Multiplication as Equal Groups

The most common situation, and the only one we usually start with, is multiplication as repeated addition:



Another sub-type of the  equal group structure is one that we usually associate with measuring.



In all these situations, we are replicating a set of  a fixed size, many times.

We can represent this structure using groups, arrays or on a number line as well as in a number sentence.

When we know the size and number of groups, the problem is multiplication. We know the factors or parts, what we are looking for is the product or the whole amount. E.g.:

When we know the product but we don’t know one of the factors or parts,  the problem becomes a  missing factor  multiplication or division situation. E.g.:


Division as Equal Groups

Even though we think of equal group multiplication as repeated addition, we tend not to think of equal group division as repeated subtraction. That’s because in this structure, we are far more likely to be engaged in sharing and grouping situations.

When we are sharing a known number of items between a known number of groups, we are performing partition division.  We are finding how many items in each group.


When we are grouping a known number of items, and we know how many are  to be in each group, we are performing quotition division. We are finding how many groups we can make.

In the next post we will look at the other key multiplicative structure, multiplication and division as comparison. For now, we will leave you with you with a list of Mathletics resources that might be helpful in developing your students’ understanding of multiplication and division as equal groups.


Multiplication and Division – Multiple representations of multiplication as repeated addition

Multiplication – Linking groups and arrays with repeated addition

Multiplication and Division – Sharing (Partition) and Grouping (Quotition)

Downloadable Workbook



Rainforest Maths


References and other useful resources

Booker, G., Bond, D., Sparrow, L., & Swan, P. (2014). Teaching primary mathematics. Pearson Higher Education AU.

Haylock, D. (2010). Mathematics explained for primary teachers. London: Sage Publications.

Walle, J. Van de, Karp, K., & Bay-Williams, J. (2014). Elementary and middle school mathematics: Teaching developmentally. Pearson Education.

NZ Maths Teaching Multiplication and Division – Revised Edition

The Improving Mathematics Education in Schools (TIMES) Project