# What if I had 12 fingers?

A Yr4 teacher is currently finding it difficult to stretch the most mathematically able students in her class – how to provide depth of understanding rather than just front-loading them with content they will learn anyway in secondary school.

I spent an afternoon with four students, trying to put into practice the vision that you can choose any topic and make it as difficult as you like. We thought about place value.

Warm-up:

Some interesting misconceptions being born here, that crop up later in secondary school:

• A must be equal to 1, because it is the first letter in the alphabet.
• The value of A must be the same in question 1 and question 2

Some absolutely outstanding vocalisation of thought process here:

The Task: Counting with different numbers of fingers.

We used this table to try and write the same number in different bases. This forced us to think really hard about place value, and the patterns that are common across different number systems.

Reflections

• We should have used physical representations initially (the classic secondary maths teacher’s mistake…). Here are 15 blocks. I can either group them into one 10 and five 1s, or into one 8 and 7 ones… (Thanks Margherita for this observation!)
• In the next session we might look at Happy Numbers, explore this calculator that converts between bases, explore Kaprekar’s Constant in different bases, the 1089 trick in different bases…
• Margherita was struck by the attitude of the students – the joy at being given a difficult problem. “This is HARD!” they crowed delightedly. Contrast to the “This is HARD!” some of the secondary students moan lethargically. How can we cultivate this love of challenge, and ensure that it doesn’t get lost as students become older?
• There was one student in particular that Lisa (the Yr4 teacher) found amazingly strong at Maths. We did not know who he/she was, and would have been unable to pick him out from the group at the end of the session. Why does the class teacher’s assessment of ability not match ours? Our session concentrated on doing simple things in unusual settings and being able to talk through the process – maybe he is doing different problems in class?

I would love to continue working with Primary Students, and cannot wait for the Middle School next year.