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

Fair Sharing: Whole Numbers, Leftovers and Mixed Numbers

B1.6 A1About 35 minutes
Learning goals
  • I can share up to 20 things equally among 2, 3, 4, 5, 6, 8 or 10 people.
  • I can use a drawing to show a fair share.
  • I can decide what to do with leftovers.
  • I can name a share as a mixed number, like 3 and one half.

Words to know

fair share
When everyone gets the same amount.
sharer
A person (or group) who gets a share.
leftover
What is left after everyone has an equal share of the whole things.
mixed number
A whole number and a fraction together, like 3 and one half.
fraction
A number that names equal parts of a whole, like one half or two fifths.

Remember from Grade 2

In Grade 2 you shared up to 10 things among 2, 3, 4 or 6 people. Some shares were whole numbers, some had halves, and some were fractions like two thirds. This year you will share up to 20 things among 2, 3, 4, 5, 6, 8 or 10 people.

After skating

Five friends come home from the outdoor rink. Grandma has 15 mini muffins. How can the friends share them fairly?

One way: deal them out one at a time, like cards, until they are all gone. Another way: draw 5 plates and put the same number on each plate.

A plate of blueberry muffins on a kitchen counter next to a snowy window.
Muffins after skating! To share them fairly, deal them out one at a time until every friend has the same number. AI-generated image
plate 1plate 2plate 3plate 4plate 5
15 muffins shared fairly on 5 plates. Each plate has 3 muffins.

Each friend gets 3 muffins. Check: 3 + 3 + 3 + 3 + 3 = 15. ✔

When the share comes out even, every person gets a whole number of things.

Worked example

Example 1: An even share

6 kids share 18 crackers fairly. How many does each kid get?

  1. Draw 6 circles, one for each kid.
  2. Deal out the crackers one at a time, around and around.
  3. Each circle ends up with 3 crackers. Check: 3 + 3 + 3 + 3 + 3 + 3 = 18.

Each kid gets 3 crackers.

What about leftovers?

4 friends share 14 granola bars. Deal them out: each friend gets 3 bars. That uses 12 bars. There are 2 bars left over.

What should we do with the leftovers? It depends on what we are sharing:

  • Granola bars, pizzas and pancakes can be cut into equal pieces. We can share the leftovers too!
  • Balloons, toy cars and hockey cards can't be cut. The leftovers stay left over (maybe you can save them, or give them to someone else).
Friend 1Friend 2Friend 3Friend 4
14 granola bars shared by 4 friends. Each friend gets 3 whole bars and one half of a bar.

To share the 2 leftover bars among 4 friends, cut each bar in half. That makes 4 halves, one for each friend. Each friend gets 3 and one half bars.

3 and one half is a mixed number: a whole number (3) and a fraction (one half) together.

Worked example

Example 2: Sharing leftovers in fifths

5 friends share 17 pancakes. How much does each friend get?

  1. Deal out the whole pancakes: each friend gets 3. That uses 15 pancakes.
  2. There are 2 pancakes left over (17 − 15 = 2).
  3. There are 5 friends, so cut each leftover pancake into 5 equal pieces: fifths.
  4. 2 pancakes × 5 pieces = 10 fifths. Deal them out: each friend gets 2 fifths.

Each friend gets 3 and two fifths pancakes.

Friend 1Friend 2Friend 3Friend 4Friend 5
17 pancakes shared by 5 friends. Each friend gets 3 whole pancakes and two fifths of a pancake.
Worked example

Example 3: Leftovers we can't cut

8 kids share 20 hockey cards. How many does each kid get?

  1. Deal them out: each kid gets 2 cards. That uses 16 cards.
  2. There are 20 − 16 = 4 cards left.
  3. We shouldn't cut hockey cards! So 4 cards are left over.

Each kid gets 2 cards, and 4 cards are left over.

Worked example

Example 4: More pizzas than people

4 friends share 6 pizzas. How much does each friend get?

  1. Deal out the whole pizzas: each friend gets 1. That uses 4 pizzas.
  2. There are 2 left. Cut each one in half: 4 halves.
  3. Each friend gets one more half.

