Level 3 Award in Mathematics for numeracy Teaching: Session 2: - - PowerPoint PPT Presentation
Level 3 Award in Mathematics for numeracy Teaching: Session 2: Number Gail Lydon & Claire Collins Welcome! While we are waiting for colleagues to join the webinar note in the chat window: What you have highlighted in your ILP that you
Level 3 Award in Mathematics for numeracy Teaching: Session 2: Number Gail Lydon & Claire Collins
Welcome! While we are waiting for colleagues to join the webinar note in the chat window:
you plan to work on first
spotted during the last week
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Swan Principles
Using the principles to consider how to self support your development (what works for you?) Mathematical modelling
Anglia Ruskin University. Harvard System. [online] Available at: https://libweb.anglia.ac.uk/referencing/harvard.htm [Accessed 12 June 2017].
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Session aim
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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? Would an approximation do?
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Overseas visitors
How useful would an approximation be?
a comparison
Proportional reasoning
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Direct proportion - unitary
litres £ x 15 x 15 x 0.6 x 0.6 1 15 0.6 ?
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Direct proportion – non-unitary
litres £ x 10/4 x 10/4 x 7/4 4 10 7 ? x 7/4
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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. Percentage increase and decrease
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Direct proportion – representing the pattern
Original Reduced price
x 67%
£y y x 0.67 y x 0.67 x 1.5
x150%
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Direct proportion – using an example
£100 £67 £67 x1.5 yx1.005
1.005y £100.5
Direct proportion – seeing more patterns
Original Increased price
x 200%
y y x 2 2y x 0.5
x50%
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y 1.5y or 3/2y (3/2y)x 2/3 y y
Up by
Down by 1/3
After the session please download and print R3 and have a play – you need to experience this one
Reduced price
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?
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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?
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A formula for compound interest
A = total amount P = principal or original investment r = rate (as a decimal) n = number of years
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Laws of indices
When expressions with the same base are multiplied, the indices are added.
When expressions with the same base (i.e. the ‘like’ terms) are divided the indices are subtracted.
Remember we have to have like terms – we can’t multiply
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Standard form
Have a look at R7.
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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
Standard form
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Compound measures
speed = distance time distance = speed x time time = distance speed
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Can you use some of the techniques we have looked at to solve some speed and distance problems?
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The 3 formulas for Speed, Time & Distance:
Speed = Distance Time Time = Distance Speed Distance = Speed x Time
Remember them from this triangle:
D S T Solving for Speed Solving for Time Solving for Distance
D S T
A windsurfer travelled 28 km in 1 hour 45 mins. Calculate his speed. Speed = Distance Time 28 1•75 = = 16 km/h 1 hour 45 mins Answer: His speed was 16 km / hour
2 hour 30 mins Answer: He travelled 125 km
A salesman travelled at an average speed of 50 km/h for 2 hours 30 mins. How far did he travel?
D S T
Distance = Speed x Time = 50 x 2•5 = 125 km
Answer: It took 9 hours 15 minutes A train travelled 555 miles at an average speed of 60
D S T
Time = Distance Speed 555 60 = = 9•25 hours = 9 hours 15 mins
Question for you to work on:
Proportional reasoning Compound measures Standard form
A few questions for you to have a go at
1. A company usually sends 9 people to install a security system in an
three people to do the same job. How much time should be scheduled to complete the job? 2. A dog trainer has to feed vitamins to his adult dogs. The dosage for adult dogs weighing 20 pounds is 2 teaspoons per day. He needs to feed vitamins to a male dog weighing 75 pounds and to a female dog weighing 7 pounds. Determine the correct dosage for both male and female dogs. Note any assumptions you have made. 3. What speed covers 27 miles in 3 hours? 4. At 13mph, how far do you travel in 2 hours? 5. Write the number 0.00037 in standard form. 6. Write 6.43 x 105 as an ordinary number. 7. Work out the value of 2 x 107 x 8 x 10-12 Give your answer in standard form. 8. Work out the value of 3 x 10-5 x 40,000,000 9. The surface area of Earth is 510,072,000km2 . The surface area of Jupiter is 6.21795 x 1010km2. The surface area of Jupiter is greater than the surface area of Earth. How many times greater? Give you answer in standard form.