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. They will use their own informal recordings to represent their strategies and communicate effectively with others. Students will also deepen their understanding of the operations themselves and the inverse relationship between multiplication and division.

Syllabus outcome

  • MAO-WM-01 develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly
  • MA2-RN-01 applies an understanding of place value and the role of zero to represent numbers to at least tens of thousands
  • MA2-MR-01 represents and uses the structure of multiplicative relations to 10 × 10 to solve problems

National Numeracy Learning Progression

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

  • MuS2: Perceptual multiples

  • MuS3: Figurative (imagined units)

  • MuS4: Repeated abstract composite units

  • MuS5: Coordinating composite units

  • MuS6: Flexible strategies for single digit multiplication and division

  • MuS7: Flexible strategies for multiplication and division

Task outline

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

Division strategies

Task 1: Factors fun

Students explore division, work out a solution and explain their thinking (one activity).

Task 2: Factors and products

Students create various models and representations for the factors of whole numbers (one activity).

Task 3: What do I know about partitioning?

Students explore the various ways to partition a dividend (one activity).

Task 4: 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 5: Remainders game

Students play the remainders game to reinforce division with remainders (one activity).

Multiplication strategies

Task 6: Chicken scramble

Students choose a counting strategy to quantify a large collection of items using counting strategies (one activity).

Task 7: Finding dice totals

Students find ways to group the dice and use mental strategies to determine the most effective way to calculate the total (two activities).

Task 8: Doubles fill

Students play the doubles fill game to builds number sense by connecting quantities with symbols and language. (one activity).

Task 9: Array bingo

Students play a game of bingo with arrays to help students see how numbers can be represented (one activity).

Task 10: Multiplication toss

Students develop multiplicative automaticity through this game using grid paper to represent multiplication (one activity).


  • Numeracy

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  • Teaching, Learning and Student Wellbeing
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