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FACTS YOU MUST KNOW!
USEFUL MEASUREMENTS
DISTANCE/LENGTH:
WEIGHT:
KILOMETRE (km) = 1,000m
KILOGRAM (kg) = 1,000g
METRE (m) = 100cm
GRAM (g) = 1,000mg
CENTIMETRE (cm) = 10mm
MILLIGRAM (mg)
MILLIMETRE (mm)
MONEY:
VOLUME:
LITRE (l) = 1,000ml
CENTILITRE (cl) = 10ml
MILLILITRE (ml)
One Pound = 100 pennies
£1 = 100p
50p = £0.50 pound
25p = £0.25 pound
75p = £0.75 pound
10 x 10p = £1
20p x 5 = £1
10% of one pound is 10p
50% of one pound is 50p
What other things
do I need to know?
Even and odd numbers
Follow these simple rules for adding
even and odd numbers:
Odd + Even = Odd
Division, or The
Odd + Odd = Even
Fraction Problem
Even + Even = Even
As you can see, there are rules that
Follow these simple rules for
subtracting even and odd numbers:
Even - Even = Even
Even - Odd = Odd
Odd - Odd = Even
tell what happens when you add,
subtract, or multiply even and odd
numbers. In any of these operations,
you will always get a particular kind of
whole number.
But when you divide numbers,
something tricky can happen—you
might be left with a fraction. Fractions
are not even numbers or odd numbers,
Follow these simple rules for multiplying
because they are not whole numbers.
even and odd numbers:
They are only parts of numbers, and can
Even x Even = Even
Even x Odd = Even
Odd x Odd = Odd
be written in different ways.
For example, you can't say that the
fraction 1/3 is odd because the
denominator is an odd number. You could
just as well write that same fraction as
2/6, in which the denominator is an even
number.
The terms “even number” and “odd
number” are only used for whole
numbers and their opposites.
Square Numbers
A square number is the result when you
multiply a number by itself (49 is a
square number because 7 X 7= 49)
Square Root
The sum could look like this 6 x 6 =
A square root goes the other way:
Or it could look like this 62
I know… All square numbers 100 or less:
1, 2, 4, 9, 16, 25, 36, 49, 64, 81, 100
3 squared is 9, so a square root of 9
is 3
Here are a few examples of how you
arrive at a square number:
1 Squared = 12 = 1 × 1
The symbol for a square root is this:
√
=
1
2 Squared = 22 = 2 × 2 =
4
3 Squared = 32 = 3 × 3 =
9
4 Squared = 42 = 4 × 4 = 16
5 Squared = 52 = 5 × 5 = 25
6 Squared = 62 = 6 × 6 = 36
The sum can look like this: √9 = 3
A square root of a number is a value
that can be multiplied by itself to
give the original number.
A square root of 9 is 3, because
when 3 is multiplied by itself you
get 9.
Remembering the
square numbers and square roots
will be no problem if you know your
times tables!
Dividing by 10, 100
and 1,000
Being able to divide by 10, 100 and 1,000
is useful when you want to convert
between units. Here are some rules and
examples, starting with pounds and
pence.
Divide by 100 to change pence into
pounds.
Example:
225 p = 225 ÷ 100 = £2.25
Divide by 1,000 to change grams into
kilograms.
Example:
1,500 g = 1,500 ÷ 1,000 = 1.500 kg =
1.5 kg
Divide by 1,000 to change millilitres into
litres.
Example:
Equivalent decimals,
fractions and
percentages
I know… Equivalent decimals, fractions
and percentages:
1 whole = 1 = 100%
3/4 = 0.75 = 75%
1/2 = 0.5 = 50%
1/4 = 0.25 = 25%
1/5 = 0.2 = 20%
750 ml = 750 ÷ 1,000 = 0.750 l = 0.75 l
Divide by 1,000 to change metres into
kilometres.
Example:
750 m = 750 ÷ 1,000 = 0.750 km =
0.75 km
Divide by 100 to change centimetres
into metres.
