Monday, December 30, 2013

TRICKS TO LEARN THE MULTIPLICATION FACTS

Multiplication Tricks


You'll find help for children who are trying to memorize and develop strategies to learn the timetable facts. More and more in my teaching career, I'm seeing that children no longer memorize their multiplication tables. With the math curriculum as extensive as it is, teachers cannot afford to take the time to ensure that students learn the basic facts. Parents are partners in the process and will have greater opportunities for their children to succeed in math if they support the learning of the basics at home. Work with your children to ensure that they do not fall between the cracks. Help your children learn the facts. There are many tricks to teach children multiplication facts in mathematics. Some tricks that I used to use in my classroom are listed here. If you know of some that I may have missed, drop into the forum and let everyone know. I'll add them to this list as I see them.
The 9 Times Quickie
1. Hold your hands in front of you with your fingers spread out.
2. For 9 X 3 bend your third finger down. (9 X 4 would be the fourth finger etc.)
3. You have 2 fingers in front of the bent finger and 7 after the bent finger.
4. Thus the answer must be 27.
5. This technique works for the 9 times tables up to 10.
The 4 Times Quickie
1. If you know how to double a number, this one is easy.
2. Simply, double a number and then double it again!
The 11 Times Rule #1
1. Take any number to 10 and multiply it by 11.
2. Multiply 11 by 3 to get 33, multiply 11 by 4 to get 44. Each number to 10 is just duplicated.
The 11 Times Rule #2
1. Use this strategy for two digit numbers only.
2. Multiply 11 by 18. Jot down 1 and 8 with a space between it. 1 --8.
3. Add the 8 and the 1 and put that number in the middle: 198
Deck 'Em!
1. Use a deck of playing cards for a game of Multiplication War.
2. Initially, children may need the grid (below) to become quick at the answers.
3. Flip over the cards as though you are playing Snap.
4. The first one to say the fact based on the cards turned over (a four and a five = Say "20") gets the cards.
5. The person to get all of the cards wins!
6. Children learn their facts much more quickly when playing this game on a regular basis.
Seeing the Patterns
1. Use a multiplication grid or let your students/children create one.
2. Look carefully at all of the patterns, especially when the numbers correspond with the facts e.g., 7X8 and 8X7 = 56
3. Let students/children practice the 'fast adding' which is what multiplication is.
4. When students can count by 3s, 4s, 5s 6s, etc. they will automatically know their multiplication tables. 
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Thursday, June 6, 2013

Lists of mathematics topics

Areas of basic mathematics

These lists include topics typically taught in secondary education or in the first year of university.

Areas of advanced mathematics 

As a rough guide this list is divided into pure and applied sections although in reality these branches are overlapping and intertwined.

Pure mathematics 

Algebra 

Algebra includes the study of algebraic structures, which are sets and operations defined on these sets satisfying certain axioms. The field of algebra is further divided according to which structure is studied; for instance, group theory concerns an algebraic structure called group.

Calculus and analysis 


Fourier series approximation of square wave in five steps.
Calculus studies the computation of limits, derivatives, and integrals of functions of real numbers, and in particular studies instantaneous rates of change. Analysis studies the same subjects, but on a more rigorous level, and also topics that evolved from calculus.

Geometry and topology 


Ford circles—A circle rests upon each fraction in lowest terms. Each touches its neighbors without crossing.
Geometry is initially the study of spatial figures like circles and cubes, though it has been generalized considerably. Topology developed from geometry; it looks at those properties that do not change even when the figures are deformed by stretching and bending, like dimension.

Combinatorics 

Combinatorics concerns the study of discrete (and usually finite) objects. Aspects include "counting" the objects satisfying certain criteria (enumerative combinatorics), deciding when the criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and finding algebraic structures these objects may have (algebraic combinatorics).

Logic 


Venn diagrams are illustrations of set theoretical, mathematical or logical relationships.
Logic is the foundation which underlies mathematical logic and the rest of mathematics. It tries to formalize valid reasoning. In particular, it attempts to define what constitutes a proof.

Number theory 

Number theory studies the natural, or whole, numbers. One of the central concepts in number theory is that of the prime number, and there are many questions about primes that appear simple but whose resolution continues to elude mathematicians.

Applied mathematics 

Dynamical systems and differential equations 


Phase portrait of a continuous-time dynamical system, the Van der Pol oscillator.
A differential equation is an equation involving an unknown function and its derivatives.
In a dynamical system, a fixed rule describes the time dependence of a point in a geometrical space. The mathematical models used to describe the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish each spring in a lake are examples of dynamical systems.

Mathematical physics 

Mathematical physics is concerned with "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories".1

Computing 


Ray tracing is a process based oncomputational mathematics.
The fields of mathematics and computing intersect both in computer science, the study of algorithms and data structures, and in scientific computing, the study of algorithmic methods for solving problems in mathematics, science and engineering.

Information theory and signal processing 

Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Historically, information theory was developed to find fundamental limits on compressing and reliably communicating data.
Signal processing is the analysis, interpretation, and manipulation of signals. Signals of interest include sound, images, biological signals such as ECG, radar signals, and many others. Processing of such signals includes filtering, storage and reconstruction, separation of information from noise, compression, and feature extraction.

Probability and statistics 


The "bell curve"—the probability density function of the normal distribution.
Probability theory is the formalization and study of the mathematics of uncertain events or knowledge. The related field of mathematical statistics develops statistical theory with mathematics. Statistics, the science concerned with collecting and analyzing data, is an autonomous discipline (and not a subdiscipline of applied mathematics).

Game theory 

Game theory is a branch of mathematics that uses models to study interactions with formalized incentive structures ("games"). It has applications in a variety of fields, includingeconomics, evolutionary biology, political science, social psychology and military strategy.

Mathematical statements 

A mathematical statement amounts to a proposition or assertion of some mathematical fact, formula, or construction. Such statements include axioms and the theorems that may be proved from them, conjectures that may be unproven or even unprovable, and also algorithms for computing the answers to questions that can be expressed mathematically.

General concepts 

Mathematical objects 

Among mathematical objects are numbers, functions, sets, a great variety of things called "spaces" of one kind or another, algebraic structures such as rings, groups, or fields, and many other things.

Equations named after people 

About mathematics 

Mathematicians 

Mathematicians study and research in all the different areas of mathematics. The publication of new discoveries in mathematics continues at an immense rate in hundreds of scientific journals, many of them devoted to mathematics and many devoted to subjects to which mathematics is applied (such as theoretical computer science and theoretical physics).

Work of particular mathematicians 

Reference tables 

List of mathematical reference tables

Integrals 

In calculus, the integral of a function is a generalization of area, mass, volume, sum, and total. The following pages list the integrals of many different functions.

Journals 

Meta-lists 

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