Lessons · Time and the sky
The shadow clock
Put a stick in the ground and mark its shadow every hour. By evening there is a clock on the lawn that nobody wound.
When
Any month of the year
Outside
About 30 minutes
What it teaches
Measuring the same thing repeatedly, comparing lengths, and reading a sequence of numbers as a shape.
What is going on
The shadow is shortest when the sun is highest, and the sun is highest at solar noon — which is almost never twelve o'clock. Your clock is set to a time zone that can be half an hour of longitude wide, daylight saving moves it another hour, and the earth's own orbit runs a little fast in one part of the year and slow in another. So a shadow clock and a wristwatch disagree by up to three quarters of an hour, and the shadow is the one telling the truth about the sun. That gap is the most teachable thing in the sky: it is the difference between a natural fact and a human agreement, standing on your lawn where a child can see both.
What to look for
- Where the shortest shadow points. In the northern hemisphere it is very nearly due north, and a compass will agree with it to within a few degrees
- How much faster the shadow moves in the first and last hour than around the middle of the day
- Whether the stones curve. In summer they bow one way, in midwinter the other, and at the equinoxes they fall almost in a straight line
- The shadow of something with a hole in it — a colander, a tree in leaf. Every spot of light is a little image of the sun
First, outside
What to do
What to take
- A straight stick, about knee-high
- Stones or pegs to mark with
- A tape measure or a piece of string
- 1
Push the stick into open ground first thing in the morning. Somewhere the sun reaches all day.
- 2
Every hour, put a stone at the tip of the shadow. Say the time out loud each time.
- 3
Measure the shadow at each visit, in whatever unit you like — footsteps work, and so does the four-year-old's arm.
- 4
At the end of the day, stand back and look at the curve of stones. Ask which stone is closest to the stick, and why.
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
- “Stand in the shadow. Now jump out of it. In, out.”
- “Put the stone here, right at the end. Good. One stone.”
- “Is the shadow long or short? Say long.”
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
- “How many of your steps is the shadow? Heel to toe, no gaps.”
- “It was twelve steps this morning and it is five now. Is it getting longer or shorter?”
- “Where do you think it will be after lunch? Put a stick where you guess, and we'll check.”
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 the time and the length each hour. Seven numbers by teatime.”
- “Which hour had the shortest shadow? That is when the sun was highest — near enough to noon, though not exactly, and that is worth arguing about.”
- “Do it again in a month. Same stick, same spot. Is the shortest shadow longer or shorter than it was?”
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
Stands on the stones and moves them. Give them their own stick and their own stone somewhere harmless.
About 4
Measures in footsteps with gaps between them, or with one big step and three small ones. The unit has to be the same every time, which is the whole idea of a unit, and it is worth saying out loud.
About 6
Predicts the next stone in a straight line from the last two. Let them be wrong; the curve is the interesting part, and being wrong about it once is how it gets noticed.
How you know it landed
They ask what the shadow does in winter. That is the question the lesson is for, and the only honest answer is to leave the stick in and find out.
Rungs of the ladder this builds
Then, five minutes on screen
The same idea, drilled
Which group is bigger, and by how much — the comparison the shadow measurements are made of.
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
The shortest shadow points due north in the northern hemisphere. Check it against a compass and see how close the lawn got.
The same day, on a slider
Your own shadow, hour by hour
Worked out from the sun's real position at your coordinates, so the shadow points where your shadow points and is as long as your shadow is. Use it to check the stones on the lawn, or to see ahead to where the next one goes.
The shadow clock
This draws your own shadow, at your own latitude, hour by hour — so it needs to know where you are. Set a location anywhere on the site and come back.
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 time and the sky
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