G: Learning to use multiplication and division to solve problems


Target group: Students in years 5–8

Focusing on:

  • applying advanced additive strategies to multiplication and division problems
  • flexibly using knowledge of basic facts.


Teacher observation over a range of activities

The student may be able to solve addition and subtraction problems with numbers of three or more digits, using different strategies that depend on the numbers involved. The student may not have strategies beyond repeated addition for solving multiplication and division problems with two-digit numbers. The student may have fast and fluent recall of most of the multiplication basic facts but cannot use this knowledge to derive new facts or flexibly solve problems. For example, a student who knows the 3 and 10 times tables does not use this knowledge to solve 13 x 6. The student may not understand the inverse nature of operations, for example, if 3 x 8 = 24 then 24 ÷ 3 = 8. The student is likely to have difficulty solving problems involving fractions.

Possible barriers to the student’s progress

  1. Limited understanding of arrays
  2. Lack of confidence with basic facts
  3. Limited understanding of the inverse nature of multiplication and division

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