Recognise all the situations addition and subtraction model: joining, separating, comparing, and finding a missing part.
NUM.ADD_SUB_MEANING“I can decide whether a story needs adding or subtracting and say why.”
Given four stories (join, take-from, compare, missing-part), write a matching equation for each.
| Course | Unit | Depth | Role | Checkpoint |
|---|---|---|---|---|
| Kindergarten | Parts of numbers | intro | introduce | ✓ |
A whole with two or three parts joined by arcs, used for part-whole reasoning in either direction.
Fact families become one picture instead of four sentences.
engine: node-and-arc scene with value slots
Discrete movable objects arranged, grouped, and recounted to establish cardinality and conservation.
Separates "how many" from "the last word I said".
engine: prop_catalog instances + drag layer
An unscaled line where the learner chooses landmarks and records their own jumps.
Exposes the strategy instead of hiding it in an algorithm.
engine: freeform axis with learner-placed marks
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
NUM.ADDSUB.KEYWORDAdds whenever the word "altogether" appears, regardless of structure.
Repair: Draw the part–whole diagram before choosing an operation.
NUM.ADDSUB.COMPARE_AS_ADDTreats "how many more" as an addition of both numbers.
Repair: Model with two aligned comparison bars and mark the difference.
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.
The problem-type taxonomy is explicit: add-to, take-from, put-together, compare, each with the unknown in three positions, and a grade is expected to master specific cells of that table. Fluency within 10 is required by Grade 1 and within 20 by Grade 2.
Number bonds do the conceptual work: a whole with two parts covers addition, both subtractions, and missing-addend problems as one picture. The make-ten strategy is taught as a named method with a drawn branching step rather than left to be discovered.
Addition and subtraction are met inside problems from the start, with the condition written out and schematised before computing. Comparison problems ("how many more") are given equal weight with joining problems rather than treated as harder.
Levels A and B are addition then subtraction as pure computation: +1 sheets, then +2 sheets, and so on, with the whole fact space covered by incremental worksheet sets and timed to a standard completion time. No word problems, no diagrams.
Addition with regrouping is taught through one problem such as 8 + 5, with several student decompositions compared on the board, and the make-ten method consolidated as the efficient one at the end. The comparison, not the demonstration, is the lesson.
Facts are drilled to automaticity on timed sheets, the column algorithm is taught explicitly with worked examples, and both then recur in mixed practice indefinitely. Regrouping is presented as a procedure to execute correctly rather than a trade to understand.
Addition begins as a physical composition of golden-bead quantities carried to a shared table, with exchange happening when ten of a category accumulate. The algorithm is met only after the exchange has been performed by hand many times.
Beast Academy leans on structure rather than facts: problems reward noticing that a long sum pairs into equal totals, or that compensation makes an awkward subtraction trivial. Speed follows from insight rather than from repetition.
Small-step sequences build bridging through ten with tens frames and part-whole models, and mental strategies are taught before the column method. Missing-number equations in every position are routine from Year 1.
Story-problem types are worked deliberately across their unknown positions, with student strategies elicited and connected to one another before any algorithm is named. Number talks give a regular slot for mental strategies to be compared.