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

Same Amount, Different Names: Halves, Fourths and Eighths

B1.7About 35 minutes
Learning goals
  • I can show that one half, two fourths and four eighths are the same amount.
  • I can show that one fourth is the same as two eighths, and three fourths is the same as six eighths.
  • I can use equivalent fractions to solve fair-share problems.
  • I can explain why cutting each piece in half doubles the number of pieces.

Words to know

equivalent fractions
Fractions that name the same amount of the same whole, like one half and two fourths.
halves, fourths, eighths
A whole cut into 2, 4 or 8 equal parts.
double
Twice as many. Cutting each piece in half doubles the number of pieces.

Remember from Grade 2

In Grade 2 you found that one third and two sixths of the same whole are equal. You may also remember that one half and two fourths are equal. This year you will find many more fractions that are equal.

Three ways to cut the pie

At Thanksgiving, 4 cousins share 2 pumpkin pies that are the same size.

  • Grandpa cuts each pie in halves. There are 4 halves, so each cousin gets one half.
  • Auntie cuts each pie in fourths. There are 8 fourths, so each cousin gets two fourths.
  • Dad cuts each pie in eighths. There are 16 eighths, so each cousin gets four eighths.

Does it matter who cuts the pie? No! Each cousin gets the same amount of pie every time.

A pumpkin pie in a glass dish cut into eight equal slices, with small pumpkins and autumn leaves around it.
This pie is cut into eighths. Four eighths cover the same amount of pie as one half, so one half = four eighths. AI-generated image
1 wholeone halftwo fourthsfour eighths
One half, two fourths and four eighths of the same strip all end at the dashed line. They are equal.

Equivalent fractions

Fractions that name the same amount of the same whole are called equivalent fractions.

one half = two fourths = four eighths

Why does this work?

Start with halves. Cut each half into 2 equal pieces. Now there are 4 pieces: fourths. Your one half became two fourths.

Cut each fourth in half again. Now there are 8 pieces: eighths. Your two fourths became four eighths.

Every time we cut each piece in half, we get twice as many pieces, and your share has twice as many pieces too. But it is still the same amount!

HalvesFourthsEighths
one halftwo fourthsfour eighths
—one fourthtwo eighths
—three fourthssix eighths
two halves (1 whole)four fourths (1 whole)eight eighths (1 whole)
Each row names the same amount in different ways.
Worked example

Example 1: Brownie pans

8 kids share 2 pans of brownies. How much does each kid get? Name it two ways.

  1. Way 1: Cut each pan into fourths. 2 pans make 8 fourths, one for each kid. Each kid gets one fourth.
  2. Way 2: Cut each pan into eighths. 2 pans make 16 eighths. Deal them out: each kid gets two eighths.
  3. Both ways give each kid the same amount.

Each kid gets one fourth, which is the same as two eighths, of a pan.

Worked example

Example 2: Three fourths and six eighths

4 friends share 3 pizzas. How much does each friend get? What if each pizza is cut into eighths?

  1. Cut each pizza into fourths. Each friend takes one fourth from each pizza: three fourths.
  2. Now cut each pizza into eighths instead: 3 pizzas × 8 = 24 eighths.
  3. Deal out 24 eighths to 4 friends: each gets 6 eighths.

Each friend gets three fourths, which is the same as six eighths.

three fourthssix eighths
Three fourths and six eighths of the same strip end at the same place.
Worked example

Example 3: Is it fair?

Sam gets four eighths of a sub sandwich. Lily gets one half of the same size sub. Sam says, "I have 4 pieces and you only have 1, so I have more!" Is he right?

  1. Sam's pieces are eighths. They are small.
  2. Four eighths is the same amount as one half.
  3. More pieces doesn't always mean more food.

Sam is not right. They have the same amount.

Check with strips

To check if two fractions are equal, line up fraction strips of the same length, or draw two same-size rectangles one above the other. If the shaded parts end at the same place, the fractions are equivalent.

Just for fun

What is the difference between half a sandwich and two fourths of a sandwich?

One extra cut! You still get the same amount to eat.

Hands-on activity

Fold and match

You need: your fraction strip kit (or 4 paper strips the same length) and a paper circle traced from a plate (ask for help with scissors).

  1. Lay out your whole, halves, fourths and eighths strips under each other, lined up on the left.
  2. Find all the ways to make one half. (one half, two fourths, four eighths)
  3. Find the ways to make one fourth and three fourths.
  4. Fold the paper circle in half, then in half again, then in half again. Open it. How many parts? (8) Colour one half of the circle. How many eighths did you colour? (4)

Math talk: "How do I know four eighths and one half are equal?"

Your turn

1

How many fourths are the same as one half?

2

How many eighths are the same as one half?

3

How many eighths are the same as one fourth?

4

Three fourths = ___ eighths

5

4 kids share 2 sandwiches. Each sandwich is cut into fourths. How many fourths does each kid get?

6

True or false: two fourths = four eighths

7

Which one is NOT equal to one half: two fourths, four eighths, three eighths?

More practice: warm-up

1

You fold a paper in half, then in half again. How many equal parts?

2

How many eighths make one whole?

3

One half = ___ fourths

4

Four fourths make one ___

5

Two eighths = one ___

More practice: on your own

1

Max says four eighths is more than one half because it has more pieces. Is he right?

2

8 friends share 4 pizzas. How much does each get? Name it two ways.

3

4 friends share 3 granola bars. How much does each get? Name it in fourths and in eighths.

4

Six eighths = ___ fourths

5

Describe a drawing that shows one fourth and two eighths are equal.

Challenge

1

8 kids share 6 pizzas. How much does each get? Name it two ways.

2

Which of these are equal to 1 whole: two halves, four fourths, six eighths, eight eighths?

3

A pizza is cut into eighths. Ava eats two eighths, Ben eats one fourth and Cal eats one half. Is any pizza left?

Check your understanding

Quiz

1.

One half is the same as:

2.

One fourth is the same as:

3.

Three fourths is the same as:

4.

4 kids share 2 pizzas cut into eighths. How much does each kid get?

5.

What are equivalent fractions?

6.

Which is NOT equal to one half?

For parents and teachers

Big idea: The same amount can have different fraction names. When each piece is cut into 2, there are twice as many pieces, and a share has twice as many pieces, but the amount doesn't change. The curriculum (B1.7) asks Grade 3 students to represent and solve fair-share problems that focus on equivalent fractions, including halves, fourths and eighths.

Common difficulties:

  • More pieces = more food. Children often think four eighths > one half. Use strips or real food to show they match.
  • Strips that are not the same length. Equivalent fractions only work for the same whole.
  • Unequal folding. Help line up the edges carefully.

How to help: Cut a sandwich into halves, then fourths, then eighths and talk about how many pieces make one half. Use the fraction strips. When serving pizza, ask: "If I give you two eighths, is that more or less than one fourth?"