Before Viewing

Review students’ knowledge of estimation and units of length by asking questions like:

• How tall are you in metres, in feet, in centimetres, in hands?
• How high in metres are the desks, the door?
• How long, wide, high is this room, in yards, inches, millimetres?
• If you could stand on each other’s shoulders how many students high would the school be? Roughly how many metres is that?
• If you were laid end to end on the school field how many students long would it be? Roughly how many feet is that?

Discuss what units students would use to measure:

• the length of their pencil or pen
• their journey to school
• the thickness of a hair on their head
• the length of their table

During or After Viewing

Develop the idea that standard measures allow us to compare unknown lengths with a known (standardised) length.

Discuss how and why standardisation was necessary for measures such as feet, cubits and miles. Compare the examples in the programme of the Guard’s pike and the trollurch rule to the use of yardsticks, rulers and so on.

Consider why rulers are usually 15 cm or 30 cm in length, rather than, say. 25cm.

The kite-prodding stick cost 2 florins per trollurch. Invite students to think of examples of goods that are sold using similar pricing methods. Discuss methods of calculation of cost related to their examples.

The Wizard considered a map with a scale of 1:25000. On this map 1mm would represent 25cm. Explore other similar examples.

Look at some real maps with a variety of scales, and get students to interpret their meaning in terms of units that they can visualise.

The map of the maze was drawn to a scale of 2cm:50cm, i.e. 1:25. Discuss methods for estimating distances on the maps available. Lisa estimated that 50cm (¹/₂ m) was roughly one step. Students could use local maps to estimate known journeys (for example, to and from school) and then check them by counting steps and using Lisa’s approximation.

Comments

The hand used in measuring horses is 4 inches.

The Roman mile was 1,000 ‘paces’, each ‘pace’ being 2 steps.

The foot was also a Roman unit of measurement.

The metre was originally defined as the distance along the Earth’s surface through Paris from the North Pole to the Equator divided by 10 million. It is now defined in terms of the wavelength of a particular photon emission. The metric system originated in France in the eighteenth century.

The cubit was a measure, based on the distance from the elbow to the end of the middle finger, used by the Egyptians. This was divided into seven ‘palms’ corresponding to the width of a hand; and each palm was divided into four ‘digits’ (the widths of the four fingers of the hand). Two standard cubits were identified, in order to overcome the variations of individual anatomy, and these were recorded by the construction of metal bars representing the royal cubit (about 20 ¹/₂") and the short cubit (about 17 ³/₄").

The Greeks and Romans also used cubits in their systems of measurement. A Greek cubit was about 18 ¹/₄" and a Roman cubit was about 17 ¹/₂"

A useful mapping site can be found at: http://uk.multimap.com/map/places.cgi. Maps can be downloaded for the whole of the UK, and areas can be viewed at different scales. Detailed local maps can be found by searching by postcode.

The Worksheets

Worksheet 1: Pike Lengths and Trollurches

The worksheet questions assume the students will be familiar with the programme content and characters.

The activity gives practice in converting between various units and calculating cost from a unit price. Students are asked to think about practical measurement and to make their own suggestions for suitable units.

The last activity could be extended to creating and using the troll system of measurement, with students inventing terms and conversion factors between units in the system, as well as metric equivalents. Some students may wish to create and describe their own units for weight or volume.

Worksheet 2: Supermarkets Goods

This open-ended activity builds on the idea of ‘best value’ introduced in the programme. Students may be interested in comparing the cost of organically grown with standard produce.

The purchase of goods provides many other opportunities for developing understanding of ratio, units of measurement and comparison.

Nutritional information is often given in terms of content per serving and per 100g. Students could answer questions like: How many grams of sugar would I consume if I ate a whole packet of cereal? If I ate a serving of cereal every morning, how many grams of sugar would I consume in a year? In a lifetime? How much fat, or salt, would I consume? How does this compare with eating a bar of chocolate, a bag of crisps, two slices of toast, every day?

Other discussions could be generated from questions like: Are bigger pack sizes usually better value? Are the supermarket’s own brands usually cheaper than branded products? How can you tell?

Worksheet 3: How Long Is a Stick?

This open-ended activity helps students to develop an understanding of the evolution of systems of measurement and the reasons why different systems have come to be adopted. It is hoped that students will gain an appreciation of the advantages and disadvantages of different forms of measurement and a sense of the way systems have developed through the solution of practical problems in real contexts.

The following sites may provide useful starting points for investigation:

http://www.microimg.com/science/
http://www-history.mcs.st-andrews.ac.uk/history/index.html
http://nrich.maths.org/mathsf/links/index.php3
http://home.clara.co.uk/brianp/index.html

Further Ideas

Comparing Currency Values

Information about currency values can be readily collected. Comparing prices in different currencies and planning holiday budgets allows students to work with ratios in a real context that is frequently used in examinations. Methods for conversion and comparison of prices, as well as mental approximation and estimation, can be developed. How does the Euro system work?

‘Old’ and ‘New’ Money

Students could compare prices in pounds, shillings and pence with prices in our current decimal monetary system. Interviews with grandparents or surveys of old newspapers could add interest. Some students may have access to old coins or stamps. The florin was worth 2 shillings (10p). What was a half crown, a bob, a tanner, a half penny, a guinea, a farthing, worth?

Some interesting facts about the changing values of money can be found in old arithmetic books. For example:

(1) Here are the returns for February 1912 for four different trades.

Students could find the average earnings per week of a worker in each of the trades specified, giving answers to the nearest penny. Then they could find out the present-day average rates and estimate the degree of inflation in the last century.

(2) Here are some prices for food items. Eggs were sold at 15p per dozen. Beer was bought at £2 5s 0d for a 36-gallon barrel and sold at 6d a quart. Oranges cost 5/— a hundred. Gas was sold at 3/7d per thousand cubic feet.

Again here students could compare 1912 prices with present-day prices.

(3) Here is a price list:

7d a quart for milk

2 ¹/₄ d per loaf of bread

¹/₂ d a pound for mutton

2 ¹/₂ d a pound for granulated sugar

¹/₉ d a dozen for eggs

¹/₆ d a pound for back bacon

¹/₂ d a pound for butter

Compare these price with present-day prices. With a little research, students could estimate the date when this price list was compiled.