Add and subtract flexibly by compensating, bridging through ten, and splitting by place value.
NUM.ADD_SUB_STRATEGIES“I can add and subtract two-digit numbers in my head and explain the route I took.”
Compute 68 + 25 and 91 − 47 mentally and describe two different valid routes.
| Course | Unit | Depth | Role | Checkpoint |
|---|---|---|---|---|
| Grade 2 | Mental strategies | intro | introduce | ✓ |
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
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
A 10x10 grid of 1–100 where +10 is a row and +1 is a column.
Turns base-ten structure into a map you can walk.
engine: grid with path highlighting
Scene archetype: number_line
NUM.MENTAL.ALGORITHM_ONLYMentally visualises the written algorithm digit by digit.
Repair: Require a jump recorded on an open number line instead.
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.