Place Value Bead Bank Game
Your child is sent to the bank for a number, comes back with loose beans, bundles of ten and bags of a hundred, and trades ten of anything for one of the next size up.
- Age
- 5 to 8, best at 5
- Setup
- 2 min
- Play
- 20 min or more
- Materials
- Household, or a bought set
- Mess
- None
- You
- Play along
Activity KG-A032
What you need
Four sizes of the same object, which is the entire idea. The beans cost almost nothing and the making of them is the first sitting rather than a chore to get through before the real thing.
- Small dried beans or lentilsabout 500 g Or: beads, buttons, short pasta, cotton buds. Anything that comes in thousands. Every piece has to be identical, because the whole argument rests on a bundle of ten really being ten of the loose ones. Half a kilo of small white beans is roughly a thousand of them, which is exactly what this needs.
- Paper strips for the tensx50 to 100 Or: small elastic bands. Or drinking straws with ten beans inside and both ends taped. A 2 cm strip of paper wrapped round ten beans and taped makes a bundle that lifts as one object. That is the point of it: a ten has to be one thing in the hand rather than ten things.
- Small bags or paper twists for the hundredsx10 Or: paper squares folded into packets. Or matchboxes. Ten bundles in one bag, and the bag stays shut on the walk. A hundred that can spill is a hundred that gets recounted, and a recount in the middle of a game loses everybody at the table.
- A box for the thousandx1 Or: a jar. Or a shoebox with the ten hundred-bags inside it. One object, visibly enormous next to a single bean, and heavy enough to want both arms. The weight is doing as much of the teaching here as the label on the lid.
- Four saucers, or a divided trayx1 set The four sizes have to stay in four separate places. Once loose beans get mixed in with the bundles, the exchange has nothing left to work on.
- Number cardsone set Or: slips of paper with the numbers written on in marker. Cut them so a thousands card is four digits wide, a hundreds card three, a tens card two and a units card one, all the same height. Laid on top of each other they stack right-aligned into 3425, and the stack of cards then looks like the piles on the tray.
How to set it up
- Put the four sizes in four saucers at one end of the table, in order, the thousand on the left.40 sec
- Lay the four rows of number cards in front of the bank, thousands along the top.40 sec
- Hand out a tray or a tea towel each, at the far end of the table or across the room.20 sec
- Say a number once, in full, and let her walk to the bank and back without you.20 sec
What to say and what to do
Say
Bring me three thousand, four hundred and twenty five.
You have ten of those. Take them to the bank and see what comes back.
- And then let her carry it. The walk across the room with a number in her arms is doing something a table cannot do.
Do
- Be the banker and nothing else. She asks, you exchange, and you do not check her count on the way past.
- Say the number in full every time, thousands first: three thousand, four hundred, twenty, five. The words and the piles line up, and that alignment is most of what this teaches.
- Play it with two children where you can. One fetching and one banking beats either one alone, and they should swap jobs halfway through.
Let be
- A fetch that comes back wrong. She finds it herself when the cards go on top of the piles and the two do not agree.
- The thousand box carried with both arms and a lot of ceremony. The weight is part of what it is for.
- A child who wants to open the hundred bag and count it. Let her, and let her band it back up. That is the idea being tested rather than taken on trust.
What it looks like when it is working
- She stops counting bundles one at a time and takes ten by sight.
- He notices he is holding ten tens before anyone says anything, and heads for the bank on his own.
- The card stack goes together right-aligned without being straightened.
- She starts asking for numbers to fetch instead of waiting to be given one.
What to expect at each age
At five
Fetches units and tens reliably, wants the hundreds and thousands said twice, and makes the exchange when prompted. Counts every bundle on the way.
Reading the four-digit number off the stack of cards comes later. At five the piles come first and the digits follow them.
Lasts 15 to 20 minutes
At six
Fetches all four sizes from one telling, spots ten of a kind himself, and lays the card stack to match his tray without help.
Adding two numbers together in one tray, with the carrying that follows, comes next, and it is the same exchange happening twice.
Lasts 20 to 30 minutes
At seven and eight
Adds and subtracts two four-digit numbers in the trays, and goes to the bank to break a hundred into ten tens when there is not enough to take away.
This is where written column arithmetic starts to look like a description of something she has already done with her hands.
Lasts 30 minutes or more
When it goes sideways
Each of these is the bank telling you something about the level, or about how the table is laid out.
There are beans everywhere
The bundles are coming apart in the carry, usually because the paper strips were wrapped loosely.
Wrap each strip tight and tape it to itself rather than to the beans, or move to straws with both ends taped. A bundle that survives being dropped is worth the ten minutes of remaking.
He does not see why ten tens is a hundred
He has never taken a hundred apart. Being told it is not the same as having had it in pieces on the table.
