The Reframe — Tricks With Understanding, Not Stage Magic
Speed math tricks have a reputation problem. Marketing for Vedic math and abacus programs promises that "in 6 weeks your child will multiply two-digit numbers in seconds" — and the promise is technically true. The problem is what it teaches.
A child who memorises that $97 \times 103 = 9991$ via a trick — without understanding why — has gained a parlour skill. The trick does not transfer to algebra, geometry, or word problems. It does not even transfer to similar-looking arithmetic.
A child who learns the same trick along with the algebra that powers it — $(100-3)(100+3) = 100^2 - 9$ — has gained two things: the trick and a piece of algebra they will use in Grade 8.
The right frame for speed math tricks: each trick is a window into a piece of algebra. Teach the trick and the window. The fluency comes either way; the understanding only comes when you teach both.
How to Use the Tricks Below
Each trick has three parts: the trick (the shortcut), the why (the algebra), and the try it (a problem your child can practise). Skip the why and the trick becomes rote. Skip the trick and the why is abstract algebra without an entry point.
One trick a week is plenty. Twelve weeks and your child has fifteen mental-math tools and an early understanding of algebraic identities — which is exactly the right shape for a Grade 5 or Grade 6 student.
Multiplication Tricks (1–5)
Trick 1 — Multiply by 11 (Two-Digit Numbers)
The trick. For any two-digit number $ab$, $ab \times 11 = a(a+b)b$. If $a+b > 9$, carry the 1.
Examples. $35 \times 11 = 3 (3+5) 5 = 385$. $72 \times 11 = 7 (7+2) 2 = 792$. $86 \times 11 = 8 (8+6) 6 = 8 (14) 6 = 946$ (carry the 1).
The why. $ab \times 11 = ab \times (10 + 1) = ab \times 10 + ab$. The first part shifts the digits one place left ($ab0$); adding $ab$ to it gives $a (a+b) b$ when there is no carry.
Try it. $47 \times 11$, $93 \times 11$, $58 \times 11$.
Trick 2 — Multiply Two Numbers Near 100
The trick. For two numbers near 100, say $97$ and $96$: compute the deficits (3 and 4), multiply them ($12$), and add 100 minus the deficit-sum to get the front digits.
$97 \times 96 = (100-3)(100-4) = 100 - 3 - 4 = 93$ (front), and $3 \times 4 = 12$ (back). Answer: $9312$.
The why. $(100-a)(100-b) = 10000 - 100a - 100b + ab = 100 \cdot (100 - a - b) + ab$.
Try it. $98 \times 97$. $99 \times 95$. $96 \times 94$.
Trick 3 — Multiply by 5
The trick. Multiplying by 5 is "multiply by 10, then halve." $47 \times 5 = 470 / 2 = 235$.
The why. $5 = 10/2$. So $n \times 5 = n \times 10 / 2$.
Try it. $36 \times 5$. $84 \times 5$. $127 \times 5$.
Trick 4 — Multiply by 9 with Fingers
The trick. Hold up ten fingers. To compute $7 \times 9$, fold down the 7th finger. The fingers to the left of the fold (6) are the tens; the fingers to the right (3) are the ones. Answer: $63$.
The why. $n \times 9 = n \times (10 - 1) = 10n - n$. For $n = 7$: $70 - 7 = 63$. The finger fold is a physical version of this subtraction.
Try it. $8 \times 9$. $4 \times 9$. $6 \times 9$.
Trick 5 — Multiply by 25
The trick. Multiplying by 25 is "multiply by 100, then divide by 4." $36 \times 25 = 3600 / 4 = 900$.
The why. $25 = 100/4$.
Try it. $48 \times 25$. $20 \times 25$. $13 \times 25$.
Squaring Tricks (6–9)
Trick 6 — Squaring Numbers Ending in 5
The trick. For any number $n5$, $(n5)^2 = n \times (n+1) \cdot 100 + 25$.
