Groups and Arrays in Multiplication
Two powerful visual tools for understanding multiplication are equal groups and arrays. Both help you see why multiplication works the way it does.
Equal Groups
When objects are arranged into groups of the same size, you can multiply to find the total.
3 groups of 6 apples = 3 × 6 = 18 apples
| Groups | Size of each group | Multiplication | Total |
|---|---|---|---|
| 4 | 5 | 4 × 5 | 20 |
| 6 | 3 | 6 × 3 | 18 |
| 2 | 9 | 2 × 9 | 18 |
Arrays
An array is a rectangular arrangement of objects organised into rows and columns.
A 4-row by 6-column array = 4 × 6 = 24
Arrays reveal the commutative property: rotating the array (swapping rows and columns) gives the same total.
4 × 6 = 24 and 6 × 4 = 24 (same array, different orientation)
Arrays and Area
An array of unit squares is exactly how we calculate area. A rectangle 5 units wide and 3 units tall has an area of 5 × 3 = 15 square units. Arrays are the visual bridge between multiplication and area.
Key Takeaways
- Equal groups and arrays are visual models of multiplication.
- Rows × columns = total items in the array.
- Rotating an array shows that a × b = b × a.
- Arrays connect directly to the concept of area.
Practice Questions
- Draw an array to represent 3 × 7.
- A class has 5 rows of desks with 6 desks in each row. How many desks are there?
- Write the multiplication for an array with 8 rows and 4 columns.
- Show that 3 × 9 = 9 × 3 using arrays.
- A garden has 6 rows of plants with 10 plants per row. How many plants in total?