Well, first grade is over, and 2nd grade math is on. The general picture is still more important than details.
2nd grade math curriculum differs from country to country, but the basics are pretty much the same.

Math is important. We use it everyday. But we don’t use everything that we learned. So keep that in mind.
In math everything can be understood if you explain it well – step by step, and practice it enough times.

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

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

Numbers – In 2nd grade, children read, write and mentally add/subtract whole numbers to 20. Add and subtract to 100.

Identify, match, order, and estimate whole numbers to 1000. Understand place value of 10s and 1s, i.e. 1 ten = 10 ones (units),
which is important for regrouping.

Skip count by 2s, 5s and 10s above 100. Simple word problems.

Revising addition commutative property (3+2 = 2+3). Introducing associative property, i.e. (2+3)+4 = 2+(3+4). Use of a number line.

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

To clarify with an example. Zero is your "home", your starting point.

So 6 – 2 is 6 steps from your "home" to the right (or forward) and then 2 steps left (or going back).
And if you put numbers on those steps – you’ll end up on number 4.

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

This trick proved to be very effective later when it comes to 3 – 5 = –2, and –3 –5 = –8.

Same goes for addition. Turning everything into a game helps a lot.

Fractions – Children learn the difference between equal and unequal parts of the whole.
Apart from halves, thirds and fourths – eighths kick in.
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Money – Still learning about values of coins. Counting, adding and subtracting up to 1 dollar.
With money you can practice regrouping literally. :-)
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Patterns – Sorting and classifying thing (shapes, numbers, pictures, objects) by common attributes or patterns.
Recognizing patterns on a chart to 100 and then applying it to the above mentioned skip counting.
Try to identify a pattern in the world around us. (top)

Algebra – Number sentences, solving for unknown number, greater or less than, equal or unequal.
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Geometry – Identifying, describing, and comparing different types of 2D and 3D shapes and lines.

Identifying different shapes in everyday structures. Recognizing and comparing similar or congruent, perpendicular and parallel shapes and lines.
Determining lines of symmetry, both vertical and horizontal.
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Moving objects in different directions (left, right…) and positions (inside, outside…).
Plotting and identifying numbers on a number line and coordinate grid.
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Space – and area of 2D shapes. Using shapes to build another shape.
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Time – Calendar and clock time difference. Analog and digital clock difference.
Telling time by quarters and halves of hour.(top)

Length, Weight, Capacity – measuring with the standard and unconventional tools, comparing, and estimating.
US/UK and metric measuring system.
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Temperature – measuring, reading, and comparing different results.
Introducing Fahrenheit and Celsius system.
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Graphing – recording and presenting a number of things on tally-table, or by pictographs and bar graphs.
Giving explanations.
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