Monthly
Maths
I s s u e
Increasing
probability of
success
If you set yourself
just a few
significant goals
you have a far
better probability
of achieving them,
as this allows you
to stay focused on
what really is
important to you to
achieve.
In his Whiteboard
Wednesday video
clip: The
Probability of
Getting Tasks
Done, Max Pool
looks at how the
ability to get
everything on your
task list done
becomes less and
less probable with
the number of
tasks you load into
your week. He
uses simple
mathematics of
compounding
probabilities as an
analogy.
2 3
New Year’s Resolutions
Have you set yourself any goals for
2013? Do you expect to keep to them or
will they soon be a distant memory along
with the Christmas pudding and tinsel?
We have been researching ways in which
you and your students might set
attainable goals, and strategies for
achieving them.
Firstly, you should
choose just one
personal goal:
something that you
want to work on just for you and you
alone. Secondly, consider your multiple
roles in life, such as teacher, parent,
spouse, employee, student, writer, etc.
Focus on two of these roles, with a
resolution for each.
“Be very, very clear not only on how you
will accomplish your resolution but also
on why you want to accomplish it,” says
Michael Pantalon of Yale University
School of Medicine. According to
Srinivasan Pillay of Harvard Medical
School, for resolutions to work they have
to take root in the brain, which requires
more than simply saying or writing them.
Don’t try to set a resolution for something
that you’ve never done before or you only
do rarely – make your resolutions
reasonable. If you don’t run regularly at
the moment, don’t set yourself a five mile
run every day! It may be more attainable
and sustainable to set smaller daily goals
with a weekly target.
Click here for the MEI
Maths Item of the Month
www.mei.org.uk
J a n
2 0 1 3
Be specific: rather than resolving “to get
fit”, set a specific target over two months
and then set a new target. Instead of
making a resolution to “finish a project”,
set mini-goals such as realistic periods of
time to work on that project, and log those
hours invested, to show how realistic are
your expectations of completing that
project within a certain timeframe.
Your goals should be set up so that they
can be measured, such as by tracking
yes/no ‘goal achievement’ data on a daily
basis and recording weekly how many
days those goals were achieved. Create
a record sheet (this could be as formal as
a spreadsheet or as simple as ticking
days on a wall calendar). If you travel a
lot, make sure to take a duplicate record.
This could easily be done using a
calendar on a mobile device. Telling
everyone of your resolutions might not
help, as some people may put you under
too much pressure or chastise for your
efforts, rather than support you in
achieving your goal.
Resolutions can be revised to enable you
to stay on track. Consider making the
resolution goal 90%, so that you do not
abandon the resolution altogether the first
time that you fail to meet a goal. This
gives you 36 days on which to falter. So if
you have decided to give something up
for 2013 that you are currently doing
every other day, that means that you will
be reducing that habit from
182 days to 36, quite an
achievement!
A new MEI teaching resource is at the end of this
bulletin. Click here to download it from our website.
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Balancing input
and output
One cookie
away…
In Plus
Magazine’s article
‘Counting
calories’ Rachel
Thomas discusses
Chow and Hall's
mathematical
analysis of weight
loss as a
dynamical system.
“As well as
describing how
your weight will
change over time,
a dynamical
system also
shows when your
weight will
stabilise at a fixed
point: where your
weight will remain
the same as long
as you continue
living the same
lifestyle, in terms
of diet and
physical activity.”
Read more
Regular exercise + balanced diet
= healthy body
BBC GCSE Bitesize tells us
that calories are a measure of
the amount of energy in food.
When we eat and drink, we put energy
(calories) into our bodies. Our bodies
then use up that energy, and the more
physical activity we do, the more energy
we use. A ‘kilocalorie’ is another word for
a calorie, so 1,000 calories will be written
as 1,000kcals. Kilojoules are the metric
measurement of calories. To find the
energy content in kilojoules, multiply the
calorie figure by 4.18.
The chemical reaction that allows cells to
release energy from food is called
respiration. The speed at which such
chemical reactions take place in the body
is called the metabolic rate, which
increases as we exercise, and which
varies with several factors:





age
gender
proportion of body muscle to fat
amount of physical activity
genetic traits
The energy we put into our bodies over a
few days must be the same as the energy
we use by normal bodily functions and
physical activity so that overall the energy
in and energy used remain balanced.
The calorie content of many
foods is stated on the
packaging in the nutrition
label and in many cases there
are ‘traffic light’ indicators that tell us the
proportions of fat, saturated fats, sugar,
and salt contained in that food. These
can be easier to understand for some
than percentages of the Guideline Daily
Amount (or GDA) that are shown on other
food labels. This year, the government is
introducing a consistent system of front-of
-pack food labelling in the UK.
A combination of guideline daily amounts,
colour coding and "high, medium or low"
wording will be used to show how much
fat, salt and sugar and how many calories
are in each product.
Eat well, Move more, Live longer
The NHS Change4life
website states: “These
days, ’modern life’ can
mean that we’re a lot
less active. With so many opportunities to
watch TV or play computer games, and
with so much convenience and fast food
available, we don’t move about as much,
or eat as well as we used to.”
