WHAT IS MATHS IN CONTEXT? - The Blue School, Wells · WHAT IS MATHS IN CONTEXT? An AS equivalent Students learn to use: a modelling cycle a statistical problem solving cycle a financial

WHAT IS MATHS IN CONTEXT?

An AS equivalent

Students learn to use:

a modelling cycle

a statistical problem solving cycle

a financial problem solving cycle

spreadsheets

They will:

work on a variety of problems

use and extend their understanding of maths

select appropriate ways of reasoning

Key Outcomes

Sound understanding of mathematical concepts, skills and techniques from GCSE and beyond.

• Fluency in procedural skills, common problem-solving skills and strategies.

• Confidence in applying mathematical and statistical thinking and reasoning in a range of new and unfamiliar contexts to solve real-life problems.

• Competency in interpreting and explaining solutions of problems in context.

WHY CHOOSE MATHS IN CONTEXT?

I recognise how important maths will be in other subjects and jobs in my future

I enjoy maths !

I want to apply my maths to real life applications

It reinforces my other subjects

It is a valued qualification by higher education establishments

It is useful and supports more job opportunities

I think I am good at it ?

WHO IS IT AIMED AT? Those who need support with maths for other A

levels: for example, in business, biology,

chemistry, computing, economics, geography,

ICT, psychology, sociology or health and social

care

Students who need to continue with some

mathematics because they intend to enter a

teacher training or health professional training

course

Year 12 and 13

Two Exams taken in Year 13

Each Exam is 2 hours

No Coursework

Introduction to Quantitative Reasoning

Critical Maths

Background knowledge

Need a level 5 grade or better at GCSE

That’s it!

What do we study?

Fermi Estimates

Screening

Finance, Business and Risk

Voting Systems

Expectation

Estimation

Exponential and Log Scales

Statistical Modelling

Normal Distribution

Regression

Sample Exam QuestionsA typical ant is about 5mm long and weighs about 3mg.

An actor is about 2m tall and weighs about 80kg.

A science fiction film script includes shrinking an actor to 5mm tall.As the actor shrinks,

his weight is always directly proportional to his volume.

Compare the weight of the shrunken actor to the weight of the ant.

[5]

This question is about estimating the average speed of the earth as it travels round the

sun.

The earth travels round the sun once a year. The average distance of the earth from the

sun is 1.5x1011m.

Assume that the sun remains still and ignore the rotation of the earth about its axis.

What assumption must be made about the path of the earth to allow you to estimate its

average speed?

Carry out the estimate, giving your answer in kmh-1.

[6]

“The new mathematics GCSE will be more demanding and we anticipate that schools will

want to increase thetime spent teaching mathematics. On average secondary schools in

England spend only 116 hours per year teaching mathematics, which international

studies show is far less time than that spent on this vital subject by our competitors. Just

one extra lesson each week would put England closer to countries like Australia or

Singapore who teach 143 and 138 hours a year of mathematics respectively.”

Michael Gove 1 Nov 2013

Estimate the number of extra mathematics teachers needed to increase average

mathematics teaching time for years 7 to 11 in England from 116 hours per year up to the

kind of time taken in Australia or Singapore.

You can use the following assumptions.

There are about 500 000 school students in each year group in England.

A typical secondary school mathematics teacher teaches between 20 and 25 hours a

week.

Students are at school for 190 days a year.

Any additional assumptions you make must be clear.

[7]

The residents of a small town find the cost of their house insurance has gone up. The

insurance companies say that their risk of flooding is high. A river flows through the town.

If the river level rises by more than 2 metres above a given datum level, the town will

flood.

The residents decide to investigate the situation so that either they can refute the

insurance companies’ argument, or they can claim funding for flood defences.

The town’s archives have records going back 120 years giving the greatest height of the

water above the datum level each year. The mean of these heights is 0.61m with

standard deviation 0.48m. One of the residents tries using the Normal distribution to

model this situation.

i. Show that using the Normal distribution as a model suggests that the flood risk in this

town means that a flood can be described as a “Once in 500 years event”.

[7]

Another resident points out that she has experienced three floods and she is

not very old. She draws this frequency diagram using the records of the

greatest heights above the datum level from the town’s archives.

ii. Taking this new information into account, comment on the work the residents

have done so far and advise them how they should proceed.

[3]

Any questions?