Grade by Grade
B. Number · Adding and Subtracting

Equal Groups up to 10

B2.5About 30 minutes
Learning goals
  • I can tell if groups are equal.
  • I can make equal groups and find how many in all.
  • I can share a number of things into equal groups.
  • I can solve problems where each group is a half or a fourth.

Words to know

equal groups
Groups that each have the same number of things.
group of
"3 groups of 2" means 3 groups with 2 in each group.
share
To split things so everyone gets the same amount.
half
One of 2 equal parts of a whole. Two halves make one whole.
fourth
One of 4 equal parts of a whole. Four fourths make one whole. Also called a quarter.

Fair is equal

Three friends are sharing grapes. Ada gets 2 grapes, Ben gets 2 grapes, and Cam gets 2 grapes. Is that fair?

Yes! Everyone has the same number. These are equal groups.

3 equal groups with 2 grapes in each group.

We say: 3 groups of 2.

How many grapes in all? We can:

  • Count by 2s: 2, 4, 6
  • Add: 2 + 2 + 2 = 6

There are 6 grapes in all.

Three small white bowls in a row, each with two green grapes.
3 groups of 2: count by 2s to find 2, 4, 6 grapes in all. AI-generated image

Check every group

Groups are equal only if every group has the same number. 2, 2 and 3 are not equal groups.

Worked example

Example 1: How many in all?

There are 2 canoes. Each canoe has 4 paddles. How many paddles in all?

  1. How many groups? 2 (2 canoes).
  2. How many in each group? 4 paddles.
  3. Draw 2 circles with 4 dots in each.
  4. Add: 4 + 4 = 8. (It's a double!)

There are 8 paddles. 2 groups of 4 is 8.

2 groups of 4. 4 + 4 = 8.
Worked example

Example 2: Groups of 5

2 hands. Each hand has 5 fingers. How many fingers?

  1. 2 groups of 5.
  2. Count by 5s: 5, 10. Or add 5 + 5 = 10.

10 fingers

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5 pairs of socks. Each pair is a group of 2. Count by 2s: 2, 4, 6, 8, 10. That's 10 socks.

Sharing into equal groups

Sometimes we know how many in all and we need to share them fairly. Deal them out one at a time, like cards: one for you, one for me, until they are all gone.

Worked example

Example 3: Sharing

Dad has 8 strawberries. He shares them equally on 2 plates. How many strawberries on each plate?

  1. Draw 2 plates.
  2. Deal one strawberry to each plate, again and again: plate 1, plate 2, plate 1, plate 2...
  3. Stop when all 8 are used. Count one plate: 4.
  4. Check: 4 + 4 = 8. Yes!

Each plate gets 4 strawberries.

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8 strawberries shared on 2 plates: 4 on each plate.
Worked example

Example 4: How many groups?

There are 9 children. They make teams of 3 for a relay race. How many teams?

  1. Put 9 counters out.
  2. Make groups of 3 until none are left: group 1, group 2, group 3.
  3. Count the groups: 3.
  4. Check: 3 + 3 + 3 = 9.

There are 3 teams.

9 children in 3 teams of 3.

When each group gets part of something

Sometimes each person gets a half or a fourth of something, not a whole one.

If you cut a sandwich into 2 equal pieces, each piece is one half. 2 halves make 1 whole sandwich.

Worked example

Example 5: Halves

4 children each eat one half of a sandwich. How many whole sandwiches do they need?

  1. Each child is a group, and each group gets 1 half.
  2. Draw sandwiches cut in half. Give one half to each child.
  3. Sandwich 1 feeds 2 children. Sandwich 2 feeds 2 more children. That's all 4 children.
  4. Or count halves: 2 halves make 1 whole, so 4 halves make 2 wholes.

They need 2 sandwiches.

ABCD
2 sandwiches, each cut into 2 halves. Children A, B, C and D each get one half.
Worked example

Example 6: Fourths

A pizza is cut into 4 equal pieces. Each piece is one fourth. 8 friends each get one fourth. How many pizzas are needed?