Example:
902 cm = 902 ÷ 100 = 9.02 m
Prime Numbers
You need to know that a prime number
can only by divided by itself and 1 (13 is
a prime number because is only in the 1
and 13 times tables)
I Know… prime numbers less than 100:
1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,
41, 43, 47, 53, 59, 61, 67, 71, 73, 79,
83, 89, 97
Factors
In arithmetic, a factor is a whole
number that divides exactly into
another whole number.
For example, what are the factors
of 12? Have a go at using
multiplication facts to get an answer
of 12 in different ways.
You can write your numbers in any
order you like for a multiplication,
so:
2 × 6 is the same as 6 × 2
Here’s another way to find the
factors of 48: write your first pair
of factors with a reasonable space
between them, then move on to the
next pair until you have them all.
1 × 12 is the same as 12 × 1
3 × 4 is the same as 4 × 3
Therefore, the full list of factors of
12 is: 1, 2, 3, 4, 6, and 12.
When you get to the 6/8 pair, you
Now try to find the factors of 48.
Start with 1 and pair off your
can stop because 7 is not a factor
and you already have 8 in your list.
numbers:
Some numbers have many factors, so
1 × 48, 2 × 24, 3 × 16, 4 × 12 and 6 ×
organised way or you may miss some.
8 all make 48
Write the list in order: 1, 2, 3, 4, 6,
8, 12, 16, 24, 48
it’s a good idea to work in an
Don’t forget to include 1 and the
number itself in your list.
Practising your
times tables and really feeling
confident with them will help you
to understand how factors work!
Know your times tables!
Multiplication
1
2
3
4
5
6
7
8
9
10
1
1
2
3
4
5
6
7
8
9
10
2
2
4
6
8
10
12
14
16
18
20
3
3
6
9
12
15
18
21
24
27
30
4
4
8
12
16
20
24
28
32
36
40
5
5
10
15
20
25
30
35
40
45
50
6
6
12
18
24
30
36
42
48
54
60
7
7
14
21
28
35
42
49
54
63
70
8
8
16
24
32
40
48
56
64
72
80
9
9
18
27
36
45
54
63
72
81
90
10
20
30
40
50
60
70
80
90
100
Table
10
Practice every day to keep your maths skills
sharp and to help you solve maths problems.
Simplifying Fractions
To simplify a fraction, divide the top
and bottom by the highest number
that can divide into both numbers
exactly.
What does it mean?
Simplifying (or reducing) fractions
means to make the fraction as simple
as possible. Why say four-eighths
(4/8) when you really mean half (1/2)?
4
2
/8
(FourEighths)
/4
1
/2
(Two(One-Half)
Quarters)
Example: Simplify the fraction
24
/108:
÷2
24
108
=
÷2
12
54
÷2
÷3
6
=
27
÷2
=
2
9
÷3
Method 2
Divide both the top and bottom of
the fraction by the Greatest
Common Factor (You have to work it
out first!).
Example: Simplify the fraction
8
/12:
How do I Simplify a
Fraction?
There are two ways to simplify a
fraction:
Method 1
Try dividing both the top and bottom
of the fraction until you can't go any
further (try dividing by 2,3,5,7,...
etc).
1. The largest number that goes
exactly into both 8 and 12 is 4, so
the Greatest Common Factor is 4.
2. Divide both top and bottom by 4:
÷4
8
12
2
=
3
÷4
And the answer is:
/3
2
How do we convert a
fraction to a decimal
manually?
Decimals and place
value
Follow these easy steps:
1: Find a number that you can multiply
by the bottom of the fraction to make
it into either 10, 100 or 1,000. (Or any
1s followed by zeros.)
2: Multiply both top and bottom
numbers by that amount.
3: Then write down just the top
number, putting the decimal point in the
right place (one place from the right
hand side for every zero in the bottom
number.)
Example 1: Express 3/4 as a decimal
1: We can multiply 4 by 25 to become
100
2: Multiply top and bottom by 25
×25
3
4
=
75
100
×25
3: Write down 75 with the decimal
point 2 spaces from the right (because
100 has 2 zeros);
Answer = 0.75
The chart above shows place value.
The decimal point always stays in the
same place!
