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 & Jo Byrne

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 plan to work on first? • Add the mathematical modelling examples you have spotted during the last week to the chat window. • Your email address? 2

Swan Principles Using the principles to consider how to self support your development (what works for you?) Mathematical modelling • keep a note of the location of your reading. • Use Harvard referencing Anglia Ruskin University. Harvard System. [online] Available at: https://libweb.anglia.ac.uk/referencing/harvard.htm [Accessed 12 June 2017]. 3

Session aim • To review participants’ personal mathematics relating to number • To apply concepts of number to solve problems • To update ILPs and plan for development of personal number skills 4

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? 5

Overseas visitors How useful would an approximation be? • A good double check – picks up those ‘oops’ moments on calculators • Good for your brain • It is a skill to develop • Rounding (up or down depending on context) • A logical or mathematical method e.g. approximating by using a comparison • When is an approximation not a good idea?

Proportional reasoning 7

Direct proportion - unitary litres £ x 15 1 15 x 0.6 x 0.6 x 15 0.6 ? 8

Direct proportion – non-unitary litres £ x 10/4 4 10 x 7/4 x 7/4 x 10/4 7 ? 9

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. 10

Direct proportion – representing the pattern Reduced Original x150% x 67% price yx1.005 y x y x 0.67 x 1.5 £y or 0.67 1.005y Direct proportion – using an example £100.5 £100 £67 x1.5 £67 11

Direct proportion – seeing more patterns Increased Reduced Original x50% price x 200% price y x 2 y 2y x 0.5 y Down by Up by 1/3 one half 1.5y or (3/2y)x y y 3/2y 2/3 After the session please download and print R3 and have a play – you need to experience this one 12

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? 13

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? 14

A formula for compound interest A = P(1+r) n A = total amount P = principal or original investment r = rate (as a decimal) n = number of years 15

Laws of indices When expressions with the same base are multiplied, the indices are added. • 2 3 x 2 4 = 2 ? • 2 3 x 2 4 = 2 7 When expressions with the same base (i.e. the ‘like’ terms) are divided the indices are subtracted. • 2 3 ÷ 2 4 = ? • 2 3 ÷ 2 4 = 2 -1 Remember we have to have like terms – we can’t multiply or divide 3 3 x 2 4 = ? i.e. we can’t simplify them. 16

Standard form Have a look at R7. 17

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 10 0 m Height of a tall skyscraper 400 4 x 10 2 m Height of a mountain 8 000 8 x 10 3 m Distance between two 20 000 000 2 x 10 7 m furthest place on earth Distance from earth to 400 000 000 4 x 10 8 m moon Size of a galaxy 800 000 000 000 000 000 000 8 x 10 20 m 18

Compound measures distance = speed x time speed = distance time = distance time speed D S x T 19

Can you use some of the techniques we have looked at to solve some speed and distance problems? 20

The 3 formulas for Speed, Time & Distance : Distance Distance Distance = Speed x Time Time = Speed = Speed Time Solving for Speed Solving for Time Solving for Distance D Remember them from S T this triangle:

A windsurfer travelled 28 km in 1 hour 45 mins. Calculate his speed. Distanc e D Speed = Time S T 28 = 1 hour 45 mins 1•75 = 16 km/h Answer: His speed was 16 km / hour

A salesman travelled at an average speed of 50 km/h for 2 hours 30 mins. How far did he travel? D Distance = Speed x Time S T = 50 x 2•5 2 hour 30 mins = 125 km Answer: He travelled 125 km

A train travelled 555 miles at an average speed of 60 mph. How long did the journey take? D Time = Distance Speed S T 555 = 60 = 9•25 hours = 9 hours 15 mins Answer: It took 9 hours 15 minutes

Question for you to work on: • Proportional reasoning • Compound measures • Standard form Our next session is 21 st November. You MUST attempt the following questions and send your workings and answers to me by end of play 19 th November. Ensure that your name IS NOT on the papers as I plan to upload these onto google docs. Once I have your attempt I will invite you to the google docs so that you can see the range of answers. You will be able to make comments (always positive and constructive). Noone will know who did which piece of work (but we will know who has made the comments). If you don’t send to me then you will not see everyone else’s attempts. We will look at them together at the beginning of session 3.

A few questions for you to have a go at 1. A company usually sends 9 people to install a security system in an office building, and they do it in about 96 minutes. Today, they have only 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 10 5 as an ordinary number. Work out the value of 2 x 10 7 x 8 x 10 -12 7. Give your answer in standard form. Work out the value of 3 x 10 -5 x 40,000,000 8. The surface area of Earth is 510,072,000km 2 . The surface area of 9. Jupiter is 6.21795 x 10 10 km 2 . The surface area of Jupiter is greater than the surface area of Earth. How many times greater? Give you answer in standard form.