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Objective – Make equivalent fractions with sums of
fractions with like denominators.

½ or
1
(What
2
fraction piece is this?)
◦ 1 piece out of 2. It is half of an object.

How do you say ½ ?
◦ One half

½ equals how many fourths? (?/4)
◦ ½ = 2 fourths (2/4)

½ = ?/6
◦ Three sixths (3/6)

1/3 = ?/6
◦ Two sixths (2/6)

2/3 = ?/12
◦ Eight Twelfths (8/12)

3/5 = ?/25
◦ Fifteen Twenty-fifths (15/25)

½ = 2/ ?
◦ Two Fourths (2/4)

1/5 = 2/?
◦ Two Tenths (2/10)

2/5 = 8/?
◦ Eight Twentieths (8/20)

¾ = 9/?
◦ Nine Twelfths (9/12)

4/5 = 16/?
◦ Sixteen Twentieths (16/20)

3/9 = 6/?
◦ Six Eighteenths (6/18)

1/7 = 2/?
◦ Two Fourteenths (2/14)







½ = ?/4
4/10 = ?/5
5/6 = 45/?
35/63 = 5/?
1/3 = ?/9
8/12 = 2/?
6/7 = ?/56
1/5 = 2/?
6/9 = ?/3
45/81 = ?/9
5/8 = ?/64
¼ = ?/12
12/16 = 3/?
4/5 = 28/?
2/5 = ?/10
9/12 = ?/4
1/6 = ?/12
5/8 = 40/?
3/7 = ?/21
5/6 = ?/42
4/5 = ?/35

Mr. Hopkins has a 1 meter wire he is using to make
clocks. Each fourth meter is marked off with 5 smaller
equal lengths. If Mr. Hopkins bends the wire at ¾
meter, what fraction of the marks is that?
1/4
Bent after 3 units
3 x 5 units = 15 units
15/20 = 3/4
Mr. Hopkins bent the wire at
¾ m or at 15/20 of the meter.
bent
5 units
1 mark is 1/20 m.
¾ m is the same as 15/20 m.
1 meter
0/4
4/4




1/3 + 1/3
Using a number line, mark the end points as zero and 1.
Between zero and 1 estimate to make three parts of equal
length and label them with their fractional value.
Now show 1/3 plus 1/3 on your number line using arrows
designating lengths.
What did you get as your answer?
◦
2/3 (two thirds)

Express this as a multiplication equation and as an
addition sentence.
◦ 1/3 + 1/3 = 2 x 1/3 = 2/3

Following the same pattern of adding unit fractions by
joining lengths, show 3 fourths (3/4) on a number line.

¼+¼+¼=3x¼=¾


3/8 + 3/8 + 1/8 (3 eighths + 3 eighths + 1 eighths)
On a number line, again mark the end points as zero
and one. Between zero and one, estimate to make 8
parts of equal length. This time only label what is
necessary to show 3 eights.
3/8

The answer is?
◦ 7 eighths (7/8)
6/8 7/8
3/8

6/8 7/8
Write a math equation to represent the problem you
just demonstrated.
◦ 2 x 3/8 + 1/8 = 7/8




6/2 = 2/2 + 2/2 + 2/2 = 1 + 1 + 1 = ?
On a number line, mark the end points as 0 halves and
6 halves below the number line. Estimate to make 6
parts of equal length. This time only label 2 halves.
Record the whole number equivalents above on your
number line.
Then represent 3 x 2 halves on your number line.
0/2
1
2
3
2/2
4/2
6/2

What is the answer?
◦ 6 halves or 3

What is the unit of 3?
◦ 3 ones

Express this as an addition equation and as an
multiplication equation.
◦ 6/2 = 2/2 + 2/2 + 2/2 = 3 x 2/2 = 3
0/2
1
2
3
2/2
4/2
6/2
Think:
6/2 = 2/2 + 2/2 + 2/2
= 3 x 2/2
=3x1
=3


8 fifths = 5/5 + 3/5 = ?
Use a number line. Mark the end points as 0 fifths and
10 fifths below it. Estimate and five a value to the
halfway point.
0/5

10/5
What will be the value of the halfway point?
◦ 5 fifths.

