Numeracy
Across Learning
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Index
3
Measurements: Converting Units of Mass
4
Measurements: Converting Units of Volume
5
Measurements: Converting Units of Length 1
6
Measurements: Converting Units of Length 2
7
Time: 24 hour clock system
8
Time: Calculating Lengths of Time
9
Time: Converting minutes:seconds to seconds
10
Ratio: Using Ratio to Solve Problems
11
Direct Proportion
12
Rounding: Round Numbers to 1 Decimal Place
13
Order of Priority
14
Finding a Percentage
15
Finding a Percentage Increase
16
Decreasing by a Percentage
17
Increasing by a Percentage
18
Changing a Fractions to a Percentage
19
Working out Percentage without a Calculator
20
Working out Percentage with a Calculator
21
Speed, Distance, Time
22
Recording Data in Tables
23
Drawing Bar Charts
24
Drawing Line Graphs 1: Laying Out
25
Drawing Line Graphs 2: Points and Lines
26
Pie Charts: Reading Information from Line Graphs
27
Pie Charts: Constructing Pie Charts
28
Averages
Measurements: Converting Units of Mass
1 kg= 1000g
x1000
Kilogramme
(kg)
grams
(g)
÷1000
Examples :
Convert 2 litres to cm3
Convert 4.6 l to ml :
Convert 3000 ml to litres:
Convert 650 cm3 to l:
2 x 1000 = 2000 cm3
4.6x 1000 = 4600 ml
3000 ÷ 1000 = 3 l
650 ÷ 1000 = 0.65 l
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Measurements: Converting Units of Volume
1 litre = 1000 ml
1 ml = 1 cm3
x1000
litre
(l)
÷1000
Millilitre or
cubic centimetre
(ml or cm3)
Examples:
Convert 2kg to g :
2 x 1000 = 2000 g
Convert 4.6kg to g :
4.6x 1000 = 4600 g
Convert 3000g to kg :
3000 ÷ 1000 = 3 kg
Convert 650g to kg :
650 ÷ 1000 = 0.65 kg
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Measurements:
Converting Units of Length
1 km= 1000m
x1000
Kilometres
(km)
1m = 100cm
1cm = 10mm
x100
metres
(m)
÷1000
x10
centimetres
(cm)
÷100
÷10
millimetres
(mm)
Example 1
Convert 2m to cm :
2 x 100 = 200 cm
Convert 4km to m :
4 x 1000 = 4000 m
Convert 34cm to mm :
34 x 10 = 340 mm
Convert 50cm to m :
50 ÷ 100 = 0.5 m
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Measurements
Converting between metres and millimetres
1m = 1000mm
x100
metres
(m)
÷100
x10
centimetres
(cm)
millimetres
(mm)
÷10
metres
(m)
x1000
centimetres
(cm)
÷1000
millimetres
(mm)
Examples:
Convert 2m to mm :
Convert 3.34m to mm :
2 x 1000 = 2000 mm
3.34 x 1000 = 3430 m
Convert 4000mm to m : 4000 ÷ 1000 = 4 m
Convert 7800mm to m : 7800 ÷ 1000 = 7.8 m
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Time
Converting between the 24 hour
and 12 hour clock systems
12/24 Hour Clock
midnight
1 am
2 am
3 am
4 am
5am
6 am
7 am
8 am
9 am
10 am
11 am
0000
0100
0200
0300
0400
0500
0600
0700
0800
0900
1000
1100
midday
1 pm
2 pm
3 pm
4 pm
5 pm
6 pm
7 pm
8 pm
9 pm
10 pm
11 pm
1200
1300
1400
1500
1600
1700
1800
1900
2000
2100
2200
2300
all 24 hour clock times have 4 digits
To go from 12 hour clock to 24 hour clock
just add 12 to the pm hours:
Example 1
8 pm becomes
2000
6:30 pm becomes
1830
To go from 24 hour clock to 12 hour clock
just subtract 12 from the hours
(if it is greater than 12)
Example 2
2000 becomes
8 pm
1730 becomes
5:30 pm
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Time
Calculating lengths of time
Example 1 :
14 mins
0946
1000
Find the time difference between
09 46 hrs and 12 32 hrs
2 hours
1100
32 mins
1200
1232
Total Time = 2 hours + 14 mins + 32 mins
= 2 hours + 46 mins
Example 2 :
13 mins
0247
0300
Find the time difference between
02 47 hrs and 05 49 hrs
2 hours
0400
49 mins
0500
0549
Total Time = 2 hours + 13 mins + 49 mins
= 2 hours + 62 mins
= 2 hours + 1 hour + 2 mins
= 3 hours + 2 mins
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Time
Converting from Minutes and Seconds to Seconds
Remember: there are 60 seconds in 1 minute.
