Numeracy Rules

 NUMBER

Adding

Adding is one of the simplest areas in Maths. You basically get two numbers and add them up. For example: 10 + 2 = 12. Another example is: 5 + 2 = 7. If you need more advanced adding this is for you.

When you are adding hundreds, you would carry the one if it added up to a number over 10, then you would add it to the next number.

Multiplication

Multiplication may seem hard but, it's incredibly easy, you just need to make sure you understand it. Here, have a go at an easy multiplication sum. John has 20 beetles, his friend has twice as many beetles, how many beetles does his friend have?

Did you know the answer? It doesn't matter what order multiplication goes in your still have the same answer. ( E.g..: 5 x 3 = 15 3 x 5 = 15 )

Division

Division is JUST about sharing!

E.g. 20 divided by 4 = 5 or 4 into 20 goes 5 times. It just means the same thing. 20 divided by 23=1 r 3 there are three (3) left over. It's called a remainder. Division is just a number into a bigger number.

Ways to remember the times tables

For the nine times table, you can use finger tricks.

9 x table- Add tens & units & they will add up to 9

+1 to tens, -1 from units

The numbers are opposites of the other numbers in 9 times table (9 x 9 = 81, 2 x 9 = 18)

8 x table- Starts with 8 then units go down by 2 at a time. The tens have a pattern (08, 16, 24, 32,40,48,56,64,72,80) every fifth ten is doubles e.g: 0, 1, 2, 3, 4, 4, 5, 6, 7, 8, 8. It's always -2 from the units

5 x table- If you times 5 by an even number you ½ the number then add a 0

If you times 5 by an odd number, you take 1 away (make it even), x by 5 then add a 5.

If you x 5 by an even number it ends in a 0, if you x by an odd number it ends in a 5.

To times a number by 5, x it by 10 then halve it.

11 x table From 10 upwards & only with separate numbers that add up to less than 10. eg: 14x 11= 1+ 4 = 5 so it's 154 (put the 5 in the middle of 14)

3 x table To find if a number is divisible by 3, add the parts of the number together & if it divides by 3 then it's in the 3 x table eg: 54 = 5 + 4 = 9. 9 can be divided by 3.

10 x table to times a number by 10, write a 0 on the end.

To divide a number by 10, move the decimal place one space to the left (if there is no decimal place, put it before the last number)

100 x table- to times a number by 100, write a 00 on the end.

To divide a number by 100, move the decimal place two spaces to the left (if there is no decimal place, put it before the last two number)

In every odd times table, the answers always go ODD, EVEN, ODD, EVEN, ODD etc?

Remember:

MATHS IS ALL ABOUT RULES & PATTERNS!!!

Multiples

Multiples are exactly the same as times tables. Basically the multiples of 2 are just the numbers in the 2 times table. Try and work out the multiples of 3 to 9. If you look out for number patterns in multiples it will make everything so much more easy!

But there is an amazingly more easy way to find out multiples, do you know how? On your calculator! If you just keep adding on the same number you'll get your answers.

Square roots/ numbers

It's simple if you think about it!

A square number is found by timesing a number by itself.

A square root is the opposite, you have a square number and whatever number you timesed by itself is the square root.

Prime numbers

Prime numbers are numbers where the only numbers which can be multiplied to equal that number without any remainder are 1 and that number. All the prime numbers up to 20 are 2,3,5,7,11,13,17 and 19. And it is debatable whether 1 is a prime number.

Factors

Factors are numbers that times by another number to get the answer to a number.

1 and 20 are factors of 20 because 1 x  20  = 20. 10 x 2 = 20 and 5 x 4 = 20 as well. 1 x 40, 2 x 20, 4 x 10 and 5 x 8 all equal 40. So they are the only factors of 40.

Negative Numbers.

-4 is bigger than -7 because -4 is closer to zero (0) -7 is further away.

