Category Archives: Discovering Maths

Demand Planning

Recently in Discovering Maths we looked at the maths within supply chains and logistics. The area which I found most interesting in this was demand planning. Demand planning is a multi-step supply chain management process used to create a prediction of sales for a particular period of time (TechTarget, 2017). Used effectively demand planning can help business to improve the accuracy of their predictions, show when sales of a product are at its highest and lowest and therefore enhance the profitability of products (TechTarget, 2017).

In the workshop we had a go at creating our own demand planning sheet for a business that we had made up. At the start of the first quarter, which for any business runs from April to June, we had a budge of £5,000. The goods we had to buy from were Christmas selection boxes, champagne (bottle), soft drink (2l bottle), beer (x4cans), whole frozen turkeys, ice cream wafers (box of 10), bunch of bananas, celebration luxury hampers, crisps (x12multi pack), sherbet dib dabs, bread (loaf), milk (1l), tins of beans (x4), luxury biscuit selection, premium durian. The aim of our demand planning was to do exactly what TechTarget (2017) said, we were to work out which products we believed would be at their peak in terms of sales during this quarter in order to generate the most sales.

We continued our demand planning into quarter 2 (July – September), quarter 3 (October – December) and finally quarter 4 (January – March). Each quarter we made a profit which we were able to carry over into the next to spend on more stock and again try to generate more profits.

        

As you can see from the photos, every quarter we focused on what the season was like at this time, for example during the summer we bought ice cream cones and soft drinks, in winter we bought section boxes and luxury hampers. This however was our downfall as we didn’t consider the products that stayed reasonably high in terms of sales all year round, the biggest of these being baked beans. Due to not considering these kinds of products we ended up coming away with the lowest profit compared with the rest of the class, however we were still positive in that our demand planning did make us a profit.

The sales of the baked beans got me thinking about other products that sell well throughout the whole year, so I decided to look into this. It was very difficult to fine exactly which products make to most profit for businesses as there are lots of other aspects to consider such as shipping cost and supplier costs (Simpson, 2014). However, I did read that in the last year the supermarket chain Tescos’s profits have rose considerably compared with what they have predicted (Cox, 2017). In the Independent’s article a spokesperson for Tesco said that one of the main reasons for the rise in their profits was because of their exclusive fresh food brand (Cox, 2017). This surprised me as supermarkets cannot carry over any fresh food stock into the following quarter due to their shelf life and so many of these items need to be written off. For the supermarkets this means that they still have to pay the shipping and supplier cost even though it is likely the will not sell any all of the fresh items and therefore make no profit to take forward. However, with the fresh food products being a large contributing factor in the considerable rise in Tesco’s products it seems to me like the customers here love their fresh foods.

This is an activity I would be liketo use with a class in the upper school of primary. This is something which I think they would find enjoyable and would help them develop their knowledge in areas of mathematics such as money and percentages.

 

References:

Cox, J. (2017) Tesco Reports £1.28bn Annual Profit and First Full Year of Growth Since 2010. Available at: http://www.independent.co.uk/news/business/news/tesco-reuslts-earnings-128bn-annual-profit-first-full-year-growth-since-2010-booker-a7679401.html (Accessed on: 24th November 2017)

Simpson, E. (2014) The Hidden World of Supplying a Supermarket. Available at: http://www.bbc.co.uk/news/business-29629742 (Accessed on: 24th November)

TeachTarget (2017) Demand Planning. Available at: http://searcherp.techtarget.com/definition/demand-planning (Accessed on 27th November 2017)

Maths and Medicine

Medicine. It is something we all hate but without a doubt something we all have to take at some point in our lives. However, mathematical knowledge is something you and any medical professional need to have before administering any kind of medicine.

For some medicines it is quite easy to follow the dosage intrusions, for example with paracetamol you are advised to take between 1 and 2 500mg tablets every 4 hours within a 24 hour period. This means that the maximum does of paracetamol for an adult is 8 500mg tablets in 24 hours, ensuring there is the advised 4 hour cap between (NHS Paracetamol for Adults, No Date).  In order to prescribe yourself with paracetamol you must have mathematical knowledge about quantities, so how many is 2  and also a good understanding of time. To stop yourself from overdosing you will need to know how long 4 hours is, as well as figuring at what time these 4 hours will have past for you to take another does, if you require it.