A stop clock might show time as
2 : 25
which is 2 minutes and 25 seconds.
To change from minutes and seconds to just seconds:
Multiply the minutes by 60, then add on the seconds
Example 1 : How many seconds in 2 mins 25 secs?
2 minutes = 2 x 60 seconds = 120 sec
Add the remaining seconds
2 : 25
120 + 25 = 145 seconds.
To change from seconds to minutes and seconds:
Divide the seconds by 60.
The answer is the number of minutes.
The remainder is the number of seconds.
Example 2 :
How many minutes and seconds
are in 193 seconds?
193 ÷ 60 = 3 remainder 13
Time = 3 minutes and 13 seconds
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Ratio
Using Ratios to solve problems
Ratios can be used to compare different quantities
Example 1
The recipe for humous is as follows
2 garlic cloves, 4 ounces of chick peas, 3 ounces of olives,
5 ml of Tahina paste and 4 tablespoons of olive oil
Write the ratio of chickpeas to olives
chickpeas olives
4:3
Ratios can be used to solve problems
Example 2
A chef makes more humous than normal.
If he uses 16 chickpeas, how many olives will he need
to use?
chickpeas olives
x4
4
3
16
12
x4
The chef will need 12 olives
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Direct Proportion
Example 1
If it costs 85p for 5 Mars bars,
what is the cost of 3 Mars bars ?
Find the cost of one !
Cost of 1 mars bar :
Cost of 3 mars bars :
85 ÷ 5 = 17 p
17 x 3 = 51p
Example 2
Three nights at Marton Manor Hotel
cost £165.
How much would five nights cost ?
Find the cost of one !
Cost of 1 night :
£165 ÷ 3 = £55
Cost of 5 nights : £55 x 5 = £275
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Rounding
Round numbers to 1 decimal place
7 .2 3 cm
1st decimal
place
7.20
7.21
7.22
7.23
7.24
7.25
7.26
7.27
7.28
7.29
2nd decimal
place
7.30
7.31
7.32
7.33
7.34
7.35
7.36
7.37
7.38
7.3cm
7.2cm
7.40
7.4cm
7.24
7.24 is nearer to 7.2
7.39
7.38
7.38 nearer to 7.4
The rules for rounding to 1 decimal place are:
If the 2nd decimal place is 4 or less
- leave 1st decimal place as it is
If the 2nd decimal place is 5 or more
- add 1 to 1st decimal place
Example :
Round the numbers to 1 decimal place
(a) 9.04 9.0 (1d.p)
(b) 18.08 18.1 (1d.p)
(c) 24.25 24.3 (1d.p)
(d) 12.73
12.7 (1d.p)
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Order of Priority
Brackets then Of
then Multiply or Divide
then Add or Subtract
Example 1
Example 2
3+4x6
3+4x6+8
= 3 + 24
Multiply
then add
= 3 + 24 + 8
= 35
= 27
Example 3
Example 4
18 ÷ 6 + 3 x 4
1/3 of (3 + 6) + 5
=3+3x4
= 1/3 of 9 + 5
= 3 + 12
=3+5
= 15
=8
Divide 18 ÷ 6 = 3
then multiply
3 x 4 = 12
then add
3 + 12 = 15
Add 3 + 6 to simplify
the bracket
Then take a third of 9
Then add
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Finding a Percentage
Example 1
I got 30 out of 70 in my English test.
