Lessons · Counting
Getting to a hundred
Sunflower seeds, dried beans or maple keys, and the discovery that a hundred is not very many once it is in tens.
When
August to November
Outside
About 35 minutes
What it teaches
Counting past the fingers, and ten tens as a thing you can see.
What is going on
Ten is not special and everyone knows why we use it: we have ten fingers. What is special is the idea that a group can stand in for its contents — that once ten seeds are in a hollow you never have to look at them again and the hollow itself becomes one thing worth counting. That substitution is the whole of place value, and every child meets it as a shock rather than as a definition. It is also worth knowing that nobody, adult or child, can see more than about four things at once without counting. Past four, everyone is either counting or grouping, and grouping is faster.
What to look for
- How high they can guess accurately before it becomes a wild number. Four is typical; six is exceptional
- Whether a hundred of something big fills the jar to the same mark as a hundred of something small
- What a hundred looks like spread out against a hundred in a heap
- A seed head — a sunflower, a poppy, a dock — and how many seeds one plant is prepared to lose
First, outside
What to do
What to take
- A hundred small seeds or beans
- An ice cube tray or an egg carton
- A jar
- 1
Put ten seeds in each hollow of an egg carton. A dozen hollows: stop at ten and ask what the two spare ones are for.
- 2
Count the tens out loud, pointing: ten, twenty, thirty.
- 3
Tip the hundred into a jar and mark the level with a pen. Ask how big two hundred would look.
- 4
Next day, fill the jar to the mark with something else — acorns, pebbles, pasta — and count that. Is it a hundred too?
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
- “One seed in the hole. One. Another one — two.”
- “Full. This one's full and this one's empty.”
- “Pour them. Listen to the sound.”
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
- “Ten in each hole. Count as you drop them in.”
- “Ten, twenty, thirty — keep going. What comes after ninety?”
- “How many holes did we fill? How many seeds is that?”
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
- “Ten tens is a hundred. So how many is five tens? Fifteen tens?”
- “If half the jar is a hundred, how many seeds does the whole jar hold?”
- “Count out a hundred of something much bigger. Does it reach the same mark?”
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
Wants to pour rather than place. Pouring is a lesson too — give them a second container and let them.
About 4
Puts eleven in a hollow and does not notice. Ten has to be checkable at a glance, which is what an egg carton or an ice tray gives you and a loose pile does not.
About 6
Counts the full hollows one by one. Slow them down and count in tens out loud together; the speed difference is the argument.
How you know it landed
Faced with a big pile of something new, they start making tens without being told.
Rungs of the ladder this builds
Then, five minutes on screen
The same idea, drilled
Grouped counting on screen, in the same fives and tens the carton makes.
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 counting
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