FRACTIONS, DECIMALS F€¦ · RATIO PROPORTION Compares the sizes of 2 or more numbers or amounts....
Transcript of FRACTIONS, DECIMALS F€¦ · RATIO PROPORTION Compares the sizes of 2 or more numbers or amounts....
12
24
48= =
Fractions which areequal in value.
SIMPLIFYING FRACTIONS
Find the highestcommon factorwhich you can divideinto the numerator &the denominator.Writing the fractionusing the smaller numbers.
13=
÷3
÷3
39
TYPES OF FRACTIONS
x+3 3
412 + 3
4154= =
CONVERT MIXED FRACTION IMPROPER FRACTIONMultiply the whole number by the denominator and then addthe numerator.
CONVERT IMPROPER FRACTION A MIXED FRACTIONDivide the numerator by the denominator.
÷223
137=
7 r 1
EQUIVALENT FRACTIONS
FRACTIONS
23
DENOMINATOR
NUMERATORNUMERATORThe number at the top of the fraction,how many parts are used.
DENOMINATOR The number at the bottom part of the fraction,how many parts there are in total.
IMPROPERFRACTION A fraction that isgreater than 1.Numerator biggerthan denominator.
223
PROPERFRACTION A fraction that isless than 1.Numerator smallerthan denominator.
13
MIXEDFRACTIONWhole number and aproper fraction combined.
WHOLENUMBER
Properfraction
1 12 3 3
4or
FRACTIONS, DECIMALS& PERCENTAGES F
FRACTIONS OF AN AMOUNT
14 =of 20 20 ÷ 4 = 5
÷
FRACTIONS, DECIMALS& PERCENTAGES FFRACTIONS, DECIMALS& PERCENTAGES F
Multiply across & simplify.
Flip the second fraction and multiply.
45 4÷ = 4
541÷
89
16÷ 8
961x= 16
3= =3
2
25
49X
x
x
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DIVIDING FRACTIONS
MULTIPLYING FRACTIONS
Change the fractions so theyall have the same denominator.You can do this by multiplyingor dividing.
Order the following fractions.
It’s easy to order them now!
1920
Step 2
Step 1
x5
x5
34
34
1520=
x2
x2
710
710
1420=
20 parts
14
= 5
COMPARING ANDORDERING FRACTIONS
DIFFERENT DENOMINATORDifferent denominator – make the denominator the same by finding acommon multiple. Don’t forget to simplify!
÷4
÷4
= =+24
56
3 + 56
1
2
ADDING AND SUBTRACTING FRACTIONS
=1820
620
1220 = 3
5
845=
=+12
56
86 = 2
61 = 131
x3
x3
smallest largest
Simplest form
1
1
1
1
712
x5
x5
x3
x3==2
3715
15
10 - 315
Can’t beUKORNKƂGF
57
15X = 1
7x
x
98= 1
81=3
8 3X = 38
31X
x
x
135
45
14x=
x
x
15=
SAME DENOMINATOR Same denominator – add or subtract across, denominatorstays the same.
=++2
12512
1920
, ,, ,
34
710
£50 ÷ 5 = £10£10 x 2 = £20
25
of £50x÷ 1 part
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PERCENTAGES
Percent % means out of 100.A way of writing a fraction with a denominator of 100.
FINDING % OF A NUMBER
METHOD 1 - FIND 1% Divide by 100.
= 42% = 2%42100
0.02 =0.42 = 2100
METHOD 2 - FIND 10% Divide by 10.
35% x 65g1% = 0.65g35% = 35 x 0.65g
Find 35% of 65g. Find 70% of 25g.
Find 15% of 500g0 6 5 3 5
3 2 51 9 5 02 2 7 5
x
+1
231 1
.
.
3.591.242.35
-98.71613.90784.809
-
Line the numbers up with the decimal point on top of each other.
ADDING DECIMALS SUBTRACTING DECIMALS
ADDING &SUBTRACTING DECIMALS
DIVIDE USING LONG DIVISIONAdd decimal points at the end.
Divide without decimal point.
Count how many digits are after the decimal points in both numbers.
19.2 ÷ 5number of decimal places = 1
Add decimal points back in.
192 ÷ 5 = 38
DIVIDING DECIMALS
number of decimal places = 1
MULTIPLYING DECIMALS
A number that contains adecimal point. Decimalpoint is between theones and tenths.
