A student:

• communicates and connects mathematical ideas using appropriate terminology, diagrams
  and symbols MA4-1WM

• applies appropriate mathematical techniques to solve problems MA4-2WM

• recognises and explains mathematical relationships using reasoning MA4-3WM

• operates with ratios and rates, and explores their graphical representation MA4-7NA

Students:

Recognise and solve problems involving simple ratios (ACMNA173)

• use ratios to compare quantities measured in the same units

• write ratios using the : symbol, e.g. 4:7

• simplify ratios, e.g. 4:6=2:3, ¹/₂:2=1:4, 0.3:1=3:10

• apply the unitary method to ratio problems

• divide a quantity in a given ratio

This series addresses all five Working Mathematically components.

• Fluency: Students practice simplifying ratios, finding equivalent ratios, calculating constants of proportionality and drawing graphs to represent relationships.

• Understanding: Students explore examples of direct proportionality and inverse proportionality to enhance their understanding of these types of relationships.

• Reasoning: Students deduce the equations of direct and inverse proportionality and the relationship between the gradient and the constant of proportionality.

• Problem Solving: Students explore and compare a variety of methods of solution, including visual methods.

• Communicating: Students use diagrams and mathematical language to explain methods of solution.

Each resource includes an initial activity, supporting students who require revision of key concepts. Each resource also includes a bonus activity containing material that can extend suitable students.