Strategies for Multiplication (Common Core)

Transcription

1 Strategies for Multiplication (Common Core) 3, 6, 9, 12, 15, By eanne Armstrong

2 Table of Contents: p. 3-8 Multiplication Strategy Mini-Posters p. 9 Properties of Multiplication Mini-Poster p. 10 Multiplication Memorization Tricks Mini-Poster p Reduced-size Mini Posters (4 per page) can be printed/copied for student reference p Draw a Picture/Equal Groups: practice, homework, answer keys p Using Arrays: practice, homework, answer keys p Problem Solving using Equal Groups & Arrays (with answer key) p Skip Counting: practice, homework, answer keys p Repeated Addition: practice, homework, answer keys p Distributive Property: practice, homework, answer keys p Properties of Multiplication practice (with answer key) p Multiplication Facts Practice (including fill in the factor page & answer keys) p Multiplication Task Cards (with recording sheet and answer key) p. 56 Thank You & Credits

3 Draw a Picture (Equal Groups) 3 x 6 = 18 3 equal groups of 6 = 18

4 Use an Array 6 columns 3 rows 3 x 6 = 18

5 Skip Count 3, 6, 9, 12, 15, 18

6 Use Repeated Addition = 18

7 Use a Number Sentence (Memorization)

8 Use the Distributive Property (Decompose Numbers)

9 Properties of Multiplication Property: Definition: Examples: Zero Property Identity Property Commutative Property Associative Property Distributive Property Any number times zero equals zero Any number times one equals itself You can multiply numbers in any order When multiplying groups of 3 or more numbers, it does not matter which numbers you multiply first The sum of two numbers times a third number is equal to the sum of each addend times the third number. (This means you can break apart numbers to multiply them.) 5 x 0 = 0 0 x 9 = 0 8 x 1 = 8 1 x 12 = 12 3 x 4 = 12 4 x 3 = 12 (3 x 4) x 2 = 24 3 x (4 x 2) = x 5 = (10 + 2) x 5 (5 x 10) + (5 x 2) = 60

10 Multiplication Memorization Tricks X 2 Skip count by 2 s Or use doubles facts X 3 Skip count to the tune of Jingle Bells 3, 6, 9 12, 15 18, 21 24, 27, 30, 33, hey! X 4 Skip count to the tune of Dashing through the Snow 4, 8, 12, 16 20, 24 28, and 40 X 5 Skip count by 5 s Or use half of the 10 s fact X 6 Skip count the other factor by 5 s then by 1 s Example: 6 x x 9 Hold up 10 fingers Counting from the left, bend down the finger of the other factor. The fingers up to the left of the bent finger are the tens place. The fingers to the right of the bent finger are the ones. X 10 Add a zero to the other factor Example: 8 x 10 = x 6 = 60 X 11 Repeat the other factor (if it s a single digit) Example: 7 x 11 = x 3 = 33 X12 The other factor x 10 plus the other factor x 2 Example: 4 x 12 4 x 10= 40 4 x 2 = =48

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13 Name: Multiplication Practice Draw a Picture Draw a picture of equal groups to solve the following multiplication problems: 1. 4 x 3 = 2. 5 x 7 = 3. 3 x 8 = 4. 7 x 4 =

14 Multiplication Practice Draw a Picture (page 2) 5. Ants have six legs. How many legs do 4 ants have? 6. How many wheels are there on 7 tricycles? 7. If there are 5 pieces of gum in a pack, how many pieces of gum are there in 6 packs? 8. There are 8 crayons in a box. How many crayons are in 4 boxes?

15 1. 4 x 3 = x 7 = x 8 = x 4 = 28 Multiplication Practice Draw a Picture ANSWER KEY 5. Ants have six legs. How many legs do 4 ants have? 6 x 4 = 24 legs 6. How many wheels are there on 7 tricycles? 7 x 3 = 21 wheels 7. If there are 5 pieces of gum in a pack, how many pieces of gum are there in 6 packs? 5 x 6 = 30 pieces of gum 8. There are 8 crayons in a box. How many crayons are in 4 boxes? 8 x 4 = 32 crayons

16 Name: Multiplication Strategy: Draw a Picture - Homework Directions: Draw a picture of equal groups to solve the following multiplication problems x 4 = 2. 6 x 3 = 3. 2 x 9 = 4. 6 x 6 = 5. Michelle has 4 friends coming to her birthday party. If she gives each friend 8 stickers, how many stickers will she need in all?

