1. Maths! Level 5-6

2. Contents 5. Intro 6. Numbers 7-8. Algebra 9-10. Angles 11. Perimeter
Area
Fractions
Percentages
Collecting like terms

3. probability Pi
Nth Term
Volume
Surface Area
Co-ordinates
Translating Shapes
Rotating Shapes
Mean, Median, Mode
Ratio

4. Time
Speed, Distance, Time
Solving Equations
Plans and Elevations
Nets
Straight Line Graphs

5. Maths Introduction
Maths is an amazing science all about patterns to problem solving. We find maths all around us, we just do not know it! Mathematicians find patterns in trees on flowers and even in the sky. It is a truly amazing thing!

6. Numbers!
Numbers are one of the most interesting things in fact if they didn’t exist maths would be very strange. The Romans used to draw numbers so weird and strange. Some people would find the Roman Numerals very confusing. If we looked at them now we would say how CRAZY the roman numerals were. So we created a modern version of Roman numerals called NUMBERS!

7. What Algebra Is!
HOWEVER! Sometimes those people who think numbers are so crazy use letters instead! Why?! But when you look deeper into it you understand why it is not ugly and why people walk round town going “My best thing I ever learned at school was algebra. Its MAGIC!”

8. Understanding Algebra!
Here is why it is so beautiful!
1.H= S=8 N=6
H+17=22! S+N = 14!
3. A=10 B=4
AB=40
Ha I caught you! I bet you are probably thinking how on earth I have just worked that out! Well in algebra the secret thing is that if you see 2 letters or 1 letter and 1 number or 2 numbers next to each other you have to multiply them together1 Ah! Do you get it now?
Here are a few questions to get your brain working!
1. A= S=9 P= B=8 N=4
A -5= S divide by P= BN=
Now you are an algebra expert!

9. What angles are!
Angles are the measurement of space between two lines that meet. There are three types of angle: Acute, Obtuse and Reflex. Acute is 90 degrees or less. Obtuse is between 90 and 180 degrees and reflex is over 180 degrees. We measure angles in degrees which looks like this… We measure angles using a protractor.

10. Angle challenge!
Can you measure the following angles and tell me whether they are acute, obtuse or reflex!
Now you are amazing at angles!

11. Perimeter!
Perimeter is the total distance of round the outside of a shape.
You would measure
All four sides and
Add them up.
Have a go at finding the perimeter of these shapes. Remember to use a ruler!

12. Area of squares and rectangles!
When we find area, we find the amount of space in an object. To find the area of a square or rectangle is simple. All you have to do is multiply the width by the length and then put cm on the end! How easy! So here are some shapes, can you find the area? The measurements have been done for you! Remember to put cm on the end! 2 2
3cm
5cm
7cm
2cm
3cm
4cm

13. Area of Triangles
EASY! All you do is find the base and the height, multiply them together and divide your answer by 2! How easy. So here is an example…
Height
Base

14. But why?
Well, if I add in an extra few lines you might understand it better…
Height
Can you recognise the hidden shape? Yes your right it’s a sneaky square which is formed by two equilateral triangles! Two Isosceles and Scalene triangles make a rectangle. So all we are actually are doing is finding the area of our squares and rectangles and then dividing them by two to find the triangles area. Simple!
Base

15. Fractions Fractions are Fab! All they are is part of a whole number!
This shape is split into equal halves which as a fraction looks like this 1 2
This shape is split into equal quarters which as a fraction looks like this 1 4
This shape is split into equal thirds which as a fraction looks like this 3

16. Fantastic Fractions!
To find a fraction, count up how many parts the shape has for your denominator. 1 2
Bottom number
And then count up how many parts are shaded for your numerator. 1 2
Top number

17. Fun Fractions
Can you tell me what the fraction that is shaded is!

18. Percentages
Percentages will appear a lot when your older. Shops are always having offers! If there was 26% off of £14 then:
Find 10% by simply dividing the number by 10. Answer = £1.40
Find 5% by halving your answer of 10%. Answer = 70p
Find 1% by dividing 10% by 2.
Answer = 14p.
That is all the information we need! All we need to do Is add it altogether…

19. 10% = £1.40
5% = 70p
1% = 14p
If we need to find 26% we need to add them all up so
£ £ p + 14p = £3.64
Because we need the money to get cheaper we need to take off £3.64 from £14 so
£14 - £3.64 = £10.36! So
26% of £14 = £10.36!

20. There are 26% of all off these clothes. Can you find the new price?
Working Out
10% =
5% =
1% =
£20
Working Out
10% =
5% =
1% =
£14
£42
Working Out
10% =
5% =
1% =

21. Collecting like terms
When we collect like terms all we are really doing is simplifying the sum. E.G
3y+5y+5h+2h is the same as saying:
8y+7h See how much smaller the sum is!

22. Try these: Wow! 2b+5b+6h+2b+10h is the same as:
7+ 3y+9a+5a+4+2y is the same as:
4b+7y+3n+3+2b+6n+1 is the same as:
Wow!

