puzzMedium printable number pyramid worksheets
The medium pack is where the pyramid earns its place on the maths shelf. Each puzzle is built so that adding pairs upwards will get the child part-way and then stop dead. The clues are placed to guarantee it: somewhere in the pyramid there is a brick that can only be found by taking a known total and subtracting the one child brick that is already filled in.
This is a good deal more valuable than it sounds. Most children meet subtraction as a separate operation with its own worksheets. Here they meet it as the way back out of addition, in a context where the relationship is visible on the page — the 12 is sitting directly above the 5, and the gap next to it has to be 7. Children who work through this pack tend to stop treating "take away" and "add" as unrelated procedures.
What is in this pack
| Shape | fifteen bricks, five along the base | |
|---|---|---|
| Numbers | positive whole numbers, apex typically in the thirties | |
| Solving level | subtraction required — verified that addition alone stalls | |
| Best for | inverse-operation work, Year 3-5 / US grades 2-4 | |
- Four A4 pagesThree puzzles, then a full answer key. Print the first three only if you would rather keep the answers.
- One verified solution eachEvery puzzle is passed through a solver and discarded unless exactly one answer fits.
- No sign-up, no watermarkA direct PDF download. No email address, no account, nothing to dismiss.
- Free to photocopyUse them at home, in a classroom, at a childminder or in a holiday club.
Teaching tip. When a child announces they are stuck, do not point at the brick. Ask "is there a brick where you know the top and one of the two underneath?" — that question is the entire technique, and it works on every stall in this pack.
How to solve a number pyramid
Five bricks along the bottom, narrowing to one at the top. Everything follows from a single relationship.
- Learn the one ruleEvery brick equals the two bricks immediately below it added together. That single rule works everywhere in the pyramid, in both directions, and there are no other rules to remember.
- Fill in every pair you can addScan the pyramid for any place where two side-by-side bricks are both filled and the brick above them is empty. Add them, write the total above, and repeat. Do this until no more pairs are available — on an easy pyramid this alone finishes the puzzle.
- Turn it round and subtractNow look for a filled brick whose two children include exactly one filled brick. The missing one is the brick above minus the one you know. If the top is 12 and one brick below is 5, the other must be 7. Say it out loud as a subtraction the first few times.
- Alternate until it closesKeep swapping between adding upwards and subtracting downwards. Each new brick unlocks fresh pairs in both directions, so the pyramid tends to finish in a rush once the first few stubborn bricks fall.
- Check the topWhen every brick is filled, re-add the whole pyramid from the bottom row up. If you arrive at the same number at the apex, the pyramid is right — a wrong brick almost always shows up as a mismatch at the top.
Who this pack suits
Built so addition stalls. The child must work at least one brick out by subtracting.
How the number pyramid packs compare
| Number Pyramid pack | Ages | What it asks of them |
|---|---|---|
| Easy | 6-8 | Small numbers, apex usually under 40. Finishes with addition alone — no subtraction needed. |
| Medium | 7-10 | Built so addition stalls. The child must work at least one brick out by subtracting. |
| Tricky | 9-12 | Bigger numbers and sparser clues; needs several subtraction steps and some planning. |
Questions about this pack
Why can my child not finish this by adding?
Because the puzzle is designed that way. The clues are placed so an addition-only solver provably stalls. The missing step is downwards: find a filled brick with exactly one filled brick beneath it, and subtract to get the other one.
Is this the same as a number wall?
Yes. Number pyramid, addition pyramid, maths pyramid and number wall all describe the same puzzle — each brick is the sum of the two below it. Different schemes of work happen to use different names.
What maths does this practise?
Mental addition and subtraction, and specifically the inverse relationship between them. Because the pyramid makes that relationship spatial, children tend to grasp it here faster than from a page of "fill in the missing number" sums.
Is there always exactly one answer?
Yes. Each pyramid is solved and solution-counted before it is printed, and is discarded unless exactly one set of numbers fits the clues.
More free worksheets
Other number pyramid packs
Other kinds of puzzle
See all 17 free worksheet packs.
Hundreds more of these in the app
Puzzeroo is an iPhone and iPad app with two hundred number pyramid levels alongside three other puzzle types — eight hundred in total, all generated by the same verified engines that made this worksheet, all working fully offline with no adverts and no accounts. The worksheets and the app draw from completely separate puzzle ranges, so printing these gives nothing away.