17 Name: Multiplication Strategy: Draw a Picture Homework ANSWER KEY Directions: Draw a picture of equal groups to solve the following multiplication problems x 4 = x 3 = x 9 = x 6 = Michelle has 4 friends coming to her birthday party. If she gives each friend 8 stickers, how many stickers will she need in all? 4 x 8 = 32 stickers

18 Name: Multiplication Using Arrays - Practice Directions: Use an array to solve the following addition problems: 1. 4 x 5 = 2. 6 x 7 = 3. 3 x 8 = 4. 4 x 8 = 5. Write a multiplication sentence for this array: * * * * * * * * * * * * * * * * * * * * * * * * * 6. Write a multiplication sentence for this array: X X X X X X X X X X X X

19 Multiplication Using Arrays Practice (page 2) Use an array to solve the following problems: 7. There are 4 rows of desks in the classroom. Each row contains 9 desks. How many desks are there in all? 8. There are 3 rows of soda cans in the vending machine. If each row contains 7 cans, how many cans of soda are there altogether? 9. I planted 5 rows of flowers in my garden. If each row has 6 flowers, how many flowers do I have? 10. There are 6 rows in the parking lot. If each row has space for 8 cars, how many cars can fit into the lot in all?

20 Multiplication Using Arrays Practice ANSWER KEY Use an array to solve the following problems: 1. 4 x 5 = x 7 = x 8 = x 8 = Write a multiplication sentence for this array: 5 x 5 = 25 * * * * * * * * * * * * * * * * * * * * * * * * * 6. Write a multiplication sentence for this array: 3 x 4 = 12 X X X X X X X X X X X X 7. There are 4 rows of desks in the classroom. Each row contains 9 desks. How many desks are there in all? 4 x 9 = 36 desks 8. There are 3 rows of soda cans in the vending machine. If each row contains 7 cans, how many cans of soda are there altogether? 3 x 7 = 21 cans 9. I planted 5 rows of flowers in my garden. If each row has 6 flowers, how many flowers do I have? 5 x 6 = 30 flowers 10. There are 6 rows in the parking lot. If each row has space for 8 cars, how many cars can fit into the lot in all? 6 x 8 = 48 cars

21 Name: Multiplication Using Arrays - Homework Directions: Use an array to solve the following problems: 1. 6 x 4 = 2. 3 x 7 = 3. 5 x 8 = 4. 5 x 5 = 5. The town of Mathville is 4 blocks wide and 5 blocks long. How many square blocks are there in all?

22 Name: Multiplication Using Arrays Homework ANSWER KEY Directions: Use an array to solve the following problems: 1. 6 x 4 = 24 X X X X X X X X X X X X X X X X X X X X X X X X 2. 3 x 7 = 21 X X X X X X X X X X X X X X X X X X X X X 3. 5 x 8 = 40 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 4. 5 x 5 = 25 X X X X X X X X X X X X X X X X X X X X X X X X X 5. The town of Mathville is 4 blocks wide and 5 blocks long. How many square blocks are there in all? 4 x 5 = 20 blocks

23 Name/#: Multiplication Using Equal Groups and Arrays - Problem Solving Use an array to solve the following problems: 1. Isabelle has a sheet of stickers. It has 10 rows and there are 7 stickers in each row. How many stickers are on the sheet altogether? 2. There are 4 rows of bleachers at the baseball field. If 8 people can sit in each row, how many people can fit on the bleachers in all? 3. There are 3 shelves of cereal boxes at the grocery store. If each shelf holds 12 boxes, how many boxes of cereal are there altogether? 4. Michael collects stamps in a book. Each page in his book has 6 rows and he can put 5 stamps in each row. How many stamps can he collect on one page. (Challenge: If there are 4 pages in his book, how many stamps does he have in all?)

24 Multiplication Using Equal Groups and Arrays Problem Solving (page 2) Draw a picture of equal groups to solve the following problems: 5. I have 6 vases. If I put 4 flowers in each vase, how many flowers will there be? 6. There were 8 dogs at the park. How many legs did they have altogether? 7. I have 7 people in my family. How many eyes do we have in all? 8. I want to give every person in my class a piece of gum. There are 35 people in my class. If there are 5 pieces of gum in a pack, how many packs will I need to buy?

