3. TRANSLATE BETWEEN DIFFERENT REPRESENTATIONS FOUND IN THE WORKPLACE

• At the end of this outcome, you will be able to:• convert representations of relationships from

one form to another to reveal features of patterns and relationships

• select and develop representations of relationships to solve a problem and/or communicate/illustrate a result

Types of representation

• Graphs

• Tables and graphs

• Formulae

• Pie charts

• Bar graphs

Activity 12

1.The compound bar chart shows the state of the dams in the Western Cape in May of 2008.

Activity 12

a. Explain why two bars are used for each dam

b. Is it possible to talk about a trend between different dams?

c. What kind of trend can you talk about here?

d. Calculate the mean and range of dam fill percentages for both 2007 and for 2008.

Activity 12

e. Why are these figures published in May?f. Write a paragraph to explain to a reader what the

bar graph tells you.g. Change the horizontal compound bar charts into

vertical broken line charts on the same set of axes.h. