Apply percent reasoning to everyday money situations, including successive percentages and working backwards to the original.
MODEL.PERCENT_APPLICATIONS“I can compute tax, tip, and discounts, and find the original price from a sale price.”
Find the final cost of a $65 item with a 20% discount plus 8% tax, then find the original price of an item now $51 after 15% off.
| Course | Unit | Depth | Role | Checkpoint |
|---|---|---|---|---|
| Grade 7 | Modelling | intro | introduce | ✓ |
Rectangular bars segmented to show parts inside a whole, with the unknown drawn as a labelled gap.
Word problems become a picture you can read the equation off.
engine: segmented bar actor with labelled brace
Two parallel scales locked together so equivalent ratios line up vertically.
Makes "per one" visible and kills cross-multiply-first habits.
engine: two coupled axes with linked tick mapping
A goal bar filling over time with deposits, withdrawals, and interest visibly compounding.
Compound growth watched rather than computed once.
engine: existing piggy-bank scene archetype
Scene archetype: bar_model
MODEL.PCT.ORDERAssumes discount-then-tax and tax-then-discount give different results without checking.
Repair: Compute both orders once and compare.
One row per instructional system. Rows marked cluster carry authored treatment for this family of topics; rows marked template are derived from the system’s general pattern and are not topic-specific research. Confidence is recorded on every row.
Modelling is one of the practice standards and a high-school conceptual category, so motion, mixture, and rate problems are expected to be set up from context rather than pattern-matched to a template.
Complex multi-step word problems are the signature assessment task, and the bar model is the standard tool for making their structure visible before any equation is written.
Motion, work, and mixture problems are a central genre with their own taught techniques: the condition is tabulated, a segment schematic is drawn, and only then is an equation formed. Students meet these years earlier than in the US sequence and in far greater volume.
Word problems are largely absent from the sequence. This is the clearest structural gap in the method: a student may be several levels ahead in computation while unable to set up a two-object motion problem.
Context problems anchor whole lessons, with the tape diagram used to expose structure and student solutions compared for generality. The problem is chosen so that several routes exist.
Word problems appear as classified types with a demonstrated set-up for each (distance-rate-time, coin, mixture), practised in sets and then recurring in mixed review.
Applied problems come from the practical-life and "going out" strands — measuring, budgeting, planning a trip — rather than from a set of classified word-problem types.
Contexts are chosen so that the standard template fails, forcing genuine modelling, and solutions are compared for insight rather than for adherence to a set-up.
Problem solving is one of the three stated aims, with multi-step contextual questions standard at KS2 SATs and GCSE, commonly scaffolded by bar models.
Contexts are the entry point for new mathematics rather than an application at the end of a unit, and the modelling cycle is made explicit in high-school units.