Digits before the decimalare whole numbers anddigits after the decimalpoint are part of a number.
H
2 2 0 . 5 3T O t. h
wholenumbers
part of anumber
ROUNDING TO NEAREST:
- tenths: 1 decimal place1 digit after the decimal
- hundredths: 2 decimal places2 digits after the decimal
- thousandths: 3 decimal places3 digits after the decimal
ROUNDING DECIMALS
DIGIT AFTER5 or more round up Less than 5 round down
2.315 2.32rounded to the nearest hundredth
2.315
2.315
2.315
Check 1st digit, 2nd digit, 3rd digit…Put a 0 where there are any missing digits.
COMPARING DECIMALS
2.32 0.34 0.22 2.56 2.37 0.304
0.22 , 0.304 , 0.34 , 2.32 , 2.37 , 2.56
0.34 0.22 0.304 all start with 0
From smallest to largest
Go to 2nd digit, 2 is the smallest so 0.22 is the smallest
2.32 0.34 0.22 2.56 2.37 0.304
2.32 0.34 0.22 2.56 2.37 0.304
DECIMALS
FRACTIONS, DECIMALS& PERCENTAGES F
Step 1
MULTIPLY NORMALLYAdd decimal points at the end.
Multiply without decimal point.
Count how many digits are after the decimal points in both numbers.
Add decimal points back in.
25 x 13 = 325
0.25 x 1.3number of decimal places = 3
2 5 1 3
7 52 5 3 2 5
x
+
number of decimal places = 3
Step 1
Step 2
Step 3
Step 2
Step 3
1_1
3_4
1_2
1_3
1_4
1_5
1_8
1_10
1_100
1.0
100% 75% 50% 33% 25% 20% 12.5% 10% 1%
0.75 0.5 0.33 0.25 0.2 0.125 0.1 0.01
Fractions
Percentage
Decimals
0.9 =
DECIMALS TO FRACTIONS
910
561000.56= 9
10000.009 =
FRACTIONS TO DECIMALSDivide numerator by denominator.
28 = 2 ÷ 8 or = 0.25÷
% TO DECIMALDivide thedecimal by 100.
34 % to decimal
34 ÷ 100= 0.34
DECIMAL TO %Multiply thedecimal by 100.
0.4 x 100= 40%
0.4 to %
0.9 x 100= 90%
0.9 to %
FRACTIONS TO %Multiply the fraction to get thedenominator out of 10 or 100.
45 as a % 4
5=
= 80%
x 80100
x 20
x 20
CONVERTING FRACTIONS ->DECIMALS -> PERCENTAGES
0 t 0 t h 0 t h th
2 .2040 00 . 2 5
8
14
510
3100
1.232.503.73
+
Add orSubtract -you canadd 0’son the end
63.85121.04 84.891
+
FRACTIONS, DECIMALS& PERCENTAGES FFRACTIONS, DECIMALS& PERCENTAGES F
25
= 38.4
% TO FRACTIONSPlace wholenumber over 100.
34100
34% =
410
0.4 = 40100
= 0 t x 10
x 10
Find 1% or 10%and use thisinformation toƂPF�QVJGTpercentages.
x7
+half of 10%
70% x £2510% = £25 ÷ 10 = £2.5070% = 7 x £2.50 = £17.50
15% x 500g10% = 500 ÷ 10 = 50g5% = 25g15% of 500g = 50g +25g = 75g
35% = 22.75g
METHOD 3 - % TO FRACTION
20% = 15
20% of 40
15 of 40 = 40 ÷ 5 = 8
÷
METHOD 4 -% TO DECIMAL & MULTIPLY
30% of 150cm30% = 0.30.3 x 150cm = 45cm
38.4 3.84
325 0.325
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RATIO
PROPORTION
Compares the sizes of 2 ormore numbers or amounts.
Ratio of circles comparedto squares 3 : 5
A box of pens has 4 blue pens forevery 5 black pens. Ratio would be:
If I bought 3 boxes,ratio would be:
3 5:
4 5:
12 15:
x 3
÷ 3
÷ 3
x 3
Compares part of a wholewith the whole amount.
What proportion of a class are boys?
