Multiplicative thinking is characterised by the ability to work flexibly with concepts, strategies, and representations of multiplication and division. Students in years 5–8 who are still at the additive thinking stage urgently need to make the shift to multiplicative thinking, but this may not happen without targeted support. This resource suggests ways to support students to make this shift.

### Why is this important?

Many ALiM teachers working with year 5–8 students focus on additive strategies and Stage 5: Early Additive knowledge. However, filling in gaps in a student’s understanding of additive strategies is insufficient in terms of preparing them for the demands of the curriculum at levels 3 and 4.

The extent to which students understand multiplication and division will impact on their level of success across all strands. Multiplicative thinking is the gateway to understanding and working with place value and fractions. Students use multiplicative thinking when they calculate area and volume, find the mean of a set of data, work out a useful scale for a graph, and compare rates. Helping students in years 5–8 to make the transition to multiplicative thinking must be viewed as a priority.

Some teachers erroneously believe that students need to have fully mastered addition and subtraction before they are introduced to multiplication and division. Helping students to develop their understanding of multiplication and division can provide opportunities for students to practise their adding and subtracting skills.

Multiplicative thinking is needed for students to develop a robust understanding of place value, and an understanding of place value and partitioning is needed for multiplicative strategies. This reciprocal relationship means that the students’ understanding of multiplication and of place value can be developed simultaneously.

### Read more

- Emphasise the usefulness of multiplication
- Make links with place value
- Models of multiplication
- Develop language
- Open up problems
- References and further reading

Click to download as a PDF (1MB).