1. Grade 4
EnVisions Math
Topic 5
Power Point Lessons

2. Arrays and Multiplying by 10 and 100
Grade 4 Lesson 5-1
CCSS 4.NBT.5
Literature Link: The Grapes of Math by Greg Tang (1-2 pages of riddles)

3. Warm Up
Marisol goes to the bakery to buy cupcakes. She buys 3 carrot cupcakes for $3.00 each, 2 vanilla cupcakes for $2.00 each, and 3 mini cupcakes for $1.00 each. How much does Marisol spend in all?

4. Think and Write
Explain how you would make an array to solve the multiplication fact of 3 X 8.

5. Multiplying By 10
When you multiply anything by 10, write the number being multiplied, then add a 0.
EXAMPLE: 12 X 10= 120
144 X 10= 1,440

6. Practice! Solve these problems by using the X10 pattern. 14 X 10

7. Multiplying by 100
Just like when you multiply by 10, when you are multiplying by 100, write the number you are multiplying, then add 2 zeros.
EXAMPLE: 255 X 100= 25,500

8. Practice!
Solve!
48 X 100
183 X 100
327 X 100
829 X 100
1,243 X 100
2,348 X 100

9. Problem 1
When Steve works at the snack stand, he makes $100 for the day. If he works 2 days per week for 8 weeks, how much money does he make?

10. Problem 2
Tara’s dad drives 100 miles every day to and from work. If he works 24 days out of the month, how many miles does he drive?

11. Multiplying by Multiples of 10 and 100
Literature Link: The Grapes of Math by Greg Tang (1-2 pages of riddles)
Grade 4 Lesson 5-2
CCSS 4.NBT.5

12. Warm Up
The Amazon River is 6,437 km. long. The Mississippi River is 3,734 km. long. How much longer is the Amazon River?

13. Think and Write
What are some things that come in groups of ten?

14. Solve! 3 X 4 = ____ 3 X 40= ____ 3 X 400= ___
How would you solve this problem? Is there a pattern that can help?

15. Multiples of Ten
When you multiply by a multiple of ten (a number ending in a zero or multiple zeros), multiply the basic fact, then count the number of zeros and add that number of zeros to the end of the product.
Example: 4 X 50
4 X 5 = 20, then count zeros. 50 has 1 zero,
so the answer is 200.

16. Practice!
Solve!
4 X 80
8 X 90
12 X 40
8 X 600
900 X 4
300 X 8
700 X 7

17. Problem 1
A male lion weighs about 400 pounds. How much would 6 male lions weigh?

18. Problem 2
Adult gorillas can weigh about 300 pounds. About how much would 7 adult gorillas weigh?

19. Problem 3
A giraffe weighs about 1,800 pounds. How much would 3 giraffes weigh?

20. Problem 4
A tiger weighs about 300 kg. An Amur Leopard weighs about 50 kg. Which weighs more, a group of 3 tigers or a group of 12 leopards?

21. Breaking Apart to Multiply
Grade 4 Lesson 5-3
CCSS 4.NBT.5
Literature Link: The Grapes of Math by Greg Tang (1-2 pages of riddles)

22. Warm Up
Write a multiplication number story for the fact 8 X 3. Then, make an array to solve 8 X 3.

23. Think and Write
Describe why you might want to break apart a larger number before you multiply.

24. Breaking Numbers Apart
Let’s say you have the number 547.
How many hundreds are there?
How many tens?
How many ones?
So the number 547, broken apart, is You can use this strategy to help you multiply.

25. Breaking Apart Numbers
Practice breaking apart the following numbers into tens and ones, or hundreds-tens-ones. 28 43 89
145
737
896
Remind students that in order to use this strategy of breaking apart to multiply, they first have to be able to break apart numbers.

26. Multiplying by Breaking Apart
Let’s say you have the problem 24 X 8. You can break apart to multiply more easily.
First, break apart 24. What does it break apart into?
Now, do 20 X 8. What is that?
Next, do 4 X 8. What is your product?
Finally, add the products together. What is your sum?
= 192
You may want to model this on the board as you go step by step or have students do the steps on slates/communicator boards.

27. Practice! Use the breaking apart method to multiply. 72 X 7 84 X 6

28. Problem 1
A sweater costs $28. How much would 7 sweaters cost? Use breaking apart to solve.

29. Problem 2
A new pair of jeans costs $38. Symia wants to buy 3 pairs. How much will she spend?

30. Problem 3
Jackets cost $57 each. If Mrs. Thompson wants to buy a jacket for each of her 4 children, how much will she spend?

31. Using Mental Math to Multiply
Literature Link: The Grapes of Math by Greg Tang (1-2 pages of riddles)
Grade 4 Lesson 5-4
CCSS 4.NBT.5, 4.NBT.3, 4.OA.3

32. Warm Up
Solve!
7 X 8
6 X 4
7 X 7
8 X 9
4 X 6
6 X 8

33. Think and Write
List some times you might need to multiply numbers in your head (mental math).

34. Compensation
Compensation is when you choose numbers close to the numbers in a problem to make the math easier. Then you adjust the answer for the numbers chosen.
Remember, there are two steps to compensation: Substitute & Adjust!