Use this to remind you and to help you
when you are working out problems
involving decimal numbers.
Think of decimal
numbers as MONEY!
DATA HANDLING
Mean (average) – To find the mean of a
set of data, add up all the numbers in
the list and then divide your answer by
the number of numbers in the list,
e.g. 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 +
19 = 135
135 ÷ 9 = 15
15 is the mean (average).
Median – To find the median, order the
numbers in the list from smallest to
largest. The median is the middle
number,
e.g. 5, 3, 2, 8, 6, 9, 3
Ordered - 2, 3, 3, 5, 6, 8, 9
Mode – To find the mode, find the
number that occurs most often in the
list,
e.g. 2, 8, 25, 26, 3, 26, 25, 9, 26
2, 3, 8 and 9 occur once
25 occurs twice
26 occurs 3 times
5 is the median
26 is the mode
If there are two middle numbers in the
list, add them together and divide by 2
to find the median,
e.g. 4, 9, 23, 16, 8, 45, 12, 14
Ordered - 4, 8, 9, 12, 14, 16, 23, 45
Add together the two middle numbers,
12 and 14
12 + 14 = 26 ÷ 2 = 13
13 is the median
Range – To find the range of a set of
data, find the lowest number in the list
and subtract it from the highest
number in the list.
e.g. 56, 94, 36, 19, 66, 12
12 is the lowest number in the list
94 is the highest number in the list
94 – 12 = 82
82 is the range of the set of data
Shapes
Basic information about shapes is
something you need to know!
How to calculate the perimeter of
a shape
Square
All sides equal
Opposite sides parallel
All angles 90°
Four lines of symmetry
Perimeter is the distance around a
two-dimensional shape.
Rectangle
Opposite sides equal
Opposite sides parallel
All angles 90°
Two lines of symmetry
Perimeter = l + w + l + w
Parallelogram
Opposite sides equal
Opposite sides parallel
Opposite angles equal
Rhombus
All sides equal
Opposite sides parallel
Opposite angles equal
Two lines of symmetry
Example: the perimeter of this
rectangle is 7+3+7+3 = 20
How to calculate the area of a
shape
Example: What is the area of this
rectangle?
Kite
Two pairs of equal,
adjacent sides
One pair of opposite
equal angles
One line of symmetry
Trapezium
One pair of parallel
sides
Isosceles trapezium
One pair of parallel
sides
Base angles equal
Non-parallel sides
equal
One line of symmetry
The formula is:
Area = w × h
w = width
h = height
We know w = 5 and h = 3, so:
Area = 5 × 3 = 15
All about triangles
Angles of shapes
Try to remember the total interior
angles for the following shapes:
A circle has = 360º
A triangle has = 180º
A square has = 360º
A pentagon has = 540º
A hexagon has = 720º
Identifying angles
An acute angle is = LESS THAN 90º
A right angle is = EXACTLY 90º
An obtuse angle is = BETWEEN 90º
AND 180º
A straight line is = EXACTLY 180º
A reflex angle is = BETWEEN 180º
AND 360º
A complete turn is = EXACTLY 360º
Have a look at the chart below to see
what these angles actually look like
Ratio and Proportion
Ratio is a way of comparing amounts of
something. It shows how much bigger
one thing is than another. For example:



use 1 measure of screen wash to
10 measures of water
use 1 shovel of cement to 3
shovels of sand
use 3 parts of blue paint to 1
part of white paint
Ratio is the number of parts to a mix.
For example, the paint mix is 4 parts,
with 3 parts blue and 1 part white.
The order in which a ratio is stated is
important. For example, the ratio of
screen wash to water is 1:10. This
means that for every 1 measure of
screen wash there are 10 measures of
water.
Mixing paint in the ratio 3:1 (3 parts
blue paint to 1 part white paint) means 3
+ 1 = 4 parts in all.
Ratio is a way in which quantities can be
divided or shared.
Example:
Share £20 between 2 people in a ratio
of 3:1.
A ratio of 3 + 1 = 4 parts, so the money
needs to be divided into 4 parts.
20 ÷ 4 = £5
If 1 person is getting 3 parts they will
have 3 × 5 = £15
The other person will have 1 part, £5.