1230
1830
+
The set of cubes below:
Proportion of grey cubes =
0.75 75% 912 3
4or or
0.25 25%or or
=
312
14
=
Proportion of blue cubes =
NUMBER SEQUENCES
The nth term rule lets you find out any term in the sequence.
Rule = n x 2 + 3 whichis written as 2n + 3
Term 1 2 3 45 7 9 11Number
14th number in the sequence would be:
3, 5, 7, 9...
Each number in a sequence is called a term.
SEQUENCE
1st term 3rd term three dots meansgoes on forever(infinite)
(“term”, “element” or “member” meanthe same thing)
2nd term 4th term
A list of numbers that are placedin an order. They follow a patternaccording to a rule.
3, 7, 11, 15, 19...
RULE: ADD 4
The next number in thesequence would be 23.
+4 +4 +4 +4
ALGEBRA
speed = distance_______
time
How long does it take to getfrom London to Manchester(240miles) at a speed of60miles/hour?
USING FORMULAE
240time60 =
distancespeedtime =
24060time =
SCALE FACTORS
UNEQUAL SHARING
By how much a shape has been enlarged. We use ratios to scale up ordown. Enlargement is changing the size of a shape (not always bigger).
SCALE FACTOR OF 2Shape B is twice thesize of shape A.
Adam, Raj & Lucy receive 1,000g of chocolate between them.Adam gets 15%, Raj gets 0.35 and Lucy gets .How many grams do they each receive?
Shape A1
2
Shape B
8 x 3 = 24y = 24
Shape A Shape B
4
x
8 12
÷3
÷3 18
y
x3
SCALE FACTOR OF 3
=Check:£105 + £35 + £7 = £210 = £35210
2+1+3 210
6
Share £210 in the ratio 2 : 1 : 3
1_2
Check: 150g + 350g + 500g = 1,000g
12 ÷ 4 = 3Scale Factor = 3
18 ÷ 3 = 6x = 6
SOLVING EQUATIONS
y = 2p + 5 + fUsing a letter torepresent a valueor number.
USING FORMULAE
Area of a triangle = bh__2
height (h)= 9cm
base(b) = 5cm
+ = 78 = 72
= 6
= 12
ALGEBRA A
RATIO &PROPORTION R
ds t
1 part = £35
(2p = 2 x p)
Check: 72 + 6 = 78 Check:726
= 12_
Substitute the lettersfor the numbers.
Step 1
Step 2
1_2
(This ratio has been scaled up.)
When p=2 and f =6, what isthe value of y?
£35 x 2 = £70 : £35 : £35 x 3 = £1052 1: 3:= 0.4
= 4 hours
y = (2 x 2) + 5 + 6y = 4 + 5 + 6y = 15
Area = 5 x 92
452= = 22.5cm2
2n + 3(2 x 14) + 328 + 3 = 31
Adam = 15% of 1,000g = 150g10% = 100g5% = 50g
Raj = 1,000g x 0.35 = 350gLucy = of 1,000g = 500g
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COMPARING NUMBERS
3TM
2, 5 5 7, 2 2 2 . 3 3 1M, HTh TTh Th, H T O . t h th
4 2, 3 1 5TTh Th, H T O
2 5, 7 3 9TTh Th, H T O
2, 4 1 5 . 6Th, H T O . t
The value of a digit according toits position within a number.
PLACE VALUE
Less than < Greater than Greater than > Less than= Equal to
10 + 5 = 154 x 6 < 7 2
24 < 49
ROUNDING
x 10/100/1,000 &÷ 10/100/1,000
TIMES TABLES UP TO 121X
123456789101112
123456789101112
24681012141618202224
2
369121518212427303336
4812162024283236404448
51015202530354045505560
61218243036424854606672
71421283542495663707784
81624324048566472808896
918273645546372819099108
102030405060708090100110120
112233445566778899110121132
1224364860728496108120132144
3 4 5 6 7 8 9 10 11 12
MULTIPLICATION & DIVISION
ADDITION & SUBTRACTION
ADDITIONInverse of subtraction.
4 2 83 9 5+1 1
8 2 3
Negative Numbers
Decreasing
+ Positive Numbers
1 2 43 5 6 7 8 9 100 -10 -9 -8 -7 -6 -5 -3 -2 -1-4
Increasing
Number lines for counting negative numbers always help!Always include 0 when counting.