Open one hundred-bag together and lay the ten bundles out in a line, then put them back. Once a week for a month, and it stops being a rule and becomes a fact about the bag.
Making a thousand is too much work
It is roughly an hour of counting, and none of it has to happen before the game can start.
Start with units, tens and hundreds only, which is about twenty minutes of building. Add the thousand later and build it with her; counting out the hundredth bundle is one of the better afternoons in this library.
She keeps fetching the wrong number on purpose
The fetching has become the boring half and the checking has become the game.
Swap jobs. Let her be the banker and you fetch, and make a few mistakes worth catching. The banker's side needs exactly the same knowledge and is twice as good to be caught on.
Making it harder
Four rungs on one bank. The beans never change. What changes is the size of the number being asked for.
Units and tens only
- Ready when
- This is the starting point.
- What changes
- Loose beans and bundles of ten, and numbers up to ninety nine.
- What is new
- Ten loose ones walking to the bank and one bundle walking back.
Add the hundreds
- Ready when
- He fetches a two-digit number without checking the card twice.
- What changes
- Bags of a hundred, and three-digit numbers.
- What is new
- The same trade one size up, and the discovery that it works identically.
The thousand, and a second player
- Ready when
- She fetches three digits and lays the card stack herself.
- What changes
- The thousand box, and another player who fetches a number of her own.
- What is new
- Two trays poured into one, which means exchanging in three places at once.
Taking away, and breaking a hundred
- Ready when
- He carries across all three columns without being prompted.
- What changes
- Start with a number in the tray and take one away, going to the bank to break a hundred into ten tens when there is not enough to give.
- What is new
- Exchange running downwards, which is the half of this that written borrowing depends on.
Stop when the trays have been cleared back into the bank rather than mid-exchange. Putting the beans back in order takes a minute and leaves the whole thing ready, which is most of whether it gets played again.
How to keep it safe
Dried beans, in a house that may have a smaller child in it.
- Count the bundles out and count them back into the bank at the end. A complete bank is also a floor with nothing on it.
- Keep the bank on a high shelf between games if there is a child under three in the house. Loose beans are exactly the size that goes into a nose or a mouth.
- Keep this set separate from the cooking beans, in its own box, so the bank stays complete and the dinner stays uncounted.
- Carry the thousand box with two hands, and keep the walk to the bank clear of chair legs.
Why this helps
From the guide The claims here follow our guide on how patience actually develops.
Place value is the one idea in early arithmetic that cannot be reached by counting harder. A child who counts beautifully to a hundred can still read 3425 as a long word rather than as three thousands, four hundreds, two tens and five ones. The bank turns each of those into a separate object with its own size and its own weight, so the number arrives in the arms before it ever arrives on paper.
The exchange is the other half, and it is what makes carrying and borrowing obvious years later. Ten loose beans walk to the bank and one bundle walks back, and nothing about the quantity has changed. A child who has made that trade a hundred times is not learning a rule about carrying the one. She is recognising something she has already been doing.
Skill practised: four sizes of number, traded ten for one
Nothing here has to be called maths. A five year old plays this because being sent to the bank for three thousand of something is a good job to be given.
Where a set helps
Dried beans in paper bands do this, and this page was written on them. What a printed set changes is the carry: the OtterDen Counting Rods come in fixed lengths, so a ten is one moulded piece that cannot come undone halfway across the room, and the Sorting Tray keeps the sizes in separate compartments on the walk back from the bank. Neither is needed to play. A child who banded her own hundred knows something about it that a bought ten cannot tell her.
One a week, at your child's age
We publish one new activity a week at each age, in exactly this format. The moment a child realises ten bundles will fit in one bag is worth fifteen seconds of video and is hard to write down.
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Questions parents ask
How long does building the bank take?
About twenty minutes for units, tens and hundreds, which is enough to play for months. The thousand is another hour of counting and banding, and it goes much faster with two people and a film on. Building it with your child is worth more than building it for her, and there is no reason to have it finished before the first game.
Can we use something other than beans?
Anything identical and countable: lentils, dried peas, beads, buttons, short pasta, cotton buds. The only requirement is that every piece is the same, because the bundle of ten has to be believably ten of the loose ones. Lentils are the cheapest and the fiddliest; white beans are the easiest at five.
My five year old can already count to a hundred. Is this too easy?
Counting to a hundred and knowing what a hundred is are different things, and this is about the second. Ask her to fetch a hundred and watch whether she reaches for the bag or starts counting beans one by one. That answer tells you where to start, and most five year olds start at the tens.
Do we need the number cards?
Not for the first few games, which run fine on a number said out loud. They start to matter when the digits are the thing being learnt: a card stack that reads 3425 sitting beside four piles of beans is what connects the written number to the quantity, and cutting them to four widths takes about ten minutes with a ruler.