Last year you added equal groups: 4 + 4 + 4 = 12. There is a shorter way to write it.
Step 1: Picture It
Start with something you already know.
A song with a chorus
- A song sheet could print the same chorus three times.
- Or it could print it once and say "Sing it 3 times."
- That only works if the chorus is the same every time.
Multiplication is the short way to write the same group again and again.
In 3 × 4, the 3 says how many times, and the 4 is the group.
Step 2: Let's Learn
Read it, or press Listen and follow the words.
Try it first
Noor packs 4 bags. Each bag holds 6 apples. How many apples in all?
apples
Stuck is fine. Let’s Learn shows the way next. Got it first time? You can jump ahead to Watch an Example.
Three groups of four is written 3 × 4.
Multiplication is a short way of adding equal groups. The symbol is ×.
How to read it
In 3 × 4, the 3 is how many groups and the 4 is how many in each group.
The answer has a name.
Product is the answer to a multiplication.
Step 3: Try It Yourself
Change the rows and read both sentences underneath.
4 + 4 + 4 = 12
3 × 4 = 12
3 rows of 4 makes 12.
3 × 4 = 12. 3 and 4 are a factor pair of 12.
Pairs you have found
- 3 × 4
Step 4: In Real Life
In the kitchen
An egg box holds 2 rows of 6 eggs. A cook does not count every egg. They see 2 groups of 6. So they know it is 2 × 6 = 12. Every full box is a multiplication.
Step 5: Watch an Example
One step at a time.
Watch Ana Write a Product
Ana sees 5 cups. Each cup holds 3 straws.
- Step 1
Ana counts the groups first. There are 5 cups, so 5 groups.
Watch Leo Write a Product
Leo sees 3 shelves. Each shelf holds 7 books. Leo starts, and you finish.
- Step 1
Leo counts the groups: 3 shelves. He counts one group: 7 books.
Step 6: Your Turn
Practice makes it stick.
The Sticker Shop
Problem 1 of 12
Stickers cost $2 each. Priya buys 7 stickers. How much does she pay?
dollars
The Muffin Tray
Problem 2 of 12
A tray has 3 rows. Each row holds 6 muffins. How many muffins fill the tray?
muffins
Write It the Short Way
Say it as groups of. Then find the product.
Problem 3 of 12
2 groups of 8. What is the product?
Problem 4 of 12
In 9 × 2, how many groups are there?
Problem 5 of 12
Which multiplication matches this array?
Find the Mistake
One line on each page is a slip. Find it, then fix it.
Problem 6 of 12
Dev has 5 boxes with 6 eggs in each. One line is a slip. Which?
Dev's answer for: 5 boxes, 6 eggs in each
- 15 boxes, 6 eggs in each
- 26 + 6 + 6 + 6 = 24
- Answer5 × 6 = 24
Problem 7 of 12
What should Dev's product be?
eggs
Problem 8 of 12
Maya has 4 groups of 7. One line is a slip. Which?
Maya's answer for: 4 groups of 7
- 14 groups of 7
- 24 + 7 = 11
- Answer4 × 7 = 11
Problem 9 of 12
What should Maya's product be?
Which Way?
Pick the way that fits the groups.
Problem 10 of 12
8 bags. 3 shells in each bag. Which way finds the total?
Problem 11 of 12
Three plates hold 4, 5 and 3 cookies. Which way finds the total?
Build the Groups
Build it, then check.
Problem 12 of 12
Build 5 groups of 2. Each row is a group.
1 = 1
1 × 1 = 1
1 row of 1 makes 1.
Step 7: Quick Check
Show what you know.
Question 1 of 2
4 groups of 5. What is the product?
Question 2 of 2
What does multiplication do?
Ready for more?Optional. Past the lesson, for anyone who wants it.
Stretch 1 of 2
The product is 40. Each group holds 8. How many groups?
groups
Stretch 2 of 2
Noor has 2 plates with 9 buns on each. She adds one more plate of 9. What is the new product?
buns
What You Learned
- Multiplication is a short way to add equal groups.
- 3 × 4 means 3 groups of 4.
- The answer is called the product.
For the grown-up
Multiplication is equal groups before it is a fact to recall. Three fours is three groups of four, and division is the same picture asked from the other end.
Watch for multiplication and division being learned as separate subjects. They are one relationship, and a child who sees that halves what there is to remember.
When they are stuck on a division, ask the multiplication instead: "what times 4 gives 24?" Nearly every child can answer that when they cannot answer 24 divided by 4.
The slip this lesson targets is adding the two numbers: reading 4 × 7 as 4 + 7. Ask "four groups of what?" and have them write the long way first. The other slip is multiplying groups that are not equal. A plate of 4, one of 5 and one of 3 is an addition, and checking the groups are equal comes before any times table. Dev's slip is a group left out: have them count the addends against the groups.
Multiplication is shorthand, not a new idea — Four groups of 5 can be written 5 + 5 + 5 + 5, or written 4 × 5. Both mean the same thing and both give 20. Multiplication was invented because writing out long strings of the same number is slow and easy to get wrong. Nothing about it is mysterious — it is addition, packaged.
Reading the two numbers correctly — In 4 × 5, the 4 is the number of groups and the 5 is how many are in each group. Read it as "four groups of five". The two numbers play different roles even though they sit side by side, and telling them apart is what lets you match an equation to a picture or a story.
The groups must be equal — Multiplication only applies when every group holds the same number. Three plates with 4, 4 and 4 cookies is 3 × 4. Three plates with 4, 5 and 3 is not multiplication at all — you have to add. Checking that the groups really are equal is the first thing to do before reaching for a times table.
Write it the long way first — Three plates. Four buns on each. The long way: 4 + 4 + 4 = 12 The short way: 3 × 4 = 12 The 3 is how many groups. The 4 is how many in each. Nothing new happened. It is the same adding, written shorter.