Compare two quantities by "how many times as much" rather than "how many more", and recognise which comparison a situation calls for.
RATIO.MULTIPLICATIVE_COMPARISON“I can tell whether a comparison is additive or multiplicative and write the matching statement.”
Given 6 and 18, state both the additive and the multiplicative comparison and say which a "3 times as many" story needs.
| Course | Unit | Depth | Role | Checkpoint |
|---|---|---|---|---|
| Grade 4 | Patterns and comparison | intro | introduce | ✓ |
Two stacked bars aligned at the left so difference and multiple both show as length.
Distinguishes "more than" from "times as many" visually.
engine: aligned bar pair with difference brace
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
Scene archetype: bar_model
RATIO.CMP.ADDITIVEUses subtraction where scaling is meant.
Repair: Draw both bars and show which comparison the story is asking about.
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.
Ratio and rate get a dedicated Grade 6-7 domain as the explicit bridge into algebra, with the double number line and the ratio table introduced as reasoning tools so that proportional relationships are met before cross-multiplication.
Ratio is taught as units: a 3:5 ratio is eight equal blocks, and almost every ratio problem is solved by finding the value of one block from a drawn strip. Formal proportion machinery is rarely needed.
Ratio and proportion sit inside a large body of multi-step problems about parts, rates, and scaling, worked through condition tables. Solving a proportion is the easy part; setting one up from a tangled situation is the taught skill.
Ratio appears as fraction-style computation and proportion solving within the fraction and pre-algebra levels, drilled as cross-multiplication rather than as multiplicative reasoning.
Proportional reasoning is developed through per-unit quantity, with the double number line used to keep the two measures aligned. Lessons compare a student who scaled up with one who found the unit rate.
Ratio and proportion are presented as a set-up-and-cross-multiply procedure with extensive practice, appearing in the pre-algebra book and then recurring in mixed review.
Ratio work grows out of the elementary material on multiples and proportion in geometry, particularly with the constructive triangles and similar-figure work, and is more geometric than numeric.
Ratio is treated as a route into scaling arguments and later into similar-triangle and probability reasoning, with problems where the naive proportion set-up gives the wrong answer.
Ratio and proportion are a named KS2-KS3 strand taught with bar models and ratio tables, with careful separation of part-to-part from part-to-whole and a lot of "for every" language.
The Grade 6 ratio units are among the most carefully built in the curriculum: discrete diagrams, then double number lines, then tables, with each representation introduced when the previous one becomes inconvenient.