1. Grade 4
EnVisions Math
Topic 7
Power Point Lessons

2. Arrays and multiplying 2-Digit numbers by multiples of 10
Lesson CCSS 4.NBT.5
Literature Link: Amanda Bean’s Amazing Dream by Cindy Neuschwander

3. Warm up
Complete the pattern.
14, 21, ___, ____, 42, 49, ___, ___, 70
9, ___, 15, 18, __, 24, 27, ___, 33, ___
36, 48, ___, 72, ___, 96, ___, ___, 132, 144

4. How can arrays help you multiply a 2 digit number by a multiple of 10?
Think and write
How can arrays help you multiply a 2 digit number by a multiple of 10?

5. Making 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 3 X 4, make 3 rows with 4 objects per row.

6. Array practice
Let’s review making arrays. Make an array to represent these problems and solve.
4 X 6
3 X 7
5 X 4
2 X 9

7. Making larger arrays
To build an array for a larger problem like X 15, make the left side of a rectangle that is 15 units long. This is also known as drawing a model.
Then make the top of the rectangle 20 units long.
Complete the remaining sides to complete your array.

8. Larger array practice
Solve the following problems by making an array (drawing a model).
30 X 18
40 X 12
20 X 19

9. Problem 1
Mrs. Tyrell has 20 tests to grade. Each test has 18 problems. How many problems will Mrs. Tyrell grade in all?

10. Problem 2
There are 30 teams in the soccer league. Each team has 16 players on the roster. How many soccer players are there altogether in the league?

11. Problem 3
Chef John is making 40 pans of chicken. Each pan has 22 pieces of chicken. How many pieces of chicken does Chef John make in all?

12. Using mental math to multiply 2 digit numbers
Literature Link: The Rabbit Problem by Emily Gravett
Using mental math to multiply 2 digit numbers
Lesson 7-2
CCSS 4.NBT.5, 4.OA.3

13. Warm up
Solve.
72 ÷ 8
56 ÷ 7
48 ÷ 8
42 ÷ 7

14. Think and write
Do you like using mental math to multiply, or do you prefer a different strategy? Why?

15. Mental math to multiply
Do you notice any patterns in the following problems?
20 X 20
20 X 30
20 X 40
To solve these problems, do the basic fact multiplication first. For 20 X 20, do 2 X 2=4. Then count the number of zeros, and put them on the end. Since there are 2 zeros, the product is 400.
Try 20 X 30. What is the basic fact? How many zeros should you add?

16. Multiplying with larger numbers
The same pattern applies when multiplying by hundreds. Find the basic fact and solve it first. For X 70, the basic fact is 2 X 7 = 14. Then count the zeros. There are 3 zeros, so the answer is 14,000.
Try 400 X 60.

17. Practice!
70 X 60
30 X 80
500 X 70
900 X 20
200 X 40

18. Problem 1
Erin has 30 friends coming to her party at the arcade. She decides to give 80 tickets to each friend. What is the total number of tickets that Erin will get for her friends?

19. Problem 2
Arpad scores 300 points every time he plays a game. He played the game 90 times this week. How many points did he score in all?

20. Problem 3
Mrs. Schafer has 20 students in her class. She buys 70 pencils for each student to last all school year. How many pencils does she buy altogether?

21. Problem 4
Mr. Phillips has to drive 40 miles to work and 40 miles from work every day. If he works 20 days out of the month, how many miles does he drive in all?

22. Using rounding to estimate
Literature Link: Counting on Frank by Rod Clement
Lesson CCSS 4.NBT.3, 4.OA.3

23. Warm Up
Solve.
704 – 578 1,

24. Think and Write
Explain how you round numbers to the nearest ten and hundred.

25. Rounding Review
Remember that when you round, look at the place to the RIGHT of the place that you are rounding to.
If the number is 4 or lower, round down. If the number is 5 or higher, round up.

26. Rounding Practice Round to the nearest ten, then hundred. 342 108 42298

27. Breaking Apart to Round
To solve 14 X 80, break the numbers apart into 10 X 80 and 4 X 80. Then add the products together = 1120.
How can you break apart 17 X 53? First, break 17 into 10 and 7. Round 53 to 50. Then do 10 X 50 and 7 x 50 . Add the products and get 850.

