Comparing Fractions on a number line

Created by HISD Curriculum using Google® Slides

I can compare two fractions that have the same

denominator using number lines.

Let’s Learn

Multiple Choice

Using the number lines, which two fractions are equivalent?

• 1/5 and 2/10

• 2/5 and 5/10

• 6/10 and 4/5

• 1/3 and 3/4

Multiple Choice

Which fraction is greater?
1/5 or 1/3

• 1/5

• 1/3

Multiple Choice

Which is greater?
9/10  or 1/10

• 9/10

• 1/10

Multiple Choice

Which comparison of these fractions is true

• $$\frac{1}{2}$$ > $$\frac{1}{1}$$

• $$\frac{2}{8}$$ > $$\frac{1}{8}$$

• $$\frac{1}{8}$$ = $$\frac{2}{8}$$

• $$\frac{2}{8}$$ < $$\frac{1}{8}$$

Fractions on a Number Line

Today we will practice identifying fractions on a number line.

Equivalent

Two quantities that are the same or have the
same value.

Equivalent Fractions

Fractions that name the same part of a whole
region, set, or distance on a number line.

1

2

3

6

=

=

Let’s review our vocabulary.

Whole

A defined unit (e.g., region, length, or set) of
one.

Fractional Parts

Equal-sized parts that can be composed to
equal a whole.

Fraction

A number that represents equal shares or parts of a
whole or unit.

Unit Fraction

A fraction with a numerator of 1 and a
whole-number denominator greater than zero.

1 whole

Models of Fractions by HISD Curriculum

using Microsoft® Word and 1, 2, 3 Math

Fonts under license

3

6

1

2

Created by HISD Curriculum using Google® Slides

This is a number line.

Notice it is split into equal parts between 0 and 1.

Match

Match the following

2/8

6/8

4/8

0/8

• 2/8

• 6/8

• 4/8

• 0/8

When we count the equal parts between 0 and 1...

We need to count the spaces not the ticks.

Match

Match the following

• Unit Fraction

• Fractional Part

• Fraction

• Equivalent

• Equivalent Fraction

A fraction with a numerator of 1

Equal-sized parts that can be composed to equal a whole.

A number that represents equal shares or parts of a whole or unit.

Two quantities that are the same or have the same value.

Fractions that name the same part of a whole region, set, or distance on a number line.

• A fraction with a numerator of 1

• Equal-sized parts that can be composed to equal a whole.

• A number that represents equal shares or parts of a whole or unit.

• Two quantities that are the same or have the same value.

• Fractions that name the same part of a whole region, set, or distance on a number line.

Multiple Choice

How many equal pieces are in this number line?

• 1

• 2

• 3

Fill in the Blank

Which of the following is closest to $$\frac{1}{4}$$

If there are 3 equal pieces in this number line, that means our unit is....

Created by HISD Curriculum using Google® Slides

Guiding Question: How can I use number lines to
compare fractions that have the same denominator?

0

1

Multiple Choice

If there are 3 equal pieces on this number line, are unit is..

• halves

• thirds

• fourths

Multiple Choice

• 2/3

• 1/2

• 1/4

• 1/3

Our unit is thirds.

Counting/Labeling on the number line is along the ticks.

0, 1/3, 2/3, 3/3 or 1

Created by HISD Curriculum using Google® Slides

Let’s read the math story below.

Steve and Sam ran around a track. Steve ran

of the track. Sam ran 4 of the track.

Who ran the furthest?

2

6

6

This a number line split into equal pieces.

Count the number of equal pieces.

Draw

Divide the number line into 4 equal parts. Circle $$\frac{3}{4}$$  

Make sure you count the spaces, not the ticks.

How many equal pieces between 0 and 1?

Created by HISD Curriculum using Google® Slides

Let’s use a number line to represent the math story.

0

1

The 1 represent a complete lap of the track. The 1 represents the whole.
The number line will be partitioned into 6 parts because the denominator is
6.

Steve and Sam ran around a track. Steve ran of the track. Sam ran

of the track. Who ran the furthest?

2

6

4

6

1

6

3

6

4

6

5

6

6

6

2

6

Multiple Choice

How many equal pieces between 0 and 1?

