NSW Syllabuses

# Mathematics K–10 - Stage 5.2 - Number and Algebra Ratios and Rates

## Outcomes

#### A student:

• MA5.2-1WM

selects appropriate notations and conventions to communicate mathematical ideas and solutions

• MA5.2-2WM

interprets mathematical or real-life situations, systematically applying appropriate strategies to solve problems

• MA5.2-5NA

recognises direct and indirect proportion, and solves problems involving direct proportion

## Content

• Students:
• Solve problems involving direct proportion; explore the relationship between graphs and equations corresponding to simple rate problems (ACMNA208)
• convert between units for rates, eg kilometres per hour to metres per second
• identify and describe everyday examples of direct proportion, eg as the number of hours worked increases, earnings also increase
• identify and describe everyday examples of inverse (indirect) proportion, eg as speed increases, the time taken to travel a particular distance decreases
• recognise direct and inverse proportion from graphs
• distinguish between positive and negative gradients when using a graph (Reasoning)
• interpret and use conversion graphs to convert from one unit to another, eg conversions between different currencies or metric and imperial measures
• use the equation $$\,y = kx\,$$ to model direct linear proportion where $$k$$ is the constant of proportionality
• given the constant of proportionality, establish an equation and use it to find an unknown quantity (Communicating, Problem Solving)
• calculate the constant of proportionality, given appropriate information, and use this to find unknown quantities (Problem Solving)
• use graphing software or a table of values to graph equations representing linear direct proportion

### Language

When describing everyday examples involving proportion, teachers should model common words and language structures before independent work is required, eg 'As the speed increases, the time taken to travel a particular distance decreases', 'The greater the speed, the less time is taken to travel a particular distance', 'The time taken to travel a particular distance is reduced when the speed is increased'.

### National Numeracy Learning Progression links to this Mathematics outcome

When working towards the outcome MA5.2-5NA the sub-elements (and levels) of Number patterns and algebraic thinking (NPA7) and Comparing units (CoU3) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.

The progression sub-elements and indicators can be viewed by accessing the National Numeracy Learning Progression.