← SciSim/Math Playground/Multiplication

Multiplication Playground

Build arrays of rows and columns and see what times tables really mean. Play, solve missions, crack puzzles and beat the clock.

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3 × 4 = 12

The idea, step by step

Start here. Multiplication is a fast way to count equal groups. Picture 3 rows of chairs with 4 chairs in each row. Instead of counting every chair, you can say 3 × 4 = 12. In this game, the first number is the number of rows and the second number is how many are in each row.

Repeated addition. The same array is also 4 + 4 + 4 = 12. Multiplication is a short way to write adding the same number again and again. When you count rows one by one (4, 8, 12) you are skip counting.

Turn it around. Flip the array on its side and you get 4 rows of 3. The dots are the same, so 3 × 4 = 4 × 3. This is why you only need to learn half of the times table.

Big numbers. Hard facts can be split. To find 6 × 14, split the 14 into 10 and 4. Then 6 × 10 = 60 and 6 × 4 = 24, and 60 + 24 = 84. This picture is called an area model.

Try this above. Build 5 × 6 and press Count. Flip it. Build 2 × 7 and see the doubles. Then build 7 × 8 and split it into 5 columns and 3 columns.

Questions

What does 3 × 4 mean?

It means 3 groups of 4. In this game it is shown as 3 rows with 4 in each row. The answer is 12.

Why is 3 × 4 the same as 4 × 3?

Turn a 3-by-4 array on its side and you get a 4-by-3 array. It has the same number of dots, so the answers match.

Which level should I pick?

"Just starting" uses the 1, 2, 5 and 10 times tables and skip counting. "I know the basics" covers all tables up to 10 × 10. "Challenge me" goes up to 12 × 12 and uses the area model for two-digit numbers.

Do I need to sign up?

No. It is free and needs no account. Your stars are saved in your own browser.