Learn multiplication facts in more than one direction.
Work through a transparent five-step path for every table from 1× through 12×. Study the pattern, retrieve products directly, recover missing factors, prove fluency in the existing 60-second Sprint, and finish with a 24-prompt Mastery Check that mixes both recall directions.
Start the Fact Mastery path
The Academy is an additive layer over the existing Times Tables specialist. The original 1–12 Practice, Missing Factor, Sprint 60, Weak Facts, Fact Grid and date-stable Daily remain intact. The new path organizes those skills into a visible progression without locking later steps or inventing a classroom grade.
The five-step path
Study is intentionally unscored. It shows all twelve products for one fact family and the existing strategy note for that table. The goal is to notice a usable pattern before testing memory. For example, the 4× strategy is “double, then double again,” while the 9× facts have a strong digit pattern. Marking Study complete means only that you reviewed the family; it does not pretend that seeing a list proves mastery.
Direct Recall asks the familiar question, such as 7 × 8. Every partner from 1 through 12 appears exactly once in the 12-question checkpoint. The pass mark is at least 11 of 12 correct on the first attempt. If the first answer is wrong, you get one retry so the round still teaches the fact, but the checkpoint keeps the original miss instead of converting the retry into fake first-attempt accuracy.
Missing Factor reverses the retrieval direction. Instead of typing the product for 7 × 8, you may see 7 × ? = 56 and have to recover 8. This is useful because multiplication knowledge is often needed inside division, fractions and algebraic rearrangement, where recognizing an unknown factor matters as much as reciting a product. The checkpoint again requires 11 of 12 first-attempt correct.
Fluency 60 does not create a second imitation speed test. It reuses the existing frozen Times Tables Sprint with only the selected table active. When you return to the Academy, the path reads that real local Sprint best. The checkpoint clears at 20 or more correct with at least 95% accuracy. That target is a DailyBrainArc practice checkpoint, not a population percentile, school grade or claim about what every learner should achieve.
Mastery Check mixes 24 prompts: one direct and one missing-factor question for every fact in the selected family. Clearing it requires 22 of 24 overall plus at least 10 of 12 correct in each prompt type. That prevents a strong direct-recall score from hiding weak missing-factor recall, or the reverse.
Why the path does not lock later steps
A rigid course can become frustrating when someone already knows most of a table or wants to diagnose a specific weakness. DailyBrainArc therefore shows the recommended order but keeps all five steps available. You can jump straight to a Mastery Check, open Missing Factor first, or run the Sprint without completing Study. The local progress map still shows which checkpoints have actually been cleared.
This also makes the path useful for review. A learner who mastered 6× months ago can reopen only the Mastery Check. Someone who keeps missing 6 × 7 can use Weak Facts first, then revisit the 6× and 7× families instead of repeating an entire course from the beginning.
How Weak Facts influence the recommendation
The existing Times Tables engine already stores the exact multiplication facts missed on this browser. V0.148 does not replace that queue with an opaque “weakness score.” The Academy simply counts which incomplete table families those saved misses touch. If a real weak fact involves 7×, the recommendation can prioritize the next unfinished 7× checkpoint. If there are no saved misses, it recommends the next incomplete family and step in a transparent order.
Because multiplication is commutative, one saved fact can matter to two families. A miss on 3 × 7 may reasonably make both the 3× and 7× paths relevant. The recommendation is a practice suggestion, not an assessment.
How the question sets are verified
The Academy does not carry a second hand-written multiplication bank. It derives every prompt from the existing frozen 144 ordered facts used by the Times Tables specialist: twelve partners for each table from 1 through 12. The V0.148 core deterministically shuffles those facts for Direct Recall and Missing Factor, and builds the Mastery Check from exactly twelve direct plus twelve missing-factor prompts.
An independent verifier reopens the frozen fact data, confirms the historical file hashes, checks every product against multiplication truth, generates thousands of seeded Academy rounds, and verifies determinism, prompt counts and complete 1–12 partner coverage. It also checks the exact checkpoint thresholds. This means the new curriculum layer can evolve without silently changing the older Times Tables engine or its date-stable Daily behavior.
Use the existing 12×12 Fact Grid as evidence, not decoration
The Fact Grid already summarizes local first-attempt history across the complete multiplication matrix. It remains useful after the Academy is added because it answers a different question: which exact facts have actually been seen and missed? The Academy answers where you are in a five-step learning path. Weak Facts answers what should be reviewed now. Keeping those views separate makes the progress model easier to understand.
Transfer a table into Mental Math
Fast multiplication recall becomes more useful when it survives outside a dedicated tables screen. Every Academy table therefore links to the existing Mental Math specialist with multiplication selected and that table fixed. A 7× learner can move directly into a 60-second Mental Math multiplication Sprint for 7×, while the broader Mental Math Adaptive Ladder remains available when you want mixed operations.
The two products keep separate records. Fact Mastery stores checkpoint progress for the five-step curriculum. Times Tables keeps its existing fact history, Weak Facts and Sprint bests. Mental Math keeps its own fluency history. V0.148 connects the workflow without pretending that one score is interchangeable with another.
What “mastery” means here
“Mastery” is used narrowly: the five local checkpoints defined on this page have been cleared for a table. It does not mean a permanent cognitive trait, a guaranteed school outcome or a comparison with other people. A cleared table can be rechecked later, and Weak Facts may still surface a specific miss from another mode. The app intentionally keeps these signals visible rather than collapsing them into a single mysterious level.
Why accuracy stays ahead of speed
Speed matters for fluent recall, but a fast run with frequent errors is not the goal. That is why the Fluency checkpoint has both a correct-count and an accuracy requirement, while the Direct, Missing and Mastery checkpoints score first attempts. The existing Sprint also keeps its own accuracy value. This encourages pace only after the fact family is stable enough to retrieve accurately.
A practical learning loop
Choose one table and read the Study panel. Run Direct Recall until the product questions feel stable, then Missing Factor to test the reverse direction. Use the table-specific Sprint and return to see whether Fluency has cleared. Finish with the mixed Mastery Check. If a fact enters Weak Facts, review it there until the existing three-correct-review rule retires it. Then carry the same table into Mental Math for transfer practice.
If you already know most tables, skip the linear path and use the recommendation, Weak Facts and Mastery Checks as diagnostics. If you are learning from the beginning, work table by table. The UI keeps all routes open in both cases.