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Reasoning about fractions

Fractions are a stumbling block for many children, but they can start reasoning about fractions by thinking about sharing. Download a research brief and a PowerPoint file for the first lesson in the Year 4 fractions programme. Enjoy watching the children grasp fundamental fraction concepts.

Reasoning about fractions: programme overview

Enrich your teaching of fractions beyond the concept of part-whole relations by using children’s understanding of sharing. Children can achieve insight into core fraction ideas by making connections between division, fractions and ratios. When 1 chocolate is shared among 4 children, this situation can be represented by the fraction ¼:  number 1 refers to the number of chocolates, the slash / indicates a division, and the number 4 refers to the number of children receiving a fair portion. The number ¼ indicates both the division, 1 divided by 4, and the portion that each child receives, one quarter. Our Year 4 programme Reasoning about Fractions supports the understanding of fraction equivalence and order of magnitude by connecting fractions with division and with ratios.

Programme details

The programme can be covered in 6-8 lessons delivered to the whole class using PowerPoint slides, that are annotated with guidance for teachers.

Children learn about fractions as numbers to represent relations between quantities. They become confident in using fractions.

The activities are ordered to extend children’s reasoning about fractions gradually. You can use the lessons once a week from the beginning of Year 4 to create a solid basis for your teaching of fractions.

You can download a fractions assessment to be used at the end of the programme. It will allow you to check if any concepts require further revision.

After you register, you can download the first lesson for free. In order to continue with the programme, you will need to purchase it.

The programme includes a video, Reasoning about Fractions, pre-prepared PowerPoint files for the whole class lessons, and a fractions assessment.  If you have followed the training for the Mathematical Reasoning in Year 2 programme, you will not need to purchase the video as it is included in the Mathematical Reasoning programme.

You can order children’s Workbooks, print separate pages at your school by using the PowerPoint file, or allow the children to do their own drawings as you use the PowerPoint presentations.

You can acquire a related set of more advanced lessons about quantities represented by fractions and ratios. Check the cost of available options.

Download the research brief from the research tab in the Home Page, register to access the sample lesson, and get started right away.

Make sure to read the research brief before starting. Print the PowerPoint file using the “print notes” option so that you can read the orientation for the activities.

In order to continue with the programme, you will need to purchase it.

Programme benefits

You will transform children’s intuitions about sharing and division into a solid basis for understanding ratios and fractions and for learning algebra later on.

Training & resources

Training is available online through the video Reasoning about Fractions. Resources include PowerPoint presentations for the lessons and for an assessment.


The online video Reasoning about Fractions forms the core of the training. You can download the PowerPoint used in the video and a research brief, to which you will be able to return in the future.


PowerPoints for the lessons and for an assessment will save preparation time and help you monitor children's progress. The lessons can be printed for the children's use and be saved in a folder.

EEF Trial of Mathematical Reasoning

Are you ready to register your interest in taking part in the EEF funded randomised control trial of Mathematical Reasoning in Y2? Click here.