Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
EM2007MM_G3_U03.qxd 12/19/05 11:29 AM Page 81 impos06 207:wg00004:wg00004_g3u03:layouts: Name Date HOME LINK 3 10 Time Unit 4: Family Letter Multiplication and Division Unit 4 focuses on the most common uses of multiplication and division—problems that involve equal sharing and equal grouping. In Second Grade Everyday Mathematics, children were exposed to multiplication and division number stories and multiplication and division facts. To solve multiplication and division number stories, children will refer to familiar strategies introduced in second grade: Acting out problems using concrete objects, such as counters (below) Representing problems with pictures and arrays (below) 3 4 12 2 7 14 Copyright © Wright Group/McGraw-Hill Using diagrams to sort out quantities (below) children pennies per child pennies in all 4 ? 28 A sheet of stamps has 6 rows. Each row has 3 stamps. How many stamps are on a sheet? 6 3 18 Using number models to represent solution strategies (below) Problem: Solution strategies: Each child has 2 apples. There are 16 apples. How many children have apples? 2 ? 16, or I know that 16 2 8. If there are 16 apples and each child has 2, then there must be 8 children. 81 EM2007MM_G3_U03.qxd 12/19/05 11:29 AM Page 82 impos06 207:wg00004:wg00004_g3u03:layouts: HOME LINK 3 10 Unit 4: Family Letter cont. Vocabulary Important terms in Unit 4: multiples of a number The product of the equal groups Sets with the same number of number and a counting number. For example, multiples of 2 are 2, 4, 6, and 8…. elements, such as tables with 4 legs, rows with 6 chairs, boxes of 100 paper clips, and so on. multiplication/division diagram In Everyday dividend The number in division that is being Mathematics, a diagram used to represent problems in which the total number of objects in several equal groups is being considered. The diagram has three parts: number of groups, number in each group, and total number. For example, the multiplication/ division diagram here represents this number story: There are 3 boxes of crayons. Each box has 8 crayons. There are 24 crayons in all. divided. boxes 3 crayons per box 8 crayons 24 rectangular array A 2-by-6 array of eggs quotient The result of division. In 28 4 7, 28 is the dividend, 4 is the divisor, and 7 is the quotient. remainder An amount left over when one number is divided by another number. In the division number model 16 3 ∑ 5 R1, the remainder is 1. The product of a 339 number multiplied by The number 9 is a square number. itself; any number that can be represented by a square array of dots or objects. A square array has the same number of rows as columns. In 4 3 12, 4 and 3 are the factors, and 12 is the product. product The result of multiplying two numbers. Building Skills through Games In Unit 4, your child will practice division and multiplication by playing the following games. For detailed instructions, see the Student Reference Book. Division Arrays Players make arrays with counters. They use number cards to determine the number of counters and a toss of a die to establish the number of rows. Beat the Calculator A Calculator (a player who uses a calculator) and a Brain (a player who solves the problem without a calculator) compete to see who will be first to solve multiplication problems. 82 Copyright © Wright Group/McGraw-Hill two or more numbers in a product. another number, the dividend. square number A group of objects placed in rows and columns. factor Each of the divisor In division, the number that divides EM2007MM_G3_U03.qxd 12/19/05 11:29 AM Page 83 impos06 207:wg00004:wg00004_g3u03:layouts: HOME LINK 3 10 Unit 4: Family Letter cont. Do-Anytime Activities To work with your child on concepts taught in this unit and in previous units, try these interesting and rewarding activities: 1. Together with your child, sort objects into equal groups. Discuss what you could do with any leftover objects. 2. Review multiplication-fact shortcuts: turn-around facts The order of the factors does not change the product. Thus, if you know 3 4 12, you also know 4 3 12. multiplication by 1 The product of 1 and another number is always equal to the other number. For example, 1 9 9; 1 7 7. multiplication by 0 The product of 0 and another number is always 0. For example, 4 0 0; 0 2 0. square numbers Arrays for numbers multiplied by themselves are always squares. For example, 2 2 and 4 4 are square numbers. 224 4 4 16 Copyright © Wright Group/McGraw-Hill 3. Use the , Fact Triangles (a set will be sent home later) to practice the basic facts. Act as a partner by covering one number on the card and then asking your child to create a multiplication or division number model using the other two numbers. 7 8 56 56 8 7 56 56 8 7 , 7 56 7 8 8 4. Write any number–for example, 34,056. Then ask questions like the following: How many are in the thousands place? (4) What is the value of the digit 5? (50) 5. Ask questions like the following: Is 467 518 more or less than 1,000? (less) Is 754 268 more or less than 500? (less) 83 EM2007MM_G3_U03.qxd 12/19/05 11:29 AM Page 84 impos06 207:wg00004:wg00004_g3u03:layouts: UNIT HOME LINK Unit 4: Family Letter cont. 3 410 As You Help Your Child with Homework As your child brings home assignments, you might want to go over the instructions together, have your child explain the activities, and clarify them as necessary. The answers listed below will guide you through this unit’s Home Links. 