OuiSi · Math

Patterns and rules

Beta

Grades 3–5 Teaching 35 min Plus 3 to set out, 3 to clear Class any size Set any Prep paper for the rules

set out 3′ Find something that repeats 8′ Write the rule 10′ Find the break 12′ Close 5′ clear 3′

Goal: Children find a pattern, write the rule it follows, then test that rule against the rest of the photograph — because a rule is only worth having once you know where it stops working.
Materials: One OuiSi Photo-Card set, about eight cards per pair. Paper and pencils.

Grade 3: Repeating patterns, and where they stop — about 23 min
Grade 4: Write the rule as a sentence, then test it on a second card — the full 35 min
Grade 5: Symmetry and angle, and what rule would repair a broken pattern — the full 35 min

1 · Find something that repeats

8 min

Pairs, about eight cards face up.

Find a pattern. Something that repeats — in a line, around a curve, or across the whole card.

Then push past the obvious ones.

Now find one that repeats but is not made of objects. A pattern in the light, or in the spaces.

Ridges, ripples, shadow bands, the rhythm of gaps. Patterns made of absence are harder to see and better to find.

2 · Write the rule

10 min

Write the rule your pattern follows, as a sentence somebody else could use.

Dark, light, dark, light is a rule. It gets bigger each time is a rule. Writing it is what turns noticing into describing, and vague rules get exposed in the next step.

Pairs swap cards and rules.

Use their rule on their card. Does it actually work the whole way across?

3 · Find the break

12 min

Now hunt for a break. Find a place where your pattern stops obeying your rule.

Photographs are of real things, and real things are mostly irregular, so a break is usually there — look at the very edge of the card first. If a pair genuinely cannot find one, that is a real finding and not a failure: ask them what would have to appear in the picture for their rule to break, which is the same thinking from the other end.

Then the question that makes it mathematics.

What rule would include the break? Rewrite it so the whole card obeys.

Is your new rule better, or just longer?

That last question is genuinely hard and worth sitting in. A rule with an exception bolted on is weaker than a simpler rule that fits less.

4 · Close

5 min

Read us a rule that held all the way across. Then one that broke.

Watch for

Rules too vague to test. It has a pattern is not a rule. The swap in step two catches these, which is why the swap exists.
Refusing to find a break. Some pairs defend their pattern. Ask them to look at the very edge of the card, where regularity almost always fails.
Bolting on exceptions. Except that bit over there is not a rule. Push for a genuine rewrite or an honest admission that the rule fits less than they thought.
Symmetry treated as pattern. Related but not the same. For grade 5 it is worth separating — one repeats, the other mirrors.

Adapt

Grade 3 — stop after step two. Finding and stating a rule is a complete lesson.
Grade 5 — add symmetry: find a line you could fold along, then find where the fold fails.
Want it harder — ask for the simplest rule that covers the most of the card, and defend why simpler is better.
Dyslexia and emerging writers — rules can be dictated to a partner or drawn as a sequence.
Multilingual learners — rules can be written as a repeating sketch rather than a sentence.
Science tie-in — the same move as finding a pattern in data and then finding the outlier.

Curriculum links. Identifying a repeating pattern, including one made of gaps · Stating a rule precisely enough for somebody else to apply · Testing a rule across a whole example · Finding where a rule breaks, and revising it · Weighing simplicity against coverage.
Standard codes vary by state and district — these are the skills exercised, for you to map to your own.

For grades K–2 see Shapes everywhere, which names shapes and hunts them in the room.
Screen-free. No codes and no devices. Works with any OuiSi Photo-Card set.