28. Practice! Try the breaking apart strategy to solve these. 23 X 72

29. Problem 1
Jane can make $48 every hour. If she works 26 hours, about how much money can she make? Use breaking apart to estimate and solve.

30. Problem 2
There are 23 apartments in each building. If there are 38 buildings, about how many apartments are there in all? Use breaking apart to estimate and solve.

31. Problem 3
The zoo has 31 tanks of frogs. There are 28 frogs in each tank. About how many frogs are there in all? Use breaking apart to estimate and solve.

32. Using Compatible Numbers to Estimate
Lesson 7-4
CCSS 4.NBT.5, 4.NBT.3, 4.OA.3
Literature Link: The Grapes of Math by Greg Tang (1-2 pages of riddles)

33. Warm Up
Write the multiplication and division fact family for these numbers. 6, 9, 54

34. Think and Write
Who are some people you get along very well with? People whom we get along well with and enjoy being around are people whom we are compatible with.

35. 30 is close to 31, so they are compatible.
Compatible Numbers
Compatible numbers are numbers that are close to the actual number, but easier to compute mentally.
Example: 25 is close to 24, and is easy to compute with. It is a compatible number.
30 is close to 31, so they are compatible.

36. Compatible Number Practice
Find a compatible number for each example. 28 44 81 96 98

37. Practice!
Estimate to find the product. When possible, use compatible numbers.
18 X 24
61 X 56
72 X 41
26 X 85
99 X 74

38. Problem 1
Sean has 19 Lego sets. Each set has 96 pieces. How many pieces are there in all? Estimate using compatible numbers and solve.

39. Problem 2
Danielle is making necklaces for 16 friends. Each necklace has 44 beads. How many beads will Danielle use in all? Estimate using compatible numbers and solve.

40. Problem 3
Jack is apple picking. He picks 21 apples a minute. If he picks for 34 minutes, how many apples will Jack pick? Use compatible numbers to estimate and solve.

41. Problem 4
Isabel is slicing 24 cakes. She slices each cake into 16 pieces. How many pieces does Isabel slice in all? Estimate using compatible numbers and solve.

42. Problem solving: multiple step problems
Literature Link: The Grapes of Math by Greg Tang (1-2 pages of riddles)
Lesson CCSS 4.NBT.5, 4.OA.3

43. Warm Up
Make the largest number you can using all of the digits 9, 6, 7, 4, and 2.

44. Think and Write
When do you have to do multiple steps in order to accomplish a goal?
Example: Following a recipe to make a cake takes multiple steps.

45. Steps to Problem Solving
1. Read the question carefully.
2. Underline key information such as numbers and signal words such as “in all”.
3. Circle the question that you are being asked to solve.
4. Number the parts of the question in the order that they need to be solved.
5. Check your work. Be sure you have solved all parts.

46. Problem 1
Tickets to the amusement park cost $22 for an adult and $12 for a child. How much would 4 adults and 2 children cost in all?

47. Problem 2
Serena and her sister Raisa are selling cookie dough for school. They raise $48 in all. Serena sells 4 containers of chocolate chip cookie dough and Raisa sells 4 containers of peanut butter cookie dough. If the containers each cost the same amount, how much did each container cost?

48. Problem 3
Mr. MacDonald buys 16 tomato plants and 12 pumpkin plants. He plans to plant them in rows with 4 plants per row. How many rows will Mr. MacDonald plant?

49. Problem 4
Meal
Cost
Personal Pizza & Drink
$ 7
Burger, Fries & Drink
$ 6
Hot Dog, Fries, & Drink
$ 5
Brian and his friends buy 2 pizza meals, 3 burger meals and 3 hot dog meals. How much do they spend altogether?

50. Problem 5
Aiden builds 4 snowmen and uses 12 rocks on each snowman. Christian builds 6 snowmen and uses 9 rocks on each snowman. Who uses more rocks, Aiden or Christian? How many more rocks are used?

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