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My LGBTQ Finance Project

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Cost Benefit & Risk Analysis Question Generator

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Cost Benefit & Risk Analysis Question Generator

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A Worksheet generator for Risk Analysis (similar in style to the final question of Paper 2B)

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A HW generator for the Personal Finance (3.02) section of the spec. NOTE - Tax/NI thresholds are for the tax year 2020-21 (which would be used in the Summer 2021 Paper 1) Keeps these basic skills ticking over all year

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Scott Cameron (@Scott_M_Cameron on Twitter) has some TES resources for Tax/NI, Confidence Intervals & Normal Distribution (Paper 2A)

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The Core Maths SOW/SOL (whichever you call it!) for 2020-21 based on AQA 2B

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Cat Van Saarloos (@CoreMathsCat on Twitter) Teaching Financial Maths Padlet with links to various financial resources (Including some that are here too!)

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Cat Van Saarloos (@CoreMathsCat on Twitter) Getting Started with Core Maths Padlet

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Another selection of misleading and frankly terrible graphs students could be shown

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Misleading Graphs in Real Life: Overview

Misleading graphs are sometimes deliberately misleading and sometimes it's just a case of people not understanding the data behind the graph they create. The "classic" types of misleading graphs include cases where:

The Vertical scale is too big or too small, or skips numbers, or doesn't start at zero.

The graph isn't labeled properly.

Data is left out.

But some real life misleading graphs go above and beyond the classic types. Some are intended to mislead, others are intended to shock. And in some cases, well-meaning individuals just got it all plain wrong. These are some of my favorite recent-history misleading graphs from real life.

Watch the video for a few examples:

Can't see the video? Click here.

Misleading Graphs: The Missing Baseline.

The Times leaves the rest behind...or does it?

You might be thinking that the graph on the right shows The Times makes double the sales of The Daily Telegraph. But take a closer look at the scale and you'll see although The Times does make more sales, it's only beating the competition by about 10%.

USA Today

USA today is notorious for fussy graphs that have too much information and mislead. This graph makes our welfare problem look like it's spiraling out of control. But note where the y-axis starts...at 94 million!

This one has the correct figures, but that BIG HEADLINE makes you think that 5.3% of children get spinal cord injuries...a pretty scary statistic for parents:

For the record, the real figure is about .0000003% (based on 2000 injuries per year out of a population of around 74,000,000).

Fox News Misleading Graphs.

Fox News showed this chart of what would happen if the Bush tax cuts expired. Disastrous, right? Again, check the scale (it starts at 34). All is not what it seems.

Not to keep on bashing on Fox News, but their name came up time and time again when searching for misleading graphs from real life. Here's another, designed to show that after a small drop in unemployment it went up and up in the Obama administration.

Note that the value for November (8.6) has not been plotted correctly. It's placed at the 9.0 position. That's not the only problem with this graph. It's been plotted to look like there's exponential growth when in fact, the overall employment trend is pretty stable at around 9%.

Here's what the graph should look like if it had been plotted correctly. See the difference?

Those d%$n Liberals!

A final example of this type of misleading graph. Terry Schiavo was removed from life support after a years-long court battle. CNN used a graph similar to the one below to show who agreed with the decision to remove the feeding tube.

A fist look at this graph makes it look like three times as many democrats supported the decision. But on closer inspection, note the scale on the vertical axis. Only slightly more democrats supported than republicans (62% vs. 54%).

What is the problem with these particular misleading graphs from real life? In general, graphs should show a baseline. A baseline is zero on the vertical scale. Graphs that have a missing baseline and start at some arbitrary number (34 on the Fox News image) tend to be very misleading. When you look at a graph and try to figure out if it's a true representation of what's really going on, check that baseline.

Misleading Graphs: Incomplete Data.

If you really want to make a shocking statement, make sure you only include part of the data. Take this first example of a misleading graph that proves global warming is real.

Global Warming out of Control!

What's wrong with this picture? It only shows the first half of the year, so of course temperatures are rising dramatically.

