Division as grouping
Theory
Division as grouping is a Year 3 maths skill: splitting a total into equal groups of a set size and counting how many groups you make. This page explains how to find the number of groups by making groups, skip counting and repeated subtraction, how grouping differs from sharing, how division links to multiplication, and how to read a remainder. Curriculum: VC2M3N05 / AC9M3N04.
Division as grouping means splitting a total into equal groups of a set size, then counting how many groups you make. Reading \(10 \div 5\) as grouping asks: how many groups of \(5\) are in \(10\)? The answer is \(2\), because \(2\) groups of \(5\) make \(10\).
Every grouping question has three parts. The total is what you start with. The group size is how many go in each group. The number of groups is the answer you are looking for. In \(10 \div 5 = 2\), the total is \(10\), the group size is \(5\), and there are \(2\) groups.
Grouping is not the same as sharing. In grouping you know the group size and find how many groups. In sharing you know how many groups and find how many go in each. A remainder is the amount left over when the total does not make equal groups exactly.
Division as grouping does not need formulas, but these facts help you find the answer and check it.
How to find how many groups
- Read the question. Find the total and the group size. \(35 \div 5\) has total \(35\) and group size \(5\).
- Count the groups. Skip count by the group size, or take the group size away, until you reach the total: \(5,\ 10,\ 15,\ 20,\ 25,\ 30,\ 35\).
- Write and check. The number of counts is the answer: \(35 \div 5 = 7\). Check with multiplication: \(7 \times 5 = 35\).
| \(\text{skip count}\) | \(:\) | \(8,\ 16,\ 24\) |
| \(24 \div 8\) | \(=\) | \(3\) |
There are \(3\) groups of \(8\).
| \(\text{count by }5\) | \(:\) | \(5,\ 10,\ \ldots,\ 45\) |
| \(45 \div 5\) | \(=\) | \(9\) |
It takes \(9\) notes of \(\$5\).
| \(25 \to 20 \to 15 \to 10 \to 5 \to 0\) | \(:\) | \(5\text{ jumps}\) |
| \(25 \div 5\) | \(=\) | \(5\) |
It takes \(5\) jumps of \(5\).
| \(5,\ 10,\ 15,\ 20\) | \(=\) | \(4\text{ full groups}\) |
| \(21 - 20\) | \(=\) | \(1\text{ left over}\) |
So \(21 \div 5 = 4\) remainder \(1\). To fit all \(21\) stickers you would need \(5\) groups (\(4\) full and \(1\) for the leftover).
Common pitfalls
Frequently asked questions
What is division as grouping?
Division as grouping means splitting a total into equal groups of a set size and counting how many groups you make. For example, \(10 \div 5\) asks how many groups of \(5\) are in \(10\), and the answer is \(2\).
What is the difference between grouping and sharing?
In grouping you know how big each group is and find how many groups there are. In sharing you know how many groups there are and find how many go in each group. Both are division, but they answer different questions.
How do you work out how many groups?
Skip count by the group size until you reach the total, or take the group size away again and again until you reach zero. The number of skips is the number of groups. For \(35 \div 5\), count \(5,\ 10,\ 15,\ 20,\ 25,\ 30,\ 35\), which is \(7\) groups.
What does 32 divided by 4 mean?
Read as grouping, \(32 \div 4\) asks how many groups of \(4\) are in \(32\). Count \(4,\ 8,\ 12,\ 16,\ 20,\ 24,\ 28,\ 32\), which is \(8\) groups, so the answer is \(8\).
What is a remainder?
A remainder is the amount left over when a total does not split into equal groups exactly. For example, \(21\) into groups of \(5\) makes \(4\) full groups with \(1\) left over, written as \(21 \div 5 = 4\) remainder \(1\). If every item must go in a group, you need \(1\) more group for the leftovers, so \(5\) groups.
How does skip counting help with division?
Skip counting by the group size lists the totals as you add each group: \(8,\ 16,\ 24\). The number of skips it takes to reach the total is the number of groups, which is the answer to the division.