Download Mathemateg Blwyddyn 7 – Cyfeirlyfr Rheini

Mathematics
Year 7
Parents’ Guidebook
The Mathematics Department
Ysgol Gyfun Gwynllyw
Mathematics Year 7 – Parents’ Guidebook
This booklet is intended to be a useful tool as your child undertakes their year 7
mathematics work this year. In the booklet you’ll find a description of the topics studied,
appropriate examples and a list of useful vocabulary.
These are the topics studied per term, as a rule:
Autumn Term
Special Numbers
Number patterns
Rounding
Symmetry
Place value
Polygons
Algebra
Displaying data
Spring Term
Fractions and Percentages
Area and Perimeter
Further Algebra
Angles
Probability
Solids
Summer Term
Plotting points
Graph-reading
Averages
Drawing to scale
Throughout the year, it’s important that pupils have the appropriate equipment. You child
will be given a work book during the initial lessons and it is expected that these be covered
and kept tidily at all times. The equipment definitely needed is:

Pens, pencils, rubber and sharpener.

Protractor and compass.

Scientific calculator
Special Numbers:
This topic allows pupils to become more familiar with certain types of
numbers. There will be a need to use some of these types, whereas
recognising others will be sufficient.
Odd numbers:
1, 3, 5, 7, 9 and all other numbers which finish with these digits.
Even numbers:
2, 4, 6, 8 and all other numbers which finish with these digits.
* Every number which finishes with 0 is also even, e.g. 10, 340, 1870.
Square number:
Cube number:
Prime number:
A number gotten by multiplying a number with itself: 1, 4, 9, 16, 25, ...
1x1=1
6 x 6 = 36
2x2=4
7 x 7 = 49
3x3=9
8 x 8 = 64
4 x 4 = 16
9 x 9 = 81
5 x 5 = 25
10 x 10 = 100
A number multiplied with itself three times: 1, 8, 27, 64, 125, ...
1x1x1=1
6 x 6 x 6 = 216
2x2x2=8
7 x 7 x 7 = 343
3 x 3 x 3 = 27
8 x 8 x 8 = 512
4 x 4 x 4 = 64
9 x 9 x 9 = 729
5 x 5 x 5 = 125
10 x 10 x 10 = 1000
A number that can only be divided by 1 and the number itself to have
a whole-number answer: 2, 3, 5, 7, 11, 13, 17, 19, 23, 39, 31, 37,...
Multiples:
Sequences of number which follow the multiplication tables:
Multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, ...
Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, ...
Factors:
Numbers that divide a larger number to give a whole-number answer:
The factors of 6 are 1, 2, 3, 6 because 6 divided by each of these give
a whole-number answer.
*4 is not a factor of 6 because 6 ÷ 4 = 1.5, which is not whole.
Common factor:
A number which is a factor to 2 or more numbers.
7 is a common factor of 14 and 21
Highest Common Factor: The largest number in a set of common factors
Triangular numbers
Number machines: A number is input into a machine, changed and an output gained:
Indices:
Rounding:
OUTPUT
+5
INPUT
3
+5
8
12
+5
17
-1
+5
4
Numbers noted using powers:
2 x 2 x 2 x 2 = 24
5 x 5 x 5 = 53
c x c = c2
d x d x d x d x d = d5
Numbers noted as a close number, e.g. to the nearest 10/100/whole
number...
6.8 is noted as 7 to the nearest whole number.
13 is noted as 10 to the nearest 10.
267 is noted as 300 to the nearest 100.
BUT A number that ending in 5 is rounded up every time:
3.5 → 4
15 → 20
150 → 200
BODMAS:
The order to follow when calculating answers:
BRACKETS
7  12  4  8  4  3
OF POWERS
72  4  8  4  3
DIVISION
49  4  8  4  3
MULTIPLICATION
49  4  2  3
ADDITION
SUBTRACTION
Symmetry:
49  8  3
57  3
54
Reflection: Note a mirror-line where the first side is a perfect mirror
image of the second side.
Rotation: How many tines does an object fit onto it’s original shape
when rotating around a full circle.
Rotational symmetry order: 4
Rotational symmetry order: 8
Turns:
Measure of turning in a circle:
½ turn clockwise
¼ turn clockwise
Decimals:
¼ turn anticlockwise
Use numbers with decimal points: Add and subtract in the usual way,
but ensuring that the numbers and decimal points are in columns:
12 .3
+
17 .7
4 .6
+
16 .9
13 .2
18 .6
24 .1
7 .5
- 18 .7
11 .1
5 .4
-
30 .9
When multiplying decimals there are a number of valid methods, but
this is easiest to begin: 2.5 x 4
25 x 4 = 100
÷ 10
2.5 x 4 = 10
Place value:
Put numbers in the correct columns: 7063.208, 612.059
Thousands
Hundreds
Tens
Units
Tenths
Hundredths
Thousandths
1/10
1/100
1/1000
7
0
6
3
2
0
8
0
6
1
2
0
5
9
Polygon:
Enclosed shape where each side is a straight line:
Number of
Name of
sides
polygon
3
Triangle
4
Quadrilateral
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
9
Nonagon
10
Decagon
Quadrilaterals:
Square
Rectangle
Rhombus
Trapezium
Parallelogram
Kite
Arrowhead
When discussing polygons, many unfamiliar words are used:
Algebra:
Parallel
Lines in the same direction that will never meet
Vertex
A corner of a 2D or 3D shape
Diagonal
A line drawn from one vertex to another
Convex
A shape that goes outward
Concave
A shape where some side come back into the shape
Use of letters to represent numbers. There are definite techniques for
using algebra, and it’s important to remember how to multiply:
Collect terms:
2 x a = 2a
6 x b = 6b
c x d = cd
a x a = a2
This is the methods of bringing similar terms together to simplify
expressions:
a + a + a = 3a
2b + 3b + b = 6b
5a – 2a + a = 4a
Substitution:
Put numbers is place of letters and work out values, so if a=2, b= 3
and c=5:
a+c=2+5=7
2b = 2 x b = 2 x 3 = 6
5a – 3b = (5 x a) – (3 x b) = (5 x 2) – (3 x 3) = 10 – 9 = 1
Graphs:
Pictogram
→ Pictures represent values
→ There must be a key telling how many each picture
represents
Bar chart
→ Draw axes with the quantity on the vertical axis
Pie chart
Fractions:
→ There are 360o in a circle, so ½ is 180o, ¼ is 90o...
The numerator say how many pieces are used and
the denominator tells the total amount of pieces.
In this circle, there are 3 equal parts, 2 coloured,
so the fraction of the circle coloured is
Improper fraction:
Mixed number:
2
3
This is when the numerator is more than the denominator, e.g.
A number and a fraction together, e.g.
6 23 9 15
There are specific methods for converting an improper (top-heavy)
fraction into a mixed number, and vice versa:
Improper → Mixed
Mixed → Improper
1. How many times does the
1. Multiply the large
denominator fit into the
number which the
numerator? This is the number
denominator and add
before the fraction.
the numerator. This
2. How much is left over? This is
the new numerator.
3. The denominator doesn’t
numerator.
2. The denominator
doesn’t change.
change.
16
1
3
5
5
Equivalent fractions:
is the new
19
5
2
7
7
These are different fractions with the same value:
1 2 3 11 37
  

