Multiplication is Repeated Addition
Multiplication means adding the same number many times.
We can write this as:
3 × 3 = 9
The × sign means "times" or "groups of".
3 × 3 means "3 groups of 3".
When we write 4 × 2:
• The first number (4) is the number of groups
• The second number (2) is the size of each group
So 4 × 2 means:
2 + 2 + 2 + 2 = 8
4 groups of 2 equals 8
Touch. Set out 4 plates and put 3 apples on each (counters or cubes work too). How many apples in all? 3 + 3 + 3 + 3.
Draw. Draw an array of dots: 4 rows of 3 dots — one row for each plate.
Write. 4 × 3 = 12. Now turn the drawing on its side: you get 3 rows of 4. It is the same array with the same 12 dots, so 4 × 3 = 3 × 4. You don't have to memorise the commutative law — you can see it.
Place Value: Tens and Ones · Fractions: Numerator, Denominator, and Comparing Fractions