23. Probability
Easy! All you need to do is subtract the decimal from one. E.G
The probability of rain is 0.20
The probability of NO rain is 0.80
1 – 0.20 = 0.80

24. Try these The probability of rain is 0.40
The probability of NO rain is 0.27
The probability of NO rain is 0.89

25. Pi!
Pi is a very very very very long number which people use to find the area and circumference of a circle.
The symbol of pi is …
Pi is what it is because in any circle, if you divide the circumference by the diameter you get pi…

26. Pi to the first 1000 digits!

27. Radius and diameter
The radius is a line from the centre of the circle to the edge. It is half of the diameter.
The diameter is double the radius. It is al line from one end of the circle to the other.
Radius Diameter

28. Area To find the area of a circle we need to use the radius.
Radius is R, Diameter is D,
Circumference is C, Area is A
Area
To find the area of a circle we need to use the radius.
A= Pi x r x r (Pi x radius x radius)
So if the radius is 6cm what would the area of the circle be is we take pi as 3?
3cm

29. Radius is R, Diameter is D,
Circumference is C, Area is A
Circumference
To find the circumference of the circle (perimeter) we need to use the diameter.
C= Pi x D (Pi x diameter)
So if the diameter is 12cm what would the circumference be if we take pi as 3?
12cm

30. Nth Term! Nth term is all to do with pattern and sequence. +2
The sequence goes up in 2s so the first part of the answer will be 2n.

31. To find the second part of the answer we need to add a few more numbers in…
Position of
black number
Below.
We need to remember the 2. Because if you multiply the 2 by the position of the number you get your answer so…
1 is the position of 3 so 1 x 2 = 2.
Next you need to work out how many more you need to add on from 2 to get your answer. So = 3 so your answer will be 1.
2 x 2 = 4 and = 5
3 x and = 7
The answer is then 2n +1

32. Find the nth term of these sequences
Find the nth term of these sequences. Remember it could be subtract as well! a) b)

33. Volume
The volume is how much stuff is in something. To work out the volume you need to times all 3 measurements together. The length, height and width!
Length x Height x Width = Volume
So if the length was 4cm the height was 5cm and the width was 2cm, the volume would be…
4cm x 5cm x 2cm = 40cm 3

34. Find the volume of these objects…
Height = 3cm
Width = 3cm Volume =
Length = 3cm cm 3
Height = 2cm
Width = 4cm Volume =
Length = 8cm cm 3
Height = 8cm
Width = 3cm Volume =
Length = 6cm cm 3
Height = 6cm
Width = 2cm Volume =
Length = 4cm cm 3

35. Surface Area
Surface area if when you find the area of all sides of your shape.
4cm
This cuboid is made up of 4 identical rectangles and 2 identical squares. The area of one rectangle is 40cm so now we need to multiply that by 4 which is 160cm. Therefore the area of all rectangles is 160cm. The area of one square is 16cm. So we need to multiply 16 by 2 which is 32cm. Now we need to add 160 and 32 which gives us the surface area. 160cm cm = cm 2 2 2 2 2 2 2 2

36. Try this… cm cm cm cm A B C C A B 2 Area of A (back and front)
Are of B (top and bottom)
Area of C (Ends)
Total Surface Area cm 2 cm 2 cm 2

37. Co – Ordinates!
We use co –ordinates mainly for finding places on maps. There are two axis, the x and y. The y is down and the x is along. Whenever we find co ordinates we go along then up…

38. y
Up the stairs x
Along the corridor

39. (-4, 6) would be on the red square.
(9, 4) would be on the yellow square
(7, -1) would be on the blue square.
(-2, -5) would be on the green square.

40. ( , ) ( , ) ( , ) Try these… What co- ordinate is the red square in?
What co-ordinate is the blue square in?
What co-ordinate is the yellow square in?
( , )
( , )
( , )

41. Translating shapes
The yellow square has been translated 2 right and 4 down. I have moved the square along first just like on a co- ordinates grid! Then I move the shape 4 down. The red square is where I landed!

42. Instead of saying Move the shape 2 right and 4 down we say…
(2,-4).This looks a bit like a
co-ordinate! Basically, the 2 means 2 right. If it was 2 left if would be -2 in a negative form.
4 down is -4 and then of course 4 up would be 4 in a positive form.
(2,-4) is a much easier way of saying 2 up and four down!

43. Try this!
Where would the new position be of the yellow square which moves (-3, 2)
The yellow square has moved. The red square shows the yellow squares new position. What has the shape moved?
( , )

44. Rotating shapes.
When we rotate a shape, we either rotate it around one of its points or the origin. The origin is the centre.
(0,0)

45. This shape has been rotated 90 degrees around the origin.

46. Which of the following shapes is correct after rotating the red shape 180 degrees anti-clockwise around the origin? a c d b

47. Which of the following shapes is correct after rotating the green shape 90 degrees clockwise around the origin? d b a c

48. Mean!
The mean is a value which is also known as average. We find the mean by dividing the total of a set of numbers by how many there are.
The total of these numbers is 20. There are 4 numbers so 20 divided by 4 = 5!
Therefore the mean is 5!