Each friend gets 1 and one half pizzas.

Check your share

Always check a fair share by putting it back together. For 14 bars and 4 friends: 3 + 3 + 3 + 3 = 12 whole bars, and 4 halves make 2 more bars. 12 + 2 = 14. ✔

Fair and friendly

Sharing fairly is a kind thing to do. If someone feels their share isn't fair, you can count or line up the pieces together to check. Talking calmly about it helps everyone feel good.

Just for fun

A real trick for sharing one pancake fairly between two friends: one friend cuts, and the other friend picks first. The cutter will try very hard to make two equal halves!

Hands-on activity

Pancake party

You need: paper, scissors (ask a grown-up for help) and some stuffed animals or toys to be the "friends". Or use real crackers or tortillas with a grown-up.

  1. Cut out 15 paper circles. These are pancakes.
  2. Share 11 pancakes between 2 toys. What do you do with the leftover? (Answer: each gets 5 and one half.)
  3. Share 13 pancakes among 4 toys. (Answer: 3 and one fourth each.)
  4. Share 9 pancakes among 5 toys. (Answer: 1 whole each, then 4 left. Cut each of those into fifths: 20 fifths, so each toy gets 4 more fifths: 1 and four fifths each.)
  5. Draw a picture of each share.

Math talk: "How did I decide how to cut the leftovers?"

Your turn

1

3 friends share 12 apples. How many each?

2

10 kids share 20 stickers. How many each?

3

8 kids share 16 crackers. How many each?

4

2 friends share 9 cookies. How much does each friend get?

5

4 friends share 13 brownies. How much each?

6

6 kids share 19 balloons. Balloons can't be cut. How many each?

7

5 friends share 11 pancakes. How much each?

More practice: warm-up

1

5 kids share 10 oranges. How many each?

2

4 kids share 8 muffins. How many each?

3

3 kids share 15 grapes. How many each?

4

2 kids share 5 sandwiches. How much each?

5

2 kids share 7 pizzas. How much each?

More practice: on your own

1

4 friends share 18 muffins. How much does each friend get?

2

8 kids share 17 granola bars. How much each?

3

5 kids share 14 toy cars. How many each?

4

Raj shares 10 pizzas among 4 people. He says each person gets 2 and one half. Check his answer.

5

3 friends share 16 sub sandwiches. How much each?

Challenge

1

10 people share 19 pies. How much does each person get?

2

Which gives each person more: 13 bars shared by 4, or 13 bars shared by 5?

3

Mia shares 20 strawberries fairly. Each person gets 2 and one half strawberries. How many people are sharing?

Check your understanding

Quiz

1.

5 kids share 20 apples. How many does each kid get?

2.

2 kids share 9 sandwiches. How much does each kid get?

3.

What is a mixed number?

4.

3 kids share 13 crackers. The crackers can be broken into equal pieces. How much does each kid get?

5.

4 kids share 11 balloons. Balloons can't be cut. What happens?

6.

8 friends share 17 pizzas. How much does each friend get?

For parents and teachers

Big idea: Fair sharing (equal sharing) is how children first meet fractions and division. The curriculum (B1.6) asks Grade 3 students to use drawings to represent, solve and compare fair-share problems with up to 20 items and 2, 3, 4, 5, 6, 8 or 10 sharers, including answers that are whole numbers, mixed numbers and fractions.

Common difficulties:

  • Unequal shares. Encourage dealing out one at a time and drawing a circle for each sharer.
  • Cutting leftovers into the wrong number of pieces. The number of equal pieces should match the number of sharers (5 sharers → fifths).
  • Forgetting the leftovers or cutting things that can't be cut. Ask: "Can this be cut into equal pieces?"
  • Naming mixed numbers. Say the whole part and the fraction part: "3 and one half".

How to help: Share real food fairly at snack time: crackers, tortillas, pizza slices, granola bars. Let your child decide how to cut the leftovers. We use words like "two fifths" here; writing fractions with numbers is part of the Operations unit.