Now make 10 parts of equal length from 0 fifths to 10
fifths, with the middle being 5 fifths.
0/5
5/5
10/5



Record the whole number equivalents above the line.
0
1
2
0/5
5/5
10/5
Label 8 fifths (8/5) on the number line and show the
sum of 5/5 and 3/5 on the number line.
0
1
0/5
5/5
2
8/5
10/5
Express this as an addition equation in two ways: as the
sum of fifths and as the sum of a whole number and
fifths.


5/5 + 3/5 = 8/5 or 5/5 + 3/5 = 1 3/5 or 1 + 3/5
= 1 3/5
What is another way to express 1 plus 3 fifths is?
◦ 1 and 3 fifths.

8 fifths is between what 2 whole numbers?
◦ 1 and 2
0
1
0/5
5/5
2
8/5
10/5


7/3 = 6/3 + 1/3 = 2 x 3/3 + 1/3 = ?
Use a number line. Mark the end points as 0 thirds and
9 thirds below the number line. Divide the whole length
into three equal smaller lengths and mark their values
using thirds. (Compare with a table mate after completing your number
line.)

3
0/3

3/3
6/3
What are the values of those points?
◦ 0/3, 3/3, 6/3, 9/3 or 0, 1, 2, 3
9/3



Mark the whole numbers above the number line.
0
1
2
3
0/3
3/3
6/3
9/3
Divide each of those whole number lengths into 3 smaller
lengths. Mark the number 7 thirds.
0
1
2
0/3
3/3
6/3
3
9/3
7/3
Show 7 thirds as two units of 3 thirds and one more third on
your number line and in an equation. (Compare with a tablemate
after you have completed the step.)
◦ (2 x 3/3) + 1/3 = 6/3 + 1/3 = 2 + 1/3 = 2 1/3 (7/3)
0
1
2
0/3
3/3
6/3
3
7/3
9/3




Debrief
Problem Set
Exit Ticket
Homework


1. Show each expression on a number line. Solve.
◦ a) 2/5 + 1/5
◦ c) 3/10 + 3/10 + 3/10
2. Express each fraction as the sum of two or three equal fractional
parts. Rewrite as a multiplication equation. Show letter a) on a number
line.
◦ a) 6/7

b) 9/2
c) 12/10
d) 27/5
Express each of the following as the sum of a whole number and a
fraction. Show c) and d) on a number lines.
◦ a) 9/7

b) 1/3 + 1/3 + 1/3
d) 2 x ¾ + ¼
b) 9/2
c) 32/7
d) 24/9
Marisela cut four equivalent lengths of ribbon. Each was 5 eights of a
yard long. How many yards of fabric did she cut? Express your answer
as the sum of a whole number and the remaining fractional units. Draw
a number line to represent the problem.

1) Show each expression on a number line. Solve.
◦ a) 5/5 + 2/5

b) 6/3 + 2/3
Express each fraction as the sum of two or three equal
fractional parts. Rewrite each as a multiplication
equation. Show letter b) on a number line.
◦ a) 6/9
b) 15/4

1. Show each expression on a number line. Solve.
◦ a) 4/9 + 1/9
◦ c) 2/7 + 2/7 + 2/7

2. Express each fraction as the sum of two or three equal fractional
parts. Rewrite as a multiplication equation. Show letter a) on a
number line.
◦ a) 6/11

b) 9/4
c) 12/8
d) 27/10
3. Express each of the following as the sum of a whole number and a
fraction. Show c) and d) on a number lines.
◦ a) 9/5

b) ¼ + ¼ + ¼ + ¼
d) 2 x 3/5 + 1/5
b) 7/2
c) 25/7
d) 21/9
Natalie sawed five boards of equal length to make a stool. Each was
9 tenths of a meter long. How many meters of board did she saw?
Express your answer as the sum of a whole number and the remaining
fractional units. Draw a number line to represent the problem.

Terminology and review of what a fraction is.
◦ http://www.slideshare.net/lauracstelling/fractions-powerpoint1
◦ http://www.slideshare.net/SnehalBhargava/fractions11546923
◦ http://www.slideshare.net/htaylor2010/understandingfractions (a little with ordering fractions)
◦ http://www.slideshare.net/kkerr/fraction-overview (adding,
subtracting, multiplying, and dividing fractions)
◦ http://www.slideshare.net/mstfdemirdag/fractions-8693215