Lesson
11 Estimating Sums by Rounding
Problem Solving:
Using Rounded Numbers in Bar Graphs
Estimating Sums by Rounding
How do we use rounding to estimate sums?
In Lesson 10, we used estimation to find numbers on a number line.
Now we will learn to estimate a sum using numbers on a number line.
Let’s use estimation to find 77 + 32.
We need to round the two numbers to estimate.
Decide
which number on the
Look at the number line below.
Estimate
the location of 77 by
number line is closest to the
dot. It is 80.
drawing a dot between 70 and
80, closer to 80.
Draw
a jump, or arrow, from
the dot to the number 80.
0
10
20
30
40
50
60
70
80
90
80
90
We have rounded 77 up to 80.
Now let’s round the number 32.
Estimate
the location of 32 by
drawing a dot between 30 and
40, closer to 30.
0
10
20
30
Draw
a jump from the dot to
the number 30.
40
50
60
70
We have rounded 32 down to 30.
We can rewrite the problem using the rounded numbers 80 and 30. This
would give us an estimated sum. The rounded addition problem is an
extended fact: 80 + 30 = 110.
The estimated sum is 110.
Unit 1 • Lesson 11 51
Lesson 11
Rounding helps us get a good idea about the sum of two numbers. It can
turn a more difficult problem into an extended fact.
Example 1
Estimate the sum of 47 and 21.
Round each number to the nearest ten because the greatest place value
in the numbers is the tens.
We round 47 up to 50 because 47 is closer to 50 than 40.
0
10
20
30
40
50
60
70
80
90
80
90
We round 21 down to 20 because 21 is closer to 20 than 30.
0
10
20
30
40
50
60
70
Use the rounded numbers to make the extended fact: 50 + 20 = 70.
The sum of the rounded numbers is 70.
The sum is about 70.
Now let’s estimate a sum without using number lines.
Example 2
Estimate the sum of 586 and 801.
Round each number to the nearest hundred because the greatest
place value in the numbers is the hundreds.
We round 586 up to 600 because 586 is closer to 600 than 500.
We round 801 down to 800 because 801 is closer to 800 than 900.
Use the rounded numbers to make the extended fact:
600 + 800 = 1,400.
The sum of the rounded numbers is 1,400.
The sum is about 1,400.
52 Unit 1 • Lesson 11
Even though estimating
only gives us an answer
that is close to the exact
answer, it allows us to
find a ballpark figure
quickly in our heads.
Lesson 11
How do we use rounding in the real world?
We round every day when we estimate a sum. For example, we estimate
the total price of several items to be sure we have enough money to
pay for them. Even though we do not know the exact sum, we can see
whether we can afford the items.
Example 1
Which problem is easier to solve?
Problem 1
Jack buys a fish tank for $72 and a fish for $17.
What is the total cost of the items?
Problem 2
Jack wants to buy a fish tank for $72 and a fish for $17.
He has $200 to spend. Does Jack have enough money?
In Problem 1, we need
to find the exact sum
of 72 and 17.
Problem 1 might look easier because there are only two numbers. But
in Problem 1, we need to calculate the exact sum.
In Problem 2, we need
to estimate the sum of
72 and 17.
Problem 2 is easier because we can estimate the answer. $72 is less
than $100, and $17 is less than $100.
Jack’s total purchase will be less than $200.
We can also use estimation to check how reasonable an answer is.
Example 2
Is Martha’s answer reasonable?
Martha added 586 and 801 on her calculator. She found the sum
667. Martha’s answer seems too low. We can estimate to check if it is
reasonable.
The sum of 586 and 801 should be greater than 1,000 because the sum
of 600 and 800 is 1,400.
You can make a mistake
on a calculator or with a
paper and pencil. Check
your work!
Martha should try to find an answer closer to the estimate.
Apply Skills
Turn to Interactive Text,
page 32.
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 1 • Lesson 11 53
Lesson 11
Problem Solving: Using Rounded Numbers in Bar Graphs
How do we round numbers in a graph?
Number of CDs Sold
We have looked at graphs of CD sales in previous lessons. The graph
below is a little different from the ones we have seen. Notice that the
tops of some of the bars do not touch the lines of the scale.
The Scatter Plots CD Sales
January–April
500
400
300
200
100
0
January
February
March
April
Month
We need to round the numbers in the graph to the nearest hundred to
make them easier to work with. To do this, we can use the height of the
bars in the graph to estimate the sales for each month.
Example 1
Estimate the total CD sales for January and February.
To estimate the total CD sales for January and February, we need to
round each month’s sales.
Look at the bar for January in the graph above. It is between 0 and
100 on the scale. It is closer to 100, so we round the number for
January to 100.
Now look at the bar for February. It is between 100 and 200 on the
scale. It is closer to 200, so we round the number for February to 200.
Now we can create an extended fact: 100 + 200 = 300.
The total CD sales for January and February were about 300 CDs.
Problem-Solving Activity
Turn to Interactive Text,
page 34.
54 Unit 1 • Lesson 11
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Rounding the data in
a bar graph is a quick
way to understand the
information in the graph.
Lesson 11
Homework
Activity 1
Add using traditional addition.
1.
437
+ 192
2.
629
685
+ 97
3.
709
+ 206
782
915
Activity 2
Round the numbers. Then estimate their sum.
Model Answer:
47
+ 62 50
+ 60
110
1.
69 + 81
2.
54 + 84
3.
94 + 59
4.
499 + 799
5.
589 + 927
6.
369 + 481
Activity 3
Round the numbers to the nearest hundred. Then estimate the sum.
1.
Trandon and Latisha are collecting video arcade tickets. They plan to combine
their tickets and trade them in for a big prize. Trandon has 787 tickets, and
Latisha has 445 tickets. About how many tickets do they have altogether?
2.
The Ruiz family traveled 227 miles on the first day of their trip, 329 miles on
the second day, and 179 on the third day. About how far did they travel in all?
Activity 4 • Distributed Practice
Add. Try to find the sum mentally.
1.
8+9
2.
500 + 900
3.
4,000 + 9,000
4.
70 + 60
5.
100 + 300
6.
80 + 40
Unit 1 • Lesson 11 55