Grade by Grade
B. Number · Operations: Adding, Subtracting and Equal Groups

Division: Sharing Equally

B2.6 B2.1 B2.5About 35 minutes
Learning goals
  • I can share up to 12 things equally.
  • I can find how many each person gets when sharing.
  • I can find how many equal groups I can make.
  • I can use repeated subtraction to show sharing.
  • I can check sharing with equal groups (multiplication).

Words to know

divide
To share or split a group into equal parts.
share equally
Give each person or group the same number.
fair share
A share where everyone gets the same amount.
deal out
Give one at a time to each person, around and around, until all are given out.
left over
Some things that are still there after everyone gets the same amount.

Let's start with a story

Grandpa baked 12 bannock pieces for a family picnic. There are 4 cousins. Each cousin should get the same number. How many pieces does each cousin get?

When we share a group into equal parts, we are dividing. Sharing fairly is something we do every day: snacks, toys, turns on the swing!

Way 1: Deal them out

Give one at a time to each person, around and around, until all the pieces are given out. Then count how many each person has.

  • Round 1: each cousin gets 1. (4 pieces given out)
  • Round 2: each cousin gets 1 more. (8 pieces given out)
  • Round 3: each cousin gets 1 more. (12 pieces given out. All gone!)

Each cousin gets 3 pieces.

12 pieces shared equally among 4 cousins. Each cousin gets 3.

Is it fair?

When you finish sharing, check: Does every group have the same number? Did you use all the things (or are some left over)?

Worked example

Example 1: Sharing strawberries

Share 10 strawberries equally between 2 friends. How many does each friend get?

  1. Draw 2 circles, one for each friend.
  2. Deal out the strawberries one at a time: 1 for Friend A, 1 for Friend B, again and again.
  3. When all 10 are shared, count one circle: 5.
  4. Check: 5 + 5 = 10.

Each friend gets 5 strawberries.

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10 strawberries shared between 2 friends: 5 each.

Way 2: Make groups

Sometimes we know how many go in each group, and we need to find how many groups we can make.

12 mittens. Each pair needs 2. How many pairs can we make? Make groups of 2 until all the mittens are used: 2, 4, 6, 8, 10, 12. That's 6 pairs.

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12 mittens make 6 pairs.
Worked example

Example 2: How many teams?

There are 9 kids at recess. They want to make teams of 3 for a relay race. How many teams can they make?

  1. We know how many in each group: 3.
  2. Make groups of 3 until all 9 kids are in a team: 3, 6, 9.
  3. Count the groups: 3.

They can make 3 teams.

Way 3: Take away equal groups (repeated subtraction)

Dividing is connected to subtracting. Keep taking away the same number until nothing is left. Count how many times you took away.

12 cookies, 3 on each plate. How many plates?

12 − 3 = 9 9 − 3 = 6 6 − 3 = 3 3 − 3 = 0

We took away 3 four times, so we need 4 plates.

0123456789101112−3−3−3−3
Start at 12 and jump back by 3 until you get to 0. 4 jumps means 4 groups.
Worked example

Example 3: Check with equal groups

Ana shared 8 crayons equally among 4 friends. She says each friend got 2. Is she right?

  1. Sharing and multiplying are connected. If each of 4 friends got 2, then 4 groups of 2 should make 8.
  2. 4 groups of 2: 2 + 2 + 2 + 2 = 8.
  3. That matches the 8 crayons she started with.

Yes, each friend got 2 crayons.

Worked example

Example 4: Some left over

Share 7 apples equally between 2 friends.

  1. Deal them out: each friend gets 1, then 2, then 3. That uses 6 apples.
  2. There is 1 apple left. If we give it to one friend, it's not fair.
  3. So each friend gets 3 apples, and 1 is left over. (A grown-up could cut it in half so each friend gets one more half!)

Each friend gets 3 apples, with 1 left over.

