I love Nrich. It is such a brilliant website with so many brilliant problems for students to solve. If you have not yet spent some time navigating through the nrich website, go and do this now! They have problems for all age groups and for so many topics of maths.
I always try to start my new school year as I mean to go on; in this case it is using problem solving where possible.
This week with my year 8 group we were looking at Highest Common Factor. Factors were covered last year and so they do have a concept of factors. To try and get them thinking about factors and also start to introduce common factors I used Gabriel’s problem. I used this as a starter activity so I did not specify that we were focusing on factors and HCF at this point. I gave the class about 10 – 15 minutes to attempt this task.
Essentially, the students are presented with a 3 by 3 grid in which they have to place the numbers 1 to 9 so that each row and each column multiply to the product shown. Each grid grows increasingly more difficult but each contains one number that could be a great starting point e.g. 21. I placed the first grid (the green grid) on the board with instructions and let my students attempt the problem. Some students were struggling with this and others were getting on with the task. Some students appeared reluctant to write anything down in case they were wrong. One of my classroom rules is that its Ok to be wrong, its OK for exercise books to have mistakes in as this is how we learn. Students need to learn to be resilient and to not give up because they find something hard. Once some students had started completing the first grid i presented the next few grids to them. Those who were still struggling i went and gave some hints to e.g. which number can only be made in one way? (the answer was 21 so 1 x 7 x 3). Then i would ask why can the number 7 not go in the same row as the number 40? (because it does not go into 40. Ok so its not a factor) etc. From here more of my students were able to start thinking for themselves more and soon my whole class completed the first grid. Some of my students were even able to complete the second grid.
As a class we then had a discussion about what were the students thinking about as they were completing this task. The students said they were thinking about what numbers fitted into the products. From there I asked them what was the mathematical word for this and they correctly identified factors. I asked them if there were certain numbers that could only go in certain places and they identified that 7 could only go in the column with 21 and the row with 378 etc. From here we identified what common factors were and then I was able to lead them to the idea of a highest common factor. Once we reached this point I introduced the LO and key words and used the Mr Barton idea of me as the teacher doing a whole class example and then the students having a go through your turn.
What I really enjoy about using problem solving in my lessons is the value that the tasks bring. Problem solving encourages students to think for themselves and be less reliant on me to lead the activity. It encourages team work and students talking about their thoughts and what they are doing, It encourages them to give tasks a go even if they find it difficult and usually along the way they get something wrong. This then helps them build resilience (if as a teacher I handle this carefully) and understand that its ok to be wrong as this is how we learn. Also, I like to think that its fun for the students.
Gabriel’s problem can be found here: https://nrich.maths.org/11750
The power point I used with my class is here: HCF