U.S. Traditional Long Division, Part 1 Objective To introduce U.S. traditional long division.

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1 Algorithm Project U.S. Traditional Long Division, Part 1 Objective To introduce U.S. traditional long division. etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Doing the Project Recommended Use After Lesson 6 10 Key Concepts and Skills Subtract multidigit numbers. [Operations and Computation Goal 2] Apply multiplication facts to long-division situations. [Operations and Computation Goal 3] Solve equal-sharing division problems and number stories. [Operations and Computation Goal 4] Key Activities Students explore and practice U.S. traditional long division with two- and three-digit whole numbers divided by single-digit whole numbers. Key Vocabulary U.S. traditional long division dividend divisor quotient remainder Extending the Project Mathematical Practices SMP1, SMP2, SMP3, SMP4, SMP5, SMP6, SMP8 Content Standards 4.NBT.6 Materials Math Journal 1 or 2, pp. 25P 27P Student Reference Book, pp. 24E 24H and bills (Math Masters, p. 428; optional) 0 bills (optional) coins (optional) base-10 blocks (optional) index cards (optional) Students write and solve division number stories using U.S. traditional long division. For additional practice, students solve division problems, first using the focus algorithm (partial-quotients division) and then using any algorithm they choose. Materials Student Reference Book, pp and 24E 24H Online Additional Practice, pp. 27A 27C Advance Preparation If you intend to have students use coins and bills to model the division problems, you will need 0 bills. Make several copies of Grade 3 Math Masters, page 401. Alternatively, use index cards to create 0 bills. A31

2 Date 7 Long Division with One-Digit Divisors Use any strategy to solve the problem. Time 1. The fourth-grade classes at Glendale School put on puppet shows for their families and friends. Ticket sales totaled $532, which the four classes are to share equally. How much should each class get? $ 3 Be ready to explain how you found your answer. Use U.S. traditional long division to solve each problem / 6 = / 8 = = 564 / 3 5. = 763 / 7 1 Doing the Project Solving a Division Problem (Math Journal 1 or 2, p. 25P) WHOLE-CLASS DISCUSSION Ask students to solve Problem 1 on journal page 25P. Tell them they may use play money, paper and pencil, or any other tools they wish except calculators. Discuss students solutions. $532 / 4 = 33 Expect that students will use several different methods, including sharing or other actions with play money or other manipulatives, various informal paper-and-pencil methods, and partial-quotients division. Some students may also use U.S. traditional long division. For example: Sharing play money Math Journal, p. 25P 25P-27P_EMCS_S_MJ1_G4_P07_ indd 25 3/4/11 11:57 AM $532 / 4 = 33 Sharing base-10 blocks $532 / 4 = 33 A32 U.S. Traditional Long Division, Part 1

3 Using an informal paper-and-pencil method (See margin.) Using partial-quotients division Using U.S. traditional long division Introducing Long Division WHOLE-CLASS After discussing students solutions, regardless of whether one or more students used U.S. traditional long division, demonstrate it again as described below. Illustrate each step with pictures and, if possible, act out the problem using play money. Help students make connections between the steps in the algorithm and the actions of sharing the money $8 for each class $25 + $25 + $25 + $25 + $25 + $8 = 33 NOTE Long division is very demanding. Encourage students who may be overwhelmed to make a table of easy multiples of the divisor. For example: Step 1: Step 1 Set up the problem. Think about sharing actual bills: 5 [0]s, 3 []s, and 2 []s $532 is to be shared. We say $532 is the dividend. Think of $532 as 5 [0]s, 3 []s, and 2 []s. The money is to be shared by four classes. We say 4 is the divisor. Step 2: Step 2 Share the [0]s. There are 5 [0]s, so each class gets 1 [0]. That uses up 4 [0]s and leaves 1 [0] Each class gets 1 [0]. 1 [0] each for 4 classes = 4 [0]s 1 1 [0] is left. A33

4 Step 3 Step 3: Trade the remaining [0] for 10 []s. That makes []s in all After trading the [0] for 10 []s, there are []s in all. Step 4 Step 4: Share the []s. Each class gets 3 []s. That leaves 1 [] still to be shared Each class gets 3 []s []s each for 4 classes = 12 []s 1 1 [] is left. Step 5 Step 5: Trade the last [] to be shared for 10 []s. That makes 12 []s in all After trading the [] for 10 []s, there are 12 []s in all. Step 6 Step 6: Share the 12 []s. Each class gets 3 []s Each class gets 3 []s []s each for 4 classes = 12 []s 0 0 []s are left. A34 U.S. Traditional Long Division, Part 1

