September is the birthday month of George Cadbury (19 September 1839 - 24 October 1922) the third son of John Cadbury, a Quaker, founder of Cadbury's cocoa and chocolate company. So what better reason do we need to focus on mathematics and chocolate!
Chocolate lovers may be interested to know that:
- the UK has the seventh highest consumption of chocolate in the world. Switzerland takes the top spot
- 40% of the chocolate eaten in the world is consumed in Europe
- 66% of chocolate is consumed between meals, with 22% of all chocolate consumed between 8pm and midnight
- Britain really is a nation of chocolate lovers. We eat an estimated 660 900 tonnes of chocolate a year, an average of 11 kg per person per year. This equates to about three bars a week
- the UK chocolate industry is worth £3.6 billion and sales of chocolate just keep growing and growing, with an estimated 17% increase in sales over the next five years
- about 8 000 new chocolate products were introduced worldwide last year – meaning that a new chocolate treat was launched almost every hour of every day
- chocolate makers use 40% of the world’s almonds and 20% of the world’s peanuts
- the annual consumption of cocoa beans averages around 600 000 tonnes per year
- consumers spend more than £12 billion annually on chocolate.
(sources: Divine Chocolate, TipTopTens.com)
Some of these facts make interesting starting points for data handling investigations. As a class or as a school, why not explore these questions:
- how much chocolate do we eat in a day? A week? A year?
- at what time of day do we eat most chocolate?
- how much money do we spend on chocolate each week/each year?
- which is the most popular brand of chocolate or what is our favourite chocolate bar?
Discuss other influencing factors on the data, such as Easter and the purchase and consumption of Easter eggs. Once the answers to these questions are discovered, discuss with the children how the information could be used further. How would this information be useful to chocolate retailers? Alternatively, link findings with ideas of healthy eating or look at other items that could be bought with the annual expenditure on chocolate.
sweets, photograph by
Coloured chocolates such as Smarties or M&Ms can be used to practise counting or to learn about fractions, percentages, averages and probability. Using chocolates as practical resources can provide very motivating opportunities although many children may be disappointed to find that they are unable to eat their resources at the end of the activity!
Very young children could be allocated a colour of sweet and then given all the chocolates of that colour from a tube of Smarties or a packet of M&Ms. In their group, ask the children to discuss the fairness of allocation. Can they find their number on a numberline and use this to work out Who has the most chocolates? Who has the least? Other than eating the sweets, can the problem be solved so that allocation is fair? Older children can go on to calculate the fraction or percentage of each colour of chocolate in a given group or explore What’s your favourite colour? and Do you get equal amounts of each colour?
In this scenario, ask the children to discuss their hypothesis and how they could check it. With a number of packs of the same sweets, children can explore the mean, mode, median and range of each colour and then discuss the suitability of each average. They could then look at What’s the chance that the first sweet you pull out will be your favourite colour? Ask the children to find the probability as a fraction, decimal or percentage of each colour being pulled from the bag first and then discuss why answers are different for each packet and how responses could be made more accurate. Results could be presented as a pie chart showing each colour and its percentage and then compared with retailers’ published percentages of distribution of colours. The Smarties Project shares the percentage distribution of Smarties by colour in 2009 and for those teachers using M&Ms, this forum shares findings of the distribution of M&Ms colours.
Packaging can provide some interesting starting points too.
Very young children can describe and sort chocolate boxes of different shapes and sizes. They can also explore the shapes of the faces of the containers and use them to print 2D shapes.
The internal trays of chocolate boxes can provide opportunities for counting - can children count how many holes there are and find the correct amount of ‘sweets’ or other objects to fill the tray? If the internal trays are arranged in uniform rows and columns, these can also provide contextualised opportunities for exploring arrays and the relationship between multiplication and division. Older children can unfold boxes and look at the nets they make. Having explored a range of nets and the shapes of the faces on the boxes, ask the children to design their own chocolate box and create the net to make it. Much older primary children can explore surface area by recording the dimensions of, in the first instance, a cuboid-shaped chocolate box. Ask children to calculate the area of each face and then find the total surface area. If you are able to access YouTube, this video clip looks at the downsizing of packaging and may provide a useful starting point for discussion and for investigating what any packaging may look like if it were downsized by 10% or 25%. The NRICH Christmas Chocolates activity is also a great puzzle to help develop skills of generalisation by investigating the amount of chocolates in a hexagonal-shaped box. It challenges children to consider multiple ways of looking at the structure of the problem and helps them to derive general formulae.
Chocolate box inner tray
Bars of chocolate also provide great motivation for understanding and ordering fractions as in NRICH's challenge, Chocolate. Three tables are set up with one bar of chocolate on the first, two bars of chocolate on the second and three bars of chocolate on the third table. Children are told that at any given point, the activity may end and they need to be seated at the table where they would receive the largest proportion of chocolate if it were shared equally amongst all the children at the table. As they are chosen, children have to say where they would sit and why. This PowerPoint also provides visual images to develop an understanding of fractions through using bars of chocolate.
Chocolate bar wrappers contain useful information and data for children to use in real-life problem solving situations. Ask older children to record and compare the data highlighted on each wrapper, such as the cocoa, fat, sugar and calories/energy for each bar. Per 100 g of chocolate, ask children to choose which bars are the ‘healthiest’ by looking at most cocoa, lowest fat, lowest sugar content. Ask children to present their results and discuss the reasoning behind their choice of healthiest bar. Explore the link between the amount of cocoa and calories in chocolate by using knowledge and understanding of ratio. Ask children to find the ratios of cocoa:calories for all the chocolates and consider how they can be used to compare the chocolate bars. Repeat for other comparisons such as the amount of cocoa and sugar, or fat and sugar. What other connections can they find? Are there any generalisations that can be formed?
Take a look also at Focus on...Fair Trade from Issue 33, which also provides other ideas on how to explore mathematics through chocolate and other Fair Trade products.
Chocolate Maths (from NRICH)
Did you know you could calculate your age by chocolate?
- first of all, pick the number of times a week that you eat chocolate. This number must be more than one but less than ten
- multiply this number by 2 (just to be bold)
- add 5 (for Sunday)
- multiply it by 50
- add 1 750
- add the last two digits from the year you last had a birthday. So if your last birthday was in 2010, add 10, if your last birthday was in 2011 then add 11
- now subtract the four-digit year that you were born (if you remember).
You should now have a three-digit number. The first digit will be your original number (i.e. how many times you eat chocolate each week). The next two digits give your age. Can you explain why it works?
Page header - chocolate sweets photograph by anemoneprojectors some rights reserved