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

Multiplication: Equal Groups

B2.5 B2.1About 35 minutes

Learning goals

I can describe a picture as "__ groups of __".
I can find the total of equal groups by skip counting or repeated adding.
I can show equal groups in rows (an array).
I can solve problems with groups of one half and one fourth.

Words to know

equal groups
Groups that all have the same number of things.

multiply
To find the total of equal groups. 3 groups of 4 is 12.

repeated addition
Adding the same number again and again, like 4 + 4 + 4 = 12.

skip count
Count by a number other than 1, like 2, 4, 6, 8 or 5, 10, 15.

array
Things arranged in equal rows, like eggs in a carton.

one half / one fourth
One of 2 equal parts of a whole (one half), or one of 4 equal parts of a whole (one fourth).

Let's start with a question

How many wheels are on 4 bikes? You could count every wheel: 1, 2, 3, 4, 5, 6, 7, 8. But there is a faster way! Each bike has 2 wheels. So count by 2s: 2, 4, 6, 8.

When we have equal groups and want the total, we are multiplying. In Grade 1 you made equal groups up to 10. In Grade 2 you will use bigger numbers, rows, and even groups of halves and fourths.

🚲🚲🚲🚲

4 bikes. Each bike has 2 wheels. 2, 4, 6, 8. There are 8 wheels.

Say it as "groups of"

To multiply, ask two questions:

How many groups?
How many in each group?

4 groups of 2 is 2 + 2 + 2 + 2 = 8.

Adding the same number again and again is called repeated addition. Multiplying is a fast way to do repeated addition.

3 groups of 5. 5 + 5 + 5 = 15. Skip count: 5, 10, 15.

Worked example

Example 1: Hockey teams

There are 3 teams. Each team has 5 players on the ice. How many players are on the ice?

How many groups? 3 teams.
How many in each group? 5 players.
Repeated addition: 5 + 5 + 5 = 15.
Or skip count by 5s: 5, 10, 15.

3 groups of 5 is 15. There are 15 players.

Arrays: equal rows

When things are lined up in equal rows, it's called an array. Egg cartons, muffin pans and windows are often arrays.

Each row is one equal group.

An open carton of twelve brown eggs arranged in two rows of six. — An egg carton is an array: 2 equal rows of 6 eggs. 6 + 6 = 12, so 2 groups of 6 make 12. AI-generated image

An egg carton: 2 rows of 6. 6 + 6 = 12 eggs.

4 rows of 3. 3 + 3 + 3 + 3 = 12. Skip count: 3, 6, 9, 12.

Same total, different groups

4 rows of 3 is 12. Turn it sideways and it is 3 rows of 4, which is also 12!

Just like adding, you can switch the numbers of groups and the number in each group. The total stays the same.

Worked example

Example 2: Muffin pan

A muffin pan has 3 rows with 4 muffins in each row. How many muffins?

How many groups (rows)? 3. How many in each? 4.
Repeated addition: 4 + 4 + 4.
4 + 4 = 8, and 8 + 4 = 12.

12 muffins. 3 groups of 4 is 12.

Worked example

Example 3: Skip counting by 10s

There are 6 boxes of crayons. Each box has 10 crayons. How many crayons?

6 groups of 10.
Skip count by 10s: 10, 20, 30, 40, 50, 60.

60 crayons.

Groups of halves and fourths

Sometimes each group is a part of something, like one half of a sandwich.

Remember: 2 halves make 1 whole. 4 fourths make 1 whole.

5 children each get one half of a sandwich. That's 5 halves. 2 halves make 1 whole, so 5 halves = 2 whole sandwiches and 1 half more.

Worked example

Example 4: Groups of one half

5 children each eat one half of a sandwich. How many sandwiches do they eat?

5 groups of one half = 5 halves.
Put the halves together to make wholes: 2 halves = 1 whole, 4 halves = 2 wholes.
We have 5 halves. That's 2 wholes and 1 half left over.

