Egg cartons and garden rows
An egg carton holds 2 rows of 6 — instead of counting all twelve, you see 2 groups of 6, which is what 2 × 6 means. Multiplication is the shortcut for counting equal groups and neat rows (arrays) without adding one at a time.
Groups of the same size
Multiplication is a shortcut for adding the same number many times. 3 × 4 means 'three groups of four', which is 4 + 4 + 4 = 12. We can arrange those objects in a rectangle called an array, with rows and columns.
🍏🍏🍏🍏 🍏🍏🍏🍏 🍏🍏🍏🍏 → 3 rows of 4 = 12
Simulation · Multiplication array
3 × 4 = 12
Multiplication counts equal groups — 3 rows of 4.
Change the rows and columns and watch the total. An array shows why 3 × 4 and 4 × 3 give the same answer.
Lab · Build the array
- Set the array to 2 rows and 5 columns. Read the total.
- Now swap to 5 rows and 2 columns.
- Compare the two totals.
What you should see: 2 × 5 and 5 × 2 both make 10 — multiplication can be done in either order (the commutative property).