How can you use arrays to divide whole numbers that do not divide evenly? to find how many rows of 3 are in 19 and if any are left over.

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1 ? Name 9.1 Remainders Essential Question How can you use arrays to divide whole numbers that do not divide evenly? Number and Operations 4.4.E MATHEMATICAL PROCESSES 4.1.C, 4.1.G Investigate Hands On Materials square tiles Erica and 2 friends are playing a game of dominoes. There are 19 dominoes in the set. Erica wants each player to receive the same number of dominoes. Can she divide them equally among the 3 players? Why or why not? You can use an array to find the number of dominoes each player will receive. A. Use 19 tiles to represent the 19 dominoes. Make an array to find how many rows of 3 are in 19 and if any are left over. B. Make a row of 3 tiles. C. Continue to make as many rows of 3 tiles as you can. Leftover Tiles D. Find the number of rows of three tiles and the number of tiles left over. Record your answer. _ rows of 3 tiles _ tile left over So, each player gets _ dominoes with _ domino left over. Math Talk Mathematical Processes Explain how the model helped you find the number of dominoes each player receives. Why is 1 tile left over? Module 9 311

2 Make Connections When a number cannot be divided evenly, the amount left over is called the remainder. Hands On Use square tiles to find Use 29 tiles. Use the tiles to make rows of 5. The number of tiles left over is the remainder. Leftover Tiles For 29 5, the quotient is _ and the remainder is _, or 5 r4. Math Talk Mathematical Processes How do you know when there will be a remainder in a division problem? Share and Show Use tiles or draw an array to find the quotient and remainder ) ) )

3 Name Problem Solving Multi-Step What s the Error? Leftover Tiles 9. Macy, Kayley, Maddie, and Rachel collected 13 marbles. They want to share the marbles equally. How many marbles will each of the 4 girls get? How many marbles will be left over? Frank used an array to solve this problem. He says his array represents 4 ) 13. What is his error? Look at the way Frank solved this problem. Find and describe his error. Use tiles or draw an array to model and solve the problem. So, each of the 4 girls will get _ marbles and _ marble will be left over. 10. Explain how you use an array to find the quotient and remainder. Module 9 Lesson 1 313

4 Daily Assessment Task Mathematical Processes Fill in the bubble completely to show your answer. 11. Jordyn explains to her friends how to play checkers. She has 29 minutes to explain to 3 teams. She wants to take the same number of whole minutes to explain to each team. What is the greatest number of whole minutes she can take to explain the rules to each team? A 8 minutes C 9 minutes B 4 minutes D 10 minutes 12. Use Tools Kenny wants to put 37 books on 5 shelves. He wants the same number of books on each shelf and he will put the remaining books in a box. How many books does Kenny put in the box? Use tiles or draw an array to help you find the number of books Kenny put in the box. A 6 books C 7 books B 2 books D 3 books 13. Multi-Step Barb puts 60 games into boxes to donate. Each box can hold 7 games. How many more games does Barb need so that all the boxes can have 7 games? A 3 games C 2 games B 8 games D 9 games TEXAS Test Prep 14. Rena has 23 DVDs that she wants to sort into rows of 6 each. How many DVDs will Rena have left over? A B 5 C 17 D 4

5 Homework and Practice Name Number and Operations 4.4.E MATHEMATICAL PROCESSES 4.1.C, 4.1.G 9.1 Remainders Use tiles or draw an array to find the quotient and remainder ) ) ) ) ) ) 43 Problem Solving 17. Miguel has 48 pieces of quartz. He wants to divide the pieces equally into 9 bags. How many pieces of quartz will be in each bag? How many pieces will be left over? Use tiles or draw an array to help you find the answer. 18. Lacy has 65 tickets for the school carnival. She and 6 friends will share the tickets equally. How many tickets will each person receive? How many tickets will be left over? Use tiles or draw an array to help you find the answer. Each bag will have pieces and pieces will be left over. Each person will get tickets and tickets will be left over. Module 9 Lesson 1 315

6 Lesson Check TEXAS Test Prep Fill in the bubble completely to show your answer. 19. Rebecca made 36 cookies for the school bake sale. If she puts 5 cookies in a bag, how many bags will she use? A 6 B 5 C 8 D Felix has 60 towels to stack on a store shelf. He puts 8 towels in each stack. He puts any remaining towels in a drawer below the shelf. How many towels does Felix put in the drawer? A 7 B 4 C 6 D Lynn is packing 52 books for her family s move. Each box can hold 9 books. What is the least number of boxes Lynn will need to pack all of the books? 22. Paul has 39 vocabulary cards to study. If he puts the cards in groups of 6, how many groups will he have, and how many cards will he have left over, if any? A 7 B 8 C 6 D 5 A B C D 6 groups with 3 cards left over 6 groups with 4 cards left over 6 groups with no cards left over 5 groups with 4 cards left over 23. Multi-Step Alyson has 46 beads to make bracelets. Each bracelet has 5 beads. How many more beads does Alyson need so that all the beads she has are used? 316 A 9 B 4 C 1 D Multi-Step Brad has saved $23 to spend on posters for his room. If each poster costs $4, how much more money does Brad need to save to buy 6 posters? A $6 B $4 C $3 D $1