Deficit an Ongoing Problem!

Here's another example of incomplete data. This graph makes it look like the deficit has always been high, because the graph starts in 2009. This might lead you to think that the deficit has been an ongoing problem. It hasn't: The deficit was just 1.2 percent of GDP in 2007, when the housing market collapsed.

Our Cream Beats the Itch!

I'm not sure what to say about this graph for the anti-itch cream, Lanacane.

It looks like lanacane works better than regular anti-itch cream, right? Note the lack of labels. What is this graph actually telling us? Pretty much nothing at all other than their statisticians are very good at making not-very-good graphs.

Misleading Graphs: Just Reading it Plain Wrong

Global Warming Stopped!

Here's another global warming picture, from the British tabloid the Mail on Sunday. The newspaper used it to claim that global warming had stopped.

When we read newspapers, we often think the people writing the articles are experts. In fact, the journalist who wrote the article to go with this picture ( David Rose) just didn't understand what the graph was telling him. He made two errors:

1. The graph is showing air temperatures. This is a very poor measure of global warming as much of the heat ends up in the oceans.

2. This is a very short term graph. You can't make good predictions based on a little data. If you win the first scratch-off lottery ticket you buy, it doesn't mean that your chances of winning are 100%. You would have to buy (and scratch-off) dozens or even hundreds of tickets to truly see a trend. A better graph for global warming would show the trend since the industrial revolution.

College not Worth Your Time and Money!

How about this chart that "proves" that college education just isn't worth the money any more?

The scale on this chart is fine. What Business Insider deduced from the chart is not. Have we "...lost the ubiquitous positive financial return on education"? No. David Blake read the chart without taking into account a key fact that wasn't on the chart: the cost of not going to college has diminished even more. Than means, your prospects as a high school graduate are a lot worse than your prospects as a college graduate.

Another key piece of information is on the chart itself. Note the average yearly income a college grad can expect is about $45,000 in 2010. That's per year. Over an average working lifetime (say, 43 years assuming retirement at age 65), that gives you an income of $45,000 * 43 = $1,935,000. Subtract that expensive college education ($95,000) and your net earnings are $1,840,000. Compare that to your average high school grad. They can expect to earn $1,300,000 over their lifetime (Source: The U.S. Department of Education). That's quite a difference!

The moral of the tale? Be cautious when trying to read a chart about a topic you aren't an expert in!

Wii is Floundering!

Everyone can be an expert in gaming systems, right? After all, what's there to know? How to put a disk into the console? How to hold a controller? How to fire a weapon? This graph from 2009 showed how a dismal 6% of Wii owners actually used their Wii:

Lee Evans, in his Downwards Compatible article "Adventures in Misleading Graphs" put it best:

Take a look at the top number on the graph. Only 11% of 360 owners actively use their 360 and only 10% of PS3 owners actively use their PS3. Now, let's do a little math.

There are 50 million Wii owners. 6% of that number is 3 million.

There are 30 million 360 owners. 11% of that number is 3.3 million.

There are 20 million PS3 owners. 10% of that number is 2 million.

In other words, almost the same amount across the board use their system regularly. The gap in percentages is not that great, but the graph (and the way people are reading it) makes it look like "OMG A HUEGE GAP!"

Misleading Graphs: Numbers that Don't add up

Palin for Pres!

Apparently 70% of people backed Palin in the 2012 presidential run. But wait! The Fox News statisticians have been at it again. A pie chart should add up to 100%. Not this one:

Misleading Graphs: Two Y-Axes

Job and health insurance losses accelerating!

At first glance, it looks clear that statement is true. But take a look at the graph and you'll see two y-axes. This special type of data manipulation goes beyond the classic methods to deceive. What's actually going on here (skipping the math part) is that if you extract the data from this confuddling mess of a graph you get:

Lack of insurance is increasing very slightly (from ~15 percent to ~16 percent).

Unemployment increases more rapidly (from ~4.5 percent to 7.5 percent).