For children, paracetamol dose are different to adults as the dosage changes by age and children receive their paracetamol through a liquid syrup. This image from NHS Paracetamol for Children shows the different ages and the dosage that goes with this.

Even though you receive a measuring spoon with liquid paracetamol, it is not known what age the child who is going to be taking it is and so it standard to give a 5ml spoon with a 2.5ml on the other end. This mean that if you child is 8 – 10 years they will require 7.5ml, you need to know to give them a 5ml dose and then 2.5ml, straight after each other in order to make that required does of 7.5ml. Similarly, with a 10ml does you need to know to give the child two 5ml dose in order to make a 10ml. This mathematical knowledge is essential to ensure that you do not give the child an overdose and they end up in a serious condition.

When a patient is in hospital they trust the medical professionals to help them get better and so this also means that they trust that the medical professionals have sufficient mathematical knowledge to ensure they are not given an overdose or not enough medication to help them feel better.

Some of the data medical professionals have to record look a bit like this:

 

Now I’m not going to pretend I know what these charts mean or what they can predict purely because I’m studying to be a teacher and not a medical professional. However, what I do know is that it requires a lot of mathematical knowledge to be able to create these charts, furthermore it is essential that the medical professionals have a deep understanding of what the maths is telling them and be able to interpret this into a diagnosis such as high blood pressure.

Medical professionals often have to use a person height and weight to calculate how much of a specific medicine they can receive (Hothersall, 2016). For example, say I am in hospital and require some medication, the dosage I receive based on my height of 4ft 11 and a weight of 7 stone will be smaller a smaller dose than someone who is 6ft 10, weighing 11 stone. If I was to be given the same dose of this specific medicine as the person who is 6ft 10 weighing 11 stone, it is most likely I will become more ill than what I was originally (Hothersal, 2016).

In the future I plan to take a greater interested in administering medicine and how much mathematical knowledge it requires to do so. I have been fascinated by the variety of areas of mathematics that can be used in medicine and I would like to deepen my understanding of this.

References:

Hothersall, E (2016) Numeracy: Every contact counts (or something) [PowerPoint Presentation]. ED21006 Discovering Mathematics. Available at: https://mydundee.ac.uk  (Accessed on: 13th November 2017)

NHS Paracetamol for Adults (Not Date). Available at: https://beta.nhs.uk/medicines/paracetamol-for-adults (Accessed on: 13th November 2017)

NHS Paracetamol for Children (No Date). Available at:  https://beta.nhs.uk/medicines/paracetamol-for-children (Accessed on: 13th November 2017)

Maths and Music

Are maths and music connected? This is a question I never thought I would ask myself and the answer was even more surprising… yes, they are!

At first I must say that I did not see the link between the two. In my opinion I view maths as a very structured subject. It has set formulas and for each question only one set answer, something in which music is not. Music, to me, is a way to express your feelings and emotions; it is free for you to do what you like with, you are free to make your own styles, there is not set structures and not set answers. However, even though musicians do create their own music they use maths to help them develop, express and communicate their ideas (Shah, 2010)

There are many aspects mathematical knowledge that musicians use when playing and creating music, one of the simplest aspects is being able to count, for example a musician needs to be able to count the number of beats in a bar. A musician also uses their mathematical knowledge when looking at rhythm, scales, intervals, patterns, symbols, time signatures, overtones and pitch (American Mathematical Society, 2017).

Maths is not only used to help musicians to create and play music, it is also used to help them to tune and play their instruments. Mathematics is able to explain how strings vibrate at certain frequencies and that sound ways are used to describe these mathematical theories (Shah, 2010).

However, it is not just string instruments such as violins and cellos that use their frequencies to help with tuning and playing, a pianist will also do this. But the maths is not always enough and so a pianist will use the frequencies along with their knowledge of the sound of the keys in order to tune the piano (Sangster, 2017).

Seeing first-hand the ways in which maths and music connect is something I have enjoyed. This has made me consider the possibility of using music as a way of explaining mathematical concepts such as patterns and sequences in my teaching practice. I believe that doing this well bring an element of enjoyment as well as a large amount of engagement from pupils as this would be an interactive activity that could be used with a variety of ages and stages within the primary school.