35. Steps for Mental Math
Imagine that you have to multiply 27 X 3. How can you multiply mentally?
You can round 27 to 30 because it is much easier to do 30 X 3. Try it!
You should have the product of 90. Now, think- what is the difference between 30 and 27?
You should have the difference of 3. Multiply 3 X 3 (since the original problem multiplied by 3), then subtract that product from 90 to get your actual answer.
90 – 9 = 81
Walk through this step by step with your students. Model it on the board or have students do it on slates/communicators.

36. Practice!
Try using mental math to solve.
32 X 4
48 X 3
88 X 6
119 X 3
127 X 4
326 X 7
Remind students that mental math with compensation is one strategy for solving multiplication problems. If they are truly uncomfortable with this strategy, I allow students to go back to breaking apart or “old-fashioned” multiplication. I explain that we teach students a lot of strategies so they can choose what works best, like choosing from a menu.

37. Problem 1
In the Amazon rainforest, the toucan has a bill that is 19 centimeters long. How long would 6 toucan bills be? Solve using the mental math compensation method.

38. Problem 2
A sloth sleeps about 18 hours a day. How many hours does a sloth sleep in one week? Use mental math to solve.

39. Problem 3
An Amazon River Dolphin weighs about 217 lb. How much would 5 river dolphins weigh altogether?

40. Problem 4
Piranhas can grow up to 26 cm. long. How long would 4 piranhas be in all?

41. Using Rounding to Estimate
Grade 4 Lesson 5-5
CCSS 4.NBT.5, 4.NBT.3
Literature Link: Math Attack by Joan Horton

42. Round the following numbers to the nearest ten. 148 902 3,498 5,999
Warm Up
Round the following numbers to the nearest ten.
148
902
3,498
5,999

43. Think and Write
What rules do you apply when you round numbers to the nearest ten? What rules do you apply when you round numbers to the nearest hundred?
Remind students that when rounding a number, always look to the place to the right of the number. When rounding to the nearest tens, the number in the ones place is the “boss” and tells the number in the tens place to round up or round down. When rounding to the nearest hundred, the number in the tens place is the “boss”.

44. Estimating numbers
Sometimes, you are asked to estimate numbers before multiplying, or you may choose to do this to make it easier to multiply. Can you think of any times in your life that you would estimate when you multiply?
When the number is a 2-digit number, round to the nearest ten. If it’s a 3 digit number, round to the nearest hundred. What about a 4 digit number?

45. Estimating and multiplication
Imagine you have the problem 134 X 7. How can you estimate to solve?
First, round 134 to the nearest hundred.
Then, multiply 100 X 7, and you get 700.

46. Estimate, then multiply! 43 X 7 78 X 6 312 X 4 703 X 8 1,835 X 7
Practice!
Estimate, then multiply!
43 X 7
78 X 6
312 X 4
703 X 8
1,835 X 7

47. Problem 1
A king cobra can grow to 18 feet long. About how long would 8 king cobras be altogether?

48. Problem 2
A Burmese python can weigh 187 pounds. How much would 7 Burmese pythons weigh together?

49. Problem 3
Anacondas can weigh up to 567 pounds. How much would 4 anacondas weigh together?

50. Problem 4
During one year, 7,498 people were bitten by rattlesnakes. About how many people would you estimate would be bitten in 8 years if the numbers remain about the same each year?

51. Grade 4 Lesson 5-6 CCSS 4.OA.3, 4.NBT.3, 4.NBT.5
Reasonableness
Literature Link: The King’s Chessboard by David Birch
Grade 4 Lesson 5-6
CCSS 4.OA.3, 4.NBT.3, 4.NBT.5

52. Explain how you solved each one.
Warm Up
Solve these equations.
128 = n – 29
465 = x + 217
Explain how you solved each one.

53. Think and write
When you are shopping, how can you judge if you will have enough money for your purchases?

54. reasonableness
An answer that is reasonable makes sense based on the information provided in the problem and answers the question posed by the problem.
Example: Justin wants to buy 4 DVDs that cost $10 each. He also wants to buy games that cost $9 each. Justin has $60. What is the greatest number of games that you can buy?
First solve 10 X 4, which is 40, and subtract 60 – 40, which is 20. Now, find the greatest number of games you can buy.
Round $9 to $10. How many games can he buy?

55. Solve with partners
At a garden show, Ray wants to arrange 29 plants on shelves. Each shelf holds 3 plants. Ray says he will need 10 shelves. Is his answer reasonable? Explain.
For this problem, break students into partnerships and have them work together. These problems are more difficult and partner work will allow students more practice before having to do this independently.

56. Problem 1
Shayla has used half of one dozen eggs. She says that she can make 10 more eggs. Is her answer reasonable? Explain.

57. Problem 2
A pet store has 7 empty bird cages. After the delivery was made, the pet store put 6 birds in each cage. Marco estimated that there were about 50 birds in the delivery. Is his answer reasonable? Explain.

58. Problem 3
The line for the each ride at Amusement Kingdom is about 28 minutes. Selena says that if she waits on line for 7 different rides, she will spend about 140 minutes waiting. Is her estimate reasonable? Explain.

59. Problem 4
Angelo sees that large pizzas cost $14. He estimates that 6 large pizzas would cost about $80. Is his estimate reasonable? Explain.

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