Reasoning provides children with an opportunity for deeper understanding through communication. Individually or in groups, children learn to explain and defend their ideas and analyze the reasoning of others. Historically we have done this very well in English thorough "talk for writing" and thankfully we are now getting much better at providing "talk for maths" opportunities into our own lessons. Teachers are able to assess the children's knowledge through asking “good questions,” and deliver lessons to ensure each child understands how to use math skills through thinking, talking, and doing combined with elements of fluency, reasoning and problem solving.
Having spent the last year or so such searching for the best reasoning resources to support my practice the Welsh have often offered the best. One of the most useful resources I have come across is their 'Reasoning in the Classroom' resource. Click the relevant year group and then support materials.
The Welsh Government has also written a document called 'Audit of existing resources to support the
development of mathematical reasoning in
the GCSE classroom' which although aimed at GCSE children has lots of resources to support primary school children and HA Y5/ 6. There is obvious NRICH and Kangaroo Maths but there are also lots of other useful links e.g tarcia support, I particularly like this 'Convince Me' tarcia.
Although this resource is not Welsh I can't possibly write a reasoning blog without mentioning the Mastery Overview documents created by Maths Hub which are invaluable. I can't recommend this resource highly enough if you haven't already used it. 
Reasoning in EYFS
The following EYFS resources are well worth a look through.
NRICH
Early Years Maths
An old document but still has a lot of relevant advice
NCTM - EYFS magazine
Evidencing reasoning in books
If you are in a school where evidence in books is highly valued you have two options for capturing evidence of reasoning, the most obvious being taking a photo of the activity and annotating the picture with details of the task. Another nice way though is to add a QR code linking to a video of the reasoning activity.
The easiest QR code creator I have come across is QRme.
On this site you can create a QR code linking to any web based document or a written note. I use Google Drive to save videos and then use the 'share' facility to capture the URL of the evidence. I can then simply copy it into the QR code creator website to create my unique QR code linking to the video. Once created I can copy the image and stick into Maths books for evidence. Anyone with a QR code reader can then watch the videos.
