Maths · Pioneers 11–15 · Year 10
Modelling, reasoning and multi-step problems
What does a mathematician do when they're stuck?
What you will learn
- Break a multi-step problem into stages and check reasonableness
- Build and refine a mathematical model with stated assumptions
- Use compound measures: speed, density, rates
- Construct a chain of reasoning and communicate it clearly
Helpful to know first: Ratio and proportion; Algebraic manipulation
Discover
Think first: What does a mathematician do when they're stuck? Say or jot one idea before you read on.
Learn — core route
- Fermi estimation: how many breaths in a lifetime?
- Speed-distance-time journey planning
- Assumption-listing protocol
Lessons in this subject: Learn Topics · Maths
Practise — check a common mix-up
If the answer isn't a whole number the method must be wrong.
A model is wrong if it ignores anything.
Apply / Create — Fermi Challenge Report
Estimate something unknowable (e.g. litres of water a school uses per year). State assumptions, model, calculate, check with a second method and reflect on error.
Evidence type: written report · accessible alternative always allowed (speak it, draw it, or show an adult).
How it is judged (rubric)
- Beginning: Gives a number
- Developing: Shows steps
- Secure: Assumptions stated, two methods, reasonable check
- Extending: Quantifies uncertainty and refines model
Explain — say what you did
Review later
We'll offer a quick memory check in 7, 21 and 45 days. Mark this done and your Today page will remind you gently.
For grown-ups · framework mappings
- aligned to UK NC · KS4 Reasoning; Ratio, proportion and rates of change
- aligned to Common Core · HSN-Q.A
Status: Live · reviewed
What's next?