How can we help students understand remainders?

In the Victorian Curriculum the concept of division is first introduced in Foundation through the notion of sharing. The concept of sharing them moves to visually creating equal groups, to then a more abstract expectation that students should be able to connect their multiplication facts to solve division problems. Around Year 5, students are then expected to explore the concepts of remainders. 

The concept of remainders is challenging for students. What does the remainder signify? What should be done with it? 

To support students' understanding of remainders, placing a division problem in a context can help significantly.For example, in the equation: 10➗ 3= 3 remainder 1, there are 3 equal groups and 1 remainder. But what does this remainder mean? 

Depending on the context, the remainder could signify different things, and therefore the idea of what to do with this remainder would change. Discussing what to do with remainerds is also a critical teaching point as it supports students problem solving and reasoning skills. For example, if this equation modeled the problem of 3 friends and 10 cupcakes, the remainder cupcake could be cut into thirds to equally share (which also serves as a teaching point for fractions). Alternatively, what if the problem stated there were 10 friends going out to dinner and the restaurant had tables of 3, how many tables would be needed. Automatically the answer changes to 4, as you can’t third a person! 

Storybooks are a great way to support the teaching of division problems in a context, and many lend themselves to longer investigations students can explore. Two excellent stories which can help support the mathematical investigation of division problems are: 


Have you used stories before to explore mathematics concepts? Write your recommendations in the comments. Let’s share our resources with each other! 

The Teaching Initiative PTY LTD