Lesson
7 Estimating to Check Answers
Problem Solving:
Checking Answers in Word Problems
Estimating to Check Answers
How can we use estimation to check our answers?
One of the benefits of estimating differences is that it gives us a way
to check our answers. When we use a calculator to subtract, we might
accidentally enter the wrong numbers. A calculator will only compute the
answer to the problem entered. It cannot tell whether we have entered
the numbers correctly. An estimate helps us determine if we made a
mistake. Let’s see how this strategy helped a student correct a mistake.
Miguel had to find the difference between 472 and 213 on his
calculator. When he entered the problem, he came up with the
answer 529.
472
 213
Miguel’s First
Calculator Answer
529
Then Miguel checked his work by estimating. He estimated the
difference by rounding 472 up to 500 and rounding 213 down to
200. The estimated difference was 300.
Miguel’s Estimate
472 S rounds to S 500
 213
 200
300
The estimated difference of 300 was not close to the calculator
answer of 529. Miguel knew that there must be a mistake, so he
entered the problem into his calculator again.
Now the estimate and calculator answer are close, so 259 is a
reasonable answer. Miguel must have entered the problem into the
calculator incorrectly the first time.
98 Unit 2 • Lesson 7
Miguel’s Second
Calculator Answer
259
Lesson 7
We also use estimates to check problems solved using paper and pencil.
Errors made with paper and pencil are usually regrouping errors. We
either forget to regroup or regroup incorrectly.
Improve Your Skills
It’s easy to make mistakes when subtracting. We can check the answer
with an estimate.
Traditional Subtraction
732
 591 ERROR
261
Estimate
700
 600
100
The estimated difference
of 100 is not close to the
answer found using traditional
subtraction. There must be a
mistake.
Look at how the problem was solved using traditional subtraction. Look
carefully at the tens column. Is it possible to subtract 9 from 3? No. We
need to regroup. The problem is solved correctly below.
Traditional Subtraction
6 13
732
 591 CORRECT
141
Estimate
700
 600
100
Estimation is a good way
to check if an answer is
reasonable or if an error
has been made.
Now the estimate and the answer found using traditional subtraction
are close. Estimation helped us see that 141 is a reasonable answer.
Apply Skills
Turn to Interactive Text,
page 68.
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 2 • Lesson 7 99
Lesson 7
Problem Solving: Checking Answers in Word Problems
How can estimation help us in word problems?
Estimation is also important when solving word problems. It is especially
useful when the word problems contain large numbers. We often use
calculators when we work with large numbers. There is a chance we
could enter the numbers incorrectly.
It is also easy to make an error when we use paper and pencil because
there could be many regroupings in one problem. This makes estimation
very important for checking the accuracy of our answers.
Example 1
Solve the word problem using estimation.
Problem:
You and your friends are going to see The Scatter Plots in concert.
You bought the tickets for yourself and two of your friends. If you
spent $117 total on the three tickets, and one ticket cost $39, what
is the total amount you should get back from your friends?
One of your friends used the traditional method to subtract and then
checked his answer by estimating.
Your Friend’s Answer
Estimated Answer
0 10 17
117 S rounds to S 120
 39
 40
78
80
Your friend’s answer and his estimate are very close, so he can
assume that he calculated correctly.
Problem-Solving Activity
Turn to Interactive Text, page 69.
100 Unit 2 • Lesson 7
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Lesson 7
Homework
Activity 1
Find the difference using expanded form. Then write the answer in standard form.
Model
76
70 6
70 6
60 + 10 6
60 10 + 6
60 16
 58 S − 50 8 S − 50 8 S −
S − 50 8
50 8 S − 50 8
10 8 S 10 + 8 = 18
1.
73
 44
2.
71
 23
3.
95
 59
4.
55
 26
Activity 2
Find the difference using traditional subtraction.
1.
88
 39
2.
49
716
 127
3.
589
825
 253
572
Activity 3
Solve the word problems using (1) a calculator and (2) estimation. Then
compare the numbers to check for reasonableness.
Central High School students were trying to decide on a band to play at their
homecoming dance this year. They narrowed it down to three bands and had the
students in each grade vote for their favorite band. The table below shows the
outcome of the vote.
Grade
The Scatter Plots
One Later
The Hammerheads
Seniors
Juniors
Sophomores
197
175
105
115
108
95
102
125
230
1. Which band received the most votes?
2. What was the difference in votes between the first- and second-place bands?
Check your answer by estimating.
Activity 4 • Distributed Practice
Add.
1.
1,108
+ 992
2,100
2.
2,429
+
78
2,507
3.
1,004
+ 3,008
4,012
Unit 2 • Lesson 7 101