Lessons · Measuring
Sort the stones
Heavy, light, rough, smooth, and then the harder question: can something be both?
When
Any month of the year
Outside
About 40 minutes
What it teaches
Sorting by one attribute, then by two at once, which is a grid before it is called one.
What is going on
A rounded stone has travelled. Rock breaks off angular and gets its corners knocked off by being rolled, so roundness is a record of distance in water or ice — and a smooth stone in a field a hundred kilometres from any river was almost certainly carried there by a glacier and dropped when the ice melted. Weight is the other half: two stones the same size can differ by half again in weight, because what they are made of differs. Sorting by two things at once is the step where sorting becomes a grid, and a grid is a table, and a table is how every piece of data a person will ever handle is arranged.
What to look for
- Round against angular, and where each kind is lying
- Stones with layers you can see — those were laid down as sediment, in water, and the layers are time
- A stone with a different stone inside it. Conglomerate is a stone made of older stones
- Whether it is the same rock as the bedrock nearby, or a stranger that arrived from somewhere else
First, outside
What to do
What to take
- A dozen stones, collected together
- A tray or a patch of flat ground
- Kitchen scales, indoors, for afterwards
- 1
Collect a dozen stones from one place — a beach, a stream bed, a driveway.
- 2
Sort them into two piles. Do not say how. Let each child sort them their own way, then guess each other's rule.
- 3
Now sort by weight, by hand, into heaviest to lightest. Then check on the scales and see who was wrong.
- 4
Last: two piles by size, and within each pile two piles by roughness. Four piles from two questions.
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
- “Heavy! Ooh, heavy. Now this one — light.”
- “Put the rough ones here. Rub it. Rough, or smooth?”
- “Two piles. This pile, that pile.”
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
- “Which is heavier, this one or this one? Hold one in each hand.”
- “Put them in a line, heaviest at that end, lightest at this end.”
- “How many are in the heavy pile? How many in the light one? Which has more?”
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
- “Weigh them. Write the number on a sticky note beside each one.”
- “How much heavier is the biggest than the smallest?”
- “Big and rough, big and smooth, small and rough, small and smooth. Does every stone fit one of the four?”
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
Sorts by a rule that changes halfway through. Ask them what the rule is rather than correcting it — sometimes it is a real rule and a surprising one.
About 4
Cannot order more than three by weight. Expected. Do it as a series of pairs — heavier than this one? — and the line builds itself.
About 6
Assumes bigger is heavier and stops testing. Hand them a big pumice or a light sandstone against a small dense one, and let the scales settle it.
How you know it landed
They pick up a stone on a walk and say where they think it came from. Wrong is fine; the question is the achievement.
Rungs of the ladder this builds
Then, five minutes on screen
The same idea, drilled
Which group has more, and by how many — sorting reduced to its comparison.
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
Where did the stones come from? The rock page for your area says what is under you, and rounded stones have usually travelled.
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 measuring
All the lessons →