Growing and Shrinking Patterns
One jump, repeated
A pattern in Year 2 earns its name by keeping one promise: the same jump, every time. Start anywhere, add the same amount again and again, and a growing pattern appears; subtract the same amount and the pattern shrinks. The rule is nothing more than the start and the jump. And the rule does not care what it wears — crates in a stack, hops on a track, numbers on a scoreboard all carry it equally well. This unit teaches children to recognise that promise, describe it, use it to repair gaps, and make patterns of their own.
See the jump in the stack
Objects come before numerals because a jump you can stack is a jump you believe. In the staircase, every new pile of crates carries the previous pile plus exactly three more, and the three newcomers are picked out in gold so the constant is visible rather than asserted. Ask a child what stays the same from stack to stack and what changes: the start never changes, the jump never changes, only the total grows. That sentence, in any words a seven-year-old chooses, is the whole theory of additive patterns.
Patterns live on the line
On the number track the same idea becomes travel. Each hop covers the same distance, so the landing spots are the pattern — which is exactly the skip-counting children met in Year 1, now seen as a rule rather than a chant. Hopping backwards makes a decreasing pattern, and the track quietly teaches its limit: a shrinking pattern eventually runs out of room, while a growing one would hop forever. Distance, direction, repetition — the line turns arithmetic into something the eye can follow.
The gaps know the answer
A missing element is not a mystery; it is a held position. The gaps on either side of the smudge still speak — read any two neighbours, find the jump, and apply it into the hole. The same trick works in reverse when the first term is missing: step backwards by the jump. Children who repair patterns this way are doing real algebraic reasoning — using a rule to recover information they never saw — years before anyone shows them a letter standing for a number.
Describe it like a scientist
To describe a pattern, name two things: where it starts and how it jumps. Start at 5, add 3. The discipline worth teaching is the checking: a claimed rule must survive every gap, not just the first. One wobble — a gap of 2 hiding among gaps of 3 — and the rule is dead. This habit of testing a claim against all the evidence is small here and enormous later; it is the difference between guessing a pattern and knowing one.
Two choices build everything
Creation is the strongest test of understanding, and an additive pattern asks for only two decisions: pick a start, pick a jump. The machine renders whatever a child chooses, including the awkward cases worth meeting on purpose — a shrinking jump from a small start runs out of room in two terms, which is not a failure but a discovery: decreasing patterns need headroom. Let children hunt for the longest pattern, the steepest staircase, the quickest collapse. Ownership of the rule comes from steering it.
Not everything regular is additive
Recognising a pattern means refusing to be impressed by mere regularity. The sequence 1, 2, 4, 8 grows beautifully, but its gaps widen — it multiplies instead of adding, and so it fails the constant-jump test. Naming why something is not an additive pattern sharpens the idea more than another tidy example would. That doubling sequence is not wasted, though: it returns in this strand soon, when doubling and halving carry the twos facts — the first bridge from addition to multiplication.