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

  • MA2-1WM: uses appropriate terminology to describe, and symbols to represent, mathematical ideas
  • MA2-2WM: selects and uses appropriate mental or written strategies, or technology, to solve problems
  • MA2-3WM: checks the accuracy of a statement and explains the reasoning used
  • MA2-6NA: 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

  • MuS2: uses groups or multiples in perceptual counting and sharing
  • MuS3: relies on perceptual markers to represent each group; uses equal grouping and counting without individual items visible but needs to represent the groups before determining the total; counts by twos, fives and tens, matching the count to groups of the corresponding size
  • MuS4: uses composite units in repeated addition and subtraction using the unit a specified number of times; uses skip counting and may use fingers to keep track of the number of groups as the counting occurs: determines the total or number of equal groups where the individual items cannot be seen
  • 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

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

Multiplication strategies

Task 1: Chicken scramble

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

Task 2: 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 3: Colouring arrays

Students use arrays to view ‘how many’ and ‘how much’ (one activity).

Task 4: Array flash

Students use flash cards to assist in forming concepts of area (four activities).

Task 5: Array bingo

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

Task 6: Multiplication toss

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

Task 7: 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).

Division strategies

Task 8: Factors and products

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

Task 9: What do I know about partitioning?

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

Task 10: Working with fact families

Students work with fact families to support a factor-factor-product approach to multiplication and division (one activity).

Task 11: Challenge and helper problems

Students consider the relationship between problems (one activity).

Task 12: Remainders game

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

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