Hi allyfe:
I think lljkk's list was closer to our experience - but will say that writing out the names of numbers (so eight) was actually never done at our school - Year R would have been too early for my DDs - but it should be learned in KS1 I think.
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Year R is technically still under the Early Years Foundation Skills Framework: media.education.gov.uk/assets/files/pdf/eyfs%20statutory%20framework%20march%202012.pdf
which for numeracy says:
Mathematics involves providing children with opportunities to develop
and improve their skills in counting, understanding and using numbers,
calculating simple addition and subtraction problems; and to describe shapes, spaces, and measures. (p5)
and page 9 goes on to describe details for maths goals:
Numbers: children count reliably with numbers from 1 to 20, place them in order and say which number is one more or one less than a given number.
Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer. They solve problems, including doubling, halving and sharing.
Shape, space and measures: children use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems.
They recognise, create and describe patterns. They explore characteristics of everyday objects and shapes and use mathematical language to describe them.
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So you should be working early in YR (and that is this stage) on being able to count to 20 (maybe higher)
Maybe being able to add one digit numbers to numbers up to 10 (knowing your number facts to 10)
Maybe being able to take 1 digit numbers from 10.
A lot of this can be done with piles of things: raisins, Lego blocks, baked beans, smarties....
So have 6 smarties (for example) in one pile and 3 smarties in another - how many smarties do we have all together? count up - or maybe add in jumps 6+1 = 7 and 7 + 2 = 9.
Games like snakes and ladders are really good practice for counting on (you can make it trickier by playing with two dice and asking that they don't count just by 1s but by 2s or 3s or 5s - when they're ready).
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Adding and subtracting 2-digit numbers is tricky and I think needs to include explaining place value (so that in the number 18 - the 1 is the tens column and = 1 ten and the 8 is in the units column and = 8 units). I found that this was essential for DD1 to understand how subtraction (and borrowing) works. So we played visual games with grapes = tens and raisins = units.
so 11 - 9 becomes one grape and one raisin (on one plate) take away nine raisins (which you'll put on another plate as you take them away). Gosh we don't have enough raisins do we - we can't take 9 from 1 - so we'll have to cash in our grape (our ten) for 10 raisins. Now we have 11 raisins - so let's count off the 9 (let's put them on this plate) 11 - 9 leaves just 2 raisins on our first plate so 11 - 9 = 2.
It is really helpful if as you're learning to add you work on all the ways to make numbers (not just 10 or 20, but how to make 4, 5, 6, 17, etc...) so that your child really understands number patterns.
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Shape/ weight/ measure can be done by having your DC help you cook. Even something as simple as measuring out water to boil helps then learn to understand what 1L or 500ml looks like.
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names of common 2D geometric shapes and maybe some 3D shapes (sphere, cylinder, cube) are really helpful. If you have a shape puzzle - you can talk about the shapes or tangrams is good for this.
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A lot of this was done in Year R for both my DDs through sending home maths games that worked on these areas and there were also regular drop-in maths workshops.
Finally I will say that a lot depends on the age of your child. My DDs were both closer to 5 or 5 by this point and hadn't progressed far on any of this - so I was starting to worry at this stage - if that's any help. My advice is keep a watchful eye, try and do a bit at home, but don't start to worry until Year 1. If addition/ subtraction aren't happening at all in Year 1 - ask questions. We waited another year on this for DD1 (didn't want to cause problems) and do kind of regret doing that.
HTH