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Developing opportunities and ensuring progression in the development of reasoning skills

Created on 09 May 2014 by ncetm_administrator
Updated on 15 May 2014 by ncetm_administrator

Achieving the aims of the new National Curriculum:
Developing opportunities and ensuring progression in the development of reasoning skills.

The aims of the National Curriculum are to develop fluency and the ability to reason mathematically and solve problems. Reasoning is not only important in its own right but impacts on the other two aims. Reasoning about what is already known in order to work out what is unknown will improve fluency; for example if I know what 12 × 12 is, I can apply reasoning to work out 12 × 13. The ability to reason also supports the application of mathematics and an ability to solve problems set in unfamiliar contexts.

Research by Nunes (2009) identified the ability to reason mathematically as the most important factor in a pupil’s success in mathematics. It is therefore crucial that opportunities to develop mathematical reasoning skills are integrated fully into the curriculum. Such skills support deep and sustainable learning and enable pupils to make connections in mathematics.

This resource is designed to highlight opportunities and strategies that develop aspects of reasoning throughout the National Curriculum programmes of study. The intention is to offer suggestions of how to enable pupils to become more proficient at reasoning throughout all of their mathematics learning rather than just at the end of a particular unit or topic.

We take the Progression Map for each of the National Curriculum topics, and augment it with a variety of reasoning activities (shaded sections) underneath the relevant programme of study statements for each year group. The overall aim is to support progression in reasoning skills. The activities also offer the opportunity for children to demonstrate depth of understanding, and you might choose to use them for assessment purposes as well as regular classroom activities.

Place Value Reasoning
Addition and Subtraction Reasoning
Multiplication and Division Reasoning
Fractions Reasoning
Ratio and Proportion Reasoning
Measurement Reasoning
Geometry - properties of shapes Reasoning
Geometry - position direction and movement Reasoning
Statistics Reasoning
Algebra Reasoning


The strategies embedded in the activities are easily adaptable and can be integrated into your classroom routines. They have been gathered from a range of sources including real lessons, past questions, children’s work and other classroom practice.

Strategies include:

  • Spot the mistake / Which is correct?
  • True or false?
  • What comes next?
  • Do, then explain
  • Make up an example / Write more statements / Create a question / Another and another
  • Possible answers / Other possibilities
  • What do you notice?
  • Continue the pattern
  • Missing numbers / Missing symbols / Missing information/Connected calculations
  • Working backwards / Use the inverse / Undoing / Unpicking
  • Hard and easy questions
  • What else do you know? / Use a fact
  • Fact families
  • Convince me / Prove it / Generalising / Explain thinking
  • Make an estimate / Size of an answer
  • Always, sometimes, never
  • Making links / Application
  • Can you find?
  • What’s the same, what’s different?
  • Odd one out
  • Complete the pattern / Continue the pattern
  • Another and another
  • Ordering
  • Testing conditions
  • The answer is…
  • Visualising

These strategies are a very powerful way of developing pupils’ reasoning skills and can be used flexibly. Many are transferable to different areas of mathematics and can be differentiated through the choice of different numbers and examples.


Nunes, T. (2009) Development of maths capabilities and confidence in primary school, Research Report DCSF-RR118 (PDF)



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25 September 2017 15:52
aleXm - The progression maps (reasoning) have examples of activities / problems that could be asked relating to that mathematical area.
21 September 2017 10:00
Trying to find a document relating to reasoning that has a KS1 KS2 overview of all types of reasoning questions in all areas of curiculum..can you help? Thanks
By aleXm
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21 September 2017 09:03
Trying to find a document relating to reasoning that has a KS1 KS2 overview of all types of reasoning questions in all areas of curiculum..can you help? Thanks
By aleXm
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03 January 2017 14:16
Maybe a typo? Guess it could be amended to 6_ x 4 = 256

Or maybe 3_ x 4 = 128 etc
By Redward
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12 December 2016 14:13
What is the answer to this Y4 multiplication with reasoning?

Prove It
What goes in the missing
6 __ x 4 = 512
Prove it.
By ejones50
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15 April 2016 11:09
These progression maps linked to reasoning are excellent. However, it was really hard to find them again on the website after I was initially shown them.
By naomirn
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21 January 2016 09:15
The year overviews are slightly different to these because these have examples too.

However, I do encourage my teachers to use these as a strand resource to assist with progression ;)
By j9allen
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21 January 2016 09:09
Year overviews can be found here: https://www.ncetm.org.uk/resources/42991
20 January 2016 16:32
Great resource. Are they also available by year group?
14 January 2016 08:24
Denise - it's good to hear you're finding this useful. You might want to start a discussion thread in either the Maths Cafe (https://www.ncetm.org.uk/community/141) or the Primary Forum (https://www.ncetm.org.uk/community/1210).
13 January 2016 22:50
I have started to introduce the activities like others as starters and as ways of developing and checking children's reasoning skills. These ideas have been invaluable as I have been able to pass them on to staff and they are constantly telling me how they have used the ideas to create their own for sessions. Brilliant. Is there somewhere teachers could share ones they make on this site to begin to build up a bank of ideas.
13 June 2015 10:20
What about progression maps for secondary?
By marymaybank
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29 May 2015 17:24
Fantastic ideas to develop reasoning- I am hoping to use them in both starters and plenaries to assess knowledge. Would love to hear how others are using the activities
23 April 2015 18:56
Great resource. I am using it a lot.

There seem to be some errors so check before you give them the class.
By gbatten
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20 March 2015 08:20
I am using lots of the reasoning examples as starters and challenge cards. I have only been using them for a month and already I can see a deeper understanding in my children's answers and knowledge of the areas we have coverd.
By Nomes88
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03 March 2015 21:00
An excellent sets of progression papers with great ideas on how to develop reasoning skills across the strands - well done!!
By p.rees
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04 February 2015 19:49
Have been using these as part of my oral and mental starter with my year 4 class and they are excellent - really makes the children think and use their reasoning skills - an excellent resource
By tigsytots444
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31 December 2014 16:23
A fantastic resource; thankyou
By Jack1Harry2
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06 November 2014 16:25
Very useful. Will come in handy when delivering training on planning for depth. Many thanks!
By nicolawarner
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13 July 2014 19:22
Very useful-thank you
By mdougal
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14 May 2014 20:12
The word document for addition and subtraction is not correct
By waking50
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14 May 2014 14:07
Reviewed the 'Nunes' article with my staff a couple of years ago when I introduced regular reasoning activities in maths classes across the school.

Another really useful suite of papers, thank you.
By BioNick
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