B. Number · Number Sense: Numbers to 1000 and Fractions

Shares Less Than One: Fifths, Eighths and Tenths

B1.6About 35 minutes

Learning goals

I can name equal parts: halves, thirds, fourths, fifths, sixths, eighths and tenths.
I can explain why more sharers means smaller pieces.
I can share fewer things than there are people, like 3 bars among 5 friends.
I can count fractional parts past one whole, like five fifths, six fifths.

Words to know

fifths
5 equal parts of a whole. Each part is one fifth.

eighths
8 equal parts of a whole. Each part is one eighth.

tenths
10 equal parts of a whole. Each part is one tenth.

whole
One complete thing, like a whole pizza or a whole granola bar.

equal parts
Parts that are exactly the same size.

Remember from Grade 2

You know halves, thirds, fourths and sixths. In Grade 3 you will also use fifths, eighths and tenths.

Thanksgiving dinner

At Thanksgiving, 10 people sit down to share 1 big pan of lasagna. Each person can't get a whole pan! The pan must be cut into 10 equal pieces. Each piece is one tenth of the pan.

When there are fewer things than people, each person gets a share that is less than one whole.

Equal parts in the whole	Each part is called	How many make one whole?
2	one half	two halves
3	one third	three thirds
4	one fourth (or quarter)	four fourths
5	one fifth	five fifths
6	one sixth	six sixths
8	one eighth	eight eighths
10	one tenth	ten tenths

The name of each part comes from how many equal parts make the whole.

The same whole cut into fifths, eighths and tenths. One part of each is shaded. The more parts there are, the smaller each part is.

More sharers, smaller pieces

Look at the picture. One fifth is bigger than one eighth, and one eighth is bigger than one tenth.

When more people share the same whole, the whole is cut into more pieces, so each piece is smaller.

Sharing a few things with many people

5 friends share 3 granola bars. There isn't a whole bar for everyone.

Cut each bar into 5 equal pieces (fifths), because there are 5 friends.
Each friend takes one piece from each bar.
Each friend gets 3 pieces: three fifths of a bar.

3 granola bars, each cut into fifths. One friend takes the shaded piece from each bar.

Worked example

Example 1: One thing, many sharers

8 kids share 1 pizza. How much does each kid get?

There are 8 kids, so cut the pizza into 8 equal pieces.
The pieces are eighths.
Each kid gets one piece.

Each kid gets one eighth of the pizza.

Worked example

Example 2: Three pizzas, four friends

4 friends share 3 pizzas. How much does each friend get?

There are 4 friends, so cut each pizza into fourths.
Each friend takes one fourth from each of the 3 pizzas.
That is 3 pieces, each one fourth.

Each friend gets three fourths of a pizza.

Worked example

Example 3: Tenths

10 kids share 7 fruit bars. How much does each kid get?

Cut each bar into 10 equal pieces: tenths.
Each kid takes one tenth from each of the 7 bars.

Each kid gets seven tenths of a fruit bar.

Counting fractional parts

We can count fifths just like we count apples:

one fifth, two fifths, three fifths, four fifths, five fifths

Five fifths make one whole. If we keep counting, six fifths is one whole and one more fifth: 1 and one fifth.

Five fifths make one whole. Six fifths is one whole and one fifth more.

Worked example

Example 4: Equal parts only

Leo cuts a cake into 5 pieces, but two of the pieces are much bigger than the others. Are the pieces fifths?

Fifths must be 5 equal parts.
Leo's pieces are not the same size.

No. They are 5 pieces, but they are not fifths because they are not equal.

Did you know?

You may also see fractions written with numbers, like 3/5 for three fifths. The bottom number tells how many equal parts make the whole. The top number tells how many parts we have. You will learn more about this in the Operations unit.

Just for fun

Why did the pizza go to math class?

It wanted to learn about fractions, but it got cut into eighths instead!

Hands-on activity

Make a fraction strip kit

You need: 7 strips of paper the same length (20 cm long works well), a ruler, a pencil, crayons and scissors (ask a grown-up to help with scissors).

Strip 1: leave it whole. Label it 1 whole.
Strip 2: fold it in half. Label each part one half.
Strip 3: fold it in half, then in half again. Label the fourths.
Strip 4: fold it in half three times. Label the eighths.
Strip 5: fold it into 3 equal parts, like a letter. Label the thirds.
Strip 6: fold it into thirds, then in half. Label the sixths.
Strip 7: fifths are hard to fold, so measure: mark every 4 cm on a 20 cm strip. Label the fifths.
Bonus strip: mark every 2 cm on another 20 cm strip. Label the tenths.

Line them up. Which part is the biggest? Which is the smallest? Keep your kit for the next lessons!

Your turn

A whole is cut into 8 equal parts. What is each part called?

5 friends share 1 sandwich. How much does each friend get?

5 friends share 2 pizzas. How much does each friend get?

8 people share 3 pies. How much each?

10 kids share 9 granola bars. How much each?

How many tenths make one whole?

Count by eighths: one eighth, two eighths ... What comes after seven eighths?

More practice: warm-up

How many equal parts are in fifths?

What do we call 10 equal parts of a whole?

How many fourths make one whole?

4 kids share 1 pizza. How much each?

Which piece is smaller: one half or one tenth of the same sandwich?

More practice: on your own

5 friends share 4 waffles. How much does each friend get? How do you cut them?

8 kids share 5 pizzas. How much each?

Is one eighth of a granola bar bigger or smaller than one fifth of the same bar? Explain.

Is seven fifths more or less than one whole? Explain.

10 kids share 3 sub sandwiches. How much each?

Challenge

8 people share 6 pies. How much does each person get?

Write twelve tenths as a mixed number.

Each of 5 friends got three fifths of a pizza. How many pizzas did they share in all?

Check your understanding

Quiz

What do we call 10 equal parts of a whole?

5 friends share 2 pizzas. How much does each friend get?

Which piece is the smallest? (The wholes are the same size.)

How many eighths make one whole?

10 kids share 3 bars. How much does each kid get?

Six fifths is:

For parents and teachers

Big idea: When fewer items are shared among more people, each share is a fraction less than one. The number of sharers tells how many equal parts to cut each item into. The curriculum (B1.6) includes sharers of 2, 3, 4, 5, 6, 8 and 10 in Grade 3, so fifths, eighths and tenths are new this year.

Common difficulties:

Thinking a bigger number means a bigger piece (one eighth > one fifth because 8 > 5). Use the fraction strips to compare.
Unequal parts. Fractions always need equal parts.
Cutting only one item instead of each item. With 3 bars and 5 friends, each bar is cut into fifths.

How to help: Use food you can cut fairly (tortillas, toast, granola bars) and talk about the names of the pieces. Save the fraction strip kit for the next lessons. A grown-up should handle any knife.