1. Math 5 Estimating Division
Instructor: Mrs. Tew Turner

2. In this lesson we will learn about estimating multiplication using rounding.

3. Math Warm-up What is one less than one million?

4. What is one less than one million?
Math Warm-up
What is one less than one million?
1,000,000 – 1 =
999,999

5. In this lesson we will answer the question:
How can you estimate the quotient for division problems?

6. Vocabulary
dividend- the number to be divided
24 ÷ 4 = 6
divisor- the number that is the result of multiplying two or more factors

7. Vocabulary
quotient - the number that is the result of dividing
24 ÷ 4 = 6

8. Vocabulary
compatible numbers – numbers that are easy to compute with mentally
Ex. 21 and 3 are compatible numbers in division because
21 ÷ 3 = 7 is a fast fact.

9. What is Division?
A QUICK review! division is separating items into groups, or finding the “fair share”! Division is FASTER than separating items one by one into groups, and it is a very useful skill in day to day life!
If you could NOT divide
287 ÷ 42...What would you
have to do?

10. What is Division?
287 ÷ 42=?
What could you do to find the Quotient for this problem?
You could separate 287 into 42 groups or
You could DIVIDE 287 ÷ 42

11. What is Division?
Which would be faster if you could divide?
DIVISION would be faster!
We are going to look at
ESTIMATION first when
dividing larger numbers. This is an important skill you need.

12. What is Division?
Estimating for division is a lot like estimating for multiplication.
We are going to look at
ESTIMATION first when
Dividing larger numbers.

13. Estimation in Division
Estimating is like asking “about how much?”
There are two ways you can estimate in division.

14. Estimation in Division
One way is to round to the nearest tens or hundreds.
Ex. 258 ÷ 6
Step 1: Round the dividend to the nearest tens or hundreds.

15. Estimation in Division
One way is to round to the nearest tens or hundreds.
Ex. 258 ÷ 6
Step 2: Divide using the rounded dividend.
300 ÷ 6 = 50

16. Estimation in Division
One way is to round to the nearest tens or hundreds.
Ex. 258 ÷ 6
300 ÷ 6 = 50
This quotient is an estimate.
It should be faster to get the estimate because 30 ÷ 6 = 5, which is a fast fact, then you add the final zero, because 0 ÷ 6 = 0.

17. Estimation in Division
Another way is to use compatible numbers.
Ex. 258 ÷ 6
Step 1: Find a compatible number.
For this problem you would replace 258 with 240.

18. Estimation in Division
Another way is to use compatible numbers.
Ex. 258 ÷ 6
How do you know what number is a compatible number?

19. Estimation in Division
Another way is to use compatible numbers.
Ex. 258 ÷ 6
Use the fast facts to help you choose a compatible number.
Think about fast facts for the 6 times table.

20. Estimation in Division
Another way is to use compatible numbers.
Ex. 258 ÷ 6
6 x 4 = 24
So, 24 ÷ 6 = 4
This fast fact will help to solve the problem mentally.

21. Estimation in Division
Another way is to use compatible numbers.
Ex. 258 ÷ 6
240 and 6 are compatible numbers, since 24 ÷ 6 = 4.

22. Estimation in Division
Another way is to use compatible numbers.
Ex. 258 ÷ 6
Step 2: Use mental math to solve the problem.
240 ÷ 6 = 40

23. Estimation in Division
Another way is to use compatible numbers.
Ex. 258 ÷ 6
240 ÷ 6 = 40
40 would be an underestimate since 258 was replaced with a smaller compatible number.

24. Rounding to Estimate the Quotient
Follow the Steps!
Rounding to Estimate the Quotient
Step 1: Round the dividend to the nearest tens or hundreds.
Step 2: Divide using the rounded dividend.
Easy as ....

25. Using Compatible Numbers to Estimate the Quotient
Follow the Steps!
Using Compatible Numbers to Estimate the Quotient
Step 1: Find a compatible number.
Step 2: Use mental math to solve the problem.
Easy as ....

26. Use rounding to estimate the quotient
In your Math Notebook
Use rounding to estimate the quotient
÷ 2 =
÷ 6 =
÷ 4 =
÷ 5 =
÷ 5 =
Use your math notebook to work it out if you need to!

