Model jobs completed per unit time and combine rates additively to find how long a shared task takes.
MODEL.WORK_RATE“I can solve combined work-rate problems by adding rates.”
One pipe fills a tank in 6 hours and another in 4; find how long both together take.
| Course | Unit | Depth | Role | Checkpoint |
|---|---|---|---|---|
| Algebra I (Grade 8-9) | Data and modelling | intro | introduce | ✓ |
Nothing in the atlas depends on this yet.
A ruled table of quantity, rate, and total (or was/change/now) filled in from the problem statement.
Makes motion, work, and mixture problems mechanical rather than mysterious.
engine: editable table widget with derived cells
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
A spare labelled line-segment schematic of the quantities and relations in a problem, drawn before any arithmetic.
Forces analysis of structure before computation.
engine: labelled segment graph with relation braces
Scene archetype: bar_model
MODEL.WORK.ADD_TIMESAdds the two times instead of the two rates.
Repair: Sanity check: together must be faster than either alone.
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.