Resolution Booster
The Change4life ‘Resolution Booster’
has been devised to boost your chances
of success, so that you can look forward
to a healthier New Year. We are
reminded that our chances of success are
far greater when we change just one
thing at a time. Small steps are easier to
achieve than big leaps.
Choose one resolution from those listed
on the website and start it by January 7.
Change4life will be in touch to help you
kick it off. Over 28 days the Resolution
Booster will help you keep track of what
you've achieved and support you with
relevant tips and tools.
New Year sales
savvy shopping
Cheers!
In October 2012
Tesco shoppers
were able to buy
six bottles of wine,
usually worth
£59.94, for less
than the price of
one bottle.
The problem
began when the
supermarket
launched a wine
discount promotion
offering three
bottles of selected
wine for £12. This
promotion included
bottles of ‘Ogio’
brand, normally
selling for £9.99
each.
However,
Tesco was
also running
another
promotion on
Ogio, giving
shoppers
25% off the original
price of the wine
when they bought
six or more bottles.
This meant that the
£24 wine bill was
reduced by a
further £14.99,
leaving just £9.01
to pay!
Comparing special offers
Calculating percentage reductions
Be careful of sales discounts when you
go shopping. For example, which is better
- ‘Buy one get one half price’ or ‘A third
off’? If customers find it confusing, take
heart in the fact that some retail websites
don’t always get it right. For sites allowing
the use of more than one discount the
order in which the discounts are applied
makes quite a difference.
There are several ways
of calculating
percentages; here are
two examples of
calculating the new value
of an item following a
percentage reduction. For example, you
may wish to calculate the sale price of a
TV normally priced at £360.00 that has
been reduced by 15%.
Before Christmas,
Marks and Spencer
offered 30% off
ladies’ nightwear;
additionally they were
offering ‘buy one get
one half price’. The
extra bargain for
online shoppers was
that the BOGOHP
discount was deducted off the pre-sale
price, but the 30% discount was also
deducted off the pre-sale price, e.g.
Two items
were ordered
at a pre-sale
price of £6
each.
Find 10% (360 ÷ 10 = £36), halve it to get
5% (£18) and then add them together to
get 15% (£54). Deduct this from the
original price to find the sale price:
£360 - £54 = £306
Another method is to calculate the
percentage of the original price you are
now paying for the item:
100% (full price) - 15% (discount) = 85%
(discounted price)
This value is multiplied by the original
price. Percentages can also be
expressed as fractions or decimals, 85%
being the same as 85/100 or 0.85. So:
Had the BOGOHP discount been applied
after the 30% discount the total would
have been different, e.g.
2 x £6.00
30% off Nightwear:
Subtotal
2x £4.20
BOGOHP Nightwear:
Total for this order:
One method is to use mental strategies to
calculate the amount that the item has
been reduced by:
£12.00
- £3.60
£8.40
- £2.10
£6.30
0.85 x £360 = £306
The result (£306) is the same whichever
method you use.
How many other ways
can you think of to solve
a percentage reduction
problem?
Calculating
commuting costs
Better than
average
The Passenger
Focus table (see
opposite) reveals
that the rises
aren’t as bad for
some commuters.
If you travel
between
Aylesbury and
London, your
season ticket will
have increased by
a whopping £112,
but this is a
smaller
percentage
increase (3.2%) of
the 2012 price of
£3520 than the
national average
price increase.
And now for
some good
news…
Rising rail fares
Rail fares have gone up again - season
tickets have increased by an average of
4.3%. Find out how much fares have
gone up by route and how much they
cost per mile.
A table provided by Passenger Focus
shows rail fare rises, comparing the price
of a 12-month season ticket bought in
January 2012 with one bought today.
Suppose that you travel between Bath
Spa and Bristol Temple Meads station. A
Bath Spa - Bristol Temple Meads season
ticket has increased in price by 4.3%
since January 2012, when it cost £1400.
How much will it cost you in January
2013?
You could calculate the actual amount by
which the price of your season ticket has
increased using this method:
1% of £1400 = £14
4.3% of £1400 = £14 x 4.3 = £60.20






and add this to the original ticket price:
£1400 + £60.20 = £1460.20
Or you could calculate the percentage of
your original price you now have:
100% + 4.3% = 104.3%
The season ticket
for those travelling
between Shenfield
and London has
decreased by
0.6% since
January 2012.
In order to make
decisions as to
whether to travel
by train or by car,
several factors need to be considered.
These include:
and multiply this by the original (2012)
price of your season ticket:
1.043 x £1400 = £1460.20
How many other ways can you think of to
solve a percentage increase problem?