And the Winner in the Misleading Graphs category is...

The award for in the misleading graphs in real life category goes to (drum roll please...) Fox News for this gem:

What's the real data behind this shocking graph? Are there really more people on welfare than those who have full time jobs? As Media Matters points out:

"Fox's 108.6 million figure for the number of "people on welfare" comes from a Census Bureau's account...of participation in means-tested programs, which include "anyone residing in a household in which one or more people received benefits" in the fourth quarter of 2011, thus including individuals who did not themselves receive government benefits. On the other hand, the "people with a full time job" figure Fox used included only individuals who worked, not individuals residing in a household where at least one person works."

In other words, if you live with your Mom, Dad, brother Joe and cousin Sam, and Sam was (briefly) on some kind of welfare program, that counted against you and everyone in your household.

References

Huff, D. (1993). How to Lie With Statistics. W. W. Norton & Company
Gonick, L. (1993). The Cartoon Guide to Statistics. HarperPerennial.

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Misleading graphs are sometimes deliberately misleading and sometimes it's just a case of people not understanding the data behind the graph they create. The "classic" types of misleading graphs include cases where: The Vertical scale is too big or too small, or skips numbers, or doesn't start at zero.

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Here are some misleading graphs from the 2017 UK General Election

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9 Deeply Questionable Graphs On 2017 Election Leaflets

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Every time you abuse the y-axis, a psephologist dies.

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Critical Analysis Exam questions from 2016-2018 papers (the common questions to all options)
[You will need the Preliminary Materials for these]
Courtesy of Rhys Williams (@MrWilliamsMaths on Twitter)

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Cost-Benefit Analysis Exam questions from 2016-2018 papers
Courtesy of Rhys Williams (@MrWilliamsMaths on Twitter)

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Expectation Exam questions from 2016-2018 papers
Courtesy of Rhys Williams (@MrWilliamsMaths on Twitter)

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Critical Path Analysis Exam questions from 2016-2018 papers
Courtesy of Rhys Williams (@MrWilliamsMaths on Twitter)

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The AMSP provides support for Core Maths, including a wide range of flexible professional development. These opportunities are often free and in some cases additional subsidies are available to enable more teachers to participate.

The Teacher Events Calendar below provides details of all of our professional development events, including a range of opportunities designed and delivered according to local need by our local Area Coordinators, such as one-day Core Maths courses. It is followed by details of our standard courses.
Events Calendar
Live Online Professional Development

On Demand Professional Development

Face-to-face courses

Conferences

You might also be interested in Teacher Network meetings organised by our local Area Coordinators, which focus on sharing good practice, professional development and promoting developments in teaching and learning.

If your school/college is involved in Initial Teacher Training, you might be interested to know that we can provide focused one- or two-day sessions on aspects of teaching Core Maths for groups of trainee teachers. Contact us for details.

Details of all of our professional development courses are available on our Events listing. If you have a particular need and you cannot find something suitable there, please contact your local AMSP Area Coordinator who will be able to advise you. Alternatively, please complete this expression of interest form to advise us of the type of professional development that interests you. The detail you provide will be used to alert you if professional development which matches your need is made available.

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The AMSP provides support for Core Maths, including a wide range of flexible professional development. These opportunities are often free and in some cases additional subsidies are available to enable more teachers to participate.

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Facebook Group for Level 3 Core Maths

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Log into Facebook to start sharing and connecting with your friends, family, and people you know.

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Some graphs that have circulated on Social Media (from the media) of graphs used to show statistics relating to Covid 19. What is wrong with them?

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Something I've put together for Yr11s who are remotely preparing for Core Maths in September 2020

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Question Generator for Mortgage questions

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A basic spreadsheet calculator for 2020/21 Tax, NI, Student Loans as a way to check your answers (with most 'working' shown)

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A PowerPoint I have used for RPI/CPI

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Questions Inspired By A News Story (QUIBANS)

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Questions Inspired By A News Story (QUIBANS)

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A brilliant Blog with Core Maths questions inspired by news stories

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From The Times Newspaper: The over-55s keeping classrooms going amid a teaching crisis Richard Lewis will be 70 on Tuesday. A former City ba...