Examples. $35^2 = 3 \times 4 \cdot 100 + 25 = 1225$. $65^2 = 6 \times 7 \cdot 100 + 25 = 4225$. $85^2 = 8 \times 9 \cdot 100 + 25 = 7225$.
The why. $(10n + 5)^2 = 100n^2 + 100n + 25 = 100 n(n+1) + 25$.
Try it. $45^2$, $75^2$, $95^2$, $105^2$.
Trick 7 — Squaring Numbers Near 100
The trick. For a number near 100, say $97$: $(97)^2 = (97 - 3) \cdot 100 + 3^2 = 9400 + 9 = 9409$. For $103$: $(103)^2 = (103 + 3) \cdot 100 + 3^2 = 10600 + 9 = 10609$.
The why. $(100 - a)^2 = 10000 - 200a + a^2 = 100 \cdot (100 - 2a) + a^2$.
Try it. $96^2$. $104^2$. $98^2$.
Trick 8 — Square Then Use Difference of Squares
The trick. $97 \times 103 = ?$ Notice $97 = 100 - 3$ and $103 = 100 + 3$. So $97 \times 103 = (100-3)(100+3) = 100^2 - 9 = 9991$.
The why. $(a-b)(a+b) = a^2 - b^2$. This is one of the most useful algebraic identities your child will learn.
Try it. $48 \times 52$. $95 \times 105$. $19 \times 21$.
Trick 9 — Squaring with Nearby Round Number
The trick. $47^2 = ?$ Round to 50. $50^2 = 2500$. The difference is 3, so subtract $2 \times 50 \times 3 - 3^2 = 300 - 9 = 291$. Answer: $2500 - 291 = 2209$.
The why. $(a - b)^2 = a^2 - 2ab + b^2$.
Try it. $48^2$. $52^2$. $39^2$.
Percentage Tricks (10–12)
Trick 10 — 10% and 1% Anchors
The trick. Find 10% of any number by moving the decimal one place left. Find 1% by moving it two places. Then add up.
Example. 15% of 80? 10% is 8, 5% is 4 (half of 10%), total 12.
The why. Percent means "per hundred." Moving the decimal divides by 100; 10% is dividing by 10.
Try it. 15% of 60. 25% of 80. 35% of 200.
Trick 11 — Reverse the Percentage
The trick. What is 8% of 25? Hard to do directly. Reverse it: 25% of 8. That is $8/4 = 2$. Same answer.
The why. Percent multiplication is commutative: $a% \times b = (a/100) \times b = (b/100) \times a = b% \times a$.
Try it. 4% of 75. 12% of 50. 18% of 50.
Trick 12 — Percent Increase / Decrease
The trick. A 20% increase on $80 is $80 + 16 = 96$. Or: $80 \times 1.20 = 96$. The second method scales for any percentage.
The why. A 20% increase means new value = 120% of old value = old × 1.20.
Try it. 15% increase on $200. 30% decrease on $50. 12% tip on $45.
Other Tricks (13–15)
Trick 13 — Divide by 5
The trick. Dividing by 5 is "multiply by 2, then divide by 10." $235 / 5 = 235 \times 2 / 10 = 470 / 10 = 47$.
The why. $5 = 10/2$, so dividing by 5 is multiplying by 2/10.
Try it. $145 / 5$. $320 / 5$. $87 / 5$.
Trick 14 — Add a Long Column with Cumulative Estimation
The trick. Adding 87 + 53 + 41 + 67? Round each to the nearest 10: 90 + 50 + 40 + 70 = 250. Then adjust: $-3 + 3 + 1 - 3 = -2$. Final: $250 - 2 = 248$.
The why. Sums distribute. $(a + r_a) + (b + r_b) + ... = (a + b + ...) + (r_a + r_b + ...)$.
Try it. $43 + 78 + 56 + 62$. $91 + 29 + 47 + 33$.