E.g. Put these in order of size (smallest first) -4, 5, -2, 10, -9, 2,

-7.

So the answer is -9, -7, -4, -2, 5, 10, 2.

Adding (+) and Subtracting (-)

E.g. work out these sums -2 - 9 = ? , -5 + 3 = ?

The answer is -2 + 9 = 7 and -5 + 3 = -2

Rounding

Rounding is when you round a number or a [decimal number] up or downwards to the nearest 1, 10, 100, 1000.. etc. For example: 5.2, does it round up or down?.. It rounds down to 5, because any number below 5 rounds down to the nearest 10, 0.

E.g: what do these numbers round to?

52    2.49   11

Number patterns

There are many different techniques to learning your tables. In the eight times table you just add on a ten and take two. For example 8 x 2, eight add ten, 18 take two, 16. 8 x 2 = 16.

16 add ten, 26, take two, 24. So basically you just switch the take two for add two when doing the 12 times table. For the nine times table you add on ten and take one.
There is an extremely helpful trick for the 11 times table. It only works if the number you are multiplying by is ten or more. 11 x 27. You must be thinking what, that's so hard. Well actually with this trick it's just plain easy. First of all you add the two and seven, which makes nine, then you put the two and seven each side of the number nine. The answer is 297. Here?s another one, 99 x11. Nine add nine is 18 which goes in between the two nines. 9189.

Fractions

In a fraction there's a name for the top and bottom number:

 ½ means half = 20/40 means half.

1/3 means one third = 3/9 this also means one third.

¼ this means one quarter = 2/8 this also means one quarter.

If a question says, there are 10 balls and 5 are footballs, 3 are tennis balls and two are rugby balls, what is the fraction for the amount of tennis balls.

¾ is the answer but here's how you work it out, for the bottom number. The question said there were 10 balls all together so that will be the bottom number. For the top number, the question said there was 3 tennis balls altogether so that's the top number.

Percentages (%)

Percent means out of 100.This sign % is a short way of writing percent. If something said 40% (40 percent) it would mean 40 out of 100. These are some common ones that come up quite often.1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/1 = 1.0 = 100%.

Decimals To Percentages

Times by 100, that means all you have to do is move the decimal point two places to the right.

Percentages To fractions

All you have to do is write the percentage at the top of the line (where the numerator goes) and put 100 at the bottom of the line (where the denominator goes.)

Working Out Percentages Of Questions

Of means times (x). If you were finding 15% of 60 all you have to do is change 15% into a decimal (0.15) and then do 0.15 x 60 = 9%. So the answer would be 9%.

Finding A Percentage Of Area

If there was a wall and there were 10 bricks on the wall then somebody asked you to colour in 40% then just colour in four bricks.

SHAPE

2D Shapes you need to know

A square has 4 equal sides with 90o angles.

A rectangle has equal sides with 90o angles.

A rhombus is tilted but also has 4 equal sides.

A parallelogram has two equal sides and two parallel sides.

A trapezium has one pair of parallel sides.

A kite has two opposite but hasn't got a parallel side.

Triangle

There are 4 types of triangle.

Equilateral Triangle.

It has 3 sides of equal length.

It has 3 equal angle.

Scalene triangle.

It has all 3 different length.

It has all the 3 angles different.

Right-angled Triangle.

It has 1 right angle.

Isosceles triangle.

It has 2 sides equal length.

It has 2 angles equal.

Polygons

Polygons have Straight Sides.

Pentagons have 5 sides.

Hexagon has 6 sides.

Heptagon has 7 sides.

Octagon has 8 sides.

Regular Polygons have Equal length sides.

Circles

The radius is half the diameter.

The radius is a straight line that goes from the edge of a circle to the centre

The diameter is a straight line that goes from edge to edge of a circle through the centree of the circle.

You can measure the circumference with a piece of string, just hold it around the outside of the circle, and then measure the string

That is the circumference.

