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.
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 Ana Build a Family
Ana has an array with 3 rows of 8.
- Step 1
She reads it one way: 3 × 8 = 24.
Step 5: Your Turn
Practice makes it stick.
Using the Family
Problem 1 of 2
You know 7 × 3 = 21. What is 21 ÷ 7?
The Other Way
Problem 2 of 2
You know 6 × 5 = 30. What is 30 ÷ 5?
Use the Family
1 of 4
You know 5 × 8 = 40. What is 40 ÷ 8?
2 of 4
You know 9 × 2 = 18. What is 18 ÷ 9?
3 of 4
How many facts come from one array?
4 of 4
4 and 7 make 28. What is 28 ÷ 4?
Show the Missing Part
Build it, then check.
10 is 4 and how many? Show that part.
How many
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?
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.
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.