Problem Solving at Alver Valley Schools an insight from Jade our Maths Lead
As part of our School Improvement Plan (SIP) this year, we are focusing on problem solving in maths. Following discussions at Maths Core Provision, it was clear that this is a wider focus for many schools across the county and probably across the country.
From our monitoring, we knew that as a school we were doing a lot of solving problems, but not giving children the opportunities to problem solve. Those scratch your head moments. Step back and let the children struggle moments. Becoming the facilitator, not the teacher moments.
During the autumn term, I worked with a member of each year group team to plan a unit of work following the Hampshire schemes, ensuring that we included the three main strands – Fluency, Reasoning and Problem Solving. When looking at the problem solving element, we looked at the different types of problems – working backwards, pattern spotting, logic problems, etc. We have now started plotting these onto a long term overview with hyperlinks to suggested activities within the resources we already have in school. Over the year, we are aiming for children to have exposure to a range of different types of problem solving strategies and build on these as they progress through the school.
Year 5 Problem solving a real life example
As a leader in school who regularly covers classes I am afforded opportunities to explore first hand problem solving alongside our pupils across a range of classes. Here follows an account of one of these opportunities in Year 5.
Starting off:
When I introduced the lighthouse task (pictured above) to the children, I explained that we would be looking at a different approach to problem solving and that this would be something slightly new to them that would test their resilience and challenge them. I gave the children the choice of whether they wanted to work as a table, pair or individually.
The children had 10 minutes to discuss and have a go at tackling the problem with no adult input other than reading the problem and modelling what the lighthouses did. During this time, many children were writing out calculations with the numbers they knew including the 4 operations. Some children sat with their heads in their hands and others started to draw pictures of lighthouses and annotate with the numbers.
Initial thoughts:
After ten minutes, we then shared any patterns that we had noticed at this point. We made links with our reasoning stems:
‘I know that… The reason I did this was because… I think… I tested… The pattern is…’
I also gathered some feedback on their thoughts and feelings at this point in time.
‘I’m just confused to be honest.’
‘It’s ok, harder than I thought but it got easier.’
‘Talking helped!’
‘Frustrated and confused.’
Using the feedback of others:
The children then had a further ten minutes to use what other children had shared. All children were then on task at this point and there were lots of discussions going on. Children were going to look at what others had done and most children changed to working as a table group if they had been working individually to share their findings.
Clues: At this point, I offered the children a possible way that they could record their ideas to make sense of what was happening with the lights.
Some children were already spotting the multiples whilst others needed a clue.
After being given a clue, this child took it further and started to cross off the ‘lights’.
Ending the session:
At the end of the session we shared what we had found out. Nobody had quite reached the answer but they all understood a strategy to help them get to the answer and how it linked with multiples. We then looked at multiples and revisited the term ‘common multiples’. After adding this to our working wall, we discussed how for this problem, we needed to find common multiples for 6, 8 and 10.
After thoughts:
After the session, we collated our ideas about the problem solving activity that we had done.
‘I felt like Albert Einstein because I had a lot of ideas.’
‘I felt mad, annoyed and tired.’
‘I feel good because it was my first time trying this but I think we did pretty good.’
‘It was very tricky and I didn’t understand at first.’
‘I felt confused and tired because it was hard work.’
Session 2
Starting the lesson:
This lesson followed on from the one the day before. We spoke about the problem solving skills that we had learnt and how maths is about looking for patterns and relationships.
Each child had a set of cards 0 – 9 to start with and similarly to the previous lesson, they had the choice with whom they wished to work with.
I covered up questions b and c to start with. The children were very quick to find multiples of 3 and we discussed how we could work out a multiple of 3 if it was a bigger number by adding the digits together. E.g. 351 is a multiple of 3 because 3 + 5 + 1 = 9 and 9 is a multiple of 3.
Once the children had arranged the cards to find multiples of 3, I asked them to record these on their paper.
Returning to the problem:
After 10 minutes, I drew the children back together and reminded them of the criteria of the problem. All the children were able to make multiples of 3, but many of them had forgotten that they had to use all the cards and only make 5 numbers. They were very excited to get going with this and there was a very different atmosphere during the lesson than the one before.
Next steps:
When moving onto problem b, the children found this much trickier. Most children were confident with 7 x tables and those who weren’t got their multiplication square for support, but they couldn’t find 5 numbers using all the cards. After 15 minutes on this problem, I gave the children the number 105 as one of the answers. The majority of children were then able to find the other multiples of 7.
Prime numbers:
The children remembered learning about prime numbers but nobody could remember what they were. We returned to the working wall and looked at the multiples work from yesterday, followed by some discussions about factors of numbers. I chose a couple of prime numbers to model the factors and this prompted some children about what a prime number was. We then wrote out the prime numbers to 20 and I challenged the children to work out the next two prime numbers.
Evaluation:
At the end of the lesson, we discussed how both of the lessons were problem solving lessons but we needed different skills to tackle them. I asked the children which problem solving lesson they preferred. Most children preferred the second lesson as it was more straight forward with the numbers but some favoured the Lighthouse problem.
‘I found the lighthouse problem less confusing.’
‘I liked the challenge of the lighthouse.’
‘I preferred the numbers one [second problem] because it was less challenging.’
‘I liked both. The lighthouse was a challenge and the numbers one was fun.’
Lessons for myself!