Using the Partial Quotients Strategy for Division with One-Digit Divisors
Students will be able to solve division problems with one-digit divisors and no remainder using the partial quotients strategy.
- Show your students a bag with 51 items in it like colored pencils, dominoes, or books.
- Tell your students that you would like to divide these items into three groups.
- Explain that while you could divide them one at a time into each group, you would like to be more efficient and put small, even amounts into each group repeatedly until you have used up all the items.
- Ask your students for suggestions about how to divide these items (e.g., place five items in three different groups at a time).
- Apply different students' suggestions for dividing these items until all of the items have been divided the evenly into 3 groups. Show students that each group contains 17 items. Tell students that they have figured out that 51 divided by 3 is 17.
- Tell students that this activity is preparing them to learn about partial quotient strategy for solving long division problems because it took several steps to find the quotient.
Explicit Instruction/Teacher modeling(10 minutes)
- Tell students that they will now learn how to solve division equations using the partial quotients strategy.
- Write on the board 972 ÷ 4, using a division bracket. Remind students that 4 is the divisor (the number of groups they are dividing into). The divisor goes to the left of the division bracket. 972 is the dividend (the number being divided). The dividend goes inside the bracket.
- Draw a vertical line going down from the right end of the division bracket and explain to students that this line will help to keep the partial quotients separate from the rest of the long division problem.
- Tell students there are four steps to the partial quotient strategy.
- Post a piece of chart paper and write the following steps:
- Step 1: Write a list of easy factors for the divisor (e.g., 4 X 100 = 400).
- Step 2: Subtract from the dividend an easy multiple of the divisor (e.g., 972 – 400 = 572). Record the partial quotient in the column to the right of the vertical line (100 X 4).
- Step 3: Repeat until the dividend has been reduced to zero or the remainder is less than the divisor.
- Step 4: Add the partial quotients to find the quotient.
- Model for students how to complete the equation 972 divided by 4 using the four steps of the partial quotient strategy.
- Tell students that this problem can be solved in more than one way because different partial quotients can be used each time.
Guided Practice(10 minutes)
- Write 704 ÷ 4 on the board, using a division bracket.
- Call on a student volunteer to solve this problem at the board using the four steps of the partial quotient strategy.
- Review the volunteer's work as a class to identify any possible errors.
- Write 1,820 ÷ 5 using a division bracket.
- Distribute whiteboards to each student.
- Ask students to solve this problem on their whiteboards using the partial quotient strategy.
- Instruct students to hold up their whiteboards so you can check their work.
- Review the answers as a class and answer any questions that may have arisen.
Independent working time
- Write the following equations on the board:
- 54 ÷ 3
- 216 ÷ 6
- 304 ÷ 4
- 861 ÷ 3
- 984 ÷ 8
- 1,263 ÷ 3
- Distribute math journals or binder paper.
- Tell students to solve these problems using the partial quotient strategy. Remind students to use the four steps written on the chart paper as a resource.
- Instruct students to compare their work with a partner when they are done to see if they solved the problem using the same partial quotients.
- Pre-teach how to use multiplication facts to help solve division problems. Show your students how checking to see if a divisor fits 1, 10, 100, or 1000 times is a good place to start with each problem when using partial quotients.
- Have students solve the same division problem twice using different partial quotients each time and then explain which partial quotients enabled them to solve the problem more efficiently.
- Distribute whiteboards to each student.
- Write 786 ÷ 6 on the board using a division bracket.
- Tell students to solve this problem using the partial quotient strategy.
- Instruct students to hold their whiteboards up for you to check their answers.
Review and closing(3 minutes)
- Discuss with your students what they liked or found challenging about the partial quotient strategy.
- Ask students to share other strategies for solving long division problems.
- Call on students to explain which long division strategy they prefer and why.