Understanding Multiplication

In this lesson:

• Learn what multiplication means
• Use arrays to show equal groups
• Create real-world multiplication stories

Learning Objectives

By the end of this lesson, you should be able to:

1. Explain that 5 × 7 means "5 groups of 7 objects" and find the total
2. Create or identify equal groups that match a multiplication expression
3. Describe a real-world situation for a given multiplication expression
4. Translate between repeated addition and multiplication expressions
5. Represent multiplication using an array and connect rows to "groups of"

You Already Know Repeated Addition

Last year you learned that when you add the same number over and over:

You're adding five sevens to get a total of 35.

Today we'll learn a faster way to write this idea.

What Is Multiplication?

Multiplication is a way to find the total when you have equal groups.

• A group is a collection of objects
• Equal groups means every group has the same number of objects
• Multiplication tells us: how many groups + how many in each group

The groups must be equal!

Four Groups of Six

4 groups of 6 = 4 × 6 = 24 objects

Reading Multiplication: "Groups Of"

When we see , we read it as:

• "4 groups of 6"
• The first number tells how many groups
• The second number tells how many in each group

Examples:

• means "3 groups of 5"
• means "5 groups of 2"

Multiplication and Repeated Addition

Multiplication is a shorthand for repeated addition:

• We're adding 6 four times
• Same as 4 groups of 6
• Multiplication is faster to write!

Quick Check

What does mean?

Say it using "groups of" language before you find the answer.

Think for a moment before we continue...

Arrays: Organizing Groups in Rows

An array is a rectangular arrangement of objects in rows and columns.

• Each row is one group
• All rows have the same number of objects
• Arrays make equal groups easy to see!

Example: An array with 5 rows and 7 columns shows

Array: Five Rows of Seven

5 rows with 7 in each row = 5 groups of 7 = 5 × 7

Building Arrays

To build an array for :

1. Make 3 rows (first number = number of rows)
2. Put 4 objects in each row (second number = size of each row)
3. Check: Does each row have exactly 4 objects?

If yes, you have an array for !

Counting an Array

Count row by row:

So 5 rows of 7 = 5 × 7 = 35

Quick Check

Draw an array for .

• How many rows should you make?
• How many objects in each row?

Pause and sketch it before the next slide...

Real-World Contexts for Multiplication

Multiplication describes many real-world situations:

• Food: 4 packs of juice boxes, 6 in each pack
• Furniture: 5 tables, 4 chairs at each table
• School supplies: 3 boxes of pencils, 8 in each box
• Nature: 6 flowers, 5 petals on each flower

Equal groups are everywhere!

Creating a Multiplication Story

Problem: Create a real-world story for

My story:
There are 3 shelves in a bookcase. Each shelf has 8 books.

Check: 3 groups? ✓ Each has 8? ✓ So books

Your Turn: Create a Story

Create a real-world story for .

Think about:

• What could come in groups?
• Do I have 4 groups?
• Does each group have exactly 5 objects?

Pause and write your story before moving on

From Story to Expression

Story: A classroom has 6 tables. Each table has 4 chairs.

Question: What multiplication expression shows the total number of chairs?

Solution:

• How many groups? 6 tables → 6 groups
• How many in each group? 4 chairs per table → 4 in each
• Expression: chairs

Quick Check

Which story matches ?

A) 5 friends share 3 cookies
B) 5 tricycles, each with 3 wheels
C) 5 flowers with different numbers of petals
D) 5 apples plus 3 oranges

Think carefully before choosing...

Your Turn to Practice

Try these three problems:

1. What does mean? Say it using "groups of"
2. Draw an array for
3. Write a real-world story for

Pause and work through all three before checking answers

Practice Answers

1. means "6 groups of 4" → total is 24

2. Array: 3 rows with 7 in each row (should have 21 total objects)

3. Story example: "There are 2 gardens. Each garden has 9 flowers."
→ Check: 2 groups? ✓ Each has 9? ✓

How did you do?

Key Takeaways

✓ Multiplication means equal groups - same number in every group
✓ Read as "4 groups of 6" - first number is groups, second is size
✓ Arrays show multiplication - each row is one group
✓ Multiplication connects to repeated addition:

Watch out: Always explain "groups of" first, then find the answer
Watch out: Groups must be equal - means all 3 groups have exactly 4
Watch out: Read in order - is 5 groups of 3, not 3 groups of 5
Watch out: but - addition and multiplication are different

Coming Next

Next lesson: Division

We'll learn the opposite of multiplication:

• If , then
• Breaking apart equal groups
• Fair sharing problems

Great work today on understanding multiplication!