# Flexible strategies with integers

## Learning intention

Students will learn to work with and apply their knowledge of directed number (positive and negative numbers) in a variety of contexts.

### Syllabus outcome (2022)

• 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
• MA4-INT-C-01 compares, orders and calculates with integers to solve problems

### Syllabus outcome (2012)*

• MA4-1WM communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols
• MA4-2WM applies appropriate mathematical techniques to solve problems
• MA4-3WM recognises and explains mathematical relationships using reasoning
• MA4-4NA compares, orders and calculates with integers, applying a range of strategies to aid computation.

### National Numeracy Learning Progression

• NPV9 Number and place value

• CPr8 Counting processes

### Task 1: Negative numbers around us

Students contextualise negative integers in a variety of situations.

### Task 2: Language of loss and gain board game

Students explore the language of loss and gain to contextualise negative and positive integers.

### Task 3: Zero pairs counter modelling (visuals or models)

Students use coloured counters to develop an understanding of addition and subtraction of positive and negative integers.

### Task 4: Close to zero

Students use a board game to reinforce their understanding of negative and positive integers.

### Task 5: Up, down, flying around

Students consolidate their knowledge of directed numbers by using a vertical number line.

### Task 6: Integer quick draw

Students apply additive thinking with negative and positive integers.

### Task 7: Tug of integers

Students compete to get to either end of the number line by adding and subtracting positive and negative integers.

Students roll two dice by adding and subtracting positive and negative integers to get three in a row.

### Task 9: Finding zero with opposites

Students conceptualise how zero is created by adding a positive number to the same size negative number.