Nets

A net is a 2D shape, when folded together makes a 3D shape. The square of a net, when folded up are the faces of the 3D shape. More than one net combination can fold up to a 3D shape.

Congruence

Congruent means the SAME size and SAME shape. In congruent questions there is a shape and you have to pick the shape out which is the same as the shape that is given to you.

Area

When working out the area you can do several things. If the shape isn't circular or have rounded edges you could just count the squares inside the shape. If your shape uses half squares you just add the half squares together to make a whole square, once you've counted the squares you put a mark inside them so you know if you've counted the square. The proper way to do it is to times the sides by each other. So if you have a square which is 3cm each side. The answer will be 9cm squared because 3 x 3 = 9. There are 9 squares in the big square if you do it the easy way.

If youre trying to find the area of a triangle you find the area of the square/rectangle and half the answer. If you have an odd shape, you split the shape in to two or more shapes you know.

Perimeter

Perimeter is the distance all around the outside of an area, like a fence around a field. To find out the perimeter you measure the length of each side of the area in the same unit and add the sides together. This will give you the answer. For example; there's a football pitch with four sides the lengths are 30m, 30m, 60m, 60m. Added together it equals 180m.

Symmetry

If you can draw 2 mirror lines then you say there are two lines of Symmetry. If you have 3 you say there are three lines of Symmetry.

To help you, you can use a mirror to find the Symmetry, but if you

don't have a mirror, you can use tracing paper it works just as well.

If you have a picture and if you put a mirror down the

middle, it will look exactly the same as before. The mirror line can also

be the line of Symmetry.

Volume

Volume is the height x width x the length of a 3D shape.

The unit of measuring is : cm3, m3, km3...etc.

The measuring is the same as area, but used with cubic units, NOT SQUARED. Eg:

a - height = 3cm

b - width = 2cm

c - length = 5cm

a x b x c = volume [30cm3].

Angles

What's an angle?

An angle is a measure of a turn around a point.

An angle between two lines is how much you have to turn one of the lines so that it matches up with the other one. If you make a whole turn the degrees in a circle will all add up to 360 degrees.

Angles are given different names. An acute angle is always less than 90 degrees. A right angle has got to be 90 degrees exactly. An obtuse angle is always over 90 degrees and always under 180 degrees. A reflex angle is 180 degrees and it goes up to 360 degrees. A straight line angle is always 180 degrees.

How To Use A Protractor

Draw your angle then get a protractor and put the bottom line of your protractor on the bottom line of your angle. Line the point of your protractor up on the point of your angle. Count up on the protractor what number the angle line is on, and that is the size of the angle.

MEASURE

 Reading Maps

Reading maps is coordinates with a few small differences. You might be asked to travel through a certain place/thing before you reach your goal. Also they might tell you to go so many squares right or left, down or up, and you will have to say where your goal is. All this is so simple you will get it straight off.

What you really need to know is how to read a compass. On a compass there are eight points. The first four points are the longest. The one at the top is north, the one on the side on the right is east, the on at the bottom is south and the side on the left is west. Between north and east is north east (obviously), between south and east is south east, between south and west is south west and between north and west is north west.

Coordinates

People get terrified when they are faced with finding coordinates, but really it is easier than falling of a log. A coordinate can look something like this: (4,2) but it can also have many different numbers between the brackets. To plot a coordinate, you must decide what the two numbers between the brackets are going to be. Eg: If the coordinate you are going to plot is (3,5), you must go along the x axis to three, then up the y axis to 5. The point where the two lines meet is where you put the cross. An easy way to remember this is along the corridor and up the stairs.

If you have a grid in the shape of a plus sign (+), the technique is still the same (along corridor and up/down the stairs) only now negative numbers might occur.

Imperial and Metric.

Imperial is the old way to measure things. Metric is the new way to measure things.

