Well, first grade math is a big step in every child's life. It dips into everything a little, just enough to get a general picture,
but not to deep to confuse, so strictly no details.

First grade math curriculum differs from country to country, but the basics are pretty much the same.
You don’t have to worry if your kid is not with doing well with this or that. No pressure here,
it's all about practice, practice, and then some more practice. But it's better to practice a little every day - than to practice a lot once a week.

Math is a fun and useful thing. If you start it right - it lays a good foundation throughout the whole education.

I like how time4learning
sums up first grade math in 18 parts and gives a pretty good picture about it.
Also math.about.com is giving its solid perspective.

Numbers – First grade math starts with identifying, reading and writing of whole numbers.

Then they should be able to make a distinction between bigger and smaller numbers, odd and even.

Then they should (more or less) learn how to count to 100 (forwards and backwards from any given point). Also skip count by 2s, 5s and 10s.

I would always recommend counting candies or something that motivates children.
They would want to know who got more candies. Use your imagination. Everything that’s not on paper is good. 3D objects – fruits, vegetables, toys… :-)

For odd/even numbers practice – you can use toys. You take a bunch of toys, and start grouping them in two’s,
and if every toy has a pair-friend – the number is even, or if a last toy doesn’t have a pair-friend – then the number of toys is odd.

I remember I learned skip counting by 5s and 10s while playing hide and seek (since that is how we counted to 100). (top)

But you have to be careful - in math we calculate only with even parts of a whole.

You can cut an apple in 2 unequal parts, but those are not halves, they’re just 2 parts of an apple.
So fractions are operations with equal parts aka - fractions.

Since this is first grade math – cut your apples to halves, thirds or quarters.
If we have one apple cut in half, and second in thirds – we still can’t count or group all those parts together - since halves are not equal to thirds.
They are not the same size, and in this case – they are “apples and oranges”.
But if we make them the same – i.e. cut them all (in this case) to sixths (halves to 3 parts, and thirds to half) – then we can group them and count them. (top)

Operations – in first grade math only addition and subtraction are on the table.

Adding and subtracting to 20 is a base for everything – believe it or not. The notorious regrouping doesn’t go beyond 18 (9+9, and 18-9).

So when bigger numbers and zeros kick in – with a little practice you can recognize what’s important and add and subtract to 18.
I recommend practicing adding and subtracting with coins, cards, cubes, hands, toys and apples of course. :-)

Be sure not to use fancy words like adding and subtracting for starters, but use “take” and “give me”, “together that is”, and so on.
Throw in now and then those “scary” words like addition, subtraction, plus, minus and equals, greater than, less than.

Children should be introduced to some addition and subtraction properties. For example, for addition there’s commutative property (i.e. 3+4 = 4+3).

Place value kicks in a little. One should know to recognize the 10s (tens) and 1s (ones, or units) to 100.
While adding or subtracting - one should learn to deal with 1s (units) and 10s separately.

Then there’s tricky part with regrouping, i.e. carrying and borrowing.
Children should know that 18 could be rounded to 20, and 8 or 13 to 10 (if asked to round a number to the nearest 10).

Get yourself some printable 1st grade math worksheets and practice. (top)

Money – Speaking of money – children should be introduced to pennies, nickels, and dimes. :-)

Tell them that now they can count their pocket money, or count their change, now how much more they need to buy an ice cream or a candy.
Ask them to combine coins to get a certain amount, say 10, 20, 50, 75 cents.

Money is also convenient for fractions (and percents) – if a dollar is considered as a whole. (top)

Patterns – Children learn to recognize it and fill in the missing blanks.

At first it’s easier with signs (++**--++*_--), objects and shapes, and then with numbers (1,3,5,_,9). Skip counting has a pattern also. (top)

Shapes and using them – Children should be able to identify and describe lines, 2d and 3d shapes.

Difference between straight and curved lines, 2d and 3d objects, open and closed shapes…
Recognizing whether those shapes are symmetrical or congruent or whatever.

Identifying and organizing objects in sets by different attributes (small, big, red, green, small and blue) (top)

Positions – In order to be able to orient in space and time, for first grade math, children need to know what is:

left and right, up and down, forwards and backwards

near, far, top, under, middle, inside, outside

measurement: length, width and height

time (calendar and clock - digital and analog)

It’s convenient to practice these skills with hands on activities.

As for time telling, they should know half and full hour with both clocks.

With a number line – I have had most success with board game analogy. Going right or up is a "plus" direction, and going left or down is a "minus" direction.

Here is an example for number line. Zero is your home, your starting point.

So 5 – 3 is 5 steps to the right (or forward) and then 3 steps left (or going back).

And if you put numbers on those steps – you’ll end up on number 2.

Or you can use some board game figurines, draw a number line, take a cube – and try it.

It will be also very effective later when it comes to 3 – 5 = –2, and –3 –5 = –8.

Same goes for addition. Turning everything into a game, especially for first grade math helps a lot. (top)

Space Sense – it’s down to calculating perimeter and area, and making 2D objects out of other 2D objects.

Thin rope is convenient for perimeter, and little squares (or something else) are for area.

For example you can make a square or a rectangle out of 2 right-angled triangles. (top)

Time – There’s time we look on a calendar (years, months, days), and on a clock (hours, minutes, seconds).
We use analog and digital clocks. (top)

Length, Weight, Capacity – measuring, comparing and estimating.

It can be done with conventional (measure tape, scale) and unconventional tools (elbows, fingers, steps).
Children should be able to tell what is longer, shorter, heavier, lighter, same as… (top)

Temperature – how to measure, read, and compare results. When water boils and when it freezes.
When is hot, and when is cold. (top)

Graphing – A way to record and present a number of things.

It can be done on tally-table, or by pictographs and bar graphs. (top)

Using Data – a very beginning of statistics.

Drawing conclusions from graphs, and making predictions from that data. (top)

Probability – through simple examples, get a basic feeling about what’s impossible,
what is likely, and what is least likely to happen. (top)