What is my percentage mark?
Percentage =
part x
whole
100
Step 1 Divide 30 by 70
30 x 100%
70
Step 2 Then multiply your = 42.85…%
answer by 100%
= 43%
Step 3 Round sensibly
Does your answer make sense?
Check by working out 50%
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Finding the Percentage Increase
Example 1
The volume of dough increased from
50cm3 to 74cm3 due to the effect
of yeast.
Work out the % increase
Percentage Increase =
Change x 100
starting value
Step 1 Work out the increase.
74 – 50
= 24
Step 2 Divide the increase by
= 24 x 100%
the starting volume.
50
Step 3 Multiply your answer
= 48%
by 100%
Does your answer make sense?
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Decrease by a Percentage
Example 1
After boiling a liquid (500ml) for
5 minutes the volume of liquid has
been reduced by 8%.
Work out the new amount.
Change = percentage change
100
x starting value
Step 1 Divide 8 by 100
8 x 500
100
Step 2 Multiply your answer
by 500
=40ml
Step 3 Subtract your answer
from 500
500 – 40
=460ml
Does your answer make sense?
Work out 10% mentally.
Alternative method:
Decrease by 8% = means a multiplier of 0.92
New volume = 500 x 0.92
= 460ml
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Increase by a Percentage
Example 1
The volume of dough increased by 18%
due to the effect of yeast.
At the start the volume of dough was
26cm3. Work out the new volume of
dough.
Change = percentage change
100
x starting value
Step 1 Divide 18 by 100
Step 2 Multiply your answer
by 26
Step 3 Add your answer
to 26
18 x 26
100
=4.68cm3
26 + 4.68
=30.68cm3
Does your answer make sense?
Work out a 20% increase mentally.
(i.e. 10% and double)
Alternative method:
Increase by 18% = means a multiplier of 1.18
New volume = 26 x 1.18
= 30.68cm3
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Changing a Fraction to a Percentage
Example 1
Change 1 to a percentage
8
Step 1 Divide 1 by 8
1 =0.125
8
Step 2 Multiply your answer 0.125 x100%
100%
=12.5%
Does your answer make sense?
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Working out a percentage without the calculator
The 10% Route
Example 1
Work out 65% of £46
10% = 4.60
50%= 23.00
5% = 2.30
65% = £29.90
85%:
10%
+5%
15%
100%
-15%
85%
45%:
10%
20%
40%
5%
40%
+5%
45%
17 ½% = 10% +5% +2 ½%
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Working out a percentage with the calculator
Example:
Work out 65% of £46?
= 65 x 46
100
Step 2 Multiply your answer
=£29.90
by 46
Step 1 Divide 65 by 100
Does your answer make sense?
Work out 50%.
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Speed Distance Time Questions
Use the formula triangle !
To remember the formula
Cover up the letter you need to find out
Example 1
A car travels at a speed of 40m.p.h for 3 hours
What distance does it travel?
s = 40 m.p.h
d=?
t = 3 hours
d=sxt
= 40 x 3
= 120 miles
Example 2
A lorry travels a distance of 150km in 2 hours 30mins
What speed did it travel at?
s=?
d = 150km
t = 2hrs 30mins
= 2.5 hours
s=d÷ t
= 150 ÷2.5
= 60 m.p.h
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Recording Data in Tables
Scientific data should be recorded in a table.
Step 1 Draw the table.
Underline the headings.
Step 2 Headings: Use the
variables as headings.
Time
Temperature
The input variable goes in
the first column or row.
The outcome variable goes in
the second column or row.
Step 3
Units: Put the units
in the headings
Step 4 Data: remember to
include the starting
values.
Time (mins)
Temperature
(oC)
Time (mins)
Temperature
(oC)
0
20
• A variable is something which changes.
• The input variable is the one which is
changed by the scientist.
