A number pyramid (sometimes called a number wall or number tower) is a stack of numbers. Each brick is the sum of the two bricks directly below it. It gives children a compact way to practise addition, and a missing brick can invite subtraction or another way of reasoning backwards.
The rule stays the same at every level. A three-brick bottom row produces two bricks above it, then one at the top. The shape makes the relationship visible: a brick never comes from a number elsewhere in the pyramid. In a larger wall, children repeat the same local rule for each neighbouring pair.
Start at the bottom
Suppose the bottom row is 2, 3, 4. Add neighbouring pairs to make the middle row: 2 + 3 = 5 and 3 + 4 = 7. Then add those two middle bricks: 5 + 7 = 12. The finished pyramid has 12 at the top.
Writing one addition fact at a time helps a learner see why each answer belongs where it does. The two middle sums both use the centre bottom brick; it is not counted just once.
Try a second complete example. With 1, 2, 4 on the bottom, the middle row is 3, 6, because 1 + 2 = 3 and 2 + 4 = 6. The top is 3 + 6 = 9. Change the base to 2, 1, 5 and the middle row is again 3, 6, so the top is again 9. Different bottom rows can lead to the same top; the full pyramid, not the top alone, tells the complete story.
What if a bottom brick is missing?
Consider a pyramid with 15 at the top and 3, □, 4 along the bottom. Call the missing number x. The middle bricks must be 3 + x and x + 4. Together they make the top:
(3 + x) + (x + 4) = 15
The known bottom numbers add to 7, leaving 8 for the two copies of x. So x = 4. Check by filling the whole pyramid: middle row 7, 8, and 7 + 8 = 15.
That check matters: when a lower brick is unknown, “always work bottom to top” is not enough. You may need to reason back from the top and then rebuild the pyramid to verify it.
For a missing middle brick, subtraction is often simpler. If the top is 12 and one middle brick is 7, the other must be 5, since 12 − 7 = 5. Then check whether the two bottom bricks below it really add to 5. For a missing outer bottom brick, use the known middle brick directly above its pair. For the shared centre bottom brick, use both middle bricks when known—or, as in the example above, notice that it contributes to the top twice.
Try one together
Place 4, 2, 5 on the bottom. The middle row is 6, 7 and the top is 13. Now cover the middle-left brick. A learner can recover it from 13 − 7 = 6, then confirm 4 + 2 = 6.
Why this exercise helps
Number walls connect addition and subtraction rather than treating them as separate drills. Children practise small facts, hold a short sequence of results in mind and explain how one brick depends on another. A missing value also encourages a useful habit: test a proposed answer against the whole structure, not only one equation.
It is normal for a learner to place a correct sum in the wrong brick or forget that the centre bottom brick participates in two sums. Point to the two bricks immediately beneath the target and trace each pair with a finger. If numbers are too large, begin with a smaller range and write the two addition statements beside the drawing. If the top is known but a lower value is missing, allow working backwards; that is part of the mathematics, not a shortcut.
Tips for parents and teachers
Begin with three visible bottom numbers and ask the child to explain why each middle brick has its value. Next cover one middle brick, then one outer bottom brick, and finally the shared centre bottom brick. Ask the child to say what is known, what is missing and how they will check the result. A drawing on squared paper is enough; no special materials or account are required.
For more examples, use number pyramid practice or a printable number pyramid worksheet. Start with visible bottom numbers; introduce missing bricks once the addition rule is secure.