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Miscellaneous · course 97 of 105

Mental Maths, No Calculator Needed

Do everyday maths in your head: fast multiplying, squares, percentages and tips, quick division, divisibility rules and a quick check before you say the answer.

4 modules

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What it teaches

The mental maths that saves you every day: × 11, squaring numbers ending in 5, multiplying numbers near 100, × 5 and × 25, halve-and-double; percentages built from 10% (tips, discounts, the percent swap, why +10% then −10% isn’t even); ÷ 5 and ÷ 25; divisibility rules (3, 4, 6, 9, 11); casting out nines and what it can’t catch; round-and-fix (49 × 21, $19.99 × 4). The AI asks 3 questions, places you, shows a short card per module, then gives you one problem at a time and checks your answer against its answer key (every number computed by script).

How long

37 items. A beginner who misses about a third of the items: about 65 rounds plus the 12-item final (3 sessions). A confident student: about 25 rounds plus the final (1 session). Estimates from two simulated students, not timed with a real person. The tutor gives a one-line save code at the end of each session.

The modules

4 modules, drilled one item at a time.

  1. M0

    The rules

    Concept questions

  2. M1

    Multiplying tricks

    Multiply in your head, one problem at a time

  3. M2

    Percentages and dividing

    Percentages and dividing in your head

  4. M3

    Checking and round-and-fix

    Check an answer, or round and fix

Before it teaches, it asks

  1. 1
    What do you want quicker maths for (work, tests, splitting bills, shopping), and how do you do 15% of a number today?
  2. 2
    A $60 bill. What is a 15% tip?
  3. 3
    Work out 97 × 96 in your head.

What’s exact, and what isn’t

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Straight from the course’s own notes.

Computed and proved
Every number in the answer key is exact integer or fraction arithmetic. Every trick on the cards is proved over a whole range, not just the item numbers (319,299 checks: × 11 for every two-digit number, squares ending in 5 up to 305², near-100 as arithmetic for every pair from 85 to 115, and the card’s write-the-product-beside steps for the 407 same-side pairs whose distances multiply to under 100, the divisibility rules and the ×/÷ 5 and 25 tricks for every number to 2,000, casting out nines with the card’s own digit-sum steps for every pair to 300 and every digit swap in every number to 9,999; the 10% ladder, percent-off, up-then-down, halve-and-double, round-and-fix and what-percent lines). A planted-error test (4 errors) was caught.
Sourced
Divisibility rules and casting out nines quote Wikipedia (short quotes, matched on the live pages, re-checked 2026-10-11).
Not in it yet
Square roots, calendar tricks, memorising numbers.