1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. three and seventy-two thousandths
Warm Up
Order the decimals from least to greatest.
, 18.7, 18.47
, 9.66, 9.6, 9.076
Write each in words.
18.47, 18.7, 18.74
9.06, 9.076, 9.6, 9.66
three and seventy-two thousandths
six and one thousand two hundred fifty-eight ten-thousandths

3. Calculate your age in months.
Problem of the Day
Calculate your age in months.
Possible answer: 11 yr 8 mo = 140 mo

4. Learn to estimate decimal sums, differences, products, and quotients.

5. Vocabulary
clustering
front-end estimation

6. When numbers are about the same value, you can use clustering to estimate. Clustering means rounding the numbers to the same value.

7. Additional Example 1: Health Application
Nancy wants to cycle, ice skate, and water ski for 30 minutes each. About how many calories will she burn in all? (Cycling = calories, ice skating = calories, and water skiing = calories)
The addends cluster around 170.
165.5
170
To estimate the total number of calories, round each addend to 170.
177.5
170
171.5
+ 170
Add.
510
Nancy burns about 510 calories.

8. Check It Out: Example 1
Abner wants to run, roller skate, and snow ski for 60 minutes each. About how many calories will he burn in all? (Running = calories, roller skating = calories, and snow skiing = calories)
The addends cluster around 190.
185.5
190
To estimate the total number of calories, round each addend to 190.
189.5
190
191.5
+ 190
Add.
570
Abner burns about 570 calories.

9. Look at the digit to the right of the place to which you are rounding.
If it is 5 or greater, round up.
If it is less than 5, round down.
Caution!

10. Estimate by rounding to the indicated place value.
Additional Example 2: Rounding Decimals to Estimate Sums and Differences
Estimate by rounding to the indicated place value.
A ; ones
B – ; tenths
Round to the nearest whole number.
The sum is about 12.
7 + 5 = 12
Round to the tenths.
Align.
– –0.3
Subtract.
9.4

11. Check It Out: Example 2
Estimate by rounding to the indicated place value.
A ; ones
B – ; tenths
Round to the nearest whole number.
The sum is about 10.
6 + 4 = 10
Round to the tenths.
Align.
– –0.5
Subtract.
8.4

12. Compatible numbers are close to the numbers that are in the problem and are helpful when you are solving the problem mentally.
Remember!

13. Additional Example 3: Using Compatible Numbers to Estimate Products and Quotients
Estimate each product or quotient.
A  1.98
B ÷ 26.14
35 and 2 are compatible.
35  2 = 70
So  1.98 is about 70.
75 ÷ 25 = 3
75 and 25 are compatible.
So, ÷ is about 3.

14. Check It Out: Example 3
Estimate each product or quotient.
A  4.98
B ÷ 18.52
20 and 5 are compatible.
20  5 = 100
So  4.98 is about 100.
60 ÷ 20 = 3
60 and 20 are compatible.
So, ÷ is about 3.

15. You can also use front-end estimation to estimate with decimals
You can also use front-end estimation to estimate with decimals. Front-end estimation means to use only the whole-number part of the decimal.

16. Additional Example 4: Using Front-End Estimation
Estimate a range for the sum.
Use front-end estimation.
Add the whole numbers only.
7.86 7
The whole-number values of the decimals are less than the actual numbers, so the answer is an underestimate.
36.97 36
5.40
+ 5
at least 48
The exact answer of is 48 or greater.

17. Additional Example 4 Continued
You can estimate a range for the sum by adjusting the decimal part of the numbers. Round the decimals up to 0.5 or 1.
Add the decimal part of the numbers.
0.86
1.00
Add the whole-number estimate and the adjusted estimate.
0.97
1.00
0.40
+ 0.50
The adjusted decimals are greater than the actual decimal, so is an overestimate.
2.50
= 50.50
The estimated range for the sum is from to

18. Check It Out: Example 4
Estimate a range for the sum.
Use front-end estimation.
Add the whole numbers only.
8.92 8
The whole-number values of the decimals are less than the actual numbers, so the answer is an underestimate.
47.88 47
3.41
+ 3
at least 58
The exact answer of is 58 or greater.

19. Check It Out: Example 4
You can estimate a range for the sum by adjusting the decimal part of the numbers. Round the decimals up to 0.5 or 1.
Add the decimal part of the numbers.
0.92
1.00
Add the whole-number estimate and the adjusted estimate.
0.88
1.00
0.41
+0.50
The adjusted decimals are greater than the actual decimal, so is an overestimate.
2.50
= 60.50
The estimated range for the sum is from to

20. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

21. Lesson Quiz
Estimate by rounding to the indicated place value.
; tenths
– ; nearest whole number
4.5 3
Estimate each product or quotient.
 1.82 14
÷ 3.42 3
5. The snowfall in December, January, and February was cm, cm, and cm, respectively. About how many total centimeters of snow fell during the three months?
80 cm

22. Lesson Quiz for Student Response Systems
1. Estimate by rounding to the indicated place value.
; hundredths A B C D

23. Lesson Quiz for Student Response Systems
2. Estimate by rounding to the indicated place value.
; nearest whole number
A. 10
B. 11
C. 12
D. 13

24. Lesson Quiz for Student Response Systems
3. Identify the estimate of the product of  3.81.
A. 48
B. 51
C. 64
D. 68

25. Lesson Quiz for Student Response Systems
4. Identify the estimate of the quotient of  3.91.
A. 6
B. 5
C. 4
D. 3

26. Lesson Quiz for Student Response Systems
5. The weight of three students in a class are pounds, pounds, and 45.3 pounds. Identify the total weight of the students.
A. 130 lb
B. 140 lb
C. 150 lb
D. 160 lb