Patterns in the Times Tables

Step 1: Let's Learn

Read it, or press Listen and follow the words.

Any even factor gives an even product

Anything times 2, 4, 6, 8, or 10 is even, because it is made of equal pairs.

Odd times odd is odd

3 × 5 = 15. Two odd factors are the only way to get an odd product.

The diagonal

1, 4, 9, 16, 25 sit on the diagonal. Each is a number times itself.

A pattern with a reason

Spotting a pattern is good. Saying why it happens is better.

Even tables give even answers

Every product in the 2, 4, 6, 8 and 10 tables is even, because each is a number of even-sized groups. The 5 table alternates 5 and 0. The 9 table has digits that always add to 9. Each pattern has a cause, and finding the cause is more valuable than memorising the pattern.

The diagonal of squares

Run down the diagonal of a times table grid and you get 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 — the square numbers. Their arrays are actual squares. The gaps between them go 3, 5, 7, 9, all the odd numbers in order, which is a striking pattern worth noticing.

The grid is symmetrical

Fold a times table grid along the square-number diagonal and every entry matches its partner, because 6 × 4 and 4 × 6 are equal. That symmetry is the commutative property made visible, and it is why the grid contains far fewer distinct facts than it has cells.

Step 2: Try It Yourself

Tap and try it out.

Tap a square to light every other square with the same total.

Addition chart. Rows are the first number, columns are the second, and each cell is their total.
+	0	1	2	3	4	5
0
1
2
3
4
5

Tap any square to see its number sentence.

Set the rows and columns to the same number. It makes a square.

4 × 4 = 16

4 rows of 4 makes 16.

Rows

Columns

Step 3: Watch an Example

One step at a time.

Watch Leo Explain a Pattern

Leo notices every answer in the 4 times table is even.

Step 1
He checks a few: 4, 8, 12, 16. All even.

Step 4: Your Turn

Practice makes it stick.

Odd or Even

Problem 1 of 2

Is 7 × 6 odd or even?

The Square

Problem 2 of 2

What is 6 × 6?

Spot the Pattern

1 of 3

Is 5 × 9 odd or even?

2 of 3

What is 7 × 7?

3 of 3

In the nine times table, the digits of each answer add to what?

Step 5: Quick Check

Show what you know.

Question 1 of 2

Is 8 × 7 odd or even?

Question 2 of 2

When is a product odd?

What You Learned

An even factor always makes an even product.
Only odd times odd gives an odd product.
A pattern is worth more once you can say why.