Lesson
8 Quarter Rounding
Problem Solving:
Estimating in Word Problems
Quarter Rounding
Vocabulary
What is another type of rounding?
quarter rounding
We used number lines to help us round numbers to the nearest 10,
100, or 1,000. The number lines we used were marked in intervals
of 10, 100, or 1,000 to help us locate the number and round it to the
appropriate value.
Using this number line, we can see that 104 rounds to 100, 286 rounds
to 300, 313 rounds to 300, and 470 rounds to 500.
104
0
100
286 313
200
300
470
400
We can also round to units of 25. These are called quarters,
just like the quarter coin is worth 25 cents.
If we have 53 cents, we would have about 2 quarters. We have
3 pennies more than 2 quarters, but we are very close.
If we have 70 cents, we
would have about 3
quarters. We are 1 nickel
short of having
3 quarters, but we
are very close.
If we have 92 cents, we would have about 4 quarters. We are
1 nickel and 3 pennies short, but we are very close.
This type of rounding is called quarter rounding . In quarter
rounding, we round numbers to the nearest quarter: 25, 50,
75, 100, 125, and so on. For this strategy, we can also use number
lines marked in intervals of 25 to help us round.
102 Unit 2 • Lesson 8
500
Lesson 8
Let’s look at an example of how we can use a number line when we do
quarter rounding.
Example 1
Round the numbers 30 and 68 to the nearest quarter.
0
25 30
50
68
75
100
The number 30 is between 25 and 50. It is closer to 25 than 50.
So 30 rounded to the nearest quarter is 25.
The number 68 is between 50 and 75. It is closer to 75 than 50.
So 68 rounded to the nearest quarter is 75.
How do we use quarter rounding to estimate
differences?
The quarter rounding strategy is also used to estimate differences in
subtraction. Sometimes we make a better estimate using this method
than rounding to the nearest 10, 100, or 1,000.
Example 1
Use quarter rounding to estimate the difference between 73 and 47.
First, round 73 to the nearest quarter. The number 73 rounds up to 75.
0
25
50
73 75
100
Then round 47 to the nearest quarter. The number 47 rounds up to 50.
0
25
47 50
Finally, subtract the rounded numbers. 75
100
73 75
S rounds to S
 47
 50
25
The estimated difference is 25.
Apply Skills
Turn to Interactive Text,
page 71.
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 2 • Lesson 8 103
Lesson 8
Problem Solving: Estimating in Word Problems
When can we use estimation to solve word
problems?
Sometimes we don’t need an exact computation—an estimate
is good enough. Computing with rounded numbers makes the
computation easier.
Let’s look at an example of a word problem where estimation
alone is used to solve the problem.
Example 1
Solve the word problem using estimation.
Problem:
The Scatter Plots promised fans that every concert will last at least
150 minutes. The Scatter Plots played in Orlando, Florida, last night.
The first set was 92 minutes long, and then there was a break. The
second set lasted 81 minutes. Did the concert last at least 150
minutes as promised?
We only need to estimate the total time to see if it is more than 150
minutes. Because the greatest place value in each number is the tens,
round both numbers to the nearest ten. The number 92 rounds down
to 90. The number 81 rounds down to 80.
The extended fact is 90 + 80 = 170.
Because 170 minutes is much greater than 150 minutes, we can be
confident that our estimate has sufficiently answered the problem.
Yes, the Scatter Plots’ concert in Orlando lasted at least
150 minutes.
Problem-Solving Activity
Turn to Interactive Text, page 72.
104 Unit 2 • Lesson 8
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Lesson 8
Homework
Activity 1
Subtract using expanded form. Then write the answer in standard form.
Model
44
40 4
40 4
30 + 10 4
30 10 + 4
 19 S − 10 9 S − 10 9 S −
10 9 S − 10 9
30 14
S − 10 9
20 5 S 20 + 5 = 25
1.
56
 38
2.
75
 28
3.
47
 29
Activity 2
Find the difference using traditional subtraction.
1.
327
 39
2.
288
566
 328
3.
238
621
 240
381
Activity 3
Use quarter rounding to estimate the difference.
Model48 − 23 Estimate: 50 − 25 = 25
1. 53 − 24
2. 78 − 29
3. 98 − 47
Activity 4 • Distributed Practice
Add.
1.
586
+ 273
859
2.
8,009
+ 678
8,687
3.
695
+ 365
1,060
Unit 2 • Lesson 8 105