Ratios and Rates

measurement year12 standard

Ratios and rates | NSW Curriculum Website

• MST-12-S2-05 solves practical problems involving ratios and rates

📖 Prior Knowledge

Content	Prior knowledge	Used for
Ratios and Rates	- solving ratio problems - solving rates problems	- repeated content - kilowatt-hours - fuel consumption
Properties of Geometrical Figures A	- scale drawing problems	- repeated content

Ratios

• Recognise ratios and explain their relationship with fractions
• Express a ratio in simplest form
• Determine the ratio of two quantities
• Divide a quantity in a given ratio
• Solve practical problems involving ratios
• Solve practical ratio problems involving the capture-recapture technique
• Explain the relationship between ratios and map scales and apply this relationship to solve problems in a variety of practical contexts
• Construct scale drawings, with and without using digital tools
• Estimate and compare quantities, materials and costs using measurements taken from scale drawings and building plans with commonly used symbols
• Calculate the perimeter, or area of a section of land using the Trapezoidal rule where appropriate, from a site plan, an aerial photograph, a radial survey or a map that includes a scale
• Calculate the volume of rainfall over an area using $V=Ah$, where $V$ is the volume, $A$ is the area of land and $h$ is the depth of rain, from a site plan, an aerial photograph, a radial survey or a map that includes a scale

Rates

• Explain the difference between ratios and rates
• Represent given information as a unit rate
• Convert between rates
• Make comparisons between rates in a variety of practical contexts
• Compare unit prices to determine best buys
• Use rates to solve problems in a variety of practical contexts
• Interpret and analyse distance–time graphs to solve problems related to speed, distance and time
• Examine fuel consumption rates to compare the efficiency of vehicles
• Recognise and convert between watts (W) and kilowatts (kW) using $1000\text{W}=1\text{kW}$
• Apply units of energy to calculate kilowatt hours and solve problems involving the consumption of energy