 

References:

American Mathematical Society (2017) Mathematics & Music Available at: http://www.ams.org/samplings/math-and-music (Accessed on: 6th November 2017)

Sangster, P. (2017) Discovering Maths: Music and Mathematics [PowerPoint Presentation]. ED21006 Discovering Mathematics. Available at: https://mydundee.ac.uk  (Accessed on: 6th November 2017)

Shah, S. (2010) An Exploration of the Relationship between Mathematics and Music. Available at: http://eprints.ma.man.ac.uk/1548/1/covered/MIMS_ep2010_103.pdf (Accessed on: 6th November 2017)

Maths and Art

I have never really been overly enthusiastic about maths and I have most defiantly never been enthusiastic about art. The two as individuals give me much anxiety and I often believe the myth that your either good at maths or literacy, the two never hold the same value. I also had this view towards art and so, when I realised we were going to be receiving a lecture on maths and art together, I must say I felt a strong sense of dread. However, I was amazed and how simply maths and art could be connected. My original thoughts were that we would be using our mathematical knowledge to create large portraits, how one would do this I do not know.

Piet Mondrian is one artist who bring maths and art together. He was famous for creating geometric abstract pieces of work (Piet Mondrian 1877 – 1944, no date). This abstract style he created was quite simple, he would create a grid of black and white horizontal lines on white paper. The black lines would create a variety of different sized squares and rectangles which he coloured in using only 3 primary colours; he called this piece of art Neo – Plasticism (Piet Mondrian 1877 – 1944, no date).

A mathematician whose work has artistic connections was Fibonnaci. Fibonnaci created different sequences, one of his most famous was the golden spiral.  Fibonnaci created a mathematical sequence that if you start at 1 and add the two numbers before it you will create the Fibonnaic’s sequence (Meinser, 2015). Doing this myself I found that the sequences goes in the order of 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 etc. Fibonnaci discovered that using this sequence as dimensions for squares he would be able to create a perfect spiral inside of them; today this spiral is known as the golden spiral (Meinser, 2015).

The golden spiral can be seen most of all in nature. FIbonnaci’s sequence can be seen in sunflower seeds, pinecones and pineapples (Meinser, 2015).

“Is God a mathematician? Certainly the universe seems to be reliably understood using mathematics. Nature is mathematics. The arrangements of seeds in a sunflower can be understood using Fibonacci numbers. Sunflower heads, like those of other flowers, contain families of interlaced spirals of seeds – one spiral winding clockwise, the other counter clockwise. The number of spirals in such heads, as well as the number of petals in flowers, is very often a Fibonacci number.”

(Pickover, 2009, p.100)

A progression from Fibonnaci’s golden spiral was that from using this sequence a golden ratio could be determined for line segments. This special ratio will appear when a line is spilt into two segments. We divide a line into two segments so that the ratio of the whole segment to the longer part is the same as the ratio of the longer part to the shorter part (Pickover, 2009, p.112).  The ratio is determined by using the formula:

(a + b) / b = b/a

The golden ratio is 1.61803, however not every line segment will equate to this, it will only occur if the numbers used appear in Fibonacci’s Sequence.

I started off by creating my own golden spiral, then by using the dimensions of the rectangular boxes and substituting these into the golden ratio formula I was able to determine the golden ratio. I also done this using the dimensions for my Mondrian drawing, however I was unable to determine the golden ratio in these, meaning that the dimensions did not occur in FIbonnaic’s sequence.

Maths is often used when creating patterns. Maths can be used to determine the length of the line or the size of the boxes within a pattern. One example of this is fractals, a fractal is a never ending pattern which is self-similar across different scales (Robb, 2017).

I went into the lecture on maths and art with the feeling of dread and came out in amazement. I had no idea about the variety of ways that maths could be linked with art and that I could do it. I now feel passionate about bringing maths and art together and it is something I plan on researching further to take with me onto to placement and in my career as a teacher to ensure that children do not feel the same feeling of dread I first had when I saw the title Maths and Art.

 

References:

Meisner, G (2015), Spirals and the Golden Ratio, Available at: https://www.goldennumber.net/spirals/ (Accessed on: 27th October 2017)

Pickover, C. A. (2009) The Math Book From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics. London: Sterling.

