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Multiplication as Equal Groups · Number and Place Value · CCSS.MATH.CONTENT.3.OA.A.1 · multiplication

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Multiplication as Equal Groups

with Lumi

Lumi stands in a sunlit bakery holding a tray of muffins, arranging them into neat groups of three while counting out loud with a big grin.

Explain what it means for groups to be equal in size.
Identify the number of groups and the size of each group in a picture.
Compare repeated addition to multiplication and show they give the same answer.
Calculate a product by thinking about equal groups.
Predict the total number of objects when the group size and number of groups are known.

Key terms

Multiplication: A fast way to add equal groups.
Equal groups: Groups that each have the same amount.
Product: The total answer when you multiply.
Repeated addition: Adding the same number again and again.

Counting Equal Groups

Multiplication helps you count things that come in equal groups. Think of muffins in boxes, where every box has the same number. Instead of counting each muffin one by one, you can count the groups. The first number tells how many groups you have. The second number tells how many are in each group. This works only when every group is the same size, so always check for equal groups first!

A Shortcut for Adding

Multiplication is really a faster way to add. If you have 4 groups of 3, you could add 3 plus 3 plus 3 plus 3 to get 12. That is repeated addition. But multiplying 4 times 3 gives you the same 12 much quicker! Both ways give the same answer. As the numbers get bigger, multiplication saves you lots of time and helps you find totals fast.

Worked examples

Find the total of 3 boxes with 5 toys each.

There are 3 groups, and each group has 5 toys.
You can add: 5 plus 5 plus 5 equals 15.
Or multiply faster: 3 times 5 equals 15.

Answer: 15 toys

Hey there! I'm Lumi, and I just got a job at the bakery. My first task: pack muffins into boxes. Each box holds exactly 3 muffins — no more, no less. That means every box is an EQUAL group of 3. I have 4 boxes to fill. I could count every single muffin one by one: 1, 2, 3 ... 4, 5, 6 ... 7, 8, 9 ... 10, 11, 12. Phew, that takes a while! Or I could add: 3 + 3 + 3 + 3 = 12. Better! But the FASTEST way is multiplication. I write it like this: 4 × 3 = 12. That means "4 groups of 3." Here is the big idea: multiplication counts EQUAL groups all at once. The first number tells you HOW MANY groups. The second number tells you HOW MANY are in each group. Multiply them and you get the TOTAL. Hint: if the groups are NOT all the same size, multiplication will not work — you need equal groups!

Activity

Drag the cookies onto the plates to make equal groups, then complete the multiplication sentence.

Practice

There are 4 plates with 2 cookies on each plate.

Write a multiplication sentence for 5 groups of 3.

Common mistakes to avoid

You can multiply any groups.No. The groups must all be the same size to use multiplication.
Multiplying is totally different from adding.No. Multiplying is a shortcut for adding equal groups together.

Check your understanding

There are 5 bags of apples. Each bag has 4 apples. Which multiplication sentence shows the total?

A student says 3 + 3 + 3 + 3 = 12 and 4 × 3 = 12 are the same thing. Are they right?

Which picture could you describe with the multiplication sentence 3 × 6 = 18?

Recap

Multiplication is a fast way to count equal groups. The first number is how many groups, and the second number is how many in each group. It gives the same total as repeated addition.

Reflect

What things in your kitchen come in equal groups you could multiply?