Trick 15 — The Casting-Out-Nines Check
The trick. To check $235 \times 47 = 11045$: add the digits of each number, reducing to a single digit. $235 \to 2+3+5 = 10 \to 1$. $47 \to 4+7 = 11 \to 2$. $1 \times 2 = 2$. Now check the answer: $11045 \to 1+1+0+4+5 = 11 \to 2$. Match. Likely correct.
The why. Casting out nines works because $10 \equiv 1 \pmod 9$, so the sum of digits equals the number mod 9.
Try it. Use casting-out-nines to check $128 \times 37$.
Where Most Parents Try the Wrong Order
The instinct is to start with the coolest trick — usually the multiplying-near-100 shortcut or the squaring-numbers-ending-in-5 pattern. Demo the trick, watch the child's eyes widen, repeat.
The trick lands as stage magic. Without understanding the why, the child cannot apply it to a number 27 instead of 97. They have memorised one specific pattern that does not transfer.
The right order is to start with the easiest trick (Multiply by 11), explain the why immediately, let the child try a few, then move to the next. By the time you reach the harder tricks (multiplying near 100, squaring ending in 5), the child has the habit of asking why does this work? — which is the habit that turns tricks into algebra.
Where Speed Tricks Go Sideways
Four traps:
Memorising without understanding. A child who memorises ten tricks without learning the algebra has a juggler's repertoire. Cute, but it does not transfer.
Using tricks where the standard method is faster. $23 \times 17$ is faster by the standard algorithm than by trying to force a "near 20" pattern. Speed tricks are for specific number shapes — not all arithmetic.
Treating tricks as a substitute for fluency. A child who relies on the 9s finger trick at age 12 has not built times-table fluency. The trick should be a stepping stone, not a permanent crutch.
Showing off. A child who has learned ten speed tricks may answer questions in school by saying "I knew that already" instead of doing the work. The trick was useful; the habit it created is not.
A pattern observed in Bhanzu's Grade 6 cohort: students who learn each trick alongside its algebraic identity transfer the learning to algebra class six months later. Students who learn the tricks by rote alone do not — the tricks remain isolated arithmetic skills.
When to Bring in Outside Help
Speed math tricks are not a tutoring need by themselves. A child who is conceptually solid will pick them up from a YouTube video or a book in a few weeks.
If your child is struggling with school math conceptually, speed tricks are not the right intervention — conceptual help is. A tutor or program is worth the call when the gap is conceptual, not when the gap is speed.
How Bhanzu Approaches This
At Bhanzu, speed math tricks are introduced from Grade 5 onwards as a finishing layer on top of conceptual fluency. Every trick is taught with its algebraic identity. A student who learns Trick 8 ($97 \times 103$) also learns $(a-b)(a+b) = a^2 - b^2$ — the same identity that powers difference-of-squares factoring in Grade 8 algebra.
Trainers do not introduce speed tricks before the conceptual foundation is in place. A Level 0 diagnostic catches whether a student is ready; if they are not, the foundation comes first.
Fit signal. Bhanzu fits families who want speed tricks built into a conceptual framework, not standalone shortcuts. It does not fit parents looking for a 4-week "make my child a calculator" program — those exist and produce different results.
Book a free demo class — the trainer assesses your child's conceptual fluency before introducing speed tricks. Live online globally, or in person at our McKinney, TX center.
Key Takeaways
Speed math tricks work best when paired with the algebra that powers them — not memorised by rote.
15 tricks across multiplication, squaring, percentages, and other categories cover most useful shortcuts.
One trick a week, with its why, is the right pace for a Grade 5 or 6 student.
Tricks are a finishing layer on top of conceptual fluency, not a substitute for it.
The most useful "trick" is estimation — the habit of checking whether an answer is reasonable.
Try It This Week
Pick one trick — Trick 1 (multiply by 11) is the easiest. Demonstrate it three times at the kitchen table. Then ask your child why it works. If they engage with the why, move to Trick 6 (squaring ending in 5) next week. If they only want the answer, hold off — the conceptual readiness is not there yet, and the trick will not transfer.
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