Fractions Project – What a week!

I was very fortunate last week to be working with an amazing group of P5 pupils from Newton Park Primary School in Wick who volunteered to be part of a project I’m working on.

The lockdown and the current situation we find ourselves in has many downsides, many of which will sadly be long-lasting and/or irreversible.  At the moment, everyone is trying hard to make the best out of a bad situation, myself included, and this week I was excited about the following:

  • Despite being unable to leave the house I can work with a group of children who live 3 hours away – I’m in Inverness, they are in Wick but they could have been anywhere in the world.
  • It has reinforced to me that rich learning discussions, while definitely not as easy, are definitely still possible in our current circumstances.  Although the discussions themselves required a device, the work the pupils did in between sessions was using pen and paper – no device and no parental support required.
  • It also reinforced that you can spend 45 minutes discussing the intricacies of a single problem.
    • As a child, you’ll likely learn far more than solving a page full of calculations.
    • As a teacher, you’ll likely learn far more about the child’s understanding than seeing their page full of answers.
      You don’t need to spend as long as this (45 minutes)… this was partly, again, down to the rationale behind doing the project and so the extended discussion was useful for us.

For anyone interested this was the format of our week:

Day 1: Introductions

  • The children did not know me.  I am not their teacher although I do work with and visit the school several times a year.
  • Set the first problem which had three levels of difficulty.
  • After the Google Meet, children worked on the problem independently (pupils were asked not to get help from parents and siblings) and sent pictures of their strategies to me via their teacher.

Days 2 – 5:

  • Using Google Meet, Google Slides and Google Canvas, we compared the different ways they had solved the problems and had in-depth discussions about potential misconceptions that arose and the pros and cons of the different strategies that people had used.
  • A new problem was set that had two levels of difficulty.  Children completed these independently and sent their work to me via their teacher for discussion the following day.

The purpose of the sessions was to support work that we are currently doing around developing The Highland Numeracy Progression (and Northern Alliance Progression) further to include a major update on fractions.  The work will then feed into both face-to-face teacher training and an online module that teachers can work through at their own pace.

The work is fascinating and we think teachers will find it incredibly beneficial when it’s released.

We recorded all the sessions with permission from the parents and pupils with the intention to use them for the purposes outlined above.

Here is a sample of the pupils’ work from a few different days of the project.  At some point, videos will accompany this

Take a look at the work yourself and reflect on:

  • What do the pupils understand
  • What is missing and therefore may reflect a gap in understanding and knowledge?
  • How does the work develop over the week?

The images themselves are incredibly rich but the discussions that accompanied brought everything up a level.

The progression in questioning and the numbers selected were carefully chosen, in part based on the responses that pupils gave but also to try and explore some of the ideas that we were particularly interested in… we are not suggesting that this is a sequence that you would typically follow.

A note on the levels of difficulty:
With each problem (see examples below) children are told to insert the first number in brackets into the first space and the second number into the second space.  The same problem is therefore used but has three levels of difficulty to it.

Day 1:

___ children in Mrs Ferrier’s class decide to share ___ banana loaf cakes.  If they want everyone to have the same amount with none left over, how much will they each get?

(6, 3)   (6, 5)  (5, 3)

Day 2:

At Toby’s birthday party, he has some chocolate logs for people to share.  If ___ children share ___ chocolate logs and everyone gets the same amount with none left over, how much will they each get?

(4, 3)  (8, 6)

*Is it better to share 4 chocolate logs between 3 people OR 8 chocolate logs between 6 people?  Explain your ideas.

Day 3:

Mrs Ferrier decides to do an art project with the class.  ___ children need to share ___ blocks of clay equally so everyone has the same amount and there is none left over.  How much clay do they each get?

(6, 4)   (6, 8)

Day 4:

The problem for Day 4 was a little bit different.  We asked the children to look at the work that had been created from the problem set on Day 3 where pupils had written different fractions for the same problem and the problem posed was:

  1. Does the fraction that each person has written match their drawing?  Explain your answer.
  2. Everyone solved the same problem but the fractions people wrote looked different.  The range of fractions recorded was then outlined as a reminder.
    Are these the same amounts or different amounts?  Explain your answer and use a drawing to show/prove your ideas.

    Are the fractions all written correctly or do any of them need to change?

 

This week, we’ll be doing more of the same but this time with a different year group and a different school.  I’m really looking forward to it.

I’m also looking forward to sharing the outcome, of what has been a huge piece of work, more broadly with others when we put out the updated progression and the accompanying CPD.

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