Idea 2of 24Builds onRows times columns
Turn the array, keep the product
Is 4 × 9 the same as 9 × 4?
Today you'll discover
- what turning an array does
- why the order of factors does not matter
- how one fact gives you two
Think first4 rows of 9 dots: 36 dots
4 rows of 9 is 36. How many dots are in 9 rows of 4?
Decide first, then press Next. Watch the dots as the array turns.
4 rows of 9 dots, labelled 4 rows and 9 in each row. Then the block turns a quarter turn into 9 rows of 4, and the right side reads 4 × 9 = 36 and 9 × 4. The last step shows 3 rows of 12.
See the whole ideathe big idea and the key word, in one place
The big idea
Turning an array swaps the order of the factors, but never changes the product.
Compare them4 × 9 means 4 rows of 9; 9 × 4 means 9 rows of 4. Different pictures, the same 36 dots.
Easy to get wrongSwapping works for multiplying, not dividing: 36 ÷ 4 = 9, but 4 ÷ 36 is not 9.
Key words
- factor
- a number being multiplied: in 4 × 9, the factors are 4 and 9
- commutative property
- you can multiply two factors in either order and get the same product
Ready to use it?
- Write the turned-around fact for a multiplication.
- Use a fact you know to answer its partner.