Amazon:
I think you may be confusing National Curriculum levels with school years.
MN summarises progress through NC Levels here: www.mumsnet.com/learning/assessment/national-curriculum-levels - the little blue boxes have links to more information about expected progress through these levels.
At end of Y2 - a pupil is notionally expected to be performing at NC L2b or better. (Each NC Level has lower ability (c)/ solid ability (b)/ high ability (a) sub-levels. So 3b is in fact 3 sub-levels above the notional end of Y2 expectation - which is well ahead for start of Y3 (remember we've not even finished the first term).
I'm giving some advice on how to learn about the tables below - because a lot of it is simply doubling times table facts you already know if you think about it. I think rather than sweat the schools information on maths curriculum - I'd just focus on helping your son with his times tables - which are important at this stage and do underpin a lot of later maths.
What I will say is that there are a lot of great multiplication games out there that really help to improve recall/ speed of times table facts but don't make it seem like you're 'learning':
Woodland Junior Maths Zone Times tables: resources.woodlands-junior.kent.sch.uk/maths/timestable/index.html - there are all sorts of free worksheets to print out - or if you select times table games there are links to all sorts of fun games to help improve skills/ recall/ speed.
Mutliplication dot com - has all sorts of free games: www.multiplication.com
Both of my girls got to a point where they knew there times table (or could work them out from things they did know - e.g. 6 x 7 was the same as 5 x 7 (which they did know would = 35) + 7. But weren't very fast - we found Timez Attack (a video game that starts from where you're at and quizzes you thoroughly on your times table facts - showing that they are repeated additions/ as well as traditional vertical multiplication problems) - we used the free version of the multiplication with two platforms: www.bigbrainz.com/ - but you can buy more elaborate versions if you want.
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Now I don't quite follow the division of x3, x4 and x11 being rated NC 3b - but putting that aside.
x3 is tricky - but learning to count in threes really helps. (In fact this is trippling). You can practice this with board games - like snakes and ladders - use 2 dice and have the roll be the multiple of 3. So if you roll 8 - that means move ahead 8 three's or 24 spaces.
You can use the lines on the inside of your fingers/ thumbs as a natural calculator. With thumbs - there are usually only two lines so I count each tip - but with fingers there are 3 lines (base/ middle/ upper third).
So 3 x 3 - hold up thumb and two fingers. Count base/ middle/ tip of thumb = 3, count base/ middle/ upper third of next finger = 6, count base/ middle/ upper third of next finger = 9.
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Once you know your 3s (and know that's tripling) and your 2s (and know that's doubling) in fact the times tables are relatively straight forward:
0 x anything = 0
1 x anything = itself
2 x table - counting by twos but knowing this is doubling
3 x table - counting by threes but knowoing this is tripling
4 x table (just double 2x table facts) - so 5 x 4 is the same things as 5 x 2 = 10 and then double that = 20.
5 table (already learned by counting by 5s)
6 times table (just double 3x table facts) - so 6 x 6 is the same thing as 6 x 3 = 18 and double 18 = 36.
7 times table (save for last - at the point you just need to learn 7 x 7 because you know whatever x 7 from all other tables learned).
8 times table (double 4x table facts or double 2x table facts and double again).
9 times table (there's all sorts of patterns - but hand trick is probably easiest to learn: - the pattern is to know that the answer 9 x 1 to 9 x 9 always starts one less than the multiple and then the second number is what you would add to the first to make 9. So in 3 x 9 - one less than 3 is 2. So what + 2 = 9. That's 7. So first number is 2 and second number is 7. 3 x 9 = 27.)
10 - already know from counting by 10.
11 - all sorts of tricks.
First off using x1 knowledge you can in fact know that any multiple from 11 x 1 to 11 x 9 is just twice the multiple:
1 x 11 = 11
2 x 11 = 22
3 x 11 = 33
4 x 11 = 44....
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9 x 11 = 99
10 x 11 (should know from counting by 10 - or knowing that you shift anything times 10 over one column to the left and put a place holder zero in the units column) = so 11 x 10 = 110.
That then leaves the nifty two digits x 11 trick.
Separate first and second digit - the number in the middle is the sum of the first and second digit.
So 15 x 11 = 1 - (1 + 5) - 5 = 165.
can be tricky if you have numbers which = or are greater than 10 -
so 37 x 11 = 3 - (3 + 7) - 7 = 3 - (10) - 7 = but you can't have two digits in the middle - so you have to carry
= (3 + 1) - 0 - 7 = 407.
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x12 table - is either double x6 table facts or double x3 table fact and double again.
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and that brings us back to x7 - which we know mostly from other tables except 7 x 7. There's no trick but I always find 7 x 7 is a bit of a swine - which of course rhymes with 49.
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HTH