What is the difference between 5 and -7?Difference between 5 and -7 is 12.
1 2 43 50 -6-7 -5 -3 -2 -1-4= 12
The temperature is –25 °C. How much must it rise to be at -4 °C?
NEGATIVE NUMBERS
ROMAN NUMERALS
- A letter can only be repeated 3 times.- Roman Numerals are made up by adding or subtracting numbers.- If there is a smaller value number. before a bigger one, we subtract- If there is a smaller value number after a bigger one, we add.
1 = I 6 = VI 2 = II 7 = VII 3 = III 8 = VIII 4 = IV 9 = IX 5 = V 10 = X
50 = L 100 = C 500 = D 1,000 = M
1,000 + 50 + 10 + 6 = 1066
M L X V I
N
CALCULATIONS C
add
Round to nearestten = 25,740hundred = 25,700thousand = 26,000ten thousand = 30,000
5 1. 3 4 9 6T O. t h th tth
Round to nearestone = 51tenth = 51.3
Giving an approximate value to a number.
Look at the digit before:If it’s 5 or more round up If it’s less than 5 round downLook at the digit after the one youare rounding. If you are roundingto the nearest thousand, look atthe hundreds!
1 9 . 6 3 . 19.63 x 100 = 1963
1 9 . 6 3. 19.63 ÷ 100 = 0.1963
hundredth = 51.35thousandth = 51.350
- +
÷ 10/100/1,000 x number gets bigger /÷ number gets smallerMove the decimal point tothe right (x) or left (÷) by:1 place for 102 places for 1003 places for 1,000 etc...
x
SUBTRACTIONInverse of addition.
1 10 122 0 2
5 4-9
1 4 8
SumTotalPlusAltogetherIncrease
Similar terms
DifferenceDecreaseTake awayMinusLess
Similar terms
-25°C
+10 +10 +1 = 21°C
-15°C -5°C -4°C
NUMBER &PLACE VALUE
The order in which you work outdifferent operations within acalculation.
BIDMASbrackets ( )
indices X2 / X3
division ÷addition +
multiplication x
subtraction -
Numbers that have beenmultiplied by a given number.
The first 12 multiples of 6 are:6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72
MULTIPLES
A number made when you multiplya number by itself 3 times.
2 3 = 2x 2 x 2 = 85 3 = 5 x 5 x 5 = 125
A number made when youmultiply a number by itself.
2 2 = 2 x 2 = 49 2 = 9 x 9 = 81
ORDER OF OPERATIONS
CUBE NUMBERS
A number which only has 2factors; 1 and itself.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,37, 41, 43, 47, 53, 59, 61, 67, 71...
FACTORS
PRIME NUMBERS
SQUARE NUMBERS
Numbers which can divide into agiven number without anyremainders. 1 , 24
2 , 12
3 , 8
4 , 6
Factorsof 24 are
LONG MULTIPLICATIONInverse of division. Similar terms
Doubled, tripled…PerProduct ofTimesOf
6 1 2 2 4x
+2 4 4 8
1 2 2 4 1 4,6 8 8
moveoveronespace product
xx
==
6 2 4 4 quotient
dividend
divisor
Similar terms
Share equallyPartsSplitDistributeAverage
LONG DIVISIONInverse of multiplication.
01725 425
04225175175000
prime factors - a factor which is also a prime number.
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COMPERIMETER
AREA OF TRIANGLE
Surface covered by a shape.Always ends in squared units(i.e. cm2 or m2).
AREA OF SQUARE &RECTANGLE= L x W
12
= x L x H
Height (H)
Length (L)
Height (H)
Length (L)
AREA OF PARALLELOGRAM= L x H
COMPOUND SHAPEA shape made up of 2or more other shapes.
Finding the perimeter whensides are missing:
AREA
Identify which lengths are missing.
Work out the missing lengths.
Calculate the perimeter by adding the lengths.
Length (L)
Width(W)4m
??
