Multiplicative strategies

Learning intention

Students will develop their efficiency, flexibility and confidence in using a variety of mental strategies to solve problems of a multiplicative nature.

Syllabus outcome

  • MA3-1WM: describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions

  • MA3-2WM: selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations

  • MA3-3WM: gives a valid reason for supporting one possible solution over another

  • MA3-4NA: orders, reads and represents integers of any size and describes properties of whole numbers

  • MA3-6NA: uses mental and informal written strategies for multiplication and division
  • MA3-10MG: selects and uses the appropriate unit to calculate areas, including areas of squares, rectangles and triangles

National Numeracy Learning Progression

The full National Numeracy Learning Progression details are included in the resource, available for download on this page.

  • MuS5 –MuS7 Multiplicative strategies

  • UnM7 Understanding money

  • UuM5-UuM6 Understanding unit of measurement .

Task outline

Full task descriptions are included in the resource, available for download on this page.


Task 1: Factors fun

Students play the factors fun game to explore division, work out a solution and explain their thinking (one activity).

Task 2: Remainders game

Students play the remainders game to reinforce division with remainders (two activities).

Task 3: The tiler

Students complete a multiplicative reasoning task with multiplicative thinking, based on the tiler problem solving task from reSolve (two activities).


Task 4: youcubed math cards

Students play the youcubed math cards game to practice and consolidate their learning of multiplication and division (two activities).

Task 5: Prime climb hundreds chart

Students develop knowledge of factors, multiples and vocabulary associated with multiplication and division (one activity).

Task 6: Here is a problem

Students use close positioning scaffolds to consider the relationship between problems and not treat them as separate and unrelated (one activity).

Task 7: Array bingo

Students recognise the different ways numbers can be presented in an array (two activities).

Task 8: Multiplication toss

Students play in pairs to develop multiplicative automaticity (one activity).

Task 9: Always, sometimes, never

Students reason with situations, instances and concepts that are always, sometimes or never true (one activity).

Task 10: Multiplication squares

Students use their knowledge of factors and products to find the missing element in a grid (three activities).


  • Numeracy

Business Unit:

  • Educational Standards
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