North School Maths - Exploring Fractions Using a Fraction Wall

Doug Clarke fractions

During the last PMS workshop, I was lucky to be part of some fantastic sessions centred around working with fractions. This was very timely because I was in the middle of a fraction sequence with my senior grades.

This will be an ode to Doug Clarke (and team) for sharing his fraction activities.

Please find below some of my observations

Colour in the fraction: https://files.eric.ed.gov/fulltext/EJ898705.pdf

Wow! Engaging… tick! Multilayered … tick! Ability to be differentiated … tick! Visual… tick! Explicit … tick!

This activity was a game changer for some of my students. Previous to this lesson we had worked with number lines and rope, created abstract artworks, worked on division and percentages through money, but this activity presented some fabulous ‘light bulb’ moments for my students and me.

We used this as a full lesson to begin with and a warm up for the next 4 or so lessons with tweaks and in conjunction with other fraction work. You know it was a successful activity when students still saw the value in playing the game a week later when working on their maths goals trying to make equivalent fractions every time instead of colouring in the obvious.

Observations

Students made links to the diagram and knowledge of fraction names and sizes.

At the games simplest form, they were colouring in the fractions rolled. Eg. 2/4 they coloured in 2/4. This was the entry point into this activity. It was really pleasing to see the collaboration between the students when identifying the fractions and working out possible ways of showing it.

It wasn’t long before students were able to make connections between equivalent fractions. Eg. 2/4 they coloured in 4/8. And as confidence grew, more complex answers were exciting and shared and celebrated. Eg. 2/4 became ¼ + 2/8, to 1/3 + 2/12.

I used Doug’s idea of getting the students to share their ‘best moves’ on the board as our reflection tool. Students were excited to share their special moves and explain what it looked like on their game board. It was pleasing to see students use these moves in the following session to progress in the game.

A variation I tried was using their ‘best moves’ and covering parts of the equation. They then had to pick some equations to try to work out what the full equation could have looked like. The students responded well pumped to take on the challenge. My students who would have been previously challenged by these equations utilised their game boards and were able to find solutions systematically. While others were utilising other methods to find solutions, such as finding a common denominator.

I began to notice students utilising the fraction wall as a tool to help them with other fraction work. Eg. Which fraction is bigger? What fraction is between these two fractions? What ways could you show ¾? They asked for their own fraction wall copy and we have added these to our math resources.

Reflecting

I had a really positive experience teaching this activity. The non-threatening nature of the game meant every student could access fractions and build their understanding. The visual features of the fraction wall diagram enabled some really relevant teachable moments between peers and discussions guided by the teacher. I was really excited to hear the conversations between students using the wall to justify their choices and utilise this in other activities. Playing this game for consecutive days was beneficial and thought it integrated well with my other planned ‘problem first’ activities. I found the students looked forward to it (usually setting it up quickly as they saw maths on the timetable) and wanted to share their ‘best moves’.

In addition to the ‘Colour in the fraction’ game, we played the chocolate chair scenario numerous times. The game is simple to set up and is highly engaging and a ‘teachable moment’ jackpot!

The standout factor of this game was the spotlight on reasoning. I was blown away with the conversations the students were having about fractions. Comparing, calculating, strategically thinking and all in a real, engaging context. I loved the concept so much that we played multiple games with different chocolate amounts.

The scenario that I used (fluked) was the following:

Chair 1 = 1 block, Chair 2 = 2/3 of a block, Chair 3 = ¼ of a block. 6 students lined up.

Before we played, students recorded a response to the following question: ‘ If I was the first person in the line, which chair would I stand behind and why?’ It was great to see them thinking of future actions and how the fraction would be shared. The responses were hilarious, referred to fractions in the context of a part of a chocolate bar. We watched the first 5 people choose a chair, allowing for time to justify their decision and highlighting the amount each player received. We paused on the last person and students were asked to explain where they would go and why

This is where my fluke prompted some hilarious results. The students worked out that the last person held enormous power. They had 2 possibilities of received ¼ of a block of chocolate. One option meant the others would go from 1/3 to ¼ and the students were quick to refer to this as ‘sabotage’. If she went to the last chair she would receive ¼ as well. So why not bring the others down and leave the ¼ piece of chocolate? Most students avoided 2/3 divided by 3 and were quick to dismiss this one.

Reflection

I can’t begin to say how much fun we had with this activity. The ‘buy in’ from all students was extraordinary (chocolate + learning = engagement) not only because they were excited by the idea of chocolate, but the emphasis on the reasoning aspects was exciting. They were genuinely interested in each students moves and potential power of each move. This activity has also highlighted how amazing the learning culture around mathematics in Sarah and my room is. I know it sounds boastful, but I attribute it to our relentless consistency around a ‘problem first’ approach (Peter Sullivan), inquiry practice (Kath Murdoch) and building their Mathematical Mindset Practices (Jo Boaler) As Peter Burrows would say, ‘we have shifted the goalposts’, so now students know that we value and enjoy exploring, deep thinking and explaining. The students were happy to share their thinking, strategies and join in with a conversation around the fraction scenario. They found enjoyment in figuring out the mathematics and seeing what happened.