## Introduction to

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Well, 3rd grade math is about to start. Now really "serious" math begins. You'll be in thousands, not hundreds from now on. And besides adding and subtracting - you get to multiply and divide!

Remember, 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.

3rd grade math curriculum differs from country to country, but the basics are similar.

I like how time4learning sums up 4th grade math in 17 parts and gives a pretty good picture about it. Also math.about.com is giving its solid perspective in 4 parts.

If combined – you get something like this:

Whole Numbers – read, write, order, compare and estimate numbers up to 1000. Add and subtract mentally to 20.

Add and subtract 4 digit numbers with and without regrouping (carrying, borrowing). For that purpose children ought to know regrouping numbers up to 1000.

Skip counting by 2s, 5s, 10s and 25s above 1000. Numbers lines. Rounding numbers. Memorizing multiplication and division facts to 7 or more.

Word problems with addition, subtraction, multiplication and division. Estimating sums and differences. (top)

Fractions and Decimals – understanding the difference in representing and a link between fractions and decimals.

What’s interesting to know is that percents are actually fractions with hundredths in denominator. (top)

Money – The Concept of money. Identifying money amounts from words to numbers. Adding and subtracting coins up to 10 dollars. Word problems with unit price. (top)

Algebra and Patterns – Representing and analyzing math problems using symbols.

Applying commutative and associative rule in equations.

Identifying relationships and reorganizing patterns with two or more attributes. Recognizing and describing patterns in the world around us (traffic, weather…). (top)

Geometry and Shapes – Properties of 2D and 3D shapes – comparing, sorting, and describing.

Part of an angle, solid object attributes, line segments.

Constructing 2D and 3D shapes from matches, toothpicks, little sticks. Solving geometric puzzles. Determining lines of symmetry.

Identifying and applying transformations (flips, slides, turns, 1/2 and 1/4 turn rotation) and symmetry for problems. Symmetrical figures, congruent shapes and tessellations. (top)

• Time – attributes of time, how to measure it, elapsed time and schedules. Reading and recording hours, minutes and seconds on both analog and digital clock.

• Customary and Metric system – understanding the attributes of length, and terms (such as inches, feet, yards, centimeters, meters), weight (with comparing).

Measuring perimeter, area, capacity (how 'much' can fit into something) and volume (the amount of 'space' that is taken up) (see the capacity - volume difference here).

Measuring with different tools, and making estimations.

• Temperature – measuring and comparing temperatures, and reading a thermometer.

Data and Probability – Creating and using graphs, charts, tally tables and Venn diagrams to record data with 2 or more attributes.

Applying basic concepts of probability - certainty, likelihood, and fairness of events. Making guesses based on gathered or given data (horse or car races etc).

Making various experiments, recording and interpreting the results, and making predictions (using coins, dice, cards, etc). (top)

Problem solving – using heuristics and methods for problem solving.

Including famous Polya’s four step method:

1. If you are having difficulty understanding a problem, try drawing a picture.

2. If you can't find a solution, try assuming that you have a solution and seeing what you can derive from that ("working backward").

3. If the problem is abstract, try examining a concrete example.

4. Try solving a more general problem first (the "inventor's paradox": the more ambitious plan may have more chances of success).

Determining if there is enough information. Making word problems that represent operations. (top)