I have to admit I've never heard of a Year R child working to NC Level 3 (but I'm just a Mum). I think the first thing that comes to my mind is that your son should be on the school's gifted and talented register for maths.
next - I think you should be asking for the school to allow your son to join maths classes in upper year groups, so that he can maintain his interest/ enthusiasm for the subject.
If he likes video games there are a lot of free resources out there:
math champs: www.mathschamps.co.uk/#home
Cool Maths for Kids games: www.coolmath-games.com/
Woodlands Junior School maths zone: resources.woodlands-junior.kent.sch.uk/maths/
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The school may also have resources like Education City/ My Maths/ Mangah High maths - which have lots of games that the children can play at home (and often allows them to compete against other children - which some children really respond well to).
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In terms of simple things for L3 maths:
Have him calculate distance of car journeys/ train journeys - how much travelled and how much further to go. (use it as an opportunity to teach concept of miles per hour as well - and then discuss how much longer will the journey take).
We play a game with our girls (currently Y6/ Y4) where we give them a certain amount of money (say £5) and task them to get us all a snack for that amount.
Price compare at grocery stores. Is that 2 for 1 bargain really cheaper?
Division of things amongst friends/ family: So have him work out how many biscuits/ cup cakes/ etc... each person should get - if the food is shared out equally.
Proportion is a great thing to introduce through baking/ cooking. So talking about the ratio of dry ingredients in a cake: Flour to sugar or the ratio of ingredients in a juice or smoothie (3 apples : 1 mango). Juice making is a really fun way of experimenting.
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Finally it's always worth just searching about to see what's out there:
Ted Ed Lessons has a maths section - many will be way above your son's level right now - but not all: ed.ted.com/lessons?category=mathematics - for example Sponge Bob's House is not a pineapple: ed.ted.com/featured/7mw3qRSi by the amazing Vi Hart (now working for Khan Academy) or how many ways can a deck of 52 cards be arranged? ed.ted.com/lessons/how-many-ways-can-you-arrange-a-deck-of-cards-yannay-khaikin.
More Vi Hart math doodles videos: www.youtube.com/user/Vihart/videos - the fibonacci & food shape videos are good fun.
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I realise you are searching ways to apply maths - but I think you also need to consider whether the school will be supporting your son's higher ability going forward (or he'll be left to tread water - i.e. he's a clear Level 3 now, and the school's attitude mgiht be we don't teach above NC Level 3 until Year 3). Hopefully, your school isn't like that (ours is sadly) - but if so you may need to consider supporting maths learning at home.
Your son may respond well to tutorials like Khan academy (which is free) or subscription services like Maths Whizz/ Mathletics/ Maths Factor/ Komodo Maths/ etc... - many on mumsnet have discussed pros and cons of these services - but if the school is not being particularly supportive this may be a means of moving his maths learning forward in a relatively structured/ building blocks way.
HTH