Lessons · Shapes and patterns
Patterns in bark and stone
Make a pattern from what is on the ground, then get somebody else to finish it.
When
Any month of the year
Outside
About 35 minutes
What it teaches
Repeating units — AB, ABB, ABC — which is where algebra quietly begins.
What is going on
A repeating pattern is a rule, and a rule is a thing that can be stated apart from the objects that obey it — stone, cone, stone, cone is the same rule as red, blue, red, blue and as A, B, A, B. That leap, from the things to the rule, is the leap into algebra, and it happens at four with pine cones rather than at fourteen with letters. Bark has patterns of its own worth stealing for the lesson: furrows run vertically because the trunk splits as it thickens, and the pattern a species makes is consistent enough to identify it in winter with no leaves at all.
What to look for
- Bark furrows: ash is a neat diamond net, oak is deep ridges, beech stays smooth its whole life
- Patterns that repeat and patterns that grow — a fern frond does both at once
- Whether a pattern can be read backwards and still be the same pattern
- The patterns nobody made: ripples in sand, cracks in dried mud, frost on a window
First, outside
What to do
What to take
- Whatever is underfoot: stones, cones, leaves, sticks
- A flat bit of path
- 1
Collect several of each of three things. Ten stones, ten cones, ten leaves.
- 2
Lay out stone, cone, stone, cone, stone — and stop. Ask what comes next.
- 3
Now a harder one: stone, cone, cone, stone, cone, cone. Then one with three things in the unit.
- 4
Let each of them build a pattern for the others to continue. The two-year-old's will not be a pattern; continue it anyway and see what happens.
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
- “Stone. Cone. Stone. Cone. Say it with me.”
- “Which one comes next? Put it there.”
- “Same, same, different. Point at the different one.”
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
- “Read the pattern out loud from the start. It helps — you can hear a pattern before you can see it.”
- “Stone, cone, cone. Stone, cone, cone. What comes next?”
- “Make one for me to finish. Don't tell me the rule.”
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
- “Call them A and B. A, B, B, A, B, B — say the letters instead of the things.”
- “If the pattern is three long and you lay out twenty, what is the twentieth one?”
- “Make a pattern that grows instead of repeating: one stone, two stones, three stones.”
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
Lays out a row with no rule and calls it a pattern. Continue it anyway, inventing a rule that fits, and see whether they object. Sometimes they do, and that is the day they got it.
About 4
Can continue a pattern but cannot make one. Making is much harder — it needs holding the rule while placing the objects. Start them with a rule you say out loud for them.
About 6
Reads a four-long unit as a three-long one and gets stuck. Have them say the unit aloud and clap on the first item; hearing it is what finds the length.
How you know it landed
They build one and refuse to tell you the rule, waiting for you to work it out. That is the game the lesson is trying to start.
Rungs of the ladder this builds
Then, five minutes on screen
The same idea, drilled
Continuing a unit of two, three or four — the same puzzle, laid out for them instead of by them.
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.
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.
More shapes and patterns
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