B. Number · Number Sense: Numbers to 50 and Fractions

More Sharers, Smaller Shares: Comparing Fractions

B1.8 B1.6About 30 minutes

Learning goals

I can name the share each person gets when a whole is shared by 2 to 10 people.
I can use drawings to compare shares.
I know that more sharers means each share is smaller.
I can put shares in order from biggest to smallest.

Words to know

one third
One of 3 equal parts of a whole. Used when 3 people share one thing.

one fifth
One of 5 equal parts of a whole.

one tenth
One of 10 equal parts of a whole.

fraction
A number that names part of a whole, like one half or one fourth.

Would you rather...?

There is one big birthday cake. Would you rather share it with 2 people or with 10 people?

If you want a bigger piece, share it with fewer people! In this lesson, you will compare the size of shares when the same whole is shared by different numbers of people.

Naming the shares

When a whole is shared fairly, the name of each share comes from how many equal parts there are:

Number of sharers	Equal parts	Each share is called
2	2	one half
3	3	one third
4	4	one fourth
5	5	one fifth
6	6	one sixth
7	7	one seventh
8	8	one eighth
9	9	one ninth
10	10	one tenth

Names for one share when one whole is shared fairly.

Listen for the pattern

Except for half, the share names sound like the order words: third, fourth, fifth, sixth, seventh, eighth, ninth, tenth.

Drawing the shares

Let's draw the same whole (like a long granola bar) many times. Each time, we share it with a different number of people. Look at the coloured piece in each bar.

The same size bar shared by 2, 3, 4, 5, 6, 8 and 10 people. One share is coloured in each bar.

What do you notice?

When 2 people share, each piece is big.
When 10 people share, each piece is tiny.
The more sharers there are, the smaller each share is.

This can seem surprising. 10 is a bigger number than 2, but one tenth is a smaller piece than one half!

Worked example

Comparing two shares

Which is bigger: one third of a pizza or one fifth of the same pizza?

One third means the pizza is shared by 3 people.
One fifth means the same pizza is shared by 5 people.
More people sharing the same pizza means smaller pieces. 5 people is more than 3.
Draw it to check: one piece from 3 equal parts is bigger than one piece from 5 equal parts.

One third is bigger than one fifth.

The same pizza shared by 3 (left) and by 5 (right). One third is bigger than one fifth.

Worked example

Ordering shares

Order these shares from greatest to least: one fourth, one tenth, one half.

Think about how many sharers: one fourth means 4 sharers, one tenth means 10 sharers, one half means 2 sharers.
The fewest sharers gives the biggest piece: 2 sharers, so one half is greatest.
Next is 4 sharers: one fourth.
The most sharers gives the smallest piece: 10 sharers, so one tenth is least.

one half, one fourth, one tenth

Worked example

A Thanksgiving pie

At Thanksgiving, Aunt Rosa's pumpkin pie is shared by 6 people. Uncle Dev's pumpkin pie is the same size, and it is shared by 8 people. Whose guests get bigger pieces?

Aunt Rosa's pie is cut into 6 equal pieces. Each piece is one sixth.
Uncle Dev's pie is cut into 8 equal pieces. Each piece is one eighth.
6 sharers is fewer than 8 sharers, so the pieces are bigger.

Aunt Rosa's guests get bigger pieces. One sixth is bigger than one eighth.

Big idea

When the wholes are the same size:

Fewer sharers means bigger shares.
More sharers means smaller shares.

Just for fun

A true story: a burger restaurant once sold a one-third pound burger. Many people did not buy it because they thought one third was smaller than one fourth, since 3 is less than 4. You know better: one third is bigger!

Hands-on activity

Paper strip fractions

You need: 5 strips of paper all the same length (cut from one sheet), crayons, and a ruler if you have one.

Leave the first strip whole. Label it "one whole".
Fold the second strip in half. Colour one part. Label it "one half".
Fold the third strip in half and in half again to make 4 parts. Colour one part. Label it "one fourth".
Fold the fourth strip in half 3 times to make 8 parts. Colour one part. Label it "one eighth".
Try folding the last strip into 3 equal parts (like folding a letter). Colour one part. Label it "one third".
Line up the strips. Put the coloured parts in order from biggest to smallest. What do you notice about the number of parts?

Your turn!

If 5 people share a sandwich fairly, what part does each person get?

Which is bigger: one half or one fourth of the same pizza?

Which is smaller: one sixth or one third of the same cake?

Ten children share a big watermelon. Three children share another watermelon that is the same size. Who gets bigger pieces?

Order from least to greatest: one half, one eighth, one fifth.

Order from greatest to least: one tenth, one third, one fourth.

Sam says one tenth is bigger than one half because 10 is bigger than 2. Is Sam right?

More practice: warm-up

8 people share a pizza fairly. What part does each person get?

Which is bigger: one third or one tenth of the same cake?

True or false: When more people share the same whole, each share gets bigger.

A whole is cut into 10 equal parts. What is each part called?

You want a bigger piece of pizza. Would you rather share it with 3 people or with 7 people?

More practice: on your own

Which is smaller: one fifth or one ninth of the same granola bar? How do you know?

Order from greatest to least: one third, one seventh, one fifth.

4 friends share one granola bar. 2 friends share another granola bar that is the same size. Which group gets bigger pieces?

Fill in the blank with bigger or smaller: One sixth of a cake is \_\_\_ than one fourth of the same cake.

Order from least to greatest: one half, one tenth, one third, one sixth.

Challenge

Find the mistake! Tia says one fifth is bigger than one fourth because 5 is bigger than 4. Is she right? Explain.

Which is bigger: one half of a tiny cookie or one fourth of a giant pizza? Explain.

A cake was going to be shared by 2 people. Then 2 more friends came, so now 4 people share it. Does each share get bigger or smaller? What is each share called now?

Check your understanding

Quiz

A pie is shared fairly by 3 people. What part does each person get?

Which is the biggest share of the same pizza?

Which is smaller: one fourth or one eighth of the same cake?

Which list is in order from greatest to least?

If 7 people share a pie fairly, what part does each person get?

Two pizzas are the same size. Which group gets bigger pieces?

For parents and teachers

What your child is learning: to name the shares (unit fractions) that result when one whole is shared by 2 to 10 people, and to compare and order them using drawings. The key idea is that the more equal parts a whole is cut into, the smaller each part is. Grade 1 students use words (one third, one fifth) rather than symbols like 1/3.

Common mistakes and how to help:

Thinking one tenth is bigger than one half because 10 is bigger than 2. This is the most common misconception. Fold two identical paper strips, one into 2 parts and one into 8 or 10 parts, and compare a single piece from each.
Drawing unequal parts. Remind your child that every share must be the same size. Rectangles and strips are easier to cut into equal parts than circles.
Comparing shares of different-size wholes. Make sure the wholes being compared are the same size.

Everyday practice: when sharing food, ask "If one more person joins us, will your piece get bigger or smaller?"

Math talk questions: "How do you know which piece is bigger?" "What would happen to the pieces if more people came?" "Can you draw it to show me?"