Transcript Maths! - Ladybird Learning

Maths!
Level 5-6
Contents
5. Intro
6. Numbers
7-8. Algebra
9-10. Angles
11. Perimeter
12-14. Area
15-17. Fractions
18-20. Percentages
21-22. Collecting like terms
23-24. probability
25-29. Pi
30-32. Nth Term
33-34. Volume
35-36. Surface Area
37-40. Co-ordinates
41-43. Translating Shapes
44-47. Rotating Shapes
48-53. Mean, Median, Mode
54-57. Ratio
58-60. Time
61-63. Speed, Distance, Time
64-65. Solving Equations
66-67. Plans and Elevations
68-69. Nets
70-72. Straight Line Graphs
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!
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!
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!”
Understanding Algebra!
Here is why it is so beautiful!
1.H=5
2. 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= 7
A -5=
2. S=9 P=3
S divide by P=
Now you are an algebra expert!
3. B=8 N=4
BN=
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… 12 We measure angles
using a protractor.
Angle challenge!
Can you measure the following angles
and tell me whether they are acute,
obtuse or reflex!
1.
2.
3.
4.
Now you are amazing at angles!
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!
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 cm2 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 2 on the
end!
3cm
2cm
5cm
4cm
7cm
3cm
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
But why?
Well, if I add in an extra few lines
you might understand it better…
Height
Base
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!
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
1
3
Fantastic Fractions!
To find a fraction, count up how
many parts the shape has for
your denominator. 1
Bottom
2
number
And then count up how
many parts are shaded
for your numerator. 1
2
Top
number
Fun Fractions
Can you tell me what the fraction
that is shaded is!
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…
10% = £1.40
5% = 70p
1% = 14p
If we need to find 26% we need to
add them all up so
£1.40 + £1.40 + 70p + 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!
There are 26% of all off these
clothes. Can you find the new price?
£20
Working Out
10% =
5% =
1% =
£14
Working Out
10% =
5% =
1% =
£42
Working Out
10% =
5% =
1% =
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!
Try these:
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!
Probability
Easy! All you need to do is
subtract the decimal from one.
E.G
The probability of
rain is 0.20
1 – 0.20 = 0.80
The probability
of NO rain is
0.80
Try these
The probability of
rain is 0.40
The probability of
rain is 0.75
The probability of NO
rain is 0.27
The probability of NO
rain is 0.89
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…
Pi to the first 1000 digits!
3.1415926535 8979323846 2643383279 5028841971
6939937510 5820974944 5923078164 0628620899
8628034825 3421170679 8214808651 3282306647
0938446095 5058223172 5359408128 4811174502
8410270193 8521105559 6446229489 5493038196
4428810975 6659334461 2847564823 3786783165
2712019091 4564856692 3460348610 4543266482
1339360726 0249141273 7245870066 0631558817
4881520920 9628292540 9171536436 7892590360
0113305305 4882046652 1384146951 9415116094
3305727036 5759591953 0921861173 8193261179
3105118548 0744623799 6274956735 1885752724
8912279381 8301194912 9833673362 4406566430
8602139494 6395224737 1907021798 6094370277
0539217176 2931767523 8467481846 7669405132
0005681271 4526356082 7785771342 7577896091
7363717872 1468440901 2249534301 4654958537
1050792279 6892589235 4201995611 2129021960
8640344181 5981362977 4771309960 5187072113
4999999837 2978049951 0597317328 1609631859
5024459455 3469083026 4252230825 3344685035
2619311881 7101000313 7838752886 5875332083
8142061717 7669147303 5982534904 2875546873
1159562863 8823537875 9375195778 1857780532
1712268066 1300192787 6611195909 2164201989
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
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
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
Nth Term!
Nth term is all to do with pattern
and sequence.
+2
3
5
7
9
11
The sequence goes up in 2s
so the first part of the answer
will be 2n.
13
To find the second part of the
answer we need to add a few
more numbers in…
Position of
black number
Below.
