1.3 How long is a piece of string?

end of ASSIGNMENT

There have been several attempts to reform our Western calendar with its months of different lengths. But it isn’t simple because the number of days in a year isn’t a whole number (that is why we need that peculiar way of determining leap years). It would be an improvement if all the months were the same length, and if the year could consist of four equal quarters. Many people have attempted to change the calendar, but unfortunately all these very clever ideas failed because our old system is so ingrained in our culture. If you want to read more about this, you can try looking up “calendar” in the “Encyclopaedia Britannica”. There’s a lot of material about different calendar systems in various cultures. Try finding something about the “World Calendar”.

CLASS WORK

• Starting with a line x cm long, one can make a square with four of these lines. Taking six of these squares, we can form a cube.

1 Write down the formulae for calculating (a) the area of a square and (b) the volume of a cube. Use x as the variable.

2 Now complete this table.

3 Say you had a cube that had to be measured by everyone in the class. All the side lengths of the faces are supposed to be 7cm, but not everyone measures very accurately. Then everybody uses his own measurements to calculate the volume of the cube. Will those measuring 1 mm more than 7 cm, make a bigger error in the volume than those measuring 1 mm less than 7 cm?

4 Now you have a square that has to be measured. All the side lengths are supposed to be 3 cm, but again your classmates get different measurements. Each again uses his own measurements, and calculates the area of the square. Will those measuring 3 mm more than 3 cm, make a bigger error in the area than those measuring 3 mm less than 3 cm?

THE FACE THAT LAUNCHED A THOUSAND SHIPS

• Question : What is measured in milliHelens?
• Answer: A milliHelen is the amount of beauty necessary to launch a single ship.
• Background : In Greek history, about three thousand years ago, Helen of Troy was abducted. Because she was so beautiful, her compatriots sailed out with a thousand ships to rescue her. So a mathematical joker, with reference to this tale, defined one Helen as the amount of beauty needed to launch a thousand ships.

Assessment

Measurement ω

 good  average  not so good

Assessment

Memorandum

CLASS WORK

1.1 One

1.2.1 cm of m

1.2.2 light years

1.2.3 months

1.2.4 litres

1.2.5 milligrams

1.2.6 degrees Fahrenheit

1.2.7 km ² or hectares

1.2.8 kilometres per hour

1.2.9 m ³

1.2.10 Rand or millions or billions of rand

PROJECT

Encourage originality.

HOMEWORK ASSIGNMENT

2.1 ruler or measuring tape

2.2 scale

2.3 millilitres

2.4 litres

2.5 hygrometer

2.6 speedometer

ASSIGNMENT

• Accept any reasonably practical answers. This exercise can be addressed again when the learners have mastered graphs, formulae and tables. They should then be able to improve their answers.

CLASS WORK

• The intention of this exercise is to illustrate the consequences of inaccurate calculations. If time allows, the learners can be given photocopies of squares to measure. They can complete another table and compare answers.