27. Use compatible numbers to estimate the quotient
In your Math Notebook
Use compatible numbers to estimate the quotient
÷ 8 =
÷ 7 =
÷ 3 =
÷ 4 =
÷ 5 =
Use your math notebook to work it out if you need to!

28. Use rounding to estimate the quotient
In your Math Notebook
Use rounding to estimate the quotient
÷ 2 = 800 ÷ 2 = 400
÷ 6 = 360 ÷ 6 = 60
÷ 4 = 200 ÷ 4 = 50
÷ 5 = 300 ÷ 5 = 60
÷ 5 = 1000 ÷ 5 = 200

29. Use compatible numbers to estimate the quotient
In your Math Notebook
Use compatible numbers to estimate the quotient
÷ 8 = 560 ÷ 8 = 70
÷ 7 = 280 ÷ 7 = 40
÷ 3 = 240 ÷ 3 = 80
÷ 4 = 440 ÷ 4 = 110
÷ 5 = 250 ÷ 5 = 50

30. How do you know when to round and when to use compatible numbers?
This is one example of why you need to know your fast facts!
Knowing your fast facts will help you know when to round and when to use compatible numbers.

31. How do you know when to round and when to use compatible numbers?
Which method would you use for this problem?
263 ÷ 3 =

32. How do you know when to round and when to use compatible numbers?
Does rounding help you solve this using mental math?
263 ÷ 3 =
300 ÷ 3 = ?
Yes! You can use rounding to help you find an estimate to this problem.

33. How do you know when to round and when to use compatible numbers?
Does rounding help you solve this using mental math?
545 ÷ 8 =
500 ÷ 8 = ?
No, rounding did not help to solve this mentally.

34. How do you know when to round and when to use compatible numbers?
What if we round to the nearest ten?
545 ÷ 8 =
550 ÷ 8 = ?
No, we still can not solve this mentally.

35. How do you know when to round and when to use compatible numbers?
Now, try using compatible numbers.
Remember to use your fast facts!
545 ÷ 8 =

36. How do you know when to round and when to use compatible numbers?
Think about your fast facts for the 8 times tables.
545 ÷ 8 =

37. How do you know when to round and when to use compatible numbers?
545 ÷ 8 =
560 ÷ 8 = 70

38. Problem Solving!
1. Seven friends collected cans of food for their families. The friends gathered 61 cans. Each person collected about the same number of cans. About how many cans did each student collect?
Use your Math Notebook to solve and show your work.

39. Problem Solving!
1. Seven friends collected cans of food for their families. The friends gathered 61 cans. Each person collected about the same number of cans. About how many cans did each student collect?
61 ÷ 7 = ?
63 ÷ 7 = 9
Each friend collected about 9 cans.

40. Problem Solving!
2. Toby earned $596 in 3 months for doing laundry. If he was paid the same amount each month, about how much did he earn per month?
Use your Math Notebook to solve and show your work.

41. Problem Solving!
2. Toby earned $596 in 3 months for doing laundry. If he was paid the same amount each month, about how much did he earn per month?
$596 ÷ 3 = ?
$600 ÷ 3 = $200

42. In your Math Notebook
Quick Check
1. Writing to explain: If you want to use compatible numbers to estimate 262 ÷ 7, is it better to use 210 ÷ 7 or 280 ÷ 7? Explain.
2. Jorge is putting shells into 8 boxes. He wants to put the same number in each box. About how many shells could Jorge put in each box?

43. In your Math Notebook
Quick Check
Writing to explain: If you want to use compatible numbers to estimate 262 ÷ 7, is it better to use 210 ÷ 7 or 280 ÷ 7? Explain.
It is better to use 280 ÷ 7 because 280 is closer to 262, so the estimate will be closer to the exact solution. This makes it a better estimate.

44. In your Math Notebook
Quick Check
2. Jorge is putting 258 shells into 8 boxes. He wants to put the same number in each box. About how many shells could Jorge put in each box?
258 ÷ 8 = ?
240 ÷ 8 = 30

45. Good Work with this lesson.
Today you learned how to use estimation to divide!