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Long Division Method for Whole Numbers and Decimals EM3TLG1_G6_441Z-DD_NEW.qx 6/20/08 11:56 AM Page 527 JE PRO CT Objective To review and practice the U.S. traditional long division method for whole numbers and decimals. 1 Doing the Project materials ,Recommended Use: Part A: After Lesson 2-7; Part B: After Lesson 2-8; Part C: ٗ Math Journal After Lesson 8-2 pp. 12–14 ,Key Activities ٗ Student Reference Book pp. 24E–24H and 60E–60I Students review the long division algorithm for whole numbers (Part A), decimal dividends (Part B), and decimal divisors (Part C). Key Concepts and Skills • Use long division to divide whole numbers and decimals. [Operations and Computation Goal 2] • Use long division to rename common fractions as decimals. [Number and Numeration Goal 5] • Multiply numbers by powers of 10. [Operations and Computation Goal 2] • Use the Multiplication Rule to find equivalent fractions. [Number and Numeration Goal 5] Key Vocabulary U.S. traditional long division method • divisor • dividend • short division 2 Extending the Project materials Students learn the short division algorithm for single-digit divisors. ٗ Math Journal, p. 15 Additional Information Technology This project has three parts, each of which is structured as follows: See the iTLG. 1. Students work individually to solve a problem using whatever methods they choose. 2. Solutions to the problem are examined in whole-class discussion, including solutions using long division. 3. As necessary, the class works together to use long division to solve one or more similar problems. 4. Students work in partnerships to solve problems with long division. The U.S. traditional long division method for whole numbers and decimals is introduced and practiced in a series of projects in Fourth and Fifth Grade Everyday Mathematics. If students completed those projects, then the work of this project will be review (except for the extension on short division) and students may be able to work with minimal direction from you. If your students did not complete the long division projects in fourth and fifth grades, then you should expect that they will need more support and instruction as they work on this project. In Everyday Mathematics, the U.S. traditional long division method is introduced in situations that involve sharing money equally. There are two reasons for this. One is that the U.S. traditional long division method fits most naturally with what Everyday Mathematics calls equal-sharing situations—situations in which a given amount is shared equally in a known number of shares. In applying long division to such problems, one can think about sharing the larger Project 13 441Z EM3TLG1_G6_441Z-DD_NEW.qx 6/20/08 11:56 AM Page 528 Student Page amounts—those in the left-most places in the dividend—first, and then sharing progressively smaller and smaller amounts as the algorithm moves to places further Date Time to the right in the dividend. PROJECT 13 Whole Number Long Division The other reason for using sharing money problems in early work with long division 1. The four sixth-grade classes at Linda Vista Elementary School held a is that money naturally models place value, including decimal place value through book sale to raise money for their classroom libraries. The sale raised 24E–24H $464. How much should each class get? hundredths, so using money emphasizes important place-value aspects of the long $116 division algorithm. Of course, long division is not limited to problems involving the equal sharing of money, so after initial work with such situations, students use the algorithm to solve all sorts of division problems. Still, you will notice that the opening problems in Parts A and B of this project involve sharing money. If your students Use long division to solve Problems 2–5. 2. $395 / 5 ϭ ? 3. $908 / 22 ϭ ? have little prior experience with long division, be sure to continue to use sharing $79 $41.27 money as a primary context until they understand how and why the algorithm works. Student Reference Book pages 24E–24H and 60E–60I are important resources for this project. If your students have significant prior experience with long division, they may be able to understand these pages well enough to do several parts of this project on their own. If your students have less experience with long division, you may want to refer to these pages as background. 4. 837 / 3 ϭ ? 5. 