Three Squares

What is the greatest number of squares you can make by overlapping three squares?

Two Dice

Find all the numbers that can be made by adding the dots on two dice.

Biscuit Decorations

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

Writing Digits

Writing Digits

Lee was recording some numbers:

What do you think she wrote next?
Why do you think that?

Click on the 'Show' button to find out.

She continued writing the counting numbers in order but she stopped for a rest after writing seventeen digits.
What was the last number she wrote?

She carried on until she got all the way up to the number 20.
How many digits has she written altogether now?

Can you find a way to work this out without writing the counting numbers yourself?

Why do this problem?

This problem provides meaningful practice of writing and ordering the numbers from $1$ to $20$. Learners might be curious to find out about the number of digits used in the counting sequence, which provides a different focus within a familiar context.

Possible approach

Show the class the first picture and ask them to say what they see, perhaps to a partner first and then take some ideas to share with the whole group.  Try not to dismiss any comments that do not seem relevant - children will need to get all of their observations 'off their chests' before they can focus on a more directed task.  Ask them what Lee might write next and take some ideas.  They may well make all sorts of suggestions - again try to welcome everything, encouraging learners to explain why they think that.

Reveal the second picture and discuss what Lee is doing, drawing out the fact that she is writing the counting numbers in order.  You could invite a learner to the board to write up to ten and then pause to ask how many digits have been written.  This is a good opportunity to clarify the meaning of 'digit', as opposed to 'number'.

You can then lead into the suggested questions, giving children time to work in pairs on the task.  The last question probes a little further by challenging learners to explain how they could work out the number of digits written without doing any writing themselves.  Listen out for those who have a good understanding of the structure of our number system in terms of the first nine numbers being one-digit numbers and then the numbers all the way up to and including 99 being two-digit numbers.

Key questions

Tell me about what you're doing.
What do we mean by 'digit'?
How might you do that without writing all the numbers?
What do you know about the number of digits in the counting numbers?

Possible extension

You could ask similar questions with learners counting in twos, for example.

Possible support

Children could be encouraged to use a number line.