Cost per mile of train/car travel
between departure point and
destination
Additional costs incurred by each
method of travel, e.g. car parking;
road toll charges; road tax; car
insurance (may change for
business use) depreciation on value
of car through wear and tear and
additional mileage
Number of passengers travelling
together to same destination
Cost of public transport/taxi/private
car/bicycle to and from station/
destination
Total journey time
Benefits/drawbacks of different
methods of transport, e.g. working/
reading/sleeping on train; carrying
bulky items in car; paying up front
for rail season ticket; public
transport strikes and delays; traffic
delays and diversions
Availability of different methods of
transport; convenience of
connection locations and times;
availability of parking
Rail fare data is provided, including how
much commuters are paying per mile, on
this spreadsheet. The data provides
several opportunities as a basis for
extension and enrichment activities. More
data is provided on the This is Money
website and the BBC News website.
Healthy Living: problems for
the classroom
• BMI calculator (using formulae)
• Eat well, move more, live longer (real life
calculations)
BMI Calculator
• Body Mass Index (BMI) is one of the measures that doctors
and others use to help determine how healthy a person is.
• It simply uses the person’s height and mass .
• Although the calculation is the same for adults and children,
the interpretation is different.
• For normal adults the healthy range for BMI is considered to
be 19 to 25. This changes if the person is particularly fit and
muscular.
• It is calculated using the formula:
where mass is in kg and height is in m.
𝐵𝐵𝐵 =
𝑀𝑀𝑀𝑀
𝐻𝐻𝐻𝐻𝐻𝐻 2
Using the BMI calculator
Using the formula 𝐵𝐵𝐵 =
𝑀𝑀𝑀𝑀
𝐻𝐻𝐻𝐻𝐻𝐻 2
answer the following:
What is the BMI for each of the following people:
• A man of height 1.84 m and mass 86kg?
• A woman of height 165cm and mass 62kg?
• A man of height 192cm and mass 68kg?
What is the healthy range of masses for a woman of height 165cm?
If a normal healthy man has a mass of 80kg, what height might he
be?
Many people still work with imperial measures; what would be the
BMI of a person height 5 foot 7 inches, weight 10 stone 3 pounds?
Eat well, move more, live longer
The NHS has a campaign called change4life to encourage
people to adopt healthier lifestyles…
… but how much more should a person move to balance
excess calorie intake?
A 100g bar of chocolate is approximately 500 kcals and a
35g bag of crisps is approximately 200 kcals.
How much exercise might a person need to do to balance
each of these?
Eat well, move more, live longer
The table on the next slide gives the amount of calories
burned for various forms of exercise.
Calories burned when exercising are also dependent on
body mass; figures given are for a 70kg person, exercising
for an hour.
• If a person ‘over-ate’ 1400 calories a week (equivalent to
2 chocolate bars and 2 bags of crisps) what exercise
might they do during the week to burn off exactly the
1400 calories?
• Devise a varied exercise plan for the week.
• You might like to think about putting together an
inexpensive plan that anyone could follow.
Eat well, move more, live longer
Exercise
Calories
Exercise
Calories
Aerobics
457
Hockey (field)
563
Badminton
317
Horse riding
281
Basketball
422
Housework
246
Bowling
210
Martial arts
704
Cycling (slow)
281
Mowing a lawn
387
Cycling (fast)
704
Roller blading
844
Fishing
176
Running (5mph)
563
Football
493
Skateboarding
352
Golf
317
Swimming
493
Gymnastics
281
Walking (brisk)
267
Teacher Notes
BMI calculator
• It is important to stress that BMI is just one indicator for assessing health
and fitness – and that the 19 to 25 range does not apply to children
Answers:
1.84 m and mass 86kg: 25.4
165cm and mass 62kg: 22.8
192cm and mass 68kg: 18.4
Range of masses for a woman of height 165cm: 51.7kg to 68.1kg
Mass of 80kg, what height might he be: 1.78m to 2.05m
BMI if they are 5 foot 7 height and weigh 10 stone 3 pounds: equivalent to
1.70m and 65 kg so BMI is 22.5
Teacher Notes
Eat well, move more, live longer
It should be stressed that we all need a certain amount of calories, but that
healthy living is about balancing what a person eats with how much exercise
they do.
This activity is designed for students to devise their own exercise plan, so there
are no definitive answers, but the extra table given in these notes can be used
as a quick reference guide.
On slide 5, students might make guesses about how much exercise is required
to burn off a chocolate bar or bag of crisps, this can then be ‘checked’ with the
information on later slides.
To find exercises to burn of exactly 1400 calories, students will need to
calculate to the nearest minute.
You might like to add restrictions such as ‘There must be 4 different activities
and the total exercise time should be between 3 and 4 hours”
Teacher Notes
The table below shows how many minutes it takes to burn
100 calories for each of the forms of exercise.
Exercise
Time
Exercise
Time
Aerobics
13
Hockey (field)
11
Badminton
19
Horse riding
21
Basketball
14
Housework
24
Bowling
29
Martial arts
8.5
Cycling (slow)
21
Mowing a lawn
15.5
Cycling (fast)
8.5
Roller blading
7
Fishing
34
Running (5mph)
11
Football
12
Skateboarding
17
Golf
19
Swimming
12
Gymnastics
21
Walking (brisk)
22
Sources
• BMI calculator
• Reference graphs for children’s BMI
• Calories in various foods
• List of calories burned by exercise