Transcript Numeracy Powerpoint

Numeracy Posters Index
1 Measurements : Converting Weights
2 Measurements: Converting Units of Length
3
Measurements: Converting m/m
4 Time:
5 Time :
6 Ratio:
24 hour clock system
Calculating lengths of time
Using Ratios to solve problems
7
8
9
10
Direct Proportion
Rounding
Round numbers to 1 decimal place
Order of Priority
Finding a percentage
11
12
13
14
15
16
17
18
19
20
21
Finding the Percentage Increase
Decrease by a Percentage
Increase by a Percentage
Changing a Fraction to a Percentage
Working out percentages without calculators
Working out a percentage with the calculator
Speed Distance Time Questions
Drawing Bar Charts
Pie Charts
Read information from Pie Charts
Pie Charts
Construct Pie Charts
Averages
Musselburgh Grammar School
Back
Measurements Converting Units of Mass
1 kg= 1000g
x1000
Kilogramme
(kg)
grams
(g)
÷1000
Example 1 :
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 :
Musselburgh Grammar School
650 ÷ 1000 = 0.65 kg
Back
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
Musselburgh Grammar School
Back
Measurements
Converting between metres and millimetres
1m = 1000mm
x100
metres
(m)
÷100
centimetres
(cm)
÷10
metres
(m)
x10
millimetres
(mm)
x1000
centimetres
(cm)
÷1000
millimetres
(mm)
Example 1
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
Musselburgh Grammar School
Back
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
Musselburgh Grammar School
2000 becomes
8 pm
1730 becomes
5:30 pm
Back
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
Musselburgh Grammar School
Back
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
Musselburgh Grammar School
Back
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 :
85  5 = 17 p
Cost of 3 mars bars :
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
Musselburgh Grammar School
Back
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
Musselburgh Grammar School
12.7 (1d.p)
Back
Order of Priority
Brackets
then Multiply or Divide
then Add or Subtract
Example 1
Example 2
3+4x6
3+4x6+8
= 3 + 24
Multiply
= 3 + 24 + 8
then add
= 27
= 35
Example 3
18  6 + 3 x 4
=3+3x4
= 3 + 12
Carry out Steps
Musselburgh Grammar School
Divide 18  6 = 3
then multiply
3 x 4 = 12
then add
3 + 12 = 15
= 15
Back
Finding a percentage
Example 1
I got 30 out of 70 in my English test.
What is my percentage mark?
30 x 100%
70
= 42.85…%
Step 2 Then multiply your
answer by 100%
= 43%
Step 3 Round sensibly
Step 1 Divide 30 by 70
Does your answer make sense?
Check by working out 50%
Musselburgh Grammar School
Back
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
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?
Musselburgh Grammar School
Back
Decrease by a Percentage
Example 1
After boiling a liquid (500ml) for
5 minutes the amount of liquid has
been reduced by 8%.
Work out the new amount.
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
Musselburgh Grammar School
Back
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.
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
Musselburgh Grammar School
Back
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?
Musselburgh Grammar School
Back
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%
Musselburgh Grammar School
Back
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%.
Musselburgh Grammar School
Back
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
Musselburgh Grammar School
S = D T
= 150 2.5
= 60 m.p.h
Back
Drawing Bar Charts
Example : How do I draw a bar chart?
Draw and label the
axes
Step 1
Step 2 Mark an even scale on
the vertical axes.
Freq.
Plastic Paper
Type
Freq.
Mark numbers on the
lines
Step 3 Complete the graph by
drawing in bars of the
correct height.
Each bar should have
equal width.
Plastic Paper
Type
Freq.
Plastic Paper
Type
Quantities of Litter
Step 4 Give the graph a title
Freq.
Plastic Paper
Type
•Use a sharp pencil and a ruler
•Colour the bars in
Musselburgh Grammar School
Back
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
54o 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
Musselburgh Grammar School
Back
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
Musselburgh Grammar School
o
108o 90
36o
o
54 72o
Back
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
Musselburgh Grammar School
( as it appears twice in list)
Back