25 Multiplication Using Equal Groups and Arrays Problem Solving ANSWER KEY 1. Isabelle has a sheet of stickers. It has 10 rows and there are 7 stickers in each row. How many stickers are on the sheet altogether? 10 x 7 = 70 stickers 2. There are 4 rows of bleachers at the baseball field. If 8 people can sit in each row, how many people can fit on the bleachers in all? 4 x 8 = 32 people 3. There are 3 shelves of cereal boxes at the grocery store. If each shelf holds 12 boxes, how many boxes of cereal are there altogether? 3 x 12 = 36 boxes 4. Michael collects stamps in a book. Each page in his book has 6 rows and he can put 5 stamps in each row. How many stamps can he collect on one page. (Challenge: If there are 4 pages in his book, how many stamps does he have in all?) 6 x 5 = 30 stamps per page Challenge: 30 x 4 = 120 stamps in all 5. I have 6 vases. If I put 4 flowers in each vase, how many flowers will there be? 6 x 4 = 24 flowers 6. There were 8 dogs at the park. How many legs did they have altogether? 8 x 4 = 32 legs 7. I have 7 people in my family. How many eyes do we have in all? 7 x 2 = 14 eyes 8. I want to give every person in my class a piece of gum. There are 35 people in my class. If there are 5 pieces of gum in a pack, how many packs will I need to buy? 5 x 7 = 35 I would need to buy 7 packs of gum.

26 Name: Multiplication using Skip Counting - Practice Directions: Use skip counting to solve the following multiplication problems: 1. 2 x 11 = 2. 5 x 7 = 3. 3 x 4 = 4. 4 x 5 = 5. 2 x 7 = 6. 5 x 9 =

27 Multiplication using Skip Counting - Practice (page 2) Use skip counting to solve the following problems: 7. There are 5 chairs in each row. How many chairs are there in 12 rows? 8. If each person gets 3 cookies, how many cookies would 6 people get? 9. There are 10 markers in a box. How many markers are there in 8 boxes? 10. I have five people in my family. Each one of us has 6 t-shirts. How many t-shirts do we have in all?

28 Multiplication using Skip Counting - Practice ANSWER KEY Use skip counting to solve the following problems: 1. 2 x 11 = 22 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, x 7 = 35 5, 10, 15, 20, 25, 30, x 4 = 12 3, 6, 9, x 5 = 20 5, 10, 15, x 7 = 14 2, 4, 6, 8, 10, 12, x 9 = 45 5, 10, 15, 20, 25, 30, 35, 40, There are 5 chairs in each row. How many chairs are there in 12 rows? 5 x 12 = 60 chairs 8. If each person gets 3 cookies, how many cookies would 6 people get? 3 x 6 = 18 cookies 9. There are 10 markers in a box. How many markers are there in 8 boxes? 10 x 8 = 80 markers 10. I have five people in my family. Each one of us has 6 t-shirts. How many t-shirts do we have in all? 5 x 6 = 30 t-shirts

29 Name: Multiplication using Skip Counting - Homework Directions: Use Skip Counting to solve the following multiplication problems: 1. 7 x 5 = 2. 3 x 7 = 3. 2 x 8 = 4. 4 x 4 = 5. Ms. Armstrong s class is counting around the room by 3 s. What did the fifth person say? 6. Challenge: Now Ms. Armstrong s class is counting around the room by 5 s. What will the 15th person say?

30 1. 7 x 5 = 35 Multiplication using Skip Counting Homework ANSWER KEY 2. 3 x 7 = 21 5, 10, 15, 20, 25, 30, 35 3, 6, 9, 12, 15, 18, x 8 = x 4 = 16 2, 4, 6, 8, 10, 12, 14, 16 4, 8, 12, Ms. Armstrong s class is counting around the room by 3 s. What did the fifth person say? 3, 6, 9, 12, Challenge: Now Ms. Armstrong s class is counting around the room by 5 s. What will the 15th person say? 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75

31 Name: Multiplication using Repeated Addition - Practice Directions: Use Repeated Addition to solve the following problems: 1. 8 x 4 = 2. 7 x 6 = 3. 9 x 4 = 4. 6 x 6 = 5. 3 x 7 = x 4 =

32 Multiplication Using Repeated Addition - Practice (page 2) Solve the following problems using Repeated Addition: 7. Pete loves to collect rocks. If he collects 4 rocks per day, how many rocks will he have after one week? 8. April is trying to reach a new reading goal. If she reads 12 pages every morning before school, how many pages will she have read in 5 days? 9. A tiger has 4 legs. How many legs do 6 tigers have? 10. Ian, Colin, Connor, and Jacob each have 4 cookies. How many cookies do they have altogether?