ThingsShared amongEach getsCheck (equal groups)
6233 + 3 = 6
6322 + 2 + 2 = 6
12266 + 6 = 12
12344 + 4 + 4 = 12
12433 + 3 + 3 + 3 = 12
12622 + 2 + 2 + 2 + 2 + 2 = 12
Ways to share 6 and 12 equally

Two kinds of sharing questions

  • How many does each get? You know the number of groups. Deal out one at a time. (12 bannock pieces, 4 cousins → 3 each.)
  • How many groups? You know how many go in each group. Make groups. (12 mittens, 2 in each pair → 6 pairs.)
Just for fun

A sneaky-smart sharing trick for two people: one person cuts the treat, and the other person picks first. Watch how carefully the cutter makes the pieces equal!

Hands-on activity

Snack sharing

You need: a small snack in 12 pieces (crackers, grapes, cereal) or 12 buttons, and 2, 3, 4 or 6 plates or cups.

  1. Put 12 pieces in a pile. Put out 2 plates. Deal out one at a time until all are shared. How many on each plate? (6)
  2. Put the pieces back. Now use 3 plates. How many on each? (4)
  3. Try 4 plates (3 each) and 6 plates (2 each).
  4. Try 5 plates. What happens? (Each plate gets 2, and 2 are left over. 12 can't be shared equally into 5.)
  5. Now make groups: Put 4 pieces on each plate. How many plates do you need? (3)

Math talk: "Why did each plate get fewer pieces when we used more plates?"

Your turn

1

Share 8 cookies equally between 2 children. How many does each get?

2

Share 9 stickers equally among 3 friends. How many does each get?

3

12 socks. How many pairs (groups of 2)?

4

10 kids make teams of 5. How many teams?

5

Use repeated subtraction: 8 grapes, 2 in each bag. How many bags?

6

Share 11 marbles equally between 2 friends. How many does each get? Are any left over?

More practice: warm-up

1

Share 6 crackers equally between 2 friends.

2

Share 4 pencils equally among 4 kids.

3

Share 10 toonies equally between 2 piggy banks.

4

Is this a fair share? Jo gets 3 grapes, Kim gets 4 grapes.

5

12 eggs. Put 6 in each carton. How many cartons?

More practice: on your own

1

Share 12 crayons equally among 4 children. Show your work.

2

A teacher has 12 students. She makes groups of 3. How many groups?

3

Share 10 granola bars equally among 3 children. How many does each get? How many are left over?

4

Ben says if he shares 6 apples among 3 friends, each gets 3. Check with equal groups. Is he right?

5

Write a sharing story for 8 shared among 4.

Challenge

1

You have 12 strawberries. Find all the ways to share them equally with no leftovers, using 2 to 6 plates.

2

Mia shared some crackers equally among 3 friends. Each friend got 4. How many crackers did she have?

3

Share 3 sandwiches equally between 2 children. How much does each child get?

Check your understanding

Quiz

1.

Share 10 berries equally between 2 kids. How many does each kid get?

2.

12 mittens. How many pairs (groups of 2)?

3.

Share 9 toys equally among 3 kids. How many does each kid get?

4.

Which repeated subtraction shows 8 shared into groups of 4?

5.

Share 7 cookies equally between 2 friends. What happens?

6.

Mo shared 12 pencils equally among 4 friends. Which shows how to check his answer?

For parents and teachers

Big idea: B2.6 asks children to represent division of up to 12 items as the equal sharing of a quantity, and to solve related problems with tools and drawings. B2.1 links subtraction and division: repeated subtraction of equal groups. Children also meet the "how many groups?" kind of problem, which builds toward Grade 3. The division sign (÷) is not expected in Grade 2.

Common mistakes:

  • Unequal shares. Teach "deal out one at a time" and always check that every group has the same number.
  • Mixing up the number of groups and the number in each group. Ask: "Do we know how many people, or how many each person gets?"
  • Ignoring leftovers. It's fine to have some left over; just name them.
  • Thinking more groups means more in each group. Act it out: the same 12 snacks on more plates means fewer on each plate.

How to help: Share real things fairly at home: snacks, Lego, cards for a game. Ask your child to check with repeated addition.