# 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.

## Multiplication

### 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).

## Division

### 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).