After successful inquiry lessons with both my year 7 and 8 classes I decided to try inquiry with my year 9 class.

The lesson before had been on writing numbers as the product of prime factors and this lesson was on HCF/LCM. I saw that inquiry maths had an inquiry that could be used ‘The product of two numbers is equal to the product of their highest common factor and lowest common multiple’.

I introduced the lesson by placing the prompt on the board and showing the students the question stems that they could use to help them create questions/statements. I gave the students 3 minutes to discuss their ideas with a person near them and then took in their thoughts. The picture below shows what they came up with:

Once we had done this, I then went through an example of how to find the highest common factor and lowest common multiple of a pair of numbers using prime factor decomposition (this was to link this to the prevouis learning). I then went through one example of what the prompt was suggesting due to some of the questions the students asked were ‘what does this statement mean?’ (referring to the prompt).

Due to this being the first inquiry I have done with this class, I used the guided sheets to help them form their inquiry. Below is an example of this:

The guided sheets can be found on inquiry maths and I do recommend using them to help the students know how to set out their work. I made it clear to my students that they had to show working out in their books and then put their thoughts on the sheet. This inquiry was certainly a great way for students to practise the methods for HCF and LCM.

Not only was it great for practise but the inquiry also brought out some good questions and conversations. One pair of students decided to use the numbers 60 and 79. As they worked through the question they noticed that there wasn’t a number to be placed in the middle of the venn diagram. They then concluded that this could mean that there is no HCF. From there, we discussed was it posible for the HCF to be 0? They realised that this in fact was not true and that the HCF must indeed be 1. They also made the connection it was because 79 was prime and the other number they were using was less than this hence why the HCF was 1.

I personally think this was a useful conversation to have and I started to think about is this an example I would use normally? I don’t recall a time when I have specifically done an example using prime factor decomposition where the HCF is 1 meaning that technically no number would belong in the intersection.

Another excellent thing about inquiry maths is that it encourages students to notice patterns and write down their thoughts. I actually think the statement below is excellent:

I like the fact that the student felt confident enough to write down that they were wrong. I think it is powerful for students to truly grasp that being wrong is perfectly acceptable and is actually a part of learning. That we all get things wrong but this is how we develop and move on. I hope doing these inquiries will continue to help my students search for connections and be able to admit and accept when they are wrong and see this as a normal part of learning. What an excllent learning environment to hone and to encourage. One in where all thoughts and ideas are welcome and one in which it is OK to be wrong.

Find this inquiry and many more at:

Leave a Comment