Multiplication as equal groups & arrays
In Year 3 (NSW Stage 2, outcome MA2-MR-01), students learn to see multiplication as equal groups and arrays. They read the times sign as groups of, count equal groups, and arrange objects in rows and columns to find a total.
This topic also links multiplication to repeated addition and skip counting, shows how to read an array, and explains why turning an array does not change the total. These skills give students in Stage 2 across NSW a strong start for learning their multiplication facts.
Theory
Multiplication as equal groups and arrays is a Year 3 skill: the times sign means groups of, so equal groups and arrays of rows and columns can be written as a multiplication. This page explains how multiplication links to repeated addition, how to read an array, why turning an array does not change the total, and how to work back from a total to find the number of groups.
Multiplication is a quick way to count equal groups. The times sign \(\times\) means groups of (or lots of). So \(3 \times 6\) means 3 groups of 6.
Equal groups are groups that are all the same size. To find the total you count the number of groups and the number in each group. Three groups of six is \(6 + 6 + 6 = 18\), the same as \(3 \times 6 = 18\). You can also skip count by the size of each group: \(6,\ 12,\ 18\). This is why multiplication is repeated addition of equal groups.
An array shows objects in equal rows and columns. You multiply the rows by the columns to find the total. Turn an array a quarter turn and the total stays the same, so \(3 \times 6 = 6 \times 3\).
Multiplication does not need long working, but these facts help you read equal groups and arrays.
How to find a total from equal groups or an array
- Count the groups or rows. Find how many equal groups there are, or how many rows the array has.
- Count the size of each. Find how many are in one group, or how many are in each row (the columns).
- Multiply. Write it as groups \(\times\) size, then find the total by skip counting or repeated addition.
Working back from a total
If you know the total and the size of each group, skip count by the group size until you reach the total. The number of jumps is the number of groups. If you know the number of rows instead, ask: which number times the number of rows gives the total? That number is how many are in each row.
| \(4\text{ groups of }4\) | \(=\) | \(4+4+4+4\) |
| \(4 \times 4\) | \(=\) | \(16\) |
There are \(16\) fish altogether.
| \(4\text{ rows} \times 7\text{ columns}\) | \(=\) | \(7+7+7+7\) |
| \(4 \times 7\) | \(=\) | \(28\) |
There are \(28\) stickers.
| \(7 + 7 + 7\) | \(=\) | \(3\text{ groups of }7\) |
| \(3 \times 7\) | \(=\) | \(21\) |
The total is \(21\).
| \(6\text{ groups of }5\) | \(=\) | \(6 \times 5\) |
| \(6 \times 5\) | \(=\) | \(30\) |
Maya has \(30\) crayons.
Skip count by fives until you reach \(15\), and count the jumps.
| \(5,\ 10,\ 15\) | \(\to\) | \(3\text{ jumps}\) |
| \(3 \times 5\) | \(=\) | \(15\) |
Sam makes \(3\) groups.
Common pitfalls
Frequently asked questions
What does multiplication mean?
Multiplication is a fast way to count equal groups. The times sign means groups of, so \(3 \times 6\) means 3 groups of 6, which is \(6 + 6 + 6 = 18\).
What is an array in maths?
An array is a set of objects in equal rows and columns. You multiply the number of rows by the number of columns. For example, 2 rows of 8 is \(2 \times 8 = 16\).
What is the difference between equal groups and an array?
Both show equal amounts. Equal groups are separate groups of the same size, like 4 tanks with 4 fish each. An array lines the objects up in straight rows and columns. Both can be written as a multiplication.
How is multiplication related to repeated addition?
Adding the same number again and again is the same as multiplying. For example, \(7 + 7 + 7\) is 3 groups of 7, which is \(3 \times 7 = 21\).
Does 3 times 6 mean 3 groups of 6 or 6 groups of 3?
We read \(3 \times 6\) as 3 groups of 6. Either way the total is the same, because \(3 \times 6 = 6 \times 3 = 18\). Turning an array a quarter turn does not change the total.
What does groups of or lots of mean in multiplication?
Groups of and lots of are everyday words for the times sign. So 6 lots of 5 means 6 groups of 5, which is \(6 \times 5 = 30\).