Transcript EYEMOUTH HIGH SCHOOL - KHS Home | Kelso High School

1.
Estimation & Measurement
2.
Rounding
3.
Addition, Subtraction, Multiplication & Division
4.
Scientific Notation / Standard Form
5.
Fractions
6.
Percentages
7.
Proportion
8.
Time
9.
Algebraic Expressions, Equations & Formulae
10. Co-ordinates
11. Data & Analysis
Estimation & Measurement
 Estimate / measure height and length in mm, cm, m
and angle sizes in degrees
eg. length of pencil ≈ 10cm
width of desk ≈ 0.5m
diameter of 1p coin ≈ 15mm
 Estimate / measure weight in g and kg, area in cm2,
m2 and hectares and volume / capacity in cm3, m3
and l
eg. bag of sugar ≈ 1kg
area of window ≈ 4m2
volume of drinks can ≈ 300ml
Estimation & Measurement
 Learn equivalences
100mm
1000mm
1cm3
1000cm3
10000m2
=
=
=
=
=
1cm
100cm =
1ml
1000ml =
1 hectare
1m
1l
Rounding
 Round to the nearest whole number,
10 or 100
eg.
74 to the nearest 10 = 70
347.5 to the nearest whole number = 348
 Round to any number of decimal
places or significant figures
eg.
7.51
=
3.14159 =
=
0.00231 =
7.5(1dp)
3.142 (3dp)
3.14 (3sp)
0.002 (1sf)
Rounding


When the next number is a 5 always round up


Never round as you go along – just at the end
Always round your final answer to the same level
of accuracy as your starting values
Watch out for necessary rounding
eg. If 90 children and 4 teachers go on a trip, how many
40-seater coaches would be needed ?
94  40 = 2.35 coaches which has to be rounded up
or some people will be left behind !
Addition, Subtraction, Multiplication & Division
 Subtract using decomposition (as a written method)
eg. 271
-38
233
 Do not borrow and pay back
 Calculate using alternative mental methods when
appropriate
eg. 478-99
= 379 by subtracting 100 then adding 1
eg. 1+2+3+ ……… +8+9+10
= 11 x 5
= 55
Addition, Subtraction, Multiplication & Division
 Use correct order of operations
 Remember BODMAS (or BOMDAS)
Brackets
Order
Divide
Multiply
Add
Subtract
eg.
18 – 7 x 2
= 18 – 14
=4
eg.
(14 + 12)  (6 – 4)
= 26  2
= 13
Scientific Notation or Standard Form

Write large or small numbers in standard form and vice versa
eg.




24500000 = 2.45 x 107
0.000988 = 9.88 x 104
Write as a x 10n where a is between 1 and 10
Use a calculator to carry out calculations involving standard form
eg.
To avoid confusion do not use 10x on calculator
Different calculators have different displays - learn how yours
works
Fractions

Find simple fractions of a quantity
eg.


1/5 of 70
= 70  5
= 14
eg.
2/3 of 120
= 120  3 x 2
= 80
Divide by the denominator, multiply by the numerator
Use equivalence of widely used fractions and decimals
eg.
3/10 = 0.3
eg.
Fractions

Add and subtract fractions

Common denominator for adding and subtracting

Never use decimals in a fraction question
Fractions
 Multiply fractions
Fractions

Cancel numerators and denominators first if possible to
simplify figures

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

Always write final answer as a mixed number
Always give your answer in its simplest form
Never cancel two numbers on the top/or bottom
Never use a common denominator when multiplying
Divide Fractions


To divide, invert second fraction and multiply
Don’t use a calculator for calculations involving fractions
Percentages

Find 50%, 331/3%, 10% and 1% without a calculator
and use addition to find other amounts
eg. 50% of £240
= ½ of £240
= £120
eg. 15% of £360
= 10% of £360 + 5% of £360
= £36 + £18
= £54
 Express some fractions as a percentage without a
calculator
eg.
Percentages