5 Step 7: Each class gets 33. We say 33 is the quotient. A number model is a good way to show the answer. Since there is no remainder, either Date 7 87 R2 Time Long Division with One-Digit Divisors cont / / 9 89 R1 $532 / 4 33 or $532 / 4 = 33 would be an acceptable number model for this problem. U.S. traditional long division is complicated, so you may want to work more examples with the whole class. For now, continue to use sharing money as a context and continue drawing pictures and, if possible, acting out the problems with play money. Later, the algorithm can be generalized to non-money contexts. Suggestions: 124 R1 174 R / / 5 $84 / 7 2 $785 / 5 57 $807 / 4 $201 R$3 86 / 7 12 R2 Math Journal, p. 26P 25P-27P_EMCS_S_MJ1_G4_P07_ indd 26 3/4/11 11:57 AM 22 / 8 5 R$2 468 / 5 93 R3 PARTNER Solving Long Division Problems with One-Digit Divisors (Math Journal 1 or 2, pp. 25P 27P; Student Reference Book, pp. 24E 24H) When students are ready, have them use U.S. traditional long division to solve Problems 2 on journal pages 25P 27P. They may find the examples on Student Reference Book, pages 24E 24H helpful. Students should note that Problems 6 9 involve remainders. Date 7 Time Long Division with One-Digit Divisors cont. 2 Extending the Project Writing and Solving Division Number Stories (Student Reference Book, pp. 24E 24H) PARTNER 10. Eight people visited a marine theme park. The total cost of the single-day admission tickets was $424. What was the cost per ticket? $ A national park charges an entrance fee of $3 per person. A school group visited the site. The cost was $288. How many people were in the school group? 96 people Have students write division number stories for a partner to solve using U.S. traditional long division. Again, students may find the examples on Student Reference Book, pages 24E 24H helpful. 12. A family went on a six-day boat cruise. They sailed a total of 432 miles. They sailed the same distance each day. How far did they travel each day? 72 miles. Four friends have birthdays in the same month. They decide to rent a hall to have a birthday party and split the cost evenly. The cost of renting the hall for one day is 72. How much did each friend pay? $ 43 Math Journal, p. 27P 25P-27P_EMCS_S_MJ1_G4_P07_ indd 27 3/4/11 11:57 AM A35

6 U.S. Traditional Long Division You can use U.S. traditional long division to divide. $935 4 Whole Numbers Solving Division Problems INDEPENDENT (Online Additional Practice, pp. 27A 27C; Student Reference Book, pp and 24E 24H) To begin, think about sharing $935 among 4 people:,,, and Step 1: Share the [0]s Each person gets 2 [0]s [0]s each for 4 people 1 1 [0] is left. 0 0 Online practice pages 27A 27C provide students with additional practice solving division problems. Use these pages as necessary. Encourage students to use the focus algorithm (partial-quotients division) to solve the problems on practice page 27A. Invite them to use any algorithm they wish to solve the problems on the remaining pages. Students may find the examples on Student Reference Book, pages and 24E 24H helpful. Step 2: Trade the last [0] for 10 []s. That makes []s in all []s are to be shared. Student Reference Book, p. 24E 024A-024J_EMCS_S_G4_SRB_ indd 24E 3/1/11 8:46 AM Go to to access the additional practice pages. Online Master Whole Numbers Name Date Time 7 Partial-Quotients Division Online Additional Practice continued Step 3: Share the []s. Use partial-quotients division to solve each problem Mrs. Johnson has a total of $872 that she wants to divide equally among her 8 grandchildren. How much should each grandchild get? $ Each person gets 3 []s. 3 []s each for 4 people 1 [] is left / 6 = / 9 = 36 Step 4: Trade the last [] for 10 []s. That makes 15 []s in all []s are to be shared. Copyright Wright Group/McGraw-Hill = 438 / 3 5. = 882 / 7 Student Reference Book, p. 24F Online Additional Practice, p. 27A EM3cuG4OP_27A-27C_P07.indd 27A 3/31/10 5:34 PM 024A-024J_EMCS_S_G4_SRB_ indd 24F 3/1/11 8:46 AM A36 U.S. Traditional Long Division, Part 1