Grade by Grade
B. Number · Operations: Adding and Subtracting to 1000, Multiplying and Dividing

Multiplication: The × Sign and Arrays

B2.6 B2.1About 35 minutes
Learning goals
  • I can use the × sign to write a multiplication sentence.
  • I can show multiplication with equal groups, arrays and a number line.
  • I can turn an array to show that 3 × 4 and 4 × 3 have the same product.
  • I can multiply numbers up to 10 × 10 using tools and drawings.

Words to know

multiply
Find the total of equal groups. 3 × 4 means 3 groups of 4.
×
The multiplication sign. Say "times" or "groups of".
factor
One of the numbers you multiply. In 3 × 4 = 12, the factors are 3 and 4.
product
The answer when you multiply. In 3 × 4 = 12, the product is 12.
array
Objects arranged in equal rows and equal columns.
repeated addition
Adding the same number again and again, like 4 + 4 + 4.

Remember from Grade 2

In Grade 2 you made equal groups and found the total by repeated addition: 4 groups of 3 is 3 + 3 + 3 + 3 = 12. You also learned that this is called multiplying. In Grade 3 you get a special sign for it: ×.

Let's start with a question

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

You could add: 4 + 4 + 4 = 12. Or you could write it as a multiplication sentence:

3 × 4 = 12

Say it: "3 times 4 equals 12" or "3 groups of 4 is 12."

A muffin pan seen from above holding 12 baked muffins in 3 rows of 4.
A muffin pan is a real array: 3 rows with 4 muffins in each row, so 3 × 4 = 12 muffins. AI-generated image
3 × 4= 12
An array of 3 rows with 4 in each row. 3 × 4 = 12.

The parts of a multiplication sentence

In 3 × 4 = 12:

  • 3 is the number of groups (or rows). It is a factor.
  • 4 is how many are in each group (or row). It is also a factor.
  • 12 is the total. It is the product.

Three ways to show multiplication

1. Equal groups. Draw circles for the groups and put the same number in each one.

4 groups of 5. 4 × 5 = 20.

2. An array. Put objects in equal rows. Each row is one group. Arrays are everywhere: egg cartons, muffin pans, windows, chocolate bars.

3. A number line. Make equal jumps from 0. The number of jumps is the number of groups. The size of each jump is the number in each group.

05101520+5+5+5+5
4 jumps of 5 land on 20. 4 × 5 = 20.
Worked example

Example 1: Write the multiplication sentence

An egg carton has 2 rows of 6 eggs. How many eggs?

  1. There are 2 rows (groups). There are 6 in each row.
  2. Write: 2 × 6.
  3. Repeated addition: 6 + 6 = 12.

2 × 6 = 12 eggs

2 × 6= 12
An egg carton array: 2 rows of 6.
Worked example

Example 2: Use a number line

Solve 3 × 7.

  1. 3 × 7 means 3 groups of 7.
  2. Start at 0. Jump 7 three times: 7, 14, 21.

3 × 7 = 21

071421+7+7+7
3 jumps of 7: 7, 14, 21.

Turn the array!

Look at an array of 2 rows of 5. Now turn it sideways. It becomes 5 rows of 2. Nothing was added or taken away, so the total is the same: 10.

2 × 5 = 5 × 2 = 10

This means you can multiply the factors in any order. If you know one fact, you know its turn-around fact too!

2 × 5= 10
2 rows of 5 makes 10.
5 × 2= 10
The same array turned sideways: 5 rows of 2. It still makes 10.
Worked example

Example 3: A big array

A sheet of stamps has 10 rows of 10 stamps. How many stamps?

  1. 10 × 10 means 10 groups of 10.
  2. Count by 10s, ten times: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

10 × 10 = 100 stamps. This is the biggest multiplication you need in Grade 3.

10 × 10= 100
A 10 by 10 array has 100 dots.
Worked example

Example 4: Build a fact from a fact you know

Solve 4 × 6 using 2 × 6.

  1. 2 × 6 = 12 (like the egg carton).
  2. 4 groups is double 2 groups.
  3. So 4 × 6 is double 12: 12 + 12 = 24.

4 × 6 = 24

Multiplying is faster than adding

8 + 8 + 8 + 8 + 8 is a lot of adding. Multiplying lets you say it in a short way: 5 × 8. When you learn your facts, you won't need to add at all!

Just for fun

Why are egg cartons so good at math?

They are always in an array: 2 rows of 6, every single time!

Hands-on activity

Array hunt

You need: paper, a pencil, and things from around your home.

  1. Hunt for arrays at home: egg cartons, ice cube trays, muffin pans, window panes, buttons on a TV remote, a calendar page.
  2. For each array, count the rows and how many are in each row.
  3. Write the multiplication sentence, like 2 × 6 = 12 for an egg carton.
  4. Make your own arrays with cereal pieces, coins or LEGO bricks. Build 3 × 5. Then turn it to make 5 × 3. Is the product the same?
  5. Challenge: build every array you can with 12 objects.

Math talk: "How did you know how many there were without counting each one?"

Your turn

1

Write a multiplication sentence for 3 rows of 6.

2

5 × 4 = ?

3

2 × 9 = ?

4

Draw an array for 4 × 3. What is the product?

5

Write 6 groups of 2 as a multiplication sentence.

6

Ella makes 7 jumps of 10 on a number line. Where does she land? Write the multiplication sentence.

7

Is 3 × 8 the same as 8 × 3? What is the product?

More practice: warm-up

1

2 × 3 = ?

2

4 × 2 = ?

3

1 × 7 = ?

4

Write 5 + 5 + 5 as a multiplication sentence.

5

How many in 2 rows of 10?

More practice: on your own

1

An ice cube tray has 2 rows of 8. How many ice cubes? Write the sentence.

2

7 × 3 = ? Show how you know.

3

4 × 6 = ?

4

8 × 5 = ?

5

9 × 3 = ?

Challenge

1

Find every array you can make with 12 dots. Write each multiplication sentence.

2

Solve 6 × 7. Hint: you know 5 × 7.

3

A window has 4 rows of 4 panes. A house has 3 of these windows. How many panes in all?

Check your understanding

Quiz

1.

What does 4 × 6 mean?

2.

An array has 3 rows of 5. How many in all?

3.

What is 7 × 2?

4.

What is 10 × 10?

5.

Which is equal to 5 × 3?

6.

In 6 × 4 = 24, what is 24 called?

For parents and teachers

Big idea: Grade 3 students represent multiplication up to 10 × 10 using tools and drawings, including arrays (B2.6). They also use properties of operations (B2.1); here, the commutative property (3 × 4 = 4 × 3) shown by turning an array. The × sign is new in Grade 3; Grade 2 used "groups of".

Common difficulties:

  • Adding the factors (4 × 6 = 10). Ask: "How many groups? How many in each group?" and draw it.
  • Uneven rows when drawing arrays. Use grid paper or line up objects carefully.
  • Counting every dot one by one. Encourage skip counting by rows.
  • Losing track on a number line. Count jumps with a finger or label each jump.

How to help: Point out arrays in daily life (egg cartons, muffin pans, parking lots, windows). Ask "How many rows? How many in each row? How many altogether?" and have your child say the multiplication sentence.