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

  • MA3-6NA: uses mental and informal written strategies for multiplication and division.

National Numeracy Learning Progression

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

Multiplicative strategies

  • MuS5: coordinates two composite units (mentally) as an operation; represents multiplication in various ways; represents division as sharing division and measurement or grouping division
  • MuS6: Flexible strategies for multiplication; Flexible strategies for division
  • MuS7: Flexible number properties

NAPLAN item descriptors

The relevant NAPLAN item descriptors are included in the resource, available for download on this page.

Task outline

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


Task 1: Double double

Students practice and consolidate learning with doubling tools and representations (one activity).

Task 2: Prime climb hundreds chart

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

Task 3: Array bingo

Students recognise the different ways numbers can be presented in an array (one activity).

Task 4: Multiplication toss

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

Task 5: Generalising groups as factors

Students use the region representation of multiplication and division facts, a blank 10 x 10 grid, their own representations or concrete materials to develop and communicate their strategies (one activity).

Task 6: Always, sometimes, never

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

Task 7: Multiplying by tens

Students use base 10 materials and/ or drawings to solve a 2-digit by 1-digit problem (two activities).

Task 8: Multiplication squares

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

Task 9: Open-ended problems

Students use open-ended problems to recognise how numbers can be partitioned in different ways (one activity).


Task 10: Challenge and helper problems

Students consider the relationship between problems (one activity).

Task 11: Remainders game

Students play the remainders game to reinforce division with remainders (2 activities).

Task 12: The tiler

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

Task 13: Liquorice factory

Students use an investigation task to apply multiplicative thinking (one activity).

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