5. 5 4 20; 4 5 20; 20 5 4; 20 4 5 Home Link 4 1 1. 30 apples 6. 10 6 60; 6 10 60; 60 10 6; 60 6 10 Home Link 4 2 1. 24 counters 2. 24 counters 3. 24 counters 4. 358 5. 204 6. 428 Home Link 4 7 1. 5 6 30; 6 5 30; 30 6 5; 30 5 6 Home Link 4 3 1. 5 counters per person; 0 counters remaining 2. 2 counters per person; 5 counters remaining 3. 4 weeks in January; 3 days remaining 4. 4 teams; 2 children remaining 5. 2 pencils; 4 pencils left over 8. 31 3. 2 9 18; 9 2 18; 18 2 9; 18 9 2 4. 4 7 28; 7 4 28; 28 7 4; 28 4 7 5. 9 8 72; 8 9 72; 72 9 8; 72 8 9 6. 11 jelly beans; 0 jelly beans left over 7. 577 2. 8 3 24; 3 8 24; 24 3 8; 24 8 3 9. 801 6. 6 7 42; 7 6 42; 42 7 6; 42 6 7 Home Link 4 4 Home Link 4 8 1. 6 marbles; 0 marbles left over 2. 2 cookies; 1 cookie left over 1. 7; 5; 7 5 35; 35 square units 3. 4 complete rows; 6 stamps left over 2. 6; 7; 6 7 42; 42 square units 1. 10; 10 2. 15; 15 3. 20; 20 4. 9; 9 5. 90; 90 6. 365; 365 7. 0; 0 8. 0; 0 9. 0; 0 13. 14 10. 20 11. 20 14. 15 15. 50 12. 18 Home Link 4 6 4. 9 5 45 Home Link 4 9 The following answers should be circled: 1. more than the distance from Chicago to Dallas; about 2,400 miles 1. 10; 10; 10; 10 2. 12; 12; 12; 12 3. 2 7 14; 7 2 14; 14 2 7; 14 7 2 4. 2 8 16; 8 2 16; 16 2 8; 16 8 2 84 2. about 600 miles; less than the distance from Chicago to Denver 3. more than the distance from New York to Chicago 4. less than the distance from Denver to Atlanta; more than the distance from New York to Portland; about 750 miles Copyright © Wright Group/McGraw-Hill 3. 4 8 32 Home Link 4 5 Playing Everyday Math Games at Home for Grades 3 and 4 All games require one deck of regular playing cards (with Jokers removed) and can be played by 2-3 players or teams. If using the face cards, remind everyone that J = 11, Q = 12, and K = 13. Addition Top-It 3 4 5 Practices addition facts and comparing sums Subtraction Top-It 3 4 5 Practices subtraction facts and comparing differences Use the cards from 1-10. Add more cards as the players improve. 1. Shuffle the deck and place it face down in the center. 2. Each player turns over 2 cards and calls out the sum of the numbers. Players should check each other’s sums. 3. The player with the greatest sum takes all the cards. In the case of a tie, each tied player turns over 2 more cards and calls out the sum. The player with the greater sum takes all of the cards from both plays. 4. Play ends when not enough cards are left for each player to have another turn. 5. The player who collected the most cards wins. Use the cards from 1-10. Add more cards as the players improve. 1. Shuffle the deck and place it face down in the center. 2. Each player turns over 2 cards and subtracts the smaller number from the larger number. He or she then calls out the difference of the two numbers. Players should check each other’s answers. 3. The player with the greatest difference takes all the cards. In the case of a tie, each tied player turns over 2 more cards and calls out the difference. The player with the greater difference takes all of the cards from both plays. 4. Play ends when not enough cards are left for each player to have another turn. 5. The player who collected the most cards wins. Multiplication Top-It Use the cards numbered 1-5. Add more cards as players improve. 1. Shuffle the deck and place it face down in the center. 2. Each player turns over 2 cards and multiplies the two numbers. He or she then calls out the product of the two numbers. Players should check each other’s Practices answers. multiplication facts 3. The player with the greatest product takes all the and comparing cards. In the case of a tie, each tied player turns products over 2 more cards and calls out the product. The player with the greater product takes all of the cards from both plays. 4. Play ends when not enough cards are left for each player to have another turn. 5. The player who collected the most cards wins. 3 4 5 Name That Number 3 4 5 Practices using the four operations to name numbers 1. Use all of the cards. 2. Place the deck face down in the center. Put five cards face up to the left of the deck. 3. Turn over the top card on the deck. This is the target number. 4. The first player tries to “name” the target number by adding, subtracting, multiplying, or dividing the numbers on as many of the 5 cards that are face up as possible. If the player is successful, he or she takes the target number and the other cards used to name the target number. Those cards are replaced by new cards from the deck. 5. If the player cannot name the target number, their turn is over and the next card on the top of the deck is turned over to be the target number. 6. The game is over when all of the cards in the deck have been turned over. The winner is the player who has collected the most cards. Example: If the target number is 10 and the five cards are 2, 3, 4, 7, and 8, some possible solutions are 3 + 7 = 10 (2 cards used) (2 * 3) + 4 = 10 (3 cards used) 8 + (4/2) = 10 (3 cards used) 7 – 3 + 4 + 2 = 10 (4 cards used)