Imperial units are:

• Inches
• Feet
• Yards
• Furlongs
• Miles

Metric units are:

• millimetres
• centimetres
• metres
• kilometres

Units/conversions

Units tell us the type of number of number we are working with. If you see this 10 you don't know what this means, so it could be 10 elephants or 10 squashed cucumbers. So you must always remember to put in the units in. Units don't just have to be in length it could be in volume, weight, time & temperature. Words like milli tell you how big a unit is. For example: how many millimetres are in a metre? Milli means one over one thousand so there are one thousand millimetres in a metre. It is easy to remember about multiplying by 10, 100, 1000, 10000 and so on all you have to do is. To add how ever many zeros there are to the number they are multiplying.

Make sure you know these simple conversions:

1 cm = 10 mm

1m = 100 cm

1 km = 1000 m

1tonne = 1000kg

1kg = 1000g

1 litre = 1000 ml

Time tables

Reading a time table is easy all you need to do is to look at the time and look at what someone. Here are four easy steps to reading a time table. 1. for each column and row make sure you know what it stands for. 2. If you run your finger across the row until you find the column.3. Or you can run your finger up and down the column. 4. When the row and column meet that is information you need to know.

The things that go up and down are called the columns, and the things that go side to side are called the rows. Time tables can come in different shapes, sizes and different colours. Some times they make them harder for you by putting it in 24 hour clock. Also they make it easier for you by putting it in digital time.

HANDLING DATA

Mean

The mean is really boring, it's not too big, and it's not too small its right in the middle, nothing special. Just remember the mean may not be one of your numbers and is often a decimal! It's easy to work out the mean of a list of numbers you just add them together then divide the answer by the number of numbers on your list.

For example we took a survey of six pirates to find the mean amount of legs they had. Four had one leg and two had two legs if you add 1, 1, 1, 1 ,2 and 2 you get 8 which you divide by 6 with a calculator to get the answer, 1.333333 stretching on forever of course none of the pirates have this many legs unless......no, too gory.

Mode

When people list the three main averages, not including the debatable forth: The Range, the one they normally list second is the mode. That?s because, after the mean, the mode is almost certainly the second most used average.

When people ask for the average, they mean the mean but if they want the mode, they don't say I want the average, even though the mode is an average, they say what's the most popular. This is because, traditionally, you find out the mode by using a tally chart. So say there were eight cars you would use a tally chart and mark down what colours the cars were and whichever car colour was the most popular would be the mode.

Median

The median is easy to work out; all you do is write them in order then rub out the smallest and the biggest then do the same with the new biggest and smallest, keep doing this until you are left with one number.

There can be a problem, if you have an even amount of numbers then the answer will be two numbers, the actual median would then be the exact middle of the two, say four and five the answer would be four point five!

Range

In averages, many people think there are three types: Mean, Mode and Median, but you could include a fourth, the range, which might be called an average, or might not. But it is a sort of average, so I?ve included it in this average section.

The range is when you have the smallest measurement and the biggest measurement and you take the small one from the big one. For example, if there were twelve mountains, one 440 metres high being the highest and 120 metres for the lowest the range would be 320 metres as 440-120=320.

Probability

Probability, a likely story! Probability is everywhere, for example what are the odds that the teacher will turn into a computer after being hit by a sumo hamster from Mars, you've got to admit it's pretty impossible. It's even in your dinner, if you have three types of food available there is a one in three chance that you will get any one type of food, the most classic example is a coin, it can land on heads, or tails so there is an even chance that it will land on heads. If there is a question on probability on a test there are good odds (There's that word again!) that it will involve a spinner, if you see a question like that there is a good chance you will panic don't worry. Imagine, if a spinner has three sides, two have hamsters and one has a crocodile there?s a good chance it will land on a hamster, there's also a good chance that the hamsters won't be alive much longer.

Probability tables are handy things look at this:

The more often a number appears the more likely it is that that the total of the two dice will equal it. For example as there are six sevens and there are thirty-six squares the odds the total of the two dice will be seven is 6 in 36.