This is taken from a Daily Telegraph article (with paragraphs removed to save space). Shrinkflation is speeding up at an alarming rate T...

With thanks to Cat van Saarloos for the data file, here's a Quibans from the Daily Mirror. Police release names most commonly linked wit...

From The Times Newspaper: The over-55s keeping classrooms going amid a teaching crisis Richard Lewis will be 70 on Tuesday. A former City ba...

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Items that can be used to provoke mathematical questions. Particularly useful for teachers of Core Maths.

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Fermi Estimation - Things you should know...

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Fermi Estimation - Things you should know...

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A rough what you should know with some suggested answers - this is not definitive or to be taken as exact!!

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Core Maths Fermi Estimation What you should know.... ANSWERS

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A stimulus for Estimation

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A stimulus for Estimation

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A stimulus for Estimation

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A stimulus for Estimation

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A stimulus for Estimation

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A stimulus for Estimation

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A series of graphs I will show to highlight some genuine bad graphs used in the media and how they can be used to manipulate

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@CoreMathsCat's Padlet for the Summer 2020 AQA Pre-release which will be used in the Autumn "resit" series

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A HW generator for the Analysis of Data (3.01) section of the spec. Keeps these basic skills ticking over all year

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Core Maths Skills Check Generator (Paper 1 Analysis of Data) 19-20 V1

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University of Plymouth Core Maths Subject Support

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University of Plymouth Core Maths Subject Support

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Sets of questions and teacher notes (CIMT style) for various topics

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FINANCE 1 Exchange Rates 2 Simple and Compound Interest 3 Loans and Mortgages 4 Inflation Indices 5 Tax and National Insurance

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Core Maths Level 3 Certificate - TLMaths314

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01. Box Plots, Cumulative Frequency and Histograms

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Finance Quiz in Guardian Paper (04/05/2019)

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Finance Quiz in Guardian Paper (04/05/2019)

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Working with National Numeracy Day on 15 May, we've compiled a quiz - and some tips on how to improve your skills. Answers below.
1. Overdrafts
After making a deposit, Damien's bank account went from £1,680 overdrawn to £425 in credit. How much was deposited?

(a) £1,025 (b) £2,255 (c) £1,255 (d) £2,105
2. In the shops
A radio cost £35, which then increased by 10%. A retailer has now cut 10% off the new price in a sale. What's the price now?

(a) £34.65 (b) £35.00 (c) £34.50 (d) £35.60
3. Simple interest
After a lot of searching, you find a savings account that pays interest at 1.6% AER. You are allowed to invest a maximum of £500 in the account. How much interest will you earn if you invest the maximum amount for one year?

(a) £16.00 (b) £8.00 (c) £5.16 (d) £4.88
4. Getting to work
Rail fares are set to rise by 3.5%. If a season ticket costs £1,650 now, how much will it cost after the increase, to the nearest pound?

(a) £1,654 (b) £1,665 (c) £1,708 (d) £1,995
5. Holiday money
If the current exchange rate for US dollars is £1 = $1.22, how many dollars should you get for £210, to the nearest 10 dollars?

(a) $190 (b) $230 (c) $260 (d) None of these
6. At work
FitURite garage employs one manager and nine fitters. The average (mean) salary for all employees is £16,600. If the manager's salary is £22,000, what is the average salary of the fitters?

(a) £17,000 (b) £18,500 (c) £15,800 (d) £16,000
7. At the petrol station
You have a voucher to save 10p a litre on fuel. How much would you save when filling up an empty 12 gallon fuel tank? (one gallon = 4.5 litres)

(a) £5.40 (b) £4.50 (c) £4.95 (d) £5.25
8. Splitting a restaurant bill
Three people shared a restaurant bill equally. Their meals cost £15.50, £17.00 and £16.50, and their drinks cost a total of £24.98. They left a 10% tip. How much did each person pay?