  1. One pizza has 4 fourths. That feeds 4 friends.
  2. A second pizza feeds 4 more friends. 4 + 4 = 8.
  3. So 8 fourths make 2 whole pizzas.

They need 2 pizzas.

2 pizzas, each cut into 4 equal pieces (fourths). That's 8 pieces, one for each friend.

Remember

2 halves = 1 whole.

4 fourths = 1 whole.

To find how many wholes, put the pieces together until each whole is complete.

Just for fun

Fun fact: an octopus has 8 arms. That is 2 groups of 4! Imagine it giving high fives to 8 friends at the same time.

Hands-on activity

Snack time sharing

You need: 10 small snacks (like crackers or cereal pieces), 2 to 5 small plates or bowls, and a slice of bread or a sheet of paper.

  1. Put 6 crackers out. Share them equally on 2 plates. How many on each? (3)
  2. Now share the same 6 crackers on 3 plates. How many on each? (2)
  3. Make 5 groups of 2. How many crackers in all? (10)
  4. Try sharing 10 crackers onto 4 plates. What happens? (Each plate gets 2, and 2 are left over. Not every number shares equally!)
  5. Fold a slice of bread or paper into halves, then fourths. If 3 people each get one half, how many slices do you need? (1 whole and 1 half more, so you need to cut 2 slices.)

Math talk: "How do you know your groups are equal?"

Your turn

1

4 groups of 2. How many in all?

2

2 groups of 3. How many in all?

3

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

4

You have 6 cookies. Put them in groups of 2. How many groups?

5

Are these equal groups? 3 apples, 3 apples, 4 apples

6

6 kids each get one half of an orange. How many oranges do they need?

7

A cake is cut into 4 equal pieces. 4 people each get one piece. How many cakes?

8

5 groups of 1. How many in all?

More practice: warm-up

1

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2 leaves have 2 ladybugs on each. How many ladybugs in all?

2

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Are these equal groups?

3

Count by 2s. Fill in the blanks: 2, 4, __, 8, __

4

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Each mitten holds a hand with 5 fingers. Count by 5s. How many fingers?

5

2 halves make __ whole.

More practice: on your own

1

Share 6 crackers equally on 3 plates. How many crackers go on each plate?

2

There are 10 kids. They make teams of 5. How many teams?

3

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Are these equal groups? How can you make them equal?

4

8 kids each get one half of an orange. How many oranges do they need?

5

A muffin tin has 2 rows. Each row has 5 muffins. How many muffins?

Challenge

1

Find the mistake. Jay shared 9 grapes among 3 friends. He gave them 4, 3 and 2 grapes. He says it is fair. Is he right?

2

A cake is cut into 4 equal pieces (fourths). 6 kids each want one piece. How many cakes do you need? How many pieces are left over?

3

Can you share 7 cookies equally between 2 friends without breaking any cookies? Explain.

Check your understanding

Quiz

1.

Which shows equal groups?

2.

3 boats with 3 people in each. How many people?

3.

Share 8 pucks equally among 4 players. How many does each player get?

4.

2 friends each eat one half of an apple. How many apples did they eat?

5.

5 groups of 2 is how many?

6.

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

7.

How many halves make 2 wholes?

For parents and teachers

Big idea: B2.5 is the start of multiplication and division thinking. Children solve equal-group problems (total up to 10) using objects and drawings, by counting, skip counting, and repeated addition. They do not use the × or ÷ signs yet. The curriculum also includes groups that are fractions, such as each person getting one half, which connects to the fair-share work in B1.6 and B1.7.

Common mistakes:

  • Mixing up the number of groups and the number in each group. Always ask "How many groups? How many in each group?" and draw circles for groups.
  • Unequal sharing. Teach the "deal it out" method, one at a time, and then count to check that every group has the same.
  • Thinking a half is "1". For "4 children each get one half", a child may answer 4 sandwiches. Cut real bread or paper so they can see 2 halves make 1 whole.

How to help: Everyday life is full of equal groups: pairs of shoes, wheels on 2 bikes, setting the table with 2 utensils per person, sharing snacks. Ask "How many groups? How many in each? How many in all?"