Formal written methods with place value counters

What it does on screen

The board is split down the middle. On the left is the sum set out on squared paper, one figure to a square, the way it goes in a maths book. On the right is the same sum in place value counters, each column its own colour, the same colours as the Place Value Chart.

• Pick the method and the numbers. Add, Subtract, Multiply or Divide, then type the two numbers and press Enter. Random gives a sum the same size as the one on the board, with exchanges in it.
• Next step. Each press does one step on both sides. The column being worked on lights up on the paper and on the chart at the same time.
• One line of words. Under the board a line says what just happened, like "Exchange 10 ones for 1 ten. Write 3 in the ones and the 1 under the tens."
• Back and Play. Back steps back, Play runs it through on its own, and Start again goes back to the set out sum. The arrow keys and a clicker work too.
• Hide counters, Hide working. Either side can go, giving the other one the whole board, so the class predicts the next step before you show it.

What the counters do in each method

• Addition. Both numbers are built in counters. Column by column they slide into the total row, and when there are ten or more, ten of them fly together and become one counter in the next column as the 1 is written under the line.
• Subtraction. When there are not enough ones, a ten bursts into ten ones while the tens figure is crossed out and rewritten. Across a zero it goes to the hundreds first, one exchange at a time. The counters taken away drop into their own row, so what is left is the answer.
• Multiplication. Each column is copied into lots, 4 lots of 3 tens, then exchanged. Two digit numbers get the ones row, the place holder zero, the tens row with every counter jumping a column to the left, and then the two rows added.
• Short division. The counters are dealt into the groups one column at a time. What is left over bursts into the column below, at the moment the small carried figure is written in front of the next digit, so 3 hundreds and 4 tens really do become 34 tens.

How to use it in a lesson

1. Start with the counters on their own. Hide working and step through a sum with just the counters, talking about what is happening to them.
2. Then bring the written method back. Step through the same sum again. Stop just before each exchange and ask what will be written.
3. Point at both sides. The lit column is the same column on the paper and on the chart. Ask what the small figure is worth, not just what it is.
4. Hide counters for the next one. Once they can say it, take the counters away and let them talk you through the written steps.
5. Use the pen. Write over the board to ring an exchange or have a child finish the answer.

Ideas by year group

• Year 3. Three digit addition and subtraction with one exchange. Play it slowly and pause on the exchange every time.
• Year 4. Four digit subtraction across a zero, like 5302 take away 1847. Ask why the hundreds are exchanged before the tens.
• Year 4. Two and three digit numbers times a one digit number. Count the lots on the chart before any exchange.
• Year 5. Four digit times one digit, then times a two digit number. Stop on the place holder zero and ask why it is there.
• Year 5 and 6. Short division with remainders. Predict what will be left over before the counters are dealt.
• Year 6. Hide working and give the class the counters only. Can they write the method that matches?

The misconceptions it helps with

The little 1 is just a 1. In addition it is a ten, and on the chart it arrives as one ten counter made from ten ones. It is never a one.

A 1 in front of a 2 means 1 add 2. In subtraction and division the small figure makes the digit beside it bigger by ten times itself. The counters burst into that column before the figure is used.

Take the smaller from the bigger. In 52 take away 17 a child writes 5 in the ones. Here the chart runs out of ones and has to exchange, so 7 take away 2 is never an option.

The zero in long multiplication is a trick. The counters jump a whole column to the left when you times by ten, so the empty ones column is why the zero is there.

Frequently asked questions