(a) £27.13 (b) £29.25 (c) £17.97 (d) £24.6
9. Paying the rent
Sandy's gross monthly pay is £2,250, before tax and other deductions. She pays rent of £675 per month. What percentage is this of her gross pay?

(a) 30% (b) 40% (c) 50% (d) 60%
10. What's left?
Marcus has an annual salary of £24,000, before deductions. He pays 18% of his gross salary in tax and national insurance, and another 25% of his gross pay goes on rent. How much is left each month?

(a) £1,579 (b) £1,368 (c) £1,476 (d) £1,140
11. Debts and savings
Marcia owes £4,000 on a credit card that she pays 15% interest on. She also has £4,000 in a savings account paying 2% interest. How much better-off will she be each year if she uses her savings to pay off the debt?

(a) £80 (b) £190 (c) £380 (d) £520
12. Buying a car
Dan borrows £6,000 from a finance company to buy a second-hand car. The company charges 5% interest and offers a range of repayment plans. Which of these options has the lowest total cost?

(a) 36 payments of £179.81 (b) 48 payments of £138.17 (c) 60 payments of £113.22 (d) It makes no difference - they all cost the same
13. Paying a little more
Sam and Jo take out a £185,000 repayment mortgage with a 3.5% interest rate and monthly repayments of £926 over 25 years. However, if they make additional payments of £200 every month, the mortgage will be fully repaid after just 224 monthly payments. Which of these is the best estimate of the amount they would save by making the overpayments?

(a) £25,600 (b) £15,300 (c) £9,800 (d) £18,800
14. Credit cards
In the UK, about £20,000 is spent using credit and debit cards every second. How much is spent each month? Pick the best estimate.

(a) £945 (b) £5.89bn (c) £53bn (d) £111m
Answers
1 (d); 2 (a); 3 (b); 4 (c); 5 (c); 6 (d); 7 (a);

8 (a); 9 (a); 10 (d); 11 (d); 12 (a); 13 (a); 14 (c)

Making it all add up

We asked National Numeracy, a charity, for tips on how to handle the everyday challenges of financial transactions, and how to improve your money maths. You can also go online to the National Numeracy Challenge, a free online learning tool designed to help you improve your everyday maths skills. It will give you a breakdown of your capability in five areas of numeracy, and tips on how to get better. Here's its advice on coping with everyday challenges if maths is not your strongest trait.

Keep control, even if you delegate. If someone else handles your finances, make sure you are closely involved in the process. Always examine the figures before making any decisions, so that you are in command of your financial situation both now and later down the line.

Check your understanding of percentages. This is an area where many people struggle, and it features in nearly all of the financial decisions you will make in life. Do you use the percentage button on your calculator? The difference between 0.2% and 1% may not seem much, but on a sizeable loan or investment this can make a huge difference both now and how it plays out over time.

Know when to use savings v credit. Understanding the basics about interest (especially compound interest) will help you to be better with money. Some people like to keep cash on hand for "emergencies" rather than paying off debts. This is generally a bad idea - borrowing costs more than the interest you will earn on savings, so paying off debts will cost you less.

Know when to pay more. When discussing a remortgage or investment, prepare by doing calculations in advance. In the case of a mortgage, understand how repayments would be affected by an increase in interest of 0.5%, 1%, 1.5% and so on, and how reducing the term could reduce how much you pay in total.

Audit your numeracy skills. Our ability with numbers can fluctuate throughout life. If you suspect you may be out of practice and could benefit from taking steps to improve, then the National Numeracy Challenge website can help.

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Are you able to split restaurant bills, work out mortgage interest or calculate exchange rates?

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A HW generator for the Personal Finance (3.02) section of the spec. NOTE - Tax/NI thresholds are for the tax year 2019-20 (which would be used in the Summer 2020 Paper 1) Keeps these basic skills ticking over all year