This week, Upper II students have been problem-solving with place value in mathematics. It’s not just your standard ones, tens and hundreds! They have been looking at Roman numerals beyond 1000 and identifying and explaining patterns in number sequences up to the millions!

When looking at patterns, we consider:

What do you notice?
What has changed?
What has stayed the same?
Can you think of a rule (generalisation)?
Can you test your rule to see if it’s always, sometimes or never true?
How do you know?

We can start making generalisations about number sequences when we have enough information about them. However, sometimes there can be multiple answers!

For example, complete the number sequence and describe it:

43,500, 43,510, …

Answer 1: 43,500, 43,510, 43,520, 43,530, 43,540

Explanation: The number sequence increases by ten each time.

What column or column changes and what stays the same?
The value of the tens column changes. However, eventually, when you bridge 100, the 100s column will change too. Eventually, when you bridge 1000, the value of the 1000s will change too.

Answer 2: 43,500, 43,510, 43,530, 43,560, 43600

Explanation: The number sequence increases by double the tens of the previous number. However, we noticed that this does not apply to the second number, as double 0 is still zero.

Can you think what the next three numbers will be?

Mathematical reasoning does not always have one answer and we teach our students to be creative in their thinking and to support with mathematical vocabulary to give as much detail as possible. Being “Right” or “Wrong” can sometimes be a barrier to learning, but as students progress through the school, learning to unpick answers and look for connections and possibilities in maths serves to deepen their understanding and builds resilience.