Created by Hester Sutton April 2011

The Brandywine School District

presents

The Singapore Math SeriesSession IVFractions

0 1

0 1/5 2/5 3/5 4/5 5/5 6/5

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.

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.

0 1

6

5 6

5

Area Model

Pie Diagram Rectangles

3

4

0 1

Linear Measurement Model

3/4

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: With the same denominator.

3

8

>58

Comparing the number of fractional units.

Comparing Fractions: With the same numerator.

3

4 >3

7

Comparing the size of the fractional units.

Circle the smallest fraction.

1

4

1

7

1

5

Renaming Fractions

1

2

1

2

2

44

8

2

4

4

8= =

3

4

6

8

12

16

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

Girls Boys

8 8 8 8 8

8 x 5 = 40

There are 40 children altogether.

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 numbers and Improper fractions. Improper fractionMixed number

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?

Cookie

Cookie

Cookie

Each child will get 3/5.

1 516 6

42 Children

Glasses No glasses

Next calculate the number of children who

wear glasses.

42 6 7

7

5 7 35 35 children do not wear glasses.

of the balls in a basket are green.

1

4

1

8 of the balls in a basket are purple.

If there are 240 balls in all, how many of the balls are neither green or purple?

240 8 30

30 3030 30 303030 30

5(30) 150150 of the balls are neither green or purple.

240

?

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?

Lisa

Sam

The ratio of Sam’s stamps to Lisa’s stamps is 5:15

or 1:3