33 Multiplication Using Repeated Addition - Practice ANSWER KEY Solve the following problems using Repeated Addition: 1. 8 x 4 = x 6 = x 4 = x 6 = x 7 = x 4 = Pete loves to collect rocks. If he collects 4 rocks per day, how many rocks will he have after one week? 4 x 7 = 28 rocks 8. April is trying to reach a new reading goal. If she reads 12 pages every morning before school, how many pages will she have read in 5 days? 12 x 5 = 60 pages 9. A tiger has 4 legs. How many legs do 7 tigers have? 4 x 6 = 24 legs 10. Ian, Colin, Connor, and Jacob each have 4 cookies. How many cookies do they have altogether? 4 x 4 = 16 cookies

34 Name: Multiplication using Repeated Addition - Homework Directions: Use Repeated Addition to solve the following problems: 1. 8 x 6 = 2. 7 x 4 = 3. 9 x 3 = 4. 6 x 7 = 5. If Glenn picks 6 apples every day, how many apples will he have after 4 days?

35 1. 8 x 6 = 48 Multiplication using Repeated Addition Homework ANSWER KEY 2. 7 x 4 = = = x 3 = x 7 = = = If Glenn picks 6 apples every day, how many apples will he have after 4 days? = 24 apples

36 Name: Multiplication using the Distributive Property - Practice Directions: Use the Distributive Property to solve the following problems: 1. 6 x 12 = 2. 3 x 14 = x 5 = x 8 = 5. If Glenn picks 6 apples every day, how many apples will he have after 2 weeks?

37 Multiplication using the Distributive Property Practice ANSWER KEY Directions: Use the Distributive Property to solve the following problems: 1. 6 x 12 = x 5 = 85 6 x 10 = 60 6 x 2 = x 5 = 50 7 x 5 = x 14 = x 8 = x 10 = 30 3 x 4 = x 8= 80 3 x 8 = If Glenn picks 6 apples every day, how many apples will he have after 2 weeks? 6 x 14 = 84 apples

38 Name: Multiplication using the Distributive Property - Homework Directions: Use the Distributive Property to solve the following problems: 1. 3 x 17 = x 4 = x 4 = x 3 = 5. There are 28 students in the class. If I give each student 3 stickers, how many stickers will I need?

39 Multiplication using the Distributive Property Homework ANSWER KEY 1. 3 x 17 = 51 3 x 10 = 30 3 x 7 = x 4 = x 4= 40 5 x 4 = x 4 = x 4 = 80 3 x 4 = x 32 = 96 3 x 30= 90 3 x 2 = There are 28 students in the class. If I give each student 3 stickers, how many stickers will I need? 28 x 3 = 84 stickers

40 Name: Properties of Multiplication - Practice Directions: Use what you know about the Properties of Multiplication to fill in the blanks below: 1. 3 x 17 = 17 x 2. 4 x (6 x 2) = (4 x 6) x x 0 = 4. 1 x 32 = x 5 = (10 x ) + (6 x ) x 4 = 4 x Directions: Identify the Property of Multiplication shown in the problems below: 7. (5 x 2) x 3 = 5 x (2 x 3) x 1 = x 12 = (6 x 10) + (6 x 2) 8. 5 x 7 = 35 7 x 5 = x 0 = x 6 = 6 x 9

41 Properties of Multiplication Practice ANSWER KEY Directions: Use what you know about the Properties of Multiplication to fill in the blanks below: 1. 3 x 17 = 17 x x (6 x 2) = (4 x 6) x x 0 = x 32 = x 5 = (10 x 5) + (6 x 5) x 4 = 4 x 43 Directions: Identify the Property of Multiplication shown in the problems below: 7. (5 x 2) x 3 = 5 x (2 x 3) Associative Property x 1 = 14 Identity Property x 12 = (6 x 10) + (6 x 2) Distributive Property 8. 5 x 7 = 35 7 x 5 = 35 Commutative Property x 0 = 0 Zero Property x 6 = 6 x 9 Commutative Property