10m
12m
3m
4m
12m - 4m = 8m
12m
4m
7m8m
10m
12m
3m
TIME
24 hours = 1 dayDivided into two halves:first 12 hours = amsecond 12 hours = pm
hrs min
hrs min
min secs
min secs
x 60
÷ 60 ÷ 60
x 60
ANALOGUE / DIGITAL
CONVERTING TIME
1 millennium
1 century
1 leap year
1 week
1 day
1 hour
1 minute
1 year12 months /52 weeks /365 days
1,000 years
100 years
366 days
7 days
24 hours
60 minutes
60 seconds
12
67 58 49 310 2
11 00 132314221521
16201719 18
1
10m
3m
10m - 3m = 7m
CAPACITY
Amount contained within a space.Use beakers or measuring spoonsto measure: millilitre (ml), centilitre (cl), litre (L).
METRIC
1,000 ml = 1 L
10 ml = 1 cl
x 1000
x 10
IMPERIAL
1 litre 4.5 litresor 8 pints (approx.)
= 1.76 pints= 1 gallon 12,000 ml = 12 L
0.85 L = 850 ml
÷ 1000
x20 x20
x 1000
1 pint = 568 ml20 pints = 11,360 ml
MEASUREMENT
CIRCLE
kilo – 1,000 cent – 100
1,200 cm = 12 m 0.44 m = 44 cm
8 km = 5 miles56 km = 35 miles
÷ 100
x 100
LENGTH
The measure of distance from one end to another.Use tape measures/ rulers to measure: millimeter (mm),centimeter (cm), meter (m), kilometer (km).
IMPERIAL
8 km 1 inch1 foot
= 5 miles= 2.54 cm= 12 inches= 30 cm
METRIC
10 mm = 1 cm
100 cm = 1 m
1,000 m = 1 km
x 10
x 1000
x 100
IMPERIAL
1 pound (lb) =16 ounces
1 pound (lb) =453.6 grams
METRIC
1,000 mg = 1 g
1,000 g = 1 kg
1,000 kg = 1 tonne
x 1000
x 1000
x 1000
MASS
8,000 kg = 8 tonnes0.016 kg = 16 g
16 oz = 1 lb25 oz = 1 lb 9 oz
÷ 1000
x 1000
How much matter there is in an object, similarto weight. Weight can vary depending on whereyou are (such as on the moon), mass doesn’t vary.Use scales to measure: milligram (mg) , gram (g), kilogram (kg) , tonne.
CIRCLE
RADIUSDistance halfway across acircle; radius is always halfthe length of the diameter.
CENTRE POINTCentre point of a circle.
CIRCUMFERENCEDistance all the wayaround a circle.
DIAMETERDistance rightacross the middleof a circle.
VOLUME
MONEY
PERIMETER
The distance all the wayaround a flat shape.
PERIMETER= L + L + W + W= (2x L) + (2 x W) Length
(L)
Width (W)
Space taken up by a shape.Always ends in cubed units(i.e. cm3 or m3).
VOLUME OF A CUBOID= L x W x H
Height (H)
Width (W)
Length (L)
£1 = 100p
£ 2.15 pound
pence
CONVERTING MONEY
£1 = €1.4 (approx.)We use exchange ratesto convert money to different currencies.The rates are constantly changing.
p £÷ 100 x 100
£ p
12hr7pm1am
24hr19:0001:00
Step 1
Step 2
Step 3
milli – 1/1,000centi – 1/100
x7 x7
4 + 10 + 12 +3 + 8 + 7= 44m
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Copyright © 2016 by
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Copyright © 2016 by
A circular graph divided into segments,showing the proportion of differentamounts – just like a pie! Each segmentrepresents a fraction of the total amount.
PIE CHART HOW CLASS 7TRAVEL TO SCHOOL
other
WalkBike
CarOther Bus
STATISTICS S
LINE GRAPH
MEAN
TABLE
Used to plot a set of data over an amount of time.
554456567766
FebJan
MarAprMayJunJul
AugSeptOctNovDec
SAM’S SPELLING TEST MARKS OVER 1 YEAR
STATISTICS S
PICTOGRAM
Each image represents a number.
A pictogram to show the number ofgoals scored in 15 football matches.
0 goals
1 goal
2 goals
= 2 matches
= 5 matches
= 6 matches
= 4 matches
876543210
JanFeb
MarApr
MayJun
Jul
Months
Ma
rks
AugSept
OctNov
Dec
y
x
Step 1
Step 2
Answer
MEAN (AVERAGE)Sum of all values divided bynumber of values.
What is the mean of these 4 numbers?