2 4 6 22 74
All of these are equal to 1/2.
2 6
8
22 36




5 15 20 55 90
All of these are equal to 3/5.
21
8
Simplifying fractions:
In order to simplify fractions we need to find factors of the
denominator and numerator, and then divide both by that
number:
3 is a factor of 6 and 9 so if 6 and 9 were divided by 3, the
answers would be 2 and 3, so
Percentages:
6 2
 .
9 3
Converting between decimals, fractions and simple percentages.
Decimal
Fraction
Percentage
0.01
1
100
1%
0.05
5
1
100
20
5%
0.1
10
1
10
10%
0.15
15
3
15%
0.2
20
0.25
25
1
100
4
25%
0.3
30
3
10
30%
0.4
40
2
40%
0.5
50
0.6
60
0.7
70
0.75
75
3
100
4
0.8
80
0.9
90
1
100
100
100
100
100
100
100
100
100
100
100
20
1
1
3
7
100
5
2
5
10
4
9
5
5
10
1
20%
50%
60%
70%
75%
80%
90%
100%
Area:
The amount of space inside a 2D shape, and there are formulas to
use in each case
Perimeter
Shape
Formula
Square
length x width
Rectangle
length x width
Parallelogram
base x height
Triangle
½ x base x height
Trapezium
½ x (a + b) x u
Rhombus
base x height
The total length of the sides of shapes, calculated by adding the
length of all the sides together.
Equations:
Calculate the value of a letter so that the equation is valid:
2 x  1  11
2 x  10
x5
Take away 1 from both sides
Divide both sides by 2
After getting an answer, it can be checked by putting it into the
equation:
(2 x 5) + 1 = 11


Trial and improvement:
Choose a initial value and improve it according to the answer
What is the value of x so that 2x  7  29
x
2x  7
10
27
Too small
12
31
Too large
11
29