Find percentages with a calculator
eg. 23% of £300
= 0.23 x £300
= £69

Express fractions as percentages using a calculator
eg. A caravan was bought for £3000 and sold for £3250
What was the profit as a percentage of the cost price ?
Profit = £3250 - £3000 = £250
Percentages

Carry out calculations involving percentage increase
and decrease
eg. Increase £350 by 15%
1.15 x £350
= £402.50

Always change percentages to decimals when using a
calculator

Never use the percentage button your calculator
Proportion

Use the unitary method (ie. find the value of one
first, then multiply by the required value)
eg. Direct
If 5 bananas cost 80p, what do 8 bananas cost ?
 3 bananas cost 48p
eg. Inverse
The journey time at 60km/h
is 30 minutes, so what is the
journey time at 50km/h ?
 The journey time at 50km/h is 36 minutes
Proportion


Always communicate answer
Don’t round until the last stage
Time

Convert between 12 and 24 hour clock
eg. 2327 = 11.27pm



 Do not write 2327pm
Calculate duration in hours and minutes by counting
up to the next hour then on to the required time,
including pm  am times
Remember the cross-eyed frog !
Never use the percentage button your calculator
Time


Change minutes to hours and hours to minutes
eg. 27 mins
=
=
27  60hrs
0.45hrs
eg. 0.2hrs
=
=
0.2 x 60 mins
12 mins
Use the link between time, speed and distance to
carry out related calculations
Speed = 42 km/h
Distance = 800km
D
S
T
Algebraic Expressions, Equations & Formulae
Solving Equations

By balancing / using the flag method

Performing the same operation to each side of the equation

Doing ‘undo’ operations eg. undo ‘+’ with ‘-’

Using statements like
“multiply both sides by …”
Algebraic Expressions, Equations & Formulae



One equal sign per line, written underneath each other
Work down the page
Write the letter ‘x’ differently from a multiplication sign
 Never change side, change sign
 Do not write ‘nonsense’ statements, such as 2x = 6 = 3
Algebraic Expressions, Equations & Formulae
Formulae




Write down the formulae first
Substitute clearly
Simplify the expression
Communicate answer fully
 Always show all steps in working
 Always substitute first, then re-arrange as necessary to solve the equation
Co-ordinates

Cartesian Co-ordinates are pairs of numbers separated by a
comma and enclosed in brackets. Each pair of numbers gives
the position of a point relative to an origin O, eg. (3,4) is 3
units to the right along the x-axis and 4 units in the positive
y-direction and (-3, -2) is 3 to the left and 3 down.
 The points are marked where the lines cross, and not in the spaces
 The order matters in that (3, 4) is not in the same place as (4, 3)
(Remember: along the corridor then up (or down) the stairs !)
Data and Analysis





Use a pencil and ruler
Give the graph a title
Label lines
Label the frequency up the side
Label on lines, not on spaces
Bar Graph
 Construct and interpret bar graphs
eg.


Make sure each bar has equal width
Label each bar in its centre
Line Graph
 Construct and interpret line graphs
The distance a gas travels over time has
been recorded in the table below
Distance travelled by a gas over time
 Plot points neatly using a cross or dot
 If the lower point of a graph has been
missed out, use a jagged line to show this
Scatter Graph
 Construct and interpret scatter graphs
 Draw a line of best fit when there is a correlation
Pie Charts
 Construct pie charts involving simple
fractions, decimals or percentages
eg. 30% of pupils travel to school by bus
10% by car, 55% walk and 5% cycle
Bus
Car
Walk
Cycle
30% of 360°
10% of 360°
55% of 360°
5% of 360°
= 108°
= 36°
= 198°
= 18°
360°

check
Pie Charts
 Construct pie charts of raw data
eg. 20 pupils were asked “what is your favourite subject?”
Replies were Maths 5, English 6, Science 7, Art 2
Maths
English
Science
Art
5  20 x 360° = 90°
6  20 x 360° = 108°
7  20 x 360° = 126°
2  20 x 360° = 36°
360°

check