7, 4, 11, 2
Add all values.7 + 4 + 11 + 2 = 24
÷ by the number.of values24 ÷ 4 = 6
The mean value is 6.
TEMPERATURE IN CAPE TOWN& MOSCOW OVER ONE WEEK
302520151050
-5-10-15
Mon Tue
Wed Thu
Fri
Sat
Sun
Day
Tem
pe
ratu
re (
°C)
Cape Town
Moscow
0901
0909
0918
0925
The table shows items sold at a cafe over a weekend.
Use the information alreadythere to complete the table.
Scone
67
33
100
Total
272
304
576
Coffee
104
79
183
Tea
60
41
101
Cake
41
151
192
Sat
Sun
TOTAL
80
70
60
50
40
30
20
10
00
5 10 15 20 25 30 35Time (minutes)
Tem
pe
ratu
re (
°C)
40 45 50
y
x
As time passesthe temperatureof the drinkcools down.
THE TEMPERATURE OF A HOT DRINK OVER AN HOUR
BAR GRAPHS
Mode of Transport
89
76543210 Bus Walk Car Bike Other
Nu
mb
er
of
Ch
ildre
n
y
x
A graph that uses bars to represent values and data.
HOW CLASS 7 TRAVEL TO SCHOOL
9 3 3 8 5WalkBus Car Bike Other
What fraction of the class travel by bus & car?
Total numberof children = 28bus + car = 9 + 3 = 12
DISTANCE/ TIME GRAPH
Used to plot distance over timefrom a certain point.Fflat line indicates a rest period.
The graph shows Anne’s journeyfrom home to her friend’s party.She stops to buy a gift. How longdid Anne spend at the gift shop?
This table shows the data from a survey of 90 people about theirfavourite pizza toppings.
Draw a pie chart for the datain the table.
Angles around a point = 360°
Step 1 360° ÷ 90 people = 41 person is represented by 4°.
Step 2 Multiply each row by 4.
Step 3 Draw a circle & use aprotractor to markeach side.
Margherita 22 x 4 = 88°
x 4 = 48°
x 4 = 196°
x 4 = 28°
favoritepizza toppings
Numberof people
Vegetarian 12
Pepperoni
Hawaiian
49
7
Total 90
Angle
Margherita Vegetarian
PepperoniHawaiian
Travel bybus & car:
1228
37=
÷4
÷4
8070605040302010
00
5 10 15 20 25 30 35Time
(mintues)
stationary
rest period = 15 minutes
steadyspeed
Dis
tan
ce (
me
ters
)
40
y
USING TIMETABLE
MEAN
0756
0807
0817
0825
0806
0817
0827
0835
0817
0828
0838
0845
0831
0839
0848
0855
0841
0849
0858
0905
0851
0859
0908
0915
Mya lives in Wyke Regis Smugglers. She has an 8:30am appointment atPortland Ripcroft. What is the latest bus she can take to make it on time?
Mya’s appointment is at 8:30 am. The latest bus she can take is the onewhich arrives in Portland Ripcroft at 08:25. This means she has to takethe 07:56 bus from Wyke Regis Smugglers.
Wyke RegisSmugglers
0729
0737
0747
0755
0736
0747
0757
0805
0746
0757
0807
0815
VictoriaSquare
EastonSquare
PortlandRipcroft
104 + 60 + 41= 205272 - 205 = 67
2D SHAPES
2D SHAPEFlat shape that has2 dimensions (length, width).
POLYGONShape with straight sides.
PARALLEL LINES2 or more lines which stay the samedistance apart and never meet, representedby smaller lines crossing the pair of parallel lines.
PERPENDICULAR LINES Meet to make aright angle.
POINT OFINTERSECTIONWhere 2 or morelines meet.
GEOMETRY
REGULAR POLYGONEqual sides & equal angles.
IRREGULAR POLYGONSides/ angles of different sizes.
CROSS SECTION
TRIANGLES
A view into the inside of theshape. When you cut the shape,you can see the cross section.
CROSS SECTION
EQUILATERAL TRIANGLE3 equal sides & 3 equal angles.
RIGHT ANGLED TRIANGLE• Can be isosceles or scalene.
1 angle = 90°
SCALENE TRIANGLE3 different angles &
3 different sides.
