An array of 4 by 6 involves three numbers: 4, 6, and 24.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Try it first
Sam's array has 3 rows of 7. He writes 3 × 7 = 21. Which division does the same array show?
Stuck is fine. Let’s Learn shows the way next. Got it first time? You can jump ahead to Watch an Example.
Four facts
4 × 6 = 24, 6 × 4 = 24, 24 ÷ 4 = 6, and 24 ÷ 6 = 4.
One gives you all four
Learn any one of them properly and the other three come with it.
Step 2: Try It Yourself
Tap and try it out.
24
4
6
- 4 × 6 = 24
6 + 6 + 6 + 6 = 24
4 × 6 = 24
4 rows of 6 makes 24.
How many
10 is a full ten.
4 and 6 make 10.
Step 3: In Real Life
On a school bus
A bus has 4 rows of 6 seats, so 4 × 6 = 24 seats. When 24 children get on, the driver knows they fill exactly 4 rows, because 24 ÷ 6 = 4. One fact family covers the whole bus.
Step 4: Watch an Example
One step at a time.
Watch Priya Build a Family
Priya has an array with 4 rows of 8.
- Step 1
Priya reads it by rows: 4 × 8 = 32. The three numbers are 4, 8 and 32.
4 × 8 = 32
4 rows of 8 makes 32.
RowsIn each row
Watch Leo Start From One Fact
Leo knows just one fact: 6 × 3 = 18. Leo starts, and you finish.
- Step 1
The three numbers are 6, 3 and 18. The product is 18.
Step 5: Your Turn
Practice makes it stick.
The Kite Stall
Problem 1 of 12
Kites cost $4 each. Ravi pays $36. He knows 9 × 4 = 36. How many kites did he buy?
kites
The Parking Lot
Problem 2 of 12
A parking lot has 6 rows of cars, 42 cars in all. Dev knows 6 × 7 = 42. How many cars are in each row?
cars
Use the Family
The answer is already in the fact you know.
Problem 3 of 12
You know 6 × 8 = 48. What is 48 ÷ 6?
Problem 4 of 12
You know 7 × 9 = 63. Which is the turned-round fact?
Problem 5 of 12
Look at the array. Which three numbers are in its family?
Find the Mistake
One line on each page is a slip. Find it, then fix it.
Problem 6 of 12
Ravi starts the family for 3 rows of 9. One line is a slip. Which?
Ravi's family for 3 rows of 9
- 13 × 9 = 27
- 29 × 3 = 27
- Answer27 ÷ 9 = 9
Problem 7 of 12
What should 27 ÷ 9 be?
Problem 8 of 12
Maya writes the divisions for 8 × 9 = 72. One line is a slip. Which?
Maya's divisions for 8 × 9 = 72
- 18 × 9 = 72
- 272 ÷ 8 = 9
- Answer9 ÷ 72 = 8
Problem 9 of 12
Which fact should line 3 be?
Same Family?
A family uses the same three numbers in every fact.
Problem 10 of 12
Which fact is in the family of 6 × 9 = 54?
Problem 11 of 12
All three facts are true. Two are in one family. Which one is from a different family?
Build the Array
Build it, then check.
Problem 12 of 12
Build the array that shows 40 ÷ 8 = 5. Each row is a group of 8.
1 × 1 = 1
1 ÷ 1 = 1
1 row of 1 makes 1.
Step 6: Quick Check
Show what you know.
Question 1 of 2
You know 6 × 4 = 24. What is 24 ÷ 6?
Question 2 of 2
How many facts come from the numbers 3, 5 and 15?
Ready for more?Optional. Past the lesson, for anyone who wants it.
Stretch 1 of 2
Ana's array is a square: 7 rows of 7. So 7 × 7 = 49. How many different facts does it make?
Stretch 2 of 2
A family has 7 and 56 in it. 56 is the product. What is the third number?
What You Learned
- Three numbers make four facts.
- Two multiplications and two divisions.
- Learning one hands you the other three.
For the grown-up
This lesson is where the child writes the four related multiplication and division equations for a given array. 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 misconception this lesson targets is that a division is a new fact to look up. A child who knows 6 × 3 = 18 can be stopped cold by 18 ÷ 6, and the cure is the question "six times what makes 18?". Two smaller slips show up on paper: starting a division with a factor (9 ÷ 72 = 8), and answering a division with the factor just divided by (27 ÷ 9 = 9). Maya's and Ravi's pages are those two. Both are cured by saying the family out loud: the same three numbers, and the product first in every division.
Four facts from three numbers — From 3, 4 and 12: 3 × 4 = 12, 4 × 3 = 12, 12 ÷ 3 = 4, and 12 ÷ 4 = 3. Same three numbers, four true sentences. The largest number is the product, and it stands alone after the equals sign in the multiplications and starts both divisions.
One array shows all four — Draw a 3-by-4 array. Count by rows and you get 3 × 4. Count by columns and you get 4 × 3. Ask how many rows are needed for 12 with 4 in each and you get 12 ÷ 4. Ask how many in each row for 3 rows and you get 12 ÷ 3. One picture, four questions.
The families with only two facts — When the two factors are the same, as in 5 × 5 = 25, the family collapses: 5 × 5 = 25 and 25 ÷ 5 = 5, and that is all. These are called square numbers, and their arrays are actual squares. They are worth learning early because they anchor the tables around them.
Three numbers, four sentences — The numbers are 3, 4 and 12. 3 × 4 = 12 4 × 3 = 12 12 ÷ 3 = 4 12 ÷ 4 = 3 One fact learned properly is four facts you can use.