• 6

• 7

• 8

Open Ended

Paulie says this number line represents the fractional unit fourths. Samantha says this number line represents the fractional unit eighths. Who is correct? Why?

There are 7 equal pieces in this number line between O and 1.

Our unit is sevenths.

Created by HISD Curriculum using Google® Slides

0
1

Let’s use a number line to represent the distance
Steve ran around the track.

1

6

2

6

3

6

4

6

5

6

6

6
=

We can represent two sixths on the number line by moving to the distance of
two sixths on the number line. Count two equal-sized interval “jumps” or
distance starting at zero. This represents the distance that Steve ran around
the track.

Multiple Choice

If there are seven equal pieces, what is our unit?

• sixths

• sevenths

• halves

Explanation Slide...

Samantha is correct because the number line is divided into eight equal pieces.

Let's count and label our number line.

I started it for you, if we keep going ....

what fraction shows the dot?

Created by HISD Curriculum using Google® Slides

Let’s use a number line to represent the distance Sam
ran around the track.

We can represent four sixth on the number line by moving to the distance of
four sixth on the number line. Count four equal-sized interval “jumps” or
distance starting at zero. This represents the distance that Sam ran around the
track.

0
1

1

6

2

6

3

6

4

6

5

6

6

6
=

Multiple Choice

The dot is at what fraction?

• 1/7

• 3/7

• 5/7

Fill in the Blank

What fraction is represented by the bolded intervals on the number line?

The dot is at 5/7 on the number line.

Created by HISD Curriculum using Google® Slides

Let’s compare the distance of Steve and the
distance of Sam. Who ran the furthest?

Steve

Sam

This is a number line from 0-1

How many equal pieces?

Remember count the spaces

Multiple Select

Which TWO number lines show equivalent fractions?

Choose TWO correct answers.

• W

• X

• Y

• Z

Multiple Choice

How many equal pieces?

• 7

• 8

• 4

Created by HISD Curriculum using Google® Slides

Let’s use numbers and symbols to compare the
distances of Steve and Sam.

Steve

Sam

Sam ran the furthest on the
track. Sam’s number line
extends further than Steve’s
number line.

4

6

is greater than

is less than

2

6

2

6

4

6

2

<

4

6

4

>

2

6

6

6

Did you remember to the count the spaces?

There are eight.

What's our unit?

Hotspot

Click to plot where $$\frac{3}{4}$$ and $$\frac{2}{5}$$ would be on these two number lines.

Multiple Choice

If there are eight equal pieces, what's our unit?

• halves

• fifths

• eighths

Multiple Choice

Which comparison of these fractions is true

• $$\frac{1}{2}$$ > $$\frac{1}{1}$$

• $$\frac{2}{8}$$ > $$\frac{1}{8}$$

• $$\frac{1}{8}$$ = $$\frac{2}{8}$$

• $$\frac{2}{8}$$ < $$\frac{1}{8}$$

We are counting by eighths.

Where is the dot? At what fraction?

Drag and Drop

Look at the model.

Complete the following statement about the shaded part of the models?

$$\frac{3}{6}$$ is ​ ​ ​ ​

Placeholder

to $$\frac{3}{8}$$ because both fractions show the same amount shaded.

Drag these tiles and drop them in the correct blank above

not equivalent

equivalent

Multiple Choice

The dot is at what fraction?

• 3/8

• 1/8

• 5/8

Drag and Drop

Look at the model.

Complete the following statement about the shaded part of the models?

$$\frac{1}{4}$$ is ​ ​ ​

Placeholder

​ ​ to $$\frac{3}{12}$$ because both fractions show the same amount shaded.

Drag these tiles and drop them in the correct blank above

equivalent

not equivalent

Poll

How are we liking fractions on a number line?

• :) Great!

• :| Ok!

• :( Yuck.

Dropdown

​

Select answer

is ​

Select answer

to ​ ​ ​

Select answer

​ ​ ​ ​ because both fractions show the same amount shaded.​

Multiple Choice

Look at the models.

Which statement is true about the shaded part of the models?

• All of the models are not equivalent because they do not show the same amount shaded.

• Only model 1 and 4 are equivalent because both show the same amount shaded.

• All of the models are equivalent because they all show the same amount shaded.

• None of the models are equivalent.