QMAK Vedic Mathematics
Unit 1 · Patterns, Pairs & Powers
Numbers have personalities, secret partnerships, and hidden powers. In this unit you'll meet numbers in a whole new way — not as things to memorise, but as patterns to recognise and play with.
Lesson 1 of 5
Every number has a personality. Let's meet them.
Grade 3 · CoreBefore you write a number, picture it as a shape made of dots. Can you arrange it into neat pairs — or is there always one left over?
That's the whole secret. Evens pair up perfectly. Odds always have one lone dot sticking out.
Yellow = Odd · Navy = Even · Odd numbers always have a "lonely" dot with no partner
Here's something interesting. Mix odds and evens and you get predictable results every time:
The number 1 has a special power — it switches any number's identity. Add 1 to an odd and it becomes even. Add 1 to an even and it becomes odd. That's the personality of 1.
The Number Ladder — adding 1 each time zigzags between odd and even. Highlighted in pink: 3 + 4 = 7
Every odd number has a "lonely" extra dot. When two odd numbers join, their two lonely dots partner up — and suddenly everything pairs perfectly. No dot left behind = even!
Without calculating — just use the rules to predict whether the answer is odd or even.
Lesson 2 of 5
Add odd numbers in order. Watch what happens.
Grade 3–4 · CoreStart with 1. Keep adding the next odd number. The answers form a perfect pattern that you can actually see.
1 = 1 · 1+3 = 4 · 1+3+5 = 9 · 1+3+5+7 = 16
Do you see it? Every answer is a perfect square! (1×1, 2×2, 3×3, 4×4...)
Each coloured "L-shape" (called a gnomon) adds the next odd number. Notice how every result is a perfect square!
You don't have to add all the way through. Count how many odd numbers you've added — that's the side of your square. Five odds added? That's 5×5 = 25. Ten odds added? That's 10×10 = 100. Done!
Use pebbles or marbles to build each sum if it helps. Predict the answers to the later ones using the pattern — you shouldn't need to add them up!
Now PREDICT — don't add, just use the pattern:
🤔 Your conclusion: What shape do all the answers make? What does adding the first n odd numbers always give you?
Lesson 3 of 5
The odd number trick goes up a whole dimension.
Grade 4 · ExtensionIn Lesson 2, adding groups of consecutive odd numbers gave you perfect squares (2D). Now we go 3D — and the same odd numbers produce perfect cubes.
The trick is that you group the odd numbers in a specific way:
Odd numbers split into groups produce perfect cubes. Each group is one number bigger than the last.
Each cube needs one more odd number than the previous. 1³ uses 1 odd. 2³ uses 2 odds. 3³ uses 3 odds. And you always pick up right where the last group finished!
Add each group of odd numbers, then write the cube it makes.
Lesson 4 of 5
Every number has partners that complete it.
Grade 3 · CoreA complement is a partner that makes a number complete. For the number 7, its complements are all the pairs that add up to exactly 7:
0+7 · 1+6 · 2+5 · 3+4 · 4+3 · 5+2 · 6+1 · 7+0
The most important complements to memorise are pairs for 9 and 10. These pop up constantly in mental maths.
Every row = 10. Navy + Mint always completes the pair. Each bar is a visual proof!
Use your complement knowledge — don't count on your fingers!
To find a 9-complement, use your hands! Hold up all 10 fingers. Put down the number of fingers matching your digit. The fingers left on that side = the complement. Try it for 9-7: put down 7, see 2 remaining → 2+7=9 ✓
Fill in the missing partner. Work from memory — no counting!
Lesson 5 of 5
Subtract from 1,000 in two seconds. Seriously.
Grade 4 · ExtensionWhat's 1,000 − 784? Most people would write it out and borrow across columns. Instead, try this one-move method:
Subtract each digit from 9, except the very last digit — subtract that one from 10.
All digits from 9 · Last digit from 10
Think of 1,000 as 999 + 1. Subtracting from 999 means each digit subtracts from 9. The remaining "1" takes the last digit up one extra, which is why we use 10 for the final digit. It's the complement relationship built into our Base 10 number system.
The same complement idea appears in clocks. If it's 6:45, you know there are 15 minutes left to 7:00 — because 45 + 15 = 60. Babylonian maths, 5,000 years old, still in use today!
Worked Examples
67 from 100:
9−6 = 3
10−7 = 3
Answer: 33 ✓
888 from 1,000:
9−8 = 1
9−8 = 1
10−8 = 2
Answer: 112 ✓
Apply the rule digit by digit — no pencil borrowing needed. Show your working next to each answer.
This technique works for multiplication too. If you know your complements of 9 and 10, you can multiply large numbers close to 1,000 mentally. Here's a peek at what's coming in future units:
8,976 × 9,998 = ?
Deficiency of 8,976 from 10,000: 9−8/9−9/9−7/10−6 = 1,024
Deficiency of 9,998 from 10,000: 0,002
Cross-subtract & multiply deficiencies: (8976−2) / (1024×2)
= 89,742,048
This single technique solves multiplications that most adults would need a calculator for. It all starts with knowing your pairs for 9 and 10 cold.
Unit 1 Complete 🎉
QMAK Vedic Mathematics · Unit 1 of ?
Grade 3–4 · The Number Universe
Next unit coming soon.