• The outcome variable is the result of
the experiment.
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Drawing Bar Charts
Example : How do I draw a bar chart?
Step 1
Step 2
Labels: Draw and
label the axes
Scale: Mark an even scale
on the vertical axes.
Freq.
Plastic Paper
Type of litter
Freq.
Mark numbers on the lines
Plastic Paper
Types of litter
Step 3
Bars: Complete the graph
by drawing in bars of the
correct height.
Freq.
Plastic Paper
Types of litter
Each bar should have
equal width.
Step 4 Give the graph a title
Quantities of Litter
Freq.
Plastic Paper
Types of litter
• Use a sharp pencil and a ruler
• You may want to colour the bars in
(but it is not essential)
• Note: For a histogram, the bars
should be touching.
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Drawing Line Graphs 1: Laying out
Example : How do I lay out a line graph?
Step 1
Label the Axes.
Draw and label the axes.
y axis
(outcome)
x axis (input variable)
The input variable goes on
the x-axis, the outcome
variable goes on the y-axis.
Use the headings from the
table of data.
Temperature
(oC)
Time (minutes)
Remember the Units
Step 2 Scale: Mark an even scale
on the both axes.
Mark the numbers on the
lines.
80
Temperature 60
(oC)
40
20
0
0 2 4 6 8 10 12
Time (minutes)
The steps on the scale should
be either 1, 2, 5, 10, 20, 50
(like coins)
Step 3
Give the graph a title
•Use a sharp pencil and a ruler
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Drawing Line Graphs 2: Points and Lines
Example : How do I plot the data on a
line graph?
Step 1
Scale:
80
Work out the smaller steps.
How big are the steps of
each small box on each axis?
Step 2
60
40
20
0
Points:
Mark each point with a tiny
dot.
Work out exactly where to
put it. Count both up and
down to check.
Step 3 Line or Curve:
80
60
Temperature 40
(oC)
20
0
0 2 4 6
8 10 12
Time (minutes)
Join the dots.
If the points are scattered around a
straight line, use a ruler to draw a line of
best fit.
If the lines form a curve, draw the curve
freehand.
Note: Some subjects have specific rules about the type of line to use.
•Use a very sharp pointed pencil.
•Make a tiny dot but you can draw a
circle round it to make it more obvious.
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Pie Charts
Read information from Pie Charts
Pie Charts are used to display all types of information
Hint : The angles in a
pie chart all up to 360º
Example 1
A survey of pupils favourite sport was
done. 300 pupils were asked
o
108o 90
36o
o
54 72o
This is number
of pupils asked
How many pupils liked football ?
The angle for football is 108º.
The total angle is 360º.
Number liking football = 108 x 300
360
= 108 ÷ 360 x 300
= 90
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Pie Charts
Construct Pie Charts
Pie Charts are used to display all types of information
Example 1
A survey of pupils favourite sport was
done. 300 pupils were asked
Favourite Sport
The results are shown in
the table
Rugby
75
Football
90
Display the results in a
pie chart
Cricket
45
Ice Hockey
60
Squash
30
To get the angle for Football
Number liking football = 90
Total number asked
= 300
Angle= 90 x 360
300
= 90 ÷ 300 x 360
= 108º
o
108o 90
36o
o
54 72o
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Averages
There are 3 types of Averages.
Which one are you trying to find out?
Mean: this is usually what people think of as average
Median: this is the middle number
Mode: this is the number that appears most often
Example 1
Look at the following ages of children attending
an after school club
5, 3 , 7, 6, 7
a)Find the mean
Add up the numbers = 5 + 3 + 7 + 6 + 7 = 28
Divide this total by how many numbers are in
the list
so Mean = 28 ÷ 5 = 5.6
b)Find the median
Rewrite list in order 3 ,5 ,6, 7, 7
Middle number
3 ,5 ,6, 7, 7
Median = 6
c)Find the mode
Mode = the number which appears most often
Mode = 7
( as it appears twice in list)
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