975 / 75 ϭ ? The directions provide an outline for each part of this project; you will need to adjust 279 13 your approach depending on your students’ experience with long division. 1 Doing the Project Math Journal, p. 12 PARTNER ▼ Part A: Whole Number U.S. ACTIVITY Traditional Long Division (Math Journal, p. 12; Student Reference Book, pp. 24E–24H) Ask students to solve Problem 1 on journal page 12. Once students have solved the problem individually, they should check their work with a partner’s work and check the reasonableness of the calculated results. As students work, circulate to help and note what methods they are using. Student Page Whole Numbers U.S. Traditional Long Division Method: Single-Digit Divisors U.S. traditional long division is another method you can use to divide. Share $957 among 5 people. Step 1: Share the $100 s. Step 2: Trade 4 $100 s for 40 $10 s. That makes 45 $10 s in all. 1 Ò Each person gets 1 $100 . 1 5ͤ9ෆ5ෆ7ෆ 5ͤ9ෆ5ෆ7ෆ Ϫ5 Ò 1 $100 each for 5 people Ϫ5 4 Ò 4 $100 s are left. 45 Ò 45 $10 s are to be shared. Step 3: Share the $10 s. Step 4: Share the $1 s. 19 Ò Each person gets 9$10 s. 191 Ò Each person gets 1 $1 . 5ͤ9ෆ5ෆ7ෆ 5ͤ9ෆ5ෆ7ෆ Ϫ5 Ϫ5 45 45 Ϫ45 Ò 9 $10 s each for 5 people Ϫ45 0 Ò 0 $10 s are left. 07 Ò 7$1 s are to be shared. Ϫ5 Ò 1 $1 each for 5 people 2 Ò 2 $1 s are left. $957 / 5 ∑ $191 R$2 Each person gets $191; $2 is left over. Divide. 1. 840 / 7 ϭ ? 2. 6ͤ9ෆ8ෆ4ෆ 3. 4ͤ5ෆ3ෆ9ෆ 4. 5,280 / 6 ϭ ? Check your answers on page 424. 24E Student Resource Book, p. 24E 441AA Project 13 Long Division EM3TLG1_G6_441Z-DD_NEW.qx 6/20/08 11:56 AM Page 529 Discuss solutions as a class. Expect that students will use several Student Page different methods, including partial-quotients division, informal Whole Numbers paper-and-pencil approaches, and the U.S. traditional long The U.S. traditional long division method is not limited Note to dividing money. division method. Discuss methods other than long division The “leading” 0 in the quotient is shown in the problem to help you understand the long division first, and then work through the long division solution method. It should not be included in the answer. step-by-step. Highlight the connections between steps in the 3,628 / 5 ϭ ? U.S. traditional long division method and the process of sharing Think about the problem as dividing 3,628 into 5 equal shares. money. See Student Reference Book, page 24E for an example of Step 1: Start with the thousands. Step 2: So trade 3 thousands for 30 hundreds. Share the hundreds. the connections. 0 Ò There are not enough thousands 07 Ò Each share gets 7 hundreds. 5ͤ3ෆ6ෆ2ෆ8ෆ to share 5 ways. 5ͤ3ෆ6ෆ2ෆ8ෆ Ò 36 hundreds Ϫ35 Ò 7 hundreds 5 shares As necessary, use long division to solve one or more similar 1 Ò 1 hundred is left. problems with the whole class, including problems with multidigit Step 3: Trade 1 hundred for 10 tens. Step 4: Trade 2 tens for 20 ones. divisors. (See Student Reference Book, pages 24G and 24H for a Share the tens. Share the ones. 072 Ò Each share gets 2 tens. 0725 Ò Each share gets 5 ones. 5ͤ3ෆ6ෆ2ෆ8ෆ 5ͤ3ෆ6ෆ2ෆ8ෆ discussion of the U.S. traditional long division method with Ϫ35 Ϫ35 12 Ò 10 tens ϩ 2 tens 12 Ϫ multidigit divisors.) As students solve the problems related to Ϫ10 Ò 2 tens 5 shares 10 28 Ò 20 ones ϩ 8 ones 2 Ò 2 tens are left. Ϫ25 Ò 5 ones 5 shares money, ask them to evaluate the reasonableness of their solutions 3 Ò 3 ones are left. in the context of the original situation. Suggestions: 3,628 / 5 ∑ 725 R3 Share $359 among 6 people. • 1. 5,376 / 6 = ? 2. 6ͤ8ෆ,5ෆ8ෆ6ෆ 3. 4ͤ6ෆ,9ෆ2ෆ3ෆ 4. 8,029 / 3 = ? Check your answers on page 424. • Share $8,295 among 5 people. 24F • Share $2,859 among 25 people. Student Resource Book, p. 24F When students are ready, ask them to solve Problems 2–5 on journal page 12. Encourage students to share their solutions and the strategies they utilized. Student Page Student Page Whole Numbers Whole Numbers 7720 / 25 ϭ ? U.S. Traditional Long Division Method: Make a table of easy multiples of the divisor. Multidigit Divisors 25 25 ء 1 .Double 25 50 25 ء You can use the U.S. traditional long division method to divide 2 .25 ء and 1 25 ء Add 2 75 25 ء by larger numbers. 3 .25 ء Double 2 100 25 ء 4 .25 ء Halve 10 125 25 ء 5 Share $681 among 21 people. .25 ء Double 3 150 25 ء 6 .25 ء Double 4 200 25 ء Make a table of easy multiples of the divisor. This can help you decide how many to share at 8 .Move the decimal point one place to the right 250 25 ء each step.
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