The Brandywine School District
presents
The Singapore Math Series
Session IV
Fractions
Created by Hester Sutton April 2011
A fraction is a point on the number line.
For example, to locate 6/5 we start at 0, find the step size
so that 5 equal steps gets us to 1.
Then take 6 such steps, landing at the point called 6/5.
0
0
1/5
2/5
3/5
4/5
5/5
1
6/5
When counting or measuring we always have
some unit in mind.
Example:
I have 3 cups of flour.
We use fractions when there is a given unit, called
the whole unit, but we want to measure using a
smaller unit, called the fractional unit.
Numerator is the number of fractional units.
Denominator names a fractional unit by specifying
how many fractional units make one whole unit.
6
5
0
6
5
1
Area Model
Pie Diagram
Rectangles
3
4
Linear Measurement Model
3/4
0
1
Bar Diagrams are just thickened number lines.
3/4
Set Model
If a class of
20 students
contains 15
girls and 5
boys then ¾
of the
students are
girls.
Fractions are introduced at the end of Grade 2,
but does not proceed to the next step, addition
and subtraction of fractions, until Grade 4.
Comparing Fractions:
>
3
8
With the same denominator.
5
8
Comparing the number of fractional units.
Comparing Fractions:
3
4
>
With the same numerator.
3
7
Comparing the size of the fractional units.
Circle the smallest fraction.
1
4
1
7
1
5
Renaming Fractions
124
284
1
2
4
=
=
2
4
8
12
63
16
84
Mother opened a quart of milk and poured 1/5 of the
quart for Kate and 2/5 for Ryan. How much was left?
Quart of Milk
Kate
Ryan
2/5 of the quart was left.
?
4/5 of the children in the choir are girls. If there are 8
boys, how many children are there altogether?
Children in the choir
8
8
8 x 5 = 40
8
8
Girls
There are 40 children altogether.
8
Boys
Peter had 400 stamps. 5/8 of them were Singapore stamps and
the rest were U.S. stamps. He gave 1/5 of the Singapore stamps
to his friend. How many stamps did he have left?
400 stamps
Singapore Stamps
?
U.S. Stamps
7/8 x 400 = 7 x (1/8 x 400) = 7 x 50 = 350
Peter had 350 stamps left.
Mixed number
numbers and Improper
Improper fractions.
fraction
is a whole number plus a fraction.
is a fraction where the numerator is
greater than the denominator.
5 children want to share 3 giant cookies equally.
How much should each one get?
Each child will get 3/5.
Cookie
Cookie
Cookie
42 Children
Next calculate the
number of children who
wear glasses.
7
Glasses
No glasses
42  6  7
1 5
1 
6 6
5  7  35
35 children do not wear glasses.
1
1
of the balls in a basket are green.
of the balls in a basket are purple.
8
4
If there are 240 balls in all, how many of the balls are
neither green or purple?
?
30 30 30 30 30 30 30 30
240
240  8  30
5(30)  150
150 of the balls are neither green or purple.
Adding Fractions
2 1

3 4
8 3 11
 
12 12 12
Sam has 3/7 as many stamps as Lisa. If Sam
gives 1/6 of his stamps to Lisa, what will be the
ratio of the number of Sam’s stamps to Lisa’s?
Sam
Lisa
The ratio of Sam’s stamps to Lisa’s stamps is 5:15
or 1:3