Lessons · Shapes and patterns
Count the petals
Flowers do not have random numbers of petals. Three, five, eight and thirteen come up again and again, and a six-year-old can find that out in an afternoon.
When
April to September
Outside
About 40 minutes
What it teaches
Counting small sets accurately, then noticing that a set of counts has a pattern in it.
What is going on
A growing tip puts out each new part about 137.5 degrees round from the last one. That angle is irrational — no whole number of turns ever brings it back to the start — so nothing ever lands directly above anything older, and nothing shades anything else. The counts that fall out of that packing are the Fibonacci numbers, which is why three, five, eight and thirteen turn up so often in spirals. Petals are a looser case: five is genuinely the commonest number in this half of the plant world, but every mustard has four, and four is not in the sequence at all. Teaching the pattern honestly, exceptions included, is better than teaching a tidier version that a child can disprove in a hedge.
What to look for
- Whether what looks like six is really three and three again — lilies and trilliums nearly always are, and the two rings sit at different heights
- Daisies and asters: what look like petals are whole flowers, and the yellow middle is hundreds more
- Flowers that fold one way only — peas, snapdragons, orchids. They have a left and a right, like a face
- Where the bees land, and whether the markings point them in
First, outside
What to do
What to take
- Paper
- A pencil
- Somewhere with several kinds of flower — a verge is better than a garden
- 1
Find a flower. Count the petals without picking it — get your nose down to it instead.
- 2
Write the number down. Draw the flower badly beside it; the drawing is how they look twice.
- 3
Do ten flowers. Do not choose them to be different — take what is there.
- 4
Now read the list of numbers aloud. Three, five, five, five, eight, five, thirteen… ask what they notice.
Out loud
What to say to each of them
All three at once, off the same bucket of acorns. Read down the column that matches the child in front of you.
2
Point and name
- “Flower! What colour? Point at a petal. Just one petal.”
- “One, two, three. Three petals. Say three.”
- “Smell it. Do not pick it — it stays where it is so the bees can find it.”
Subitising — seeing that a group is two without counting it — and the idea that a number word belongs to a thing you are touching.
4
Count and compare
- “Touch each petal once as you count. Start where the sun is and go all the way round.”
- “Five. Now find another flower with five. Are they the same kind?”
- “Which flower has the most petals of all the ones we've found?”
One-to-one correspondence: one number word per object, the last word you said is how many there were. Then more, fewer, and the same.
6
Tally and figure
- “Write each number down as we go. Ten flowers, ten numbers.”
- “Look at your list. Which numbers keep coming back? Which ones never turn up at all?”
- “Three, five, eight, thirteen. Add three and five — what do you get? Now add five and eight.”
Grouping as a way of counting past what fingers hold, and subtraction as the distance between two numbers rather than a taking-away.
When it is not working
What going wrong looks like
Most of what looks like failing is a child standing at a known place on a known ladder. Knowing which place changes what you do next, and it is usually not more practice.
About 2
Pulls the petals off. Expected. Move to a fallen flower or a dandelion in a lawn where it costs nothing, and keep the pointing finger for the ones still standing.
About 4
Counts round and round and never stops, because there is no edge to a circle. Give them a starting mark — a blade of grass laid across one petal — and the problem disappears.
About 6
Wants the sequence to be a law and is annoyed by the mustards. Sit with the annoyance; it is the correct scientific feeling. Collect the exceptions on purpose and the annoyance turns into a project.
How you know it landed
They come back with a number you did not ask for. A six-year-old who says the buttercups by the gate are all fives has started a survey.
Rungs of the ladder this builds
Then, five minutes on screen
The same idea, drilled
Counting small groups fast, which is what petal-counting on a windy day turns into.
Why this order
The walk first, the game after. Reversed, the walk becomes the price of the game, and a child who has learned that outside is what you do before the screen has learned the wrong thing very efficiently.
If they want more
Those numbers — 1, 1, 2, 3, 5, 8, 13, 21 — each one the sum of the two before it. Count the spirals on a pine cone or a sunflower head and they turn up again.
When you have done it
Ticking it keeps it off the next season plan, and nothing else.
We look, we count and we put it back. Nothing goes in a mouth — not a berry, not a mushroom, not a leaf. That is the whole rule, and it is the same rule every time.
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