42 Multiplication Facts Practice #1 Name: 4 x 5 6 x 3 7 x 7 8 x 2 6 x 5 3 x 3 9 x 4 4 x 8 5 x 9 11 x 4 6 x 8 9 x 3 4 x 4 6 x 4 7 x 8 4 x 2 6 x 7 8 x 3 3 x 7 2 x 2 5 x 7 12 x 3 5 x 5 6 x 6 7 x 4

43 Multiplication Facts Practice # 1 ANSWER KEY 4 x 5 6 x 3 7 x 7 8 x 2 6 x x 3 9 x 4 4 x 8 5 x 9 11 x x 8 9 x 3 4 x 4 6 x 4 7 x x 2 6 x 7 8 x 3 3 x 7 2 x x 7 12 x 3 5 x 5 6 x 6 7 x

44 Multiplication Facts Practice #2 Name: 9 x 4 3 x 5 6 x 7 8 x 3 2 x 7 5 x 5 4 x 8 11 x 3 6 x 6 8 x 2 7 x 5 9 x 3 5 x 8 4 x 6 12 x 2 4 x 3 7 x 3 9 x 6 4 x 7 8 x 8 9 x 5 3 x 6 8 x 7 12 x 0 9 x 1

45 Multiplication Facts Practice #2 ANSWER KEY 9 x 4 3 x 5 6 x 7 8 x 3 2 x x 5 4 x 8 11 x 3 6 x 6 8 x x 5 9 x 3 5 x 8 4 x 6 12 x x 3 7 x 3 9 x 6 4 x 7 8 x x 5 3 x 6 8 x 7 12 x 0 9 x

46 Note: The following page is for multiplication facts practice, but you will notice that it looks a little different. At the top of the page there is a line that says Fill in the factor: Simply choose a factor and students will multiply all of the numbers in the boxes by that factor. This is a terrific paper saver! Rather than printing out new test/practice pages, you can just change the factor at the top of the page and students have a brand new set of facts to practice. This works well for independent practice/homework and for timed multiplication tests. It can be differentiated for students working on different multiplication facts. This page also works well in sheet protectors for use with dry-erase markers.

47 Multiplication Facts Practice Fill in the Factor: Name: Directions: Multiply the following numbers by the factor filled in on the line above. For example, if the factor on the line above is 8, then the first problem would be 8x5. x 5 x 3 x 7 x 2 x 6 x 3 x 4 x 8 x 9 x 11 x 9 x 3 x 4 x 6 x 8 x 2 x 7 x 3 x 1 x 2 x 10 x 12 x 5 x 0 x 4 x 0 x 11 x 1 x 10 x 12

48 Directions: 1. Choose a task card. 2. Decide which strategy to use. 3. Solve the multiplication problem. Make sure to show your work in the correct box on the Recording Sheet.

49 7 x 5 = 8 x 6 = 12 x 4 = x 18 = There are 2 wheels on a bike. How many wheels are on 12 bikes? 9 x 7 =

50 I have 7 people in my family. We have 5 toes on each foot and we each have 2 feet. How many toes do we have in all? 7 x 7 = Write a multiplication sentence for this array: X X X X X X X X X X X X There are 6 bananas in a bunch. How many bananas are in 4 bunches? Crayons come in a box of 16. How many crayons are in 5 boxes? 4 x 8 =

51 8 x 7 = There are 9 children at the party. If each child gets 3 cookies, how many cookies are there in all? There are 9 rows of seats at the theater. Each row has 11 seats. How many seats are there in all? Marco runs 3 miles per day. How many miles does he run in a week? There are 4 students at each table. There are 8 tables. How many students are there? 17 x 3 =

52 Write a multiplication sentence for this array: X X X X X X X X X X X X X X X X X X X X If Marley reads 5 pages per day, how many days will it take him to read 40 pages? There are 7 different types of crackers at the store. There are 6 boxes of each type. How many boxes of crackers are there? , 23. There are 8 pieces of candy in each box. How many pieces of candy are in 5 boxes? There are four rows of flowers in my garden and each row has 9 flowers. How many flowers are in the garden in all? 11 x 8 =

53 Name: Multiplication Task Cards - Recording Sheet

54 Multiplication Task Cards - Recording Sheet (page 2)

55 Subtraction Task Cards ANSWER KEY wheels toes bananas crayons x 4 = miles cookies students seats x 5 = pieces days flowers boxes

56 Thank you for purchasing this product!! Fonts: Credits: Graphics/Borders/Backgrounds: