#Measurement #Year12 #Standard >[!info]- [Ratios and rates | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-standard-11-12-2024/content/n12-tba2/fa96edbda5) >- MST-12-S2-05 solves practical problems involving ratios and rates ## 📖 Prior Knowledge | Content | Prior knowledge | Used for | | ---------------------------------------------- | ---------------------------------------------------- | -------------------------------------------------------------- | | [[Stage 4/Ratios and Rates\|Ratios and Rates]] | - solving ratio problems<br>- solving rates problems | - *repeated content*<br>- kilowatt-hours<br>- 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