1
2
3
4
5
6
3
5
7
9
11
13
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 2 + 1 = 3 so your
answer will be 1.
2 x 2 = 4 and 4 + 1 = 5
3 x 2 + 6 and 6 + 1 = 7
The answer is then 2n +1
Find the nth term of these sequences.
Remember it could be subtract as well!
a)
b)
1
2
3
4
5
5
8
11
14
17
1
2
3
3
7
11
4
5
15
19
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…
3
4cm x 5cm x 2cm = 40cm
Find the volume of these objects…
Height = 3cm
Width = 3cm
3
Volume =
cm
Volume =
3
Length = 3cm
Height = 2cm
Width = 4cm
Length = 8cm
cm
Height = 8cm
Width = 3cm
Volume =
Length = 6cm
3
cm
Height = 6cm
Width = 2cm
Length = 4cm
Volume =
3
cm
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
2
is 40cm so now we need to multiply that by 4 which
2
is 160cm.
Therefore the area of all rectangles is
2
2
160cm. The area of one square is 16cm.
So we
2
need to multiply 16 by 2 which is 32cm. Now we
need to add 160 and 32 which gives us the surface
2
2
2
area. 160cm + 32cm
= 192cm
Try this…
A
B
C
C
A
B
Area of A (back and front)
cm2
Are of B (top and bottom)
cm2
Area of C (Ends)
cm2
Total Surface Area
cm
2
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…
x
Along the corridor
(-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.
Try these…
What co- ordinate is What co-ordinate is
the red square in?
the blue square in?
(
,
)
(
,
)
What co-ordinate is
the yellow square in?
(
,
)
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!
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!
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?
(
,
)
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)
This shape has been rotated
90 degrees around the origin.
Which of the following shapes is correct after
rotating the red shape 180 degrees anticlockwise around the origin?
a
c
d
b
Which of the following shapes is correct after
rotating the green shape 90 degrees
clockwise around the origin?
d
b
a
c
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.
4 6 5 5
The total of these numbers is 20.
There are 4 numbers so 20 divided
by 4 = 5!
Therefore the mean is 5!
Find the mean of these sets of
numbers!
3 7
6
2
7
9
2
4
Mean is
1
5
Mean is
3
Mean is
Mode!
The mode is the number that
occurs the most often.
2 6 3 2 5
The mode would be 2.
Find the mode of these
numbers!
5
7
12
5
3
9
2
7
Mode is
2
12
3 Mode is
5
3
9 Mode is
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.
3
4
7
The median is 4
4
5
7
2
5 + 7 = 12
12 divided by 2 = 6
The median is 6.
Find the median of these number
sequences!
4 5
4
7
3
6
8
2
2
9
13
15
21
33
2
Median =
Median =
6
Median =
18
Median =
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.
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
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 40 – 4 = 10
Then, 3 x 10 = 30 so 30L is blue.
Try these…
There are 60L of paint altogether.
The ratio of green to yellow
paint is 2:3.
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?
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?
:
Sammy finishes cricket at 10.10. 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?
:
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?
Speed, Distance and Time
Take a look at this alphabetical
order triangle. This is all we
need to find speed, distance and
time…
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)
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.
Solving equations!
Find the value of x if:
3x + 2 = 32
We basically need to work
backwards. So 32 – 2 = 30
30 – 3 = 10. So x = 10
Try these:
What is x if:
2x - 2 = 22
What is y if:
9y – 2 = 70
What is a if:
11a + 7 = 51
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
What are the correct plans and
elevations of the shapes?
A
B
C
A
B
C
A
B
C
Nets
Nets are the layout of the shape.
When you fold up the net you
will end up with the shape.
Net
Shape
Are these correct nets of the
following shapes?
Incorrect
Correct
Incorrect
Correct
Incorrect
Correct
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.
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.
Can you find the – and + part of the equations
for these lines.
A
B
C
Line A
Y=
Line B
Y = 0.5X
Line C
Y = 3X
I hope that you found my maths
powerpoint useful and fun.
If you did why not try looking at
my other powerpoint on SPAG.
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