Learn
Patterns and shapes
Living things do not grow to random numbers. Count the petals on twenty flowers and the same few numbers keep turning up; count the spirals on a pine cone and you get eight one way and thirteen the other, on cone after cone. A four-year-old can find this out in an afternoon, and a six-year-old can start to ask why — which is a better question than most of the ones in a maths book.
Look and count. Nothing goes in a mouth.
Counting
The petal numbers
Get down to the flower rather than picking it, and touch each petal once as you count. Write the number down. Ten flowers is enough for the pattern to show itself.
| Petals | What has them | Where to look |
|---|---|---|
| 3 | Trillium, iris, most liliesDamp woodland in spring; garden beds. What looks like six on a lily is two rings of three. | Damp woodland in spring; garden beds. What looks like six on a lily is two rings of three. |
| 4 | Every mustard — and there are hundredsRoadsides and gardens all summer. Four petals in a cross is what gives the family its old name. | Roadsides and gardens all summer. Four petals in a cross is what gives the family its old name. |
| 5 | Buttercup, wild rose, geranium, apple and cherry blossom, columbineEverywhere, all season. By a long way the commonest number to find. | Everywhere, all season. By a long way the commonest number to find. |
| 6 | Snowdrop, many onions and garlicsEarly spring. Often really three and three again, so look for the two rings. | Early spring. Often really three and three again, so look for the two rings. |
| 8 | Cosmos, some larkspurs, bloodrootLate summer borders; bloodroot in rich spring woodland. | Late summer borders; bloodroot in rich spring woodland. |
| 13, 21, 34 | Daisies, asters, black-eyed SusanLate summer fields. These are not petals but ray florets, and the count varies head to head — which is the honest, interesting part. | Late summer fields. These are not petals but ray florets, and the count varies head to head — which is the honest, interesting part. |
Say this out loud to the six-year-old
Three, five, eight, thirteen, twenty-one — each one is the two before it added together. That sequence is real and it turns up all over the place. But four is just as common as five in a hedgerow, and four is not in the sequence at all. So it is a strong habit rather than a law, and the flowers that break it are worth collecting on purpose. A pattern you can find exceptions to is a better thing to own than one you have been told is always true.
Spirals
Things to go and count
Spirals are where the pattern is strongest, and the reason is something a child can act out: a plant putting out each new leaf about a hundred and thirty-seven degrees round from the last one never lands a leaf directly above an older one, so none of them sits in another’s shade. Stand in the garden and turn that far each time you put down a stone. The stones never line up.
A pine cone, looked at from the flat end
8 one way, 13 the other
Follow one spiral with a finger and count how many it takes to get round. Then follow the other way. Small cones often go 5 and 8.
A pineapple, from the shop
8, 13 and 21
Three sets of spirals at three angles. Easiest of the lot, and it comes with lunch.
A sunflower head, seeds and all
34 and 55, or 55 and 89
Too many to count without a pen. Mark the starting seed, draw the spiral on a photograph.
A fern fiddlehead in spring
One spiral, unrolling
Come back to the same one each day for a week and see how far it has opened.
A snail shell
About three turns
Each turn is wider than the last by roughly the same amount, which is what makes it a spiral rather than a coil.
The way a twig splits
Usually into 2
Follow one branch from the trunk to a leaf, counting the forks. Then another. Are they the same?
Symmetry
Folding things in half
One fold
A leaf, a feather, a butterfly, your own face. Fold a leaf down the midrib and the two edges very nearly meet — nearly, because a real leaf is never exact, and spotting the gap is the sharper skill. Elm leaves are lopsided at the base on purpose and are the best ones to hand a four-year-old who thinks the answer is always yes.
Many folds
A buttercup folds five ways. A starfish folds five ways. A snowflake folds six. Cut a paper circle, fold it in half three times and snip the edge — open it out and count the repeats. That is the same arithmetic as the flower, done with scissors.
No folds at all
A snail shell does not fold onto itself any way at all, and neither does a spiral. Ask which pile a pine cone goes in — it is a genuinely hard question, and there is no wrong answer at six.
Pick the matching half. The youngest gets the pattern game instead, which is the same idea one rung down.
Repeats
Make one, then finish one
Stone, cone, stone, cone. Then stone, cone, cone. Then three things instead of two. Laying out a repeat and asking somebody else to continue it is the whole of early algebra, done with what is on the path. The full lesson is here.
What comes next — two things, then three, then four.