ISOSCELES TRIANGLE2 equal sides & 2 equal angles.
60°
60° 60°90°
2D SHAPES
are parallel
Kite
External External External
External External External
Trapezium
3D SHAPES
3 dimensions(length, width, height).
CUBE CUBOID
CYLINDERCONE
SQUARE BASED PYRAMID
TRIANGULARBASED PYRAMID
SPHERE
FACEEDGELine where two
VERTEXPlace where two or more
PRISMSame cross section across
GEOMETRY G
GEOMETRY G
Parallelogram
Heptagon
DecagonNonagon
Pentagon Hexagon
NET
A pattern which folds tomake a 3D shape.There can be more than 1
CUBE
NET OFA CUBE
NET OF ATRIANGULAR
BASED PYRAMID
Dodecagon
QUADRILATERALS -
Rhombus
SquareRectangle
Copyright © 2016 by
Copyright © 2016 by
Octagon
COORDINATES
FINDING COORDINATES
Coordinates are a set of numbers that show us the exact position (x, y).
x first – along the corridorthen y – up or down the stairs y is the vertical axis
x
Point A has the co-ordinates (3,5)0 1 2 3 4 5 6 7 8 9
Ax
y
2 4 6 8-8 -6 -4 -2-2
-4
-6
-8
8
6
4
2
4 quadrants
Record the coordinates known on the x and y axis.
Use the information to work out the missing coordinate.
x x
y
D = (2,2)
A B = (8,8)8
2
2 8
C = (8,2)
A = (2, 8)
X Y +
X Y
X Y+ +
X Y+
Step 1
Step 2
Answer
ANGLE RULES
RIGHT ANGLEAn angle that is
equal to 90°.
STRAIGHT LINE ANGLEAngles on a straight
line add up to 180°.a° + b° = 180°
3 right angles are equal to a turn.
Worth 3 x 90° = 270°Add up to 270°.
3_4
FULL TURN – 360°ANGLES AROUNDA POINT
360°4 right angles are
equal to a full turn.Angles around a point
add up to 360°.a° + b° + c° + d° + e° = 360°
TURN – 270°3_4
VERTICALLY OPPOSITE ANGLESAngles which are vertically
opposite from each other are equal in size.
45° xx = 45°
TURN – 90°1_4
TURN – 180°1_2
ANGLES IN AQUADRILATERAL(4 SIDED SHAPE)
Interior angles add up to 360°.
a° + b° + c° + d° = 360°
a° b°
c° d°
ANGLES IN ATRIANGLE
Add up to 180°.a° + b° + c° = 180°
b°
a°
c°
ANGLES IN A REGULAR POLYGONExternal angles add up to 360°.a° + b° + c° + d° + e° = 360°
a°
a°
b°
b°
Internalangle
Externalangle
170
1016
02
0
18018
0
015
030
140
40
130
50
120
60
110
70
100
80
90
90
80
100 110
7060
50130 40140 30150 2
0160
10170
0
120
ANGLES
TYPES OF ANGLES
MEASURING ANGLES
1. Place the centre point of the protractor on the vertex of the angle.2. Line up the base line (0 line) of the protractor with one of the angle rays.3. To find the angle, always read from 0, look at the number the second ray crosses.
angle = 35°
ACUTE ANGLEless than 90°
OBTUSE ANGLEmore than 90°less than 180°
REFLEX ANGLEmore than 180°less than 360°
RIGHT ANGLE90°
GEOMETRY
TRANSFORMATION
REFLECTIONFlips a shape across the line of reflection.
Line of SymmetryA line that divides a shape equally in two.
TRANSLATIONMovement of a shape,doesn’t change size or direction.
Can be translated horizontally,vertically or both.
Mirror LineLine used when reflecting a shape.
ROTATIONA circular movement,centre point stays fixed.
Centre point
x
y
anti-clockwise
clockwise
COMPASS DIRECTIONS
Written as 2 squares rightand 3 squares up.
y
A
B
A TO B2 right &3 up
B TO A2 left &3 down
Use a compassto tell directions. N
NE
SE
NW
SW
S
W E
GEOMETRY G
GEOMETRY G
x
c°
c°
b°
d°
d°
e°
e°
a°
There are different ways to transform a shape - reflect, rotate, translate.
Copyright © 2016 by
Copyright © 2016 by