Wednesday, September 17, 2008

First Lessons in Arithmetic: Lesson XV. - adding three numbers



As a mathematical operation, addition follows several important patterns. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication. All of these rules can be proven, starting with the addition of natural numbers and generalizing up through the real numbers and beyond. General binary operations that continue these patterns are studied in abstract algebra.
Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some animals. In primary education, children learn to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.
Lessons in this series:


Monday, September 15, 2008

First Lessons in Arithmetic: Lesson XIV - Addition tables of sevens and eights



Addition math worksheet:







Thursday, September 11, 2008

Basic Math - Lesson 2 Equalities and Inequalities



This lesson consists of providing you with a Self-Tutorial on the basics of equalities and inequalities. I go over how to write results in interval notation, inequality notation, and set (set-builder) notation. I also explain in the printed notes how to use your graphing calculator to help you make comparisons between numbers.

PDF
Printable Notes: 12 pages. 23 minutes of video.




Wednesday, September 10, 2008

Monday, September 8, 2008

Other words for times tables

Here are some other words which mean multiplication. You will need to know them.

Factors

One number is a factor of another number if it divides, or 'goes into' it exactly, with no remainders.
So, 5 is a factor of 20, but 5 is NOT a factor of 23 because if you tried to divide 23 by 5 you'd be left with a remainder of 3.

Groups of
6 groups of 2 are 12
6 x 2 = 12

Lots of
3 lots of 5 are 15
3 x 5 = 15

Multiple
Multiples are the numbers you find in any times table. The multiples of 6 are the numbers in the 6 times table, 6, 12, 18, 24 and so on.

Multiply
There are lots of ways of talking about multiplication. The sum 5 x 4 = 20 can be written as:

  • 5 times 4 = 20
  • 5 multiplied by 4 = 20
  • 5 lots of 4 are 20
  • the product of 5 and 4 is 20
  • 5 sets of 4 are 20
  • five fours are twenty

Prime number
A prime number is a number which nothing else will go into except 1 and itself. Prime numbers don't appear in any other tables.
So 3 is a prime number because only 3 and 1 go into it.
12 is NOT a prime number because lots of numbers go into it, like 1, 12, 2, 6, 4, etc.

Product
The product is the answer that you get when you multiply numbers together. The product of 3 and 4 is 12.

Sets of
3 sets of 6 are 18
3 x 6 = 18

Times
7 times 4 = 28
7 x 4 =28

Times tables grid

Know your times tables. Memorize this grid to help you with them.

Times Tables Grid

Print the grid off and highlight any times tables you find difficult.

BBC Maths: Handling data lesson - Probability



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BBC Maths: Handling Data - Mode, median and mean

BBC Maths: Handling Data - Interpreting data

Basic Math - Lesson 1 Numbers





Click here to read the pdf for lesson one

This lesson consists of providing you with a Self-Tutorial on all about the classification and sets of numbers. Learn what are natural numbers, integers, rational numbers and more. I also explain how to use your graphing calculator to input all types of numbers (integers, fractions, square roots, etc.).

Thursday, September 4, 2008

Wednesday, September 3, 2008

BBC Maths: Shape, space, measures - Transformation



QUIZ


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BBC Maths: Shape, space, measures - Shapes

BBC Maths: Shape, space, measures - Measures



=-+*: math worksheets multiplication division addition subtraction worksheets math :*+-=

BBC Maths: Shape, space, measures - Grids

Grids

1. Coordinates

  • A grid has an x-axis and a y-axis.
  • A point on a grid has two numbers to identify its position.
    These two numbers are known as the point's coordinates.
  • Coordinates are always written as the number of steps
    across first, then the number of steps up or down.

BBC Maths: Shape, space, measures - Angles



These lessons have great images:

Diagram showing the angles 360%, 90% and 180%:
Diagram showing the angles 360%, 90% and  180%

Diagram showing different angles
Diagram showing different angles

Diagram showing angles and triangles
Diagram showing angles and triangles

Diagram showing angles on a protractor
Diagram showing angles on a protractor


Perpendicular and parallel lines

BBC Maths: Numbers - Using a calculator

BBC Maths: Numbers - The number system

BBC Maths: Numbers - Subtraction

BBC Maths: Numbers - Problem solving

Problem solving

1. Money problems

  • Read the words of the problem carefully to decide whether
    to use adding, subtracting, multiplying or dividing.
  • If some of the prices in the problem are in pence and some
    are in pounds, change some of them so they are either ALL
    in pounds or ALL in pence.
  • Treat money problems just like normal number
    calculations, but remember to put the decimal point and
    pound symbol in the right place.
  • Example: You buy a talking robot for £9.87 and a magazine
    for 73p. How much will you spend altogether?
    a) First make sure both amounts are in the same units.
    73p = £0.73.
    b) Then add the two amounts by lining up the decimal
    points.
    Example of adding money: 9.87 and 0.73 = 10.60
    c) So the total you will spend is £10.60. (If you had
    worked this out on a calculator, you would have got 10.6.
    Remember to write this as £10.60.)
  • Read the words of a money problem carefully to work out
    which calculations you need to do.
  • Example: You can buy a 4-can pack of lemonade for £1.00
    or individual cans for 28p.
    Which is better value for money?
    a) Work out how much one can in the 4-can pack costs by
    dividing the price by the number of cans. £1.00 ÷ 4 = £0.25 or 25p.
    b) So the 4-can pack is better value because each can costs
    25p, that is 3p cheaper than individual cans.

2. Measures problems

  • Read the words of the problem carefully to decide whether
    to use adding, subtracting, multiplying or dividing.
  • It's really important to change the units of quantities so
    that ALL are in the same units before you start working out
    the answer.
  • Example: Sophie is 1.29 m tall. Her little brother, Josh, is
    32 cm shorter. How tall is Josh?
    a) This is a subtraction problem. You need to take away 32 cm from Sophie's height.
    But you shouldn't work out 1.29 - 32 because the 1.29 is
    in metres and the 32 is in centimetres.
    Change so both are in the same units. 1.29 m = 129 cm.
    b) Then carry out the subtraction. 129 - 32 = 97 cm.
    c) So Josh is 97 cm tall.

3. Time problems

  • Read the words of the problem carefully to decide whether
    to use adding, subtracting, multiplying or dividing.
  • If some of the times in the problem are in seconds, some in
    minutes and some in hours, change some of them so they
    are either ALL in seconds, ALL in minutes or ALL in hours.
  • When reading timetables, make sure you know what type
    of information is in each column and row.
  • Example: How long does it take the 11.55 train from
    Normington to get to Kirfield?
    Timetable example
    The empty space in the table means the 10:39 train from Normington doesn't stop at Baskwell.

    a) Look along the Normington row until you reach the
    column that starts with the 11.55.
    b) Look down that column until you get to Kirfield and
    read off the time, 12.44.
    Now you need to find the difference between 11.55 and
    12.44. A good way to do this is to break up the time into
    smaller steps.
    Example: time difference between 11.55 and 12.44
    c) 5 + 44 = 49 minutes. So the 11.55 train from
    Normington takes 49 minutes to get to Kirfield.




QUIZ

BBC Maths: Numbers - Percentages

BBC Maths: Numbers - Number patterns

BBC Maths: Numbers - Multiplication

BBC Maths: Numbers - Mental maths

BBC Maths: Numbers - Fractions

BBC Maths: Numbers - Division

BBC Maths: Numbers - Decimals



QUIZ


BBC Maths: Numbers - Addition

1. Adding in your head
2. Writing it down




USA:

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