B. Number · Number Sense: Numbers to 10 000, Fractions and Decimal Tenths

Fractions of a Group and on a Number Line

B1.4 A1About 35 minutes

Learning goals

I can name a fraction of a group (set) of objects.
I can find a unit fraction of a group by sharing into equal groups.
I can show a fraction on a number line from 0 to 1.
I can explain what the numerator and denominator mean for a group and for a number line.

Words to know

set (group)
A collection of objects that we treat as one whole, like a carton of 12 eggs.

fraction of a set
Part of a group. If 3 of 5 apples are red, 3/5 of the apples are red.

number line
A line with numbers in order. We can split the space from 0 to 1 into equal parts.

A fraction can be part of a group

Last lesson, our whole was one thing, like a pan of squares or a strip of paper. But a whole can also be a group of things.

Here is a bowl of 5 apples. 3 are red and 2 are green.

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3 red apples and 2 green apples. 5 apples in all.

The whole is the group of 5 apples. So the denominator is 5.
3 of them are red. So the numerator is 3.

3/5 of the apples are red. 2/5 of the apples are green.

In a group, each object is one equal part. The apples don't need to be the same size: each one counts as 1 of the 5 objects.

A white bowl holding three red apples and two green apples. — The whole is the group of 5 apples. 3/5 of the apples are red and 2/5 are green. AI-generated image

Worked example

Example 1: Name a fraction of a set

A hockey team has 10 players on the bench. 7 are wearing helmets with face cages and 3 are wearing visors. What fraction wear visors?

The whole group: 10 players. Denominator: 10.
Players with visors: 3. Numerator: 3.

3/10 of the players wear visors. (And 7/10 wear cages.)

Finding a unit fraction of a group

What is 1/4 of 12 eggs? The denominator 4 tells us to split the group into 4 equal groups. One of those groups is 1/4.

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12 eggs shared into 4 equal groups of 3. One group, 3 eggs, is 1/4 of the eggs.

Worked example

Example 2: 1/4 of 12

A carton has 12 eggs. Dad uses 1/4 of them for pancakes. How many eggs is that?

The denominator is 4, so share the 12 eggs into 4 equal groups.
12 shared into 4 groups is 3 in each group (because 4 × 3 = 12).
The numerator is 1, so take 1 group.

3 eggs. And 3/4 of the eggs would be 3 groups: 9 eggs.

Fractions on a number line

The space from 0 to 1 on a number line is one whole. To show fifths, split that space into 5 equal jumps. Each jump is 1/5. Count the jumps from 0 to find a fraction.

A number line from 0 to 1 split into 5 equal parts. The dot is at 3/5: three jumps of one fifth from 0.

The denominator (5) tells how many equal jumps there are from 0 to 1.
The numerator (3) tells how many jumps to count from 0.
The point at 1 could also be called 5/5.

Worked example

Example 3: Find the fraction on a number line

A number line from 0 to 1 is split into 8 equal parts. A dot is on the 5th tick after 0. What fraction is it?

8 equal parts, so each part is 1/8. Denominator: 8.
The dot is 5 jumps from 0. Numerator: 5.

5/8

0 to 1 split into eighths. The dot is at 5/8, just past the middle (4/8).

Find the whole first

Before you name a fraction, always ask: "What is the whole?" Is it one object, a group, or the space from 0 to 1? Once you know the whole, the denominator is easy.

Just for fun

A dozen eggs is a fraction superstar. 1/2 of 12 is 6, 1/3 is 4, 1/4 is 3, 1/6 is 2 and 1/12 is 1. Twelve shares fairly in lots of ways!

Hands-on activity

Snack fractions

You need: a small handful of snacks or objects in two kinds (for example 6 crackers and 4 grapes, or 6 red and 4 blue buttons), a long piece of string or tape on the floor, paper and a pencil.

Part 1: Fractions of a group

Put all 10 objects in one group. That is the whole.
What fraction are crackers? What fraction are grapes? (6/10 and 4/10.)
Share the 10 objects into 2 equal groups. How many is 1/2 of 10? (5.) Now share them into 5 equal groups. How many is 1/5 of 10? (2.)

Part 2: Floor number line

Put a paper marked 0 at one end of the string and 1 at the other end.
Walk from 0 to 1 in 4 equal steps. Put a paper at each step: 1/4, 2/4, 3/4.
Have your grown-up call out a fraction, like "3/4!" Jump to it.

Math talk: "What is the whole in Part 1? In Part 2?"

Your turn

There are 8 mittens. 5 are blue. What fraction are blue?

In the bowl of apples above, what fraction are green?

What is 1/2 of 10?

What is 1/3 of 12?

A number line from 0 to 1 is split into 10 equal parts. What is the first tick after 0?

On a number line from 0 to 1 split into 3 equal parts, where is 2/3?

A class has 6 tables. 1 table is by the window. What fraction of the tables is by the window?

More practice: warm-up

4 cats and 1 dog are at the pet groomer. What fraction of the animals are cats?

What is 1/2 of 8?

What is 1/5 of 10?

On a number line from 0 to 1 cut into fourths, what fraction is halfway?

On a number line, what fraction is at the same point as 1: 6/6 or 1/6?

More practice: on your own

A box has 10 crayons. 3 are broken. What fraction are not broken?

What is 1/4 of 20? What is 3/4 of 20?

What is 1/6 of 18?

A number line from 0 to 1 has 5 equal jumps. Mia puts a dot 4 jumps from 0. What fraction is it? How many more jumps to get to 1?

Jon has 6 marbles: 2 blue, 3 red, 1 green. What fraction of the marbles are not red?

Challenge

Sam says 1/2 of 6 cookies and 1/2 of 10 cookies are the same amount, because both are one half. Is he right?

2/5 of a group is 4 marbles. How many marbles are in the whole group?

Draw (or describe) a number line from 0 to 1 and show both 1/2 and 3/10. Which is closer to 0?

Check your understanding

Quiz

7 of 10 canoes at a camp are green. What fraction are green?

What is 1/3 of 9?

What is 1/4 of 8?

A number line from 0 to 1 is cut into 6 equal parts. A dot is 5 jumps from 0. What fraction is it?

In a group of 4 dogs, 1 is asleep. What fraction are awake?

On a number line from 0 to 1, which fraction is at the same spot as 1?

For parents and teachers

Big idea: Fractions can describe part of one object, part of a group (set), or a point on a number line. All three models support B1.4 and help children see fractions as numbers.

Common difficulties:

Not knowing what the whole is. Always ask "What is the whole here?"
Counting ticks instead of jumps on a number line (calling the first tick after 0 "2/5"). Have your child put a finger on 0 and count jumps.
Thinking a fraction is always the same amount (1/2 of 6 vs 1/2 of 10). The amount depends on the size of the whole.

How to help: Ask fraction questions about everyday groups: "What fraction of the socks in this pile are white?", "Half of the 12 muffins are blueberry. How many is that?" Strand A: encourage your child to explain what the whole is before answering.