Solids:
3D objects
Sphere
Cube
Cuboid
Cone
Cylinder
Square base pyramid
(Pyramid)
Triangular base pyramid
(Tetrahedron)
Triangular prism
Hexagonal prism
Nets:
The method of drawing shapes in 2D where they can be folded to
make the necessary shape:
Net of a triangular prism
Probability:
Describing the chance an event will happen, in words and numbers:
Numbers can be used to correspond with the words:
Angles:
0
Impossible
0.5
Even chance
1
Certain
The method of noting the space between two lines, and there are
specific names for the different angles:
Acute angle
Angle between 0o
and 90o
Right angle
Angle equal to 90o
Obtuse angle
Angle between
90o and 180o
Straight angle
Angle equal to
180o
Reflex angle
Angle between
180o and 360o
A triangle’s internal angles add to give 180o.
A quadrilateral’s internal angles add to give 360o.
In isosceles triangles, two angles are equal and one different.
Opposite angles are equal.
Measure:
This topic studies the length of objects and how they can be
measured. There is some specific vocabulary in measure:
Imperial – older units such as inches, feet, yards, miles
Metric – newer units such as centimetre (cm), millimetre (mm), meter
(m), kilometre (km)
Use is also made of additional older units:
Span – the distance from the tip of the thumb to the small finger
Hand-breadth – the distance from one side of the hand to the other
Cubit – the distance from the elbow to the tip of the middle finger
Span
Hand-breadth
Cubit
We also needs to remember some important ratios:
Metric units
Imperial units
1cm
10mm
1 foot
12 inches
1m
100cm
1 yard
3 feet
1km
1000m
1 mile
1760 yards
Imperial ↔ metric units
Average:
1 inch
2.5cm
1 yard
0.9m
1 mile
1.6km
This is a general word for 4 specific types of average: mean, mode,
median and range (although this is not strictly a type of average).
Mean:
Add all the numbers, divide with the amount of numbers
Mode:
The most popular number (can be more than one mode)
Range:
The difference between the largest and smallest number
Median:
Arrange the numbers largest → smallest and choose the
number in the middle
BUT if there are two numbers in the middle (as in the example below)
add the two numbers together and halve the answer
Calculate the mean, mode, median and range of 8, 6, 9, 4, 9, 6
Mode:
6 and 9 appear twice, so the mode is 6 and 9.
Range:
9 – 4 = 5.
Mean:
(8 + 6 + 9 + 4 + 9 + 6) ÷ 6 = 42 ÷ 6 = 7
Median:
4, 6, 6, 8, 9, 9
As 6 and 8 are the middle numbers,
the median is (6 + 8) ÷ 2 = 14 ÷ 2 = 7.
It’s possible to have different answers for the 4 averages.
Co-ordinates:
The method of noting the location of points on graphs. We go
horizontally first, then vertically:
The points’ co-ordinates are:
A (-3, 4)
B (0, 5)
C (3, 0)
D (0, 3)
H (5, 0)
I (4, -3)
P( -2, 3)
S (5, -2)
T (2, -5)
W (3, -2)
Y (-4, -1)
The horizontal axis is called
the x axis, and the vertical
axis the y axis.
Vocabulary
addition
adio
inch
modfedd
rectangle
petryal
acute
angle
angle
ongl lem
index
indecs
reflection
adlewyrchiad
ongl
isosceles
isosgeles
reflex angle
ongl atblyg
area
arwynebedd
mean
cymedr
rotation
cylchdro
average
cyfartaledd
median
canolrif
rotation
troad
BODMAS
CORLAT
mile
milltir
rounding
talgrynnu
brackets
cromfachau
rhif cymysg
simplify
symleiddio
circle
cylch
mixed
number
mode
modd
square
sgwâr
collect
casglu
multiple
lluosrif
rhif sgwâr
cube
number
decimal
rhif ciwb
multiply
lluosi
square
number
square root
degolyn
net
rhwyd
substitution
amnewid
decimals
degolion
ongl aflem
subtract
tynnu
divide
rhannu
obtuse
angle
odd number
odrif
symmetry
cymesuredd
equation
hafaliad
percentage
canran
to square
sgwario
pendrwm
ailisradd
equilateral hafalochrog
percentages canrannau
top-heavy
equivalent cywerth
perimeter
perimedr
even
number
factor
eilrif
rhif cysefin
ffactor
prime
number
probability
trial and
cynnig a
improvement gwella
triangle
triongl
foot
troedfedd
quadrilateral pedrochr
fraction
ffracsiwn
range
tebygolrwydd
amrediad
triangular
number
whole
number
yard
rhif trionglog
rhif cyfan
llathen