Real-World Mathematical Modelling
Model real-world problems involving ratio, scale, volume, unit conversion, and proportional reasoning with appropriate tools, diagrams, or equations
What a learner can do afterwards
- Choose a bar model or double number line to represent a ratio problem and solve it
- Model a volume problem with a labelled diagram, apply the formula, and interpret the result in context
- Determine whether a measurement answer should be rounded and to what degree of accuracy
The lesson
When you solve a real problem, you often have to choose how to picture it first. A bar model splits a ratio into equal parts. A double number line lines up two related amounts so you can see how they grow together. Pick whichever picture matches the problem, then solve it.
A fish tank is 40 cm long, 20 cm wide, and 25 cm tall. To find its volume, multiply length by width by height: 40 x 20 x 25 = 20,000 cm cubed. Since 1000 cm cubed equals 1 litre, that tank holds 20 litres of water.
Not every answer should be rounded the same way. Money often rounds to the nearest cent, while a tank's volume might round to the nearest litre. Finish your calculation first, then round to match what you are measuring.
To model a real problem, pick a bar model, double number line, or formula, solve it, then round your answer to match what you are measuring.
Watch it
Where it sits
This opens up
Nothing builds on it yet.
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.