Simplest form: ratios can be simplified
by finding common factors.
Direct proportion: ratios are in direct
proportion when they increase or
decrease in the same ratio.
Equivalent ratios: this is when both
sides of a ratio can be multiplied or
divided by the same number to give an
equivalent ratio.
Example
There are 15 males and 12 females in a
group. What is the ratio of males to
females? Give your example in its
3 parts blue paint to 1 part white paint =
3
4
blue paint to
1
4
white paint.
If the mix is in the right proportions
we can say that it is in the correct
ratio.
simplest form.
So the ratio of males to females is
15:12. However, both sides of the ratio
can be divided by 3. Dividing 15 and 12
by 3 gives 5:4.
5:4 is the ratio in its simplest form.
5:4 and 15:12 are equivalent ratios.
Direct Proportion
Understanding proportion can help in
making all kinds of calculations. It helps
to work out the value or amount of
quantities that are either bigger or
smaller than the one about which you
have information. Here are some
examples:
Example: if you know the cost of 3
packets of batteries is £6, can you
work out the cost of 5 packets?
£2.00
You need to get used to certain
symbols and terms which sometimes
mean the same thing:
+
Plus, add, increase, together,
more, and
-
Subtract, minus, take away,
fewer, decrease, reduce, difference
X Multiply, times, product
% Divide, share, divisible by
£6.00
£2.00
Basic maths symbols
=
Equals, total
<
Less then
£2.00
£10.00
To solve this problem you need to
know the cost of 1 packet.
If 3 packets cost £6, then divide
£6 by 3 to find the price of 1
packet.
6 ÷ 3 = 2
Now you know that the batteries
cost £2 each, to work out the cost
of 5 packets you multiply £2 by 5.
2 × 5 = 10
So 5 packets of batteries cost
£10.
>
More than
If you find the less and more than
symbols tricky to remember, remind
yourself of this rhyme:
Time facts
What MUST we know and remember?
Minutes, seconds and
hours
There are 60 seconds in one minute
There are 60 minutes in one hour
Days, months and
years
There are 7 days in the week:
Monday, Tuesday, Wednesday,
Thursday, Friday, Saturday and
Sunday
A fortnight is TWO weeks
There are 24 hours in one day
There are 52 weeks in one year
AM = ANTE MERIDIEM = morning
There are twelve months in one year,
each with a different number of days.
Learn this simple rhyme to help you to
remember:
PM = POST MERIDIEM = afternoon
12 hour and 24 hour
digital times
Thirty days have September,
April, June, and November;
February has 28 alone,
All the rest have 31;
Except leap year, that's the time,
When February's days are 29
You could also count on your knuckles:
When working out
how to convert 12hr to 24hr time, if
the time is in the afternoon (after
midday/12 noon/PM) just add 12!
There are 365 days in one year, except
in a leap year where there are 366
A leap year occurs every four years
A decade is 10 years
A century is 100 years
A millennium is 1,000 years
Problem Solving Tips
When you first look at a number
problem it’s important that you read the
question first and then work out if you
need to add, subtract, multiply or
divide.
Try to find the
Step 3
Carry out the
>
calculations
easiest way of
working out the
problem - use
and answer
mental or
the problem.
written
Here’s a method you can run through in
methods.
your head to help solve problems:
Make sure you
do all the steps
Read and
needed to
What is it
Step 1
>
answer the
about?
understand the
What are you
problem.
being asked to
do?
question.
Have you
Step 4
answered the
Check that
Will a diagram
your answer
help?
works.
question?
>
Use estimation
to see if your
answer is about
Do you need to
Step 2
Work out what
calculations
you
need to do.
>
add, subtract,
multiply,
divide?
right.
Can you use a
different
method to
Have you done
check your
a similar
answer (eg
problem?
working
Underline any
key words to
help you
decide.
backwards, or
using the
inverse sum)?
Some TOP TIPS not to forget!
Change them all into
the same units to see
which is smallest!
Put them all as
the same units
so you can see
which is earliest!
Get them all as
fractions,
decimals or
percentages