieces, but you need to subtract two fourth fraction pieces.
• Show your students how you can decompose or cut apart one of the whole pieces of paper into fourths (4/4).
• Ask students how many whole pieces and fourth pieces you have now (two whole pieces and five fourth pieces) and then write this on the board: 2 5/4.
• Emphasize to students that you have not taken anything away yet.
• Rewrite the original problem on the board using the decomposed mixed number 2 5/4 − 1 2/4.
• Show students that now you can easily subtract one whole piece of paper and two fourth pieces to get one whole piece of paper and 3 fourth pieces remaining.
• Write on the board 6 3/8 − 2 4/8.
• Model for your students how to solve this using the decomposition strategy.
(5 minutes)
• Practice solving two more problems with your students using the following equations:
• 5 1/6 − 3 4/6 =
• 4 5/8 − 1 7/8 =
• Call on student volunteers to tell you what to do at each step .
• Answer any questions that students may have.
(15 minutes)
• Post the following problems for students to copy into their math journals or onto binder paper and solve:
• 6 3/5 − 2 4/5 =
• 2 3/6 − 1 5/6 =
• 7 1/4 − 4 3/4 =
• 5 1/3 − 3 2/3 =
• 3 3/8 − 2 5/8 =
• 4 1/5 − 2 4/5 =
• Circulate and offer support as needed.

Support:

• Provide students with fraction pieces so they can practice decomposing whole numbers before beginning this lesson.
• Distribute fraction pieces to students so they can build each problem and then subtract pieces to solve during Independent Work Time.

Enrichment:

• Challenge students to write their own mixed number subtraction problems to exchange with partner or give them mixed number subtraction problems with three addends.
(2 minutes)
• Distribute whiteboards to each student.
• Write this equation on the board: 6 3/7 − 3 6/7 =
• Instruct students to solve this equation on their whiteboards and to show all of their work.
• Tell students to hold up their whiteboards when they are finished so you can check their work.
(5 minutes)
• Discuss with your students what they like or find challenging about this strategy. Some students might have figured out that they can decompose and regroup in their head and make the connection to subtraction with whole numbers.
• If your students have already learned another strategy for subtracting mixed numbers, like turning them into improper fractions, ask your students to explain which method they prefer and why.