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

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

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.

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

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

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

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.

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
=

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

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

Multiple Choice

Which comparison of these fractions is true

• $$\frac{1}{2}$$ > $$\frac{1}{1}$$

• $$\frac{2}{8}$$ > $$\frac{1}{8}$$

• $$\frac{1}{8}$$ = $$\frac{2}{8}$$

• $$\frac{2}{8}$$ < $$\frac{1}{8}$$