They eat 2 and a half sandwiches.

2 pizzas cut into fourths. 8 fourths = 2 whole pizzas.

Worked example

Example 5: Groups of one fourth

8 friends each get one fourth of a pizza. How many pizzas do they need?

8 groups of one fourth = 8 fourths.
4 fourths make 1 whole pizza.
Count by 4s to make wholes: 4 fourths (1 pizza), 8 fourths (2 pizzas).

They need 2 pizzas.

Coming in Grade 3

In Grade 3 you will learn a special sign for multiplying. For now, say and write "groups of" and use repeated addition, like 4 groups of 3 = 3 + 3 + 3 + 3 = 12.

Just for fun

An octopus has 8 arms. Three octopuses have 3 groups of 8: 8, 16, 24 arms. That's a lot of high fives!

Hands-on activity

Equal group hunt

You need: your home, paper, a pencil, and small things like cereal pieces or buttons.

Hunt for equal groups at home: eggs in a carton, socks in pairs, wheels on toy cars, windows with panes, buttons on shirts.
For each one, draw it and write "__ groups of __ = __". Example: "5 pairs of socks: 5 groups of 2 = 10."
Use cereal to build an array: 3 rows of 5. Count the total by skip counting. Turn your paper. Is it 5 rows of 3 now? Is the total the same?
Half and fourth snack: cut 2 slices of bread (or paper squares) into fourths. Give one fourth to each family member or toy. How many fourths did you use? How many whole slices is that?

Your turn

🐞🐞🐞 🐞🐞🐞 🐞🐞🐞 🐞🐞🐞

How many groups? How many in each? How many in all?

Write as repeated addition and solve: 5 groups of 2.

A carton has 2 rows of 5 eggs. How many eggs?

How many fingers are on 4 hands? Skip count.

There are 3 bags with 10 marbles in each bag. How many marbles?

6 children each eat one half of an apple. How many apples do they eat?

Draw an array for 2 rows of 4. What is the total?

More practice: warm-up

Skip count by 2s to 12.

Skip count by 5s to 30.

Are these equal groups? 🍎🍎🍎 🍎🍎 🍎🍎🍎

2 groups of 6 = ?

How many halves make one whole?

More practice: on your own

A spider has 8 legs. How many legs do 3 spiders have?

Lily puts her toy cars in 5 rows of 4. How many cars? Show your thinking.

7 nickels are each worth 5 cents. How many cents is that?

4 friends each eat one fourth of a pizza. How much pizza did they eat?

Write a "groups of" sentence for 3 + 3 + 3 + 3 + 3. Then find the total.

Challenge

Show 12 as equal groups in three different ways.

9 children each get one half of a granola bar. How many granola bars are needed? Will any be left over?

Tom says 4 groups of 5 is 9. What mistake did he make?

Check your understanding

Quiz

What does 3 groups of 6 mean?

How many wheels are on 5 bikes? (Each bike has 2 wheels.)

An array has 3 rows of 5 stickers. How many stickers?

Which shows equal groups?

6 friends each get one fourth of a pie. How much pie is that?

Which is the same total as 4 groups of 2?

For parents and teachers

Big idea: B2.5 asks children to represent multiplication as repeated equal groups, including groups of one half and one fourth, using tools and drawings. B2.1 connects addition and multiplication: multiplying is repeated addition. The multiplication sign (×) and memorizing times tables are not expected in Grade 2; they come in Grade 3.

Common mistakes:

Adding the two numbers (4 groups of 5 = 9). Always ask: "How many groups? How many in each group?" and draw circles.
Unequal groups. Check that every group has the same number.
Fraction groups. Children may say 5 halves = 5 sandwiches. Use real food or paper to put halves together into wholes.

How to help: Point out equal groups everywhere: pairs of mittens, legs on chairs, eggs in a carton, wheels on cars. Practise skip counting by 2s, 5s and 10s (from the Number Sense unit) while walking or climbing stairs. Share snacks in halves and fourths.