Ratio, Proportion & Percentages
MYP Year 3 Mathematics — Number strand: Ratio, Proportion & Percentages
This whole topic is really one skill wearing different costumes: spotting the multiplicative rule that connects two quantities, and then using it correctly in both directions. A recipe scaling up, a wage going up with hours, a sale price coming down, a bag of rice getting cheaper per kilo in bulk — every one of these is asking 'what's the constant relationship here, and does it still hold?' Examiners deliberately build in traps where the relationship looks proportional but isn't (a fixed fee, a bulk discount) — your job is to test the model, not just apply a formula on autopilot.
Overview — The Shape of This Chapter
Why this all fits together
Ratios, proportion and percentages are all ways of describing how two quantities scale together. A ratio compares parts within one situation (). Proportion asks whether two ratios stay equal as the numbers change (). A percentage is just a ratio locked to a base of 100, which makes it easy to compare across totally different totals — a discount means the same rate whether it's on a $10 item or a $1000 item.
- The single most examined skill: finding the constant multiplier (call it or a % rate) from given data, then applying it to a new value.
- The single most examined trap: assuming a relationship is directly proportional when a fixed fee, base charge or bulk discount breaks that pattern.
- MYP loves 'explain' and 'justify' command terms here — a correct number with no reasoning about why the model does or doesn't hold rarely gets full marks.
The shape of the chapter
Command terms that dominate this topic's mark schemes
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| State | Give a short, precise answer with no justification expected. | AO1 Knowing & Understanding | Just the value/name — e.g. 'k = 8'. Extra working earns no bonus but also no penalty. |
| Calculate | Obtain a numerical answer showing the relevant working stages. | AO1/AO2 | Method mark for the correct setup (e.g. correct multiplier or formula), accuracy mark for the final value. |
| Apply | Use a given rule or formula in a new situation. | AO2 Investigating Patterns / AO1 | Must show the substitution step explicitly — 'plugging in' without writing the formula first often loses the method mark. |
| Explain | Give a reason that makes a relationship or result clear. | AO3 Communicating | A bare number scores 0 here — you need a sentence connecting cause and effect (e.g. 'because the graph does not pass through the origin'). |
| Justify | Give valid reasons or evidence to support a conclusion, often a yes/no decision. | AO3/AO4 | State the decision AND the numeric evidence that supports it — decision alone or evidence alone each earn partial credit at best. |
| Compare | Identify similarities and differences between two quantities or methods. | AO3 | Needs both values stated and an explicit comparative word ('more/less/by how much') — two separate numbers with no comparison sentence rarely gets the mark. |
Key point
Overview