Piet Mondrian 1877 – 1944, (No Date),  Available at: http://www.tate.org.uk/art/artists/piet-mondrian-1651 (Accessed on: 27th October 2017)

Robb, A (2017) ‘Maths and Art’, [PowerPoint Presentation], ED21006 Discovering Mathematics, Available at: https://mydundee.ac.uk (Accessed on: 27th October 2017)

Prehistoric Mathematics

1, 2, 3, 4, 5 is almost everyone’s first memory of maths, the enjoyment of being able to count. However, I have been very naive in my thinking and believed that number systems and counting have been around forever. I have recently discovered that this is not the case.

Some of the earliest evidence of mankind considering mathematically thinking can been seen on marked bones from Africa dating back to around 20,000 years ago (The Story of Mathematics, 2010). It is thought that mankind could identify the difference between having one of something and having two but they had not discovered a way of communicating this through words or symbols. It has been suggested that early mankind made markings on bone to track occurrences such as the phases of the moon, the seasons and time (All Worlds, 2015).

The first steps made towards the mathematical systems we have now were suggested to have been made for bureaucratic needs and the development of agriculture. A shared mathematical system was needing to measure land and work out taxes (The Story of Mathematics, 2010).

This video explains mankind’s first signs of mathematical thinking by looking at the Ishango Bones.

I have read through many articles while writing this post to see if there has been any final determination of what the markings on the Ishango Bones mean, however it is still unknown. The most commonly found assumption I have read is that early mankind were making these markings to track the phases of the moon but again, whether or not this is true is still unknown.

References:

All Worlds (2015) PREHISTORIC MATHEMATICS, Available at: https://www.youtube.com/watch?v=TsLqTfKtpCA (Accessed on: 6th October 2017)

International Organization for Chemical Sciences in Development (2015), The Ishango Bone. An enduring symbol of mankind’s intellectual progress and a star of archaeology from the heart of Africa, Available at: http://www.iocd.org/v2_PDF/IOCD-IshangoBrochure2015bp.pdf (Accessed on: 6th October 2017)

The Story Of Mathematics (2010), Prehistoric Mathematics, Available at: http://www.storyofmathematics.com/prehistoric.html (Accessed on: 6th October 2017)

Daunting Discovering Maths

Mathematics, one of the scariest words that can be said. I feel that I suffer from maths anxiety and so when deciding to choose the discovering maths elective I felt very nervous about what to expect. However I must say, so far so good.

From my experience of maths at school I always believed, what I now know to be one of the maths myths; it-should-be-easy suggesting not everyone has a maths brain. (University of Alabama, no date). But there was always part of me questioned this, I knew I wasn’t a maths genius; another one of the math myths but I wasn’t terribly awful at maths either, why was this? The past few lectures provided me with the answer to this – I was able to memorise formulas and structures and apply them to mathematical questions.

Another question about my own math experience started to puzzle me, if I was able to apply what I had memorised to basic mathematical questions, why did I always struggle when the format of the question was changed? For example, if the teacher put the question what is 2 + 3 in front of me I could answer within seconds but when it changed to the question “if I had 2 sweets and my friend gave me another 3, how many would I have altogether?” it would take me some time to work out what this question was asking me to do. The answer to this was simple, during my time at school I had very little practical maths lessons. I cannot remember ever having a maths lesson I didn’t realise at the time was a maths lesson or one I even found enjoyable. Boalar (2009) suggest that children, like myself, who have been taught in a very structural way do have a board range of understanding, however this understanding is not deeply engrained so is easily forgot over time. She also suggests that children who have experienced a more practical approach to mathematics were more flexible and so were able to adapt their knowledge to suit the question that was in front of them.

Since starting this module I have realised many potential ways mathematics can be enjoyable for children. I thoroughly enjoyed the latest lecture on making maths creative. Until this lecture I most likely could tell you very little about geometry and I most definitely could not tell you anything about tessellations. However, I know feel my brain is filled with so much more knowledge about these aspects of mathematics and I certainly won’t forget making my own tessellation, I even plan to make some more.

I am starting to see that discovering maths might not be so daunting after all.

References:

Boaler, J. (2009) The Elephant in the Classroom. London: Souvenir Press Ltd.

University of Alabama (no date).  Math Myths.  Available online at: http://www.ctl.ua.edu/CTLStudyAids/StudySkillsFlyers/Math/mathmyths.htm (Accessed 26th September 2017).