1. Grade 4
EnVisions Math
Topic 6
Power Point Lessons

2. Arrays and Using an Expanded Algorithm
Literature Link: The Grapes of Math by Greg Tang (1-2 pages)
Lesson 6-1
CCSS 4.NBT.5

3. Warm Up
4 X 8
9 X 7
5 X 5
3 X 6
8 X 6
7 X 7

4. Think and Write
We use arrays to solve multiplication problems by representing the problem as a number of rows with equal objects in each row. In real life what can you think of that comes in rows?
Picture albums, desks in a classroom, chairs in an auditorium, plane seats, etc.

5. Arrays
Array: A strategy used to solve a multiplication problem by drawing equal rows with an equal number of objects in each row.
Example: For the problem 2 x 4, you would make 2 rows with 4 objects in each row.

6. Partial Products with Arrays
How can you make an array to show 4 X 12?
Look at the tens and ones in the 12 as two different numbers. Make an array for 4 X 1, and another for 4 X 2.
Remember that since the 1 is in the tens place, and 4 X 1 = 4, it is really worth X 2 = 8
Now add

7. Problem 1
Thomas arranges his video games in 4 rows with 16 games in each row. Build an array to show Thomas’ games.

8. Problem 2
Sadie bakes 3 rows of cupcakes with 14 cupcakes in a row. Build an array to find out how many cupcakes Sadie baked.

9. Problem 3
Josh puts his baseball cards in 4 rows with 26 cards per row. Build an array to find how many cards Josh has in all.

10. Problem 4
Sean puts his dinosaurs into 3 rows with 22 dinosaurs in each row. Build an array to see how Sean arranged his dinosaurs and find his total number of dinosaurs.

11. Problem 5
Mariana bakes cookies in 6 rows with 16 cookies per row. Build an array to find out how many cookies Mariana baked in all.

12. Challenge
How many more stamps are in 4 rows of rocket stamps than 5 rows of flower stamps?
Type of Stamps
Number Per Row
Rocket 30
Presidents 24
Flower 22

13. Connecting the expanded and standard algorithms
Literature Link: The Grapes of Math by Greg Tang (1-2 pages)
Connecting the expanded and standard algorithms
Lesson 6-2
CCSS 4.NBT.5, 4.OA.3

14. Warm up
Write the fact family for 8, 9, and 72.

15. Think and write
What is your favorite strategy for multiplying larger numbers? Why do you prefer this strategy?

16. Expanded algorithm method
The plane can hold 72 people. How many people can 6 planes hold? 72
X 6
First do 6 X 70 = 420. Then do 6 X 2 = 12. Add
= 432.

17. Classic multiplication method
The plane can hold 72 people. How many people can 6 planes hold?
Write the multiplication number sentence. Solve with regrouping: 72
X 6

18. Solve! Solve using the expanded algorithm method. 43 X 5 64 X 4 72 X 7

19. Solve!
Solve using the classic method.
56 X 4
78 X 3
92 X 6
17 X 8

20. Problem 1
Marina makes $56 a day babysitting. If she babysits for 6 days, how much money will she make? Choose from the expanded algorithm method or the classic method and solve.

21. Problem 2
A ticket to the zoo costs $23 per person. If Mr. Shelby buys 7 tickets, how much does he spend? Choose from the expanded algorithm method or the classic method and solve.

22. Problem 3
An extra large pizza at Rino’s costs $19. If the football team buys 8 pizzas, how much money will they spend? Choose from the expanded algorithm method or the classic method and solve.

23. Problem 4
There are 27 children in each class. If there are 6 classes, how many children are there in all? Choose from the expanded algorithm method or the classic method and solve.

24. Multiplying 2 digit by 1 digit numbers
Literature Link: Anno’s Mysterious Multiplying Jar by Masaichiro and Mitsumasa Anno
Lesson CCSS 4.NBT.5, 4.OA.3

25. Warm Up
Put these numbers in order from least to greatest. 4,576 5,476 5,647 4,765

26. Think and Write
What careers require a person to master multiplication?

27. Checking Answers
When you multiply larger numbers, it is helpful to check to see if your answer is correct by using estimation. Estimation, or rounding, allows you to see if your answer is close to the estimate.
When estimating, round to the nearest TEN for the closest estimate.

28. Rounding Review
When rounding to the nearest ten, look at the ONES place.
Remember if the number is four or lower, round DOWN. If the number is five or higher, round UP.

29. Rounding Song (to the tune of “If You’re Happy & You Know It”
When you round, look at the place to the right. When you round, look at the place to the right. When you’re rounding a number always look to the right place. When you round look at the place to the right.
If the number’s 4 or lower, you round down. If the number’s 4 or lower, you round down. If the number’s 4 or lower, then the number will be smaller. If the number’s 4 or lower, you round down.
If the number’s 5 or higher, you round up. If the number’s 5 or higher you round up. If the number’s 5 or higher, then the number will be bigger. If the number’s 5 or higher, you round up.

