Transcript Number master class - presentation

Support for English, maths and ESOL
Module 7: developing the personal maths
skills of teachers and assessors
Masterclass 1: Number
Welcome!
Please introduce yourself to a colleague or two
and locate a set of cards on the table.
Looking at the cards, discuss each of the
elements of business performance and consider
which of these would be improved by better
English and maths skills.
Session aim
• To review and extend participants’
personal mathematics relating to
number
• To apply concepts of number to solve
problems
Outcomes
By the end of the session participants will have:
• Reviewed issues related to rounding, estimating and
accuracy
• Revised and consolidated understanding of direct
and inverse proportion
• Extended proportional reasoning to understanding of
inverse percentages and compound increase
• Identified and used the rules of indices
• Interpreted and calculated with numbers in standard
form
• Applied understanding of number to solve practical
problems
Overseas visitors
In 2004 a total of 26.2 million overseas visitors came to
the UK. 16.4% of these came from North America, and
they spent an average of £670 per visit.
The number of visitors from North America increased by
11.8% over the next 2 years, while the amount they
spent per visit increased by 18.1%.
What was the total amount spent by visitors from North
America in 2006?
Proportional reasoning
Direct proportion - unitary
litres
£
x 15
1
15
x 0.6
x 0.6
x 15
0.6
?
Direct proportion – non-unitary
litres
£
x 10/4
4
10
x 7/4
x 7/4
x 10/4
7
?
Compound measures
distance = speed x time
speed = distance
time
time = distance
speed
D
SxT
Percentage increase and decrease
In a sale, the prices in a shop were all
reduced by 33%.
After the sale they were all increased by 50%.
What was the overall effect on the shop
prices? Explain how you know.
Interest
Bob and Sandra are thinking of investing £1,000
in a five-year fixed rate savings scheme, paying
interest at 10% pa.
Bob says that at the end of the 5 years, their
investment will be worth £1500.
Sandra disagrees and says that it’ll be worth
more than £1600.
Who is correct and why?
Compound interest
With compound interest, the interest is added to the
investment each year (or sometimes each month or
each day)
In this case, after 5 years at 10% pa interest, the
investment will be worth:
= £1000 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1
= £1610.51
Can you use this to produce a general formula for
compound interest?
A formula for compound interest
A=
n
P(1+r)
A = total amount
P = principal or original investment
r = rate (as a decimal)
n = number of years
Standard form
Nucleus of an atom
0.00000000000001
1 x 10-14 m
Length of a virus
0.0000002
2 x 10-7 m
Diameter of the eye of a fly
0.0008
8 x 10-4 m
Diameter of a 1p coin
0.02
2 x 10-2 m
Height of a door
2
2 x 100 m
Height of a tall skyscraper
400
4 x 102 m
Height of a mountain
8 000
8 x 103 m
Distance between two
furthest place on earth
20 000 000
2 x 107 m
Distance from earth to
moon
400 000 000
4 x 108 m
Size of a galaxy
800 000 000 000 000 000 000
8 x 1020 m