Lesson
10 Numbers on a Number Line
Monitoring Progress:
Quiz 2
Numbers on a Number Line
Vocabulary
How do we find numbers on a number line?
number line
estimate
round
We use measuring tools in everyday life. Rulers measure distance.
Fuel gauges measure how much gas is in a gas tank. These
instruments help us understand a numerical value in a visual way.
A number line is a tool we can use to visualize numbers. Number
lines help us see where numbers are in relation to each other.
0
1
2
3
4
5
6
7
8
9
10
Number lines work as long as
we have at least two numbers
marked on them. Look at the
number line to the right. We
would have a hard time finding
the number 50 on this line
because there are no numbers.
With this number line, we have
a pretty good idea where 50
should be. It should be to the
right of 40. But we don’t know
exactly where 50 should be yet.
After adding another number,
we know where 50 should go.
It goes between 40 and 60 on
the number line.
40
40
40
60
50
60
As long as we have two numbers on a number line, we can find where
any other number should go on the line.
Unit 1 • Lesson 10 45
Lesson 10
When numbers are labeled on the number line, we can find their exact
location.
Example 1
Find 50 on the number line.
0
10
20
30
40
50
60
70
60
70
The number 50 is part of the scale of the number line, so we can place a
dot exactly at 50.
The dot shows the exact location of 50.
It is a little more difficult to find the location of a number on a number
line if the number is not labeled. In this case, we have to estimate the location of the number. This means we need to guess the
number’s location.
Example 2
Find 55 on the number line.
0
10
20
30
40
50
The number 55 is not labeled on the number line, so we have to estimate
its location. We know that 55 is greater than 50 and less than 60, so
the dot will be placed somewhere between these two numbers. Because
55 is halfway between 50 and 60, we place the dot halfway between
these numbers on the number line.
The dot shows the estimated location of the number 55.
46 Unit 1 • Lesson 10
Lesson 10
When we see a dot on a number line, sometimes we need to estimate
the number represented by the dot. Example 3 shows estimations for
several different dots on a number line.
Example 3
Estimate the number represented by each dot on the number line.
0
A
10
20
30
40 B
50
C60
70
The number represented by A is about 5. The dot is halfway between
0 and 10.
The number represented by B is about 43. The dot is not quite halfway
between 40 and 50. It is closer to 40.
The number represented by C is about 58. The dot is not quite halfway
between 50 and 60. It is closer to 60.
How do we use number lines to round?
When we estimate,
more than one number
can be considered a
correct estimation.
It is often easier to work with numbers using an estimation. For
example, if we are asked to guess the number of people who attended a
soccer game, we might say about 500, when the exact attendance was
487 people.
When we use an estimation of a number, we round the number to the
closest number on a number line.
Example 1
Use the number line to round to the nearest ten.
This number line is marked by tens. The number 47 is between 40 and
50. The number 47 rounds to 50 because it is closer to 50 than 40.
0
10
20
30
40
47
50
60
70
Unit 1 • Lesson 10 47
Lesson 10
Example 2
Use the number line to round to the nearest hundred.
This number line is marked by hundreds. The number 320 is between
300 and 400. The number 320 rounds down to 300 because it is closer
to 300 than 400.
0
100
200
320
300
400
500
600
700
The most confusing case is when the number we are trying to round lies
right in the middle of two numbers. In this case, we always round up to
the greater number.
Example 3
Use the number line to round to the nearest ten.
This number line is marked by tens. The number 165 is halfway between
160 and 170. When a number lies exactly halfway between two
numbers, we round up. So 165 rounds up to 170.
100
48 Unit 1 • Lesson 10
110
120
130
140
150
160
165
170
Lesson 10
What are the rules for rounding?
We have learned that we can think about numbers on a number line
to help us round. We can also use rules to help us round.
Rules for Rounding
To round to the nearest ten, look at the ones.
• If the ones are greater than or equal to 5, round up. 46
• If the ones are less than 5, round down.
32
S  50
S  30
To round to the nearest hundred, look at the tens.
• If the tens are greater than or equal to 5, round up. 180
• If the tens are less than 5, round down.
230
S
S
200
200
Improve Your Skills
How would we round 152 to the nearest hundred?
Common mistakes:
150This number is 152 rounded down to the nearest ten, not the
nearest hundred.
100This number is 152 rounded down to the nearest hundred.
Because the tens are equal to 5, we round up.
Being able to estimate
is an important skill.
The correct way to round 152 to the nearest hundred is to round up
to 200.
Apply Skills
Turn to Interactive Text,
page 30.
Monitoring Progress
Quiz 2
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 1 • Lesson 10 49
Lesson 10
Homework
Activity 1
Estimate the number represented by the dot on the number line.
Model
0
10
20
30
40
50
60
70
80
90
Answer: The number is about 65.
1.
0
10
20
30
40
50
60
70
80
90
0
10
20
30
40
50
60
70
80
90
2.
3.
0
10
20
30
40
50
60
Activity 2
Use the number line to round the number to the nearest ten.
0
10
1. 35
20
30
2. 14
40
50
3. 59
60
70
4. 15
Activity 3 • Distributed Practice
Add.
1.
378
+ 115
493
50 Unit 1 • Lesson 10
2.
437
+ 93
530
3.
585
+ 56
641
5. 67
70