1. Engage NY Math Module 2
Lesson 17: Use basic facts to estimate quotients with two-digit divisors.

2. Group Count by Multiples of 10
Count by fours up to 80 (as a class).
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80
Count by 4 tens up to 40 tens (as a class).
4 tens, 8 tens, 12 tens, 16 tens, 20 tens, 24 tens, 28 tens, 32 tens, 36 tens, 40 tens
How do you say 4 tens in standard form? 40
How do you say 16 tens in standard form?
160
How do you say 320 tens in standard form?
3,200

3. Group Count by Multiples of 10
Count by fives up to 100 (as a class).
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100
Count by 5 tens up to 50 tens (as a class).
5 tens, 10 tens, 15 tens, 20 tens, 25 tens, 30 tens, 35 tens, 40 tens, 45 tens, 50 tens
How do you say 5 tens in standard form? 50
How do you say 35 tens in standard form?
350
How do you say 450 tens in standard form?
4,500

4. Group Count by Multiples of 10
Count by sevens up to 140 (as a class).
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140
Count by 7 tens up to 70 tens (as a class).
7 tens, 14 tens, 21 tens, 28 tens, 35 tens, 42 tens, 49 tens, 56 tens, 63 tens, 70 tens
How do you say 7 tens in standard form? 70
How do you say 56 tens in standard form?
560
How do you say 700 tens in standard form?
7,000

5. Round to the Nearest Ten
21 ≈ _____
37 ≈ _____
16 ≈ _____
54 ≈ _____
73 ≈ _____
65 ≈ _____
25 ≈ _____

6. Divide by Multiples of 10, 100, and 1,000
700 ÷ 10
Say the division sentence and state the quotient.
700 ÷ 10 = 70
800 ÷ 20
Write 800 ÷ 20 as a two-step division sentence taking out the ten.
800 ÷ 10 ÷ 2
Now rewrite this in one step after solving the first division problem.
80 ÷ 2
What is the quotient? 40

7. Divide by Multiples of 10, 100, and 1,000
15,000 ÷ 30
Write 15,000 ÷ 30 as a two-step division sentence taking out the ten.
15,000 ÷ 10 ÷ 3
Now rewrite this in one step after solving the first division problem.
1,500 ÷ 3
What is the quotient?
500

8. Divide by Multiples of 10, 100, and 1,000
Follow the same procedure to answer the following problems:
15,000 ÷ 300
15,000 ÷ 100 ÷ 3 = 50
15,000 ÷ 3,000
15,000 ÷ 1,000 ÷ 3 = 5
450,000 ÷ 50
450,000 ÷ 10 ÷ 5 = 9,000
21,000 ÷ 300
21,000 ÷ 100 ÷ 3 = 70

9. Application Problem
852 pounds of grapes were packed equally into boxes for shipping. How many pounds of grapes will there be in 2 boxes? 2 8 4
lb per box
8 4 x
Note: The focus of the Application Problem is division with a one-digit divisor. This review encompasses both the meaning of and skill with division, which helps students as they learn to work with a two-digit divisor. -6 2 5
lb for 2 boxes
-2 4 1 2
There will be 568 pounds of grapes in 2 boxes.

10. Concept Development – Problem 1
402 ÷ 19
What’s the whole (dividend) in this problem?
402
What’s the divisor? 19
Let’s round the divisor first. What is 19 rounded to the nearest ten? 20
Let’s record our estimation.
402 ÷ 19 ≈ ____ ÷ 20
We need to round our whole, 402, to a number that can easily be divided by 20.
Note: The word whole is used throughout the module to indicate the dividend.

11. Concept Development – Problem 1
402 ÷ 19
402 ÷ 19 ≈ ____ ÷ 20
What should we round 402 to?
400
402 ÷ 19 ≈ 400 ÷ 20 = ?
What is 400 divided by 20?
400 divided by 10 is 40 and 40 divided by 2 is 20
So, 400 ÷ 20 = 20
Note: The word whole is used throughout the module to indicate the dividend.

12. Concept Development – Problem 2
149 ÷ 71
In your notebooks, estimate the quotient. What do we need to do first?
Round the divisor.
71 ≈ 70
149 ÷ 71 ≈ ____ ÷ 70
Now round the whole, Usually when we round, we round to place value units. But since we’re dividing, it’d be really nice if our whole was a multiple of the divisor. Round 149 to the nearest multiple of 70. Count with me by seventies.
70, 140, 210, 280
Our whole is between which of these?
140 and 210

13. Concept Development – Problem 2
149 ÷ 71
We are rounding to the nearest multiple of is closest to which multiple of 70?
140
149 ÷ 71 ≈ 140 ÷ 70
140 divided by 70 is the same as 14 divided by what? Say the division sentence.
14 ÷ 7 = 2
How do you know?
140 ÷ 70 = 140 ÷ 10 ÷ 7
Dividing by 70 is the same as dividing by 10 and then dividing by 7.
If I put parentheses like this (140 ÷ 10) ÷ 7, it’s easy to see the two expressions are equal.
So what is 140 ÷ 70 then?
Our estimated quotient is 2.

14. Concept Development – Problem 3
427 ÷ 58
In your notebooks, estimate the quotient.
What is the estimated divisor?
58 ≈ 60
427 ÷ 58 ≈ ____ ÷ 60
So 60 will be our unit. Let’s count by sixties and stop when we find a multiple near 427.
60, 120, 180, 240, 300, 360, 420, … stop!
To which number should we round the whole?
420

15. Concept Development – Problem 3
427 ÷ 58
What’s the next multiple of 60?
480
Is 427 closer to 420 or 480?
420
Let’s use 420 as our estimated whole divided by 60 is the same as what division equation?
42 ÷ 6 = 7
Share with your partner how you know.
420 ÷ 60 = 420 ÷ 10 ÷ 6 = 7
What is our estimated quotient? What’s 420 divided by 60?
Our estimated quotient is 7.

16. Concept Development – Problem 4
293 ÷ 42
In your notebooks, estimate the quotient.
Round the divisor.
42 ≈ 40
293 ÷ 42 ≈ ____ ÷ 40
So 40 will be our unit. Round the whole to a multiple of 40. Let’s count by forties and stop when we find a multiple near 293.
40, 80, 120, 160, 200, 240, 280, 320
This time we went past Our total is between which two multiples of 40?
280 and 320

17. Concept Development – Problem 4
293 ÷ 42
Visualize a number line. Which multiple is closer to 293?
280
Finish the division problem in your journal. Compare your work with a neighbor.
How did you estimate the quotient?
280 ÷ 40 = 28 ÷ 4 = 7

18. Concept Development – Problem 5
751 ÷ 93
Work independently to solve this problem in your journal.
Share your work with a neighbor?
What was your estimated divisor?
93 ≈ 90
And what is the estimated whole?
751 ≈ 720
Tell me how to estimate the quotient.
720 ÷ 90 = 72 ÷ 9 = 8

19. Exit Ticket

20. Problem Set
Display Problem Set on the board. Allow time for the students to complete the problems with tablemates.