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	Prerequisite relationships
Fractions Decimals Percentages	- Find the highest common factor (HCF) → Simplify ratios
Ratios and Rates	- Use ratios to compare quantities → Express a ratio part as a fraction of the whole - Use ratios to compare quantities → Distinguish ratios from rates - Express a ratio part as a fraction of the whole (revisited content) - Produce equivalent ratios → Simplify ratios - Simplify ratios (revisited content) - Apply the unitary method to ratio problems → Divide a quantity in a given ratio - Divide a quantity in a given ratio (revisited content) - Solve real-life ratio problems (revisited content) - Distinguish ratios from rates (revisited content) - Represent information as a simplified rate (revisited content) - Convert between units for rates (revisited content) - Solve problems involving rates (revisited content) - Determine the best buy (revisited content) - Solve problems involving related rates (revisited content) - Interpret distance–time graphs (revisited content) - Calculate speed from a distance–time graph (revisited content) - Calculate distance, speed and time → Calculate speed from a distance–time graph
Equations	- Solve one-step linear equations → Solve problems involving rates
Volume	- Convert between units of volume and capacity → Determine the best buy
Properties of Geometrical Figures A	- Determine and apply scale factors → Solve scale drawing problems - Solve scale drawing problems (revisited content)
Applications of Measurement	- Apply the Trapezoidal rule → Calculate area from a scaled plan

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