49. Find the mean of these sets of numbers!
Mean is
Mean is
Mean is

50. Mode! The mode is the number that occurs the most often. 2 6 3 2 5
The mode would be 2.

51. Find the mode of these numbers!
Mode is
Mode is
Mode is

52. Median!
The median is the middle number. However if you have 2 numbers in the middle you add them up and divide by 2 to find the number in between them.
The median is 4
5 + 7 = divided by 2 = The median is 6.

53. Find the median of these number sequences!

54. Ratio Ratio is about how one thing compares to another.
There are 3 red squares and 1 blue square.
Therefore if there were 6 red squares there would be 2 blue squares because we multiply by 2.

55. The trick to finding the ratio is to always multiply or divide the numbers by the same value. Try these…
Lisa eats 3 oranges for every 2 apples. If she eats 18 oranges, how many apples will she eat?
Oranges : Apples
3: 2
18 : ?
For every 30g of cement, William uses 11 bricks. If he uses 44 bricks, how many grams of cement will he use?
Cement : Bricks
30g : 11
? : 44

56. Finding out how much…
If the ratio of blue to red paint is 3:1 and there are 40L of paint altogether how much paint is blue? To find out this we do…
3 + 1 = – 4 = 10
Then, 3 x 10 = 30 so 30L is blue.

57. Try these…
There are 60L of paint altogether. The ratio of green to yellow paint is 2: How much green paint is there?
There are 240 sweets in a bag. The ratio of sugar to plain sweets if 17:13. How many plain sweets are
in the bag?

58. : : Time! We use time every day. It is a very useful thing in life.
Can you work out the new times?
Nicole arrives at the swimming pool at 9:15. She spends 45 minutes at the pool. When does she leave?
Bob watches a film that lasts 1 hour and 10 minutes. There is a 20 minute delay because the lighting doesn’t work. He comes out at 2:30. What time did the film start? : :

59. Sammy finishes cricket at 10. 10
Sammy finishes cricket at It takes Sammy 25minutes to drive to football from cricket and then he has 1hour and 15 minutes of football. What time did he finish football?
Ruby starts dancing at 13:45. The dancing class goes on for 1 hour and 10 minutes. She doesn’t leave until another 25 minutes. What time does Ruby leave her dancing class? : :

60. James goes to bed at 21:00. He sleeps for 9 hours but snoozes in bed for and extra 35 minutes, then he gets up. What time does he get up?
Kieron catches the 10:15 boat to Portsmouth. The boat takes 52minutes to arrive. Kieron booked a bowling lane for 11:35. How long does he have to get to the bowling place? :

61. Speed, Distance and Time
Take a look at this alphabetical order triangle. This is all we need to find speed, distance and time…

62. Distance
Speed Time
To find distance, multiply the speed by the time (ST)
To find speed, divide the distance by the time (D/T)
To find time, divide the distance by the speed (D/S)

63. Try these…
Find the distance if a car drove 5miles per minute in 4minutes.
Find the speed if a dog ran 4miles in 2minutes.
Find the time if a person ran 21metres at 1 metre per 2 seconds.

64. Solving equations! Find the value of x if: 3x + 2 = 32
We basically need to work backwards. So 32 – 2 = 30
30 – 3 = So x = 10

65. Try these: What is x if: 2x - 2 = 22 What is y if: 9y – 2 = 70
What is a if:
11a + 7 = 51

66. Plans and Elevations!
The plan of a shape is the top, What is seen from a bird looking down!
An elevation is of a shape is the side. What a snail would see!
Plan
Elevation

67. What are the correct plans and elevations of the shapes?
A B C
A B C
A B C

68. Nets
Nets are the layout of the shape. When you fold up the net you will end up with the shape.
Net Shape

69. Are these correct nets of the following shapes?
Incorrect Correct
Incorrect Correct
Incorrect Correct

70. Straight Line Graphs
Straight line graphs are straight lines on a co-ordinate grid. All they do is tell us the position and steepness of the line. The number before the x tells us how steep the line is (also known as the gradient) and the number after the + or – tells us where abouts the line crosses the y axis.

71. The bigger the number before the x the steeper the line
The bigger the number before the x the steeper the line. So 5x would be a steeper line than 2x.
If the line equation has a – then it passes through the y axis on the negative bit. If it is a + then it passes through the y axis at the positive bit.
Some equations may just be
Y =3x without a + or - because they cross through the y axis at 0. And some equations could be Y = 5 because the are flat and just cross through the y axis at 5 with no gradient.

72. Can you find the – and + part of the equations for these lines.B C
Line A Y =
Line B Y = 0.5X
Line C Y = 3X

73. I hope that you found my maths powerpoint useful and fun.
If you did why not try looking at my other powerpoint on SPAG.
Created by Liberty!

74. Thank you for using my Website!