30. Estimation Practice Round these numbers to the nearest ten. 456 712
998
1,342
5,677

31. Multiply, then Check! Multiply to solve. Then estimate to check.
45 X 7
64 X 8
32 X 9
56 X 3

32. Problem 1
A bus holds 54 people. If there are 7 buses, how many people can they hold in all? Solve, then estimate to check.

33. Problem 2
A football team has 45 players that are active on game day. How many players are active if there are 6 teams playing today? Solve, then estimate to check.

34. Problem 3
Mrs. Monroe drives 38 miles to and from work every day. How many miles does she drive this week if she works 6 days? Solve, then estimate to check.

35. Multiplying 3 and 4 digit by 1 digit numbers
Lesson CCSS 4.NBT.5
Literature Link: 7 X 9 = Trouble by Claudia Mills

36. Warm up
Put these numbers into standard form.
100, ,
Fifty two thousand forty three
500, ,
Six hundred fifty four thousand ninety two

37. Think and write
When might you have to multiply larger numbers (3 and 4 digit numbers) in your everyday life?

38. Multiplying by larger numbers
Just as in multiplying with 2 digit X 1 digit numbers, you can use either the classic multiplication method or the partial products (expanded algorithm) method.
To multiply with the classic method, you multiply and regroup if needed. Try it!
734
X 8

39. Partial products multiplication
Multiplying with partial products can be a good strategy for multiplying larger numbers. Let’s say you have to solve 456 X 8.
456
X First multiply the ones. 6 X 8= 48.
Then multiply the tens. 50 X 8 = 400.
Finally multiply the hundreds. 400 X 8 = 3200.
Add the numbers together to find the product.
= 3,648

40. Multiply! Choose the method you prefer to solve. 762 X 4 337 X 6

41. Problem 1
There are 365 days in one year. How many days are there in 6 years? Choose your preferred method and solve.

42. Problem 2
Carl makes $869 a week. How much money does he make in 4 weeks?

43. Problem 3
A plane ticket costs $287. How much would 4 plane tickets cost?

44. Multiplying by 1 Digit Numbers
Lesson 6-5
CCSS 4.NBT.5, 4.NBT.3, 4.OA.3
Literature Link: Multiplying Menace The Revenge of Rumpelstiltskin by Pam Calvert (first half of book)

45. Warm Up
Estimate, then solve.

46. Think and Write
Tell about a time when you have had to multiply three digit by one digit numbers in your everyday life.

47. Estimating to Check
When you multiply large numbers, you can check your work by estimating. If the actual sum is close to your estimate, then it is reasonable.
Rounding to the nearest ten gives you the closer estimate than rounding to the nearest hundred.

48. Rounding Roundup
Round these numbers to the nearest TEN.
283
947
698
1,031
5,259

49. Find each product. Then estimate to check for reasonableness. 449 X 4
Practice!
Find each product. Then estimate to check for reasonableness.
449 X 4
382 X 2
905 X 8
557 X 7

50. Problem 1
When Miya visits her grandmother, she drives 218 miles. If she visits her grandmother 4 times a month, how many miles does Miya drive in all? Find your product and estimate to check for reasonableness.

51. Problem 2
A male gorilla weighs about 359 pounds. How much would 7 male gorillas weigh altogether? Find your product and estimate to check for reasonableness.

52. Problem 3
Antonio makes $262 a day at work. If he works 6 days this week, how much will he make? Find your product and estimate to check for reasonableness.

53. Problem 4
Sarah is on vacation for 4 days. Every morning she buys breakfast for $12, lunch for $18 and dinner for herself and her family for $89. How much does she spend in all during her vacation? Find your product and estimate to check for reasonableness.

54. Problem Solving: Missing or Extra Information
Literature Link: Multiplying Menace The Revenge of Rumpelstiltskin by Pam Calvert (second half of book)
Problem Solving: Missing or Extra Information
Lesson 6-6
CCSS 4.NBT.5, 4.OA.3

55. Warm up
Solve.
28 X 3
47 X 8
33 X 9
16 X 7

56. Think and write
Tell about a time where you did not have enough information to solve a problem. What did you do, and were you able to solve the problem?

57. Steps to problem solving
Knowing steps to problem solving can help you in figuring out what information is needed.
1. Read the problem carefully.
2. Underline the question(s) you are being asked.
3. Circle the information you need to solve.
4. Identify the operation you will use.
5. Solve.

58. Practice problem Use the problem solving steps to solve.
Mario swam 28 laps per day. Each lap took him 3 minutes to swim. How many laps did he swim in a week?
Is there any information here that you don’t need to solve this problem? Cross it out. Then solve.

59. Practice problem 2
The length of a rectangular room is 16 feet. What is its area?
What information is missing? Why do you need this information to solve?
If the width is 7 feet, what is the area of this room?

60. Problem 1
Michaela has 4 rabbits. She buys each rabbit a cage for $28. Each cage is 42 inches long and 32 inches wide. How much does Michaela spend on the cages in all?

61. Problem 2
Eddie runs around the field 8 times. How many yards does he run in all?

62. Problem 3
Kira buys 8 watermelons for $3.25 each. Each watermelon weighs 3 pounds. How much money does Kira spend in all?

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