Find "per one" values from a ratio of quantities with different units, and use them to compare and to predict.
RATIO.UNIT_RATE“I can find a unit rate and use it to compare two offers or predict a value.”
Compare $7.50 for 3 kg with $11.60 for 5 kg by unit price and state which is the better buy.
Depth is a column, not a second topic. The same topic is taught at these depths in different years; the path table below places each rung.
Find a unit rate from a simple whole-number ratio.
Compare rates with different units and use them to predict.
Work with both unit rates of a relationship (per unit A and per unit B) and choose the useful one.
| Course | Unit | Depth | Role | Checkpoint |
|---|---|---|---|---|
| Grade 6 | Ratio and rate | advanced | review | ✓ |
| Grade 6 | Ratio and rate | intermediate | review | |
| Grade 6 | Ratio and rate | intro | introduce |
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 table of equivalent ratios scaled up and down by multiplication, not addition.
Scaling arrows make the multiplicative structure explicit.
engine: table widget with scale-factor arrows
Scene archetype: double_number_line
RATIO.RATE.INVERTDivides in the wrong order and reports kg per dollar as dollars per kg.
Repair: Write the unit in the answer every time and check it reads correctly.
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.