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Multiplication as equal groups — Mathematics, 7–10 years

Multiplication is a quick way to count equal groups. It connects repeated addition, arrays and sharing the same number of objects into each group.

Equal groups

Four bags with three apples each contain 3 + 3 + 3 + 3 apples. We write this more briefly as 4 × 3 = 12: four equal groups of three make twelve. The first number counts groups; the second tells how many are in each group.

Why multiply?

Adding equal groups one by one works, but it takes longer and makes missed groups easy. Multiplication gives one number for the whole pattern, so you can count seats in rows or objects in boxes without starting again each time.

Six rows of four

A garden has 6 rows with 4 plants in each row. Count one row: 4; double it for two rows: 8; triple that for six rows: 24. So 6 × 4 = 24 plants, and turning the array around shows 4 × 6 also equals 24.

Counting the gaps

When objects are in rows, it is easy to count the spaces between them instead of the objects. A row showing four plants has three gaps, but it still contains four plants. Mark each object or touch it as you count the group.

Packing and planning

Multiplication helps when equal groups appear in real life: 5 shelves with 8 books hold 40 books, and 3 teams of 6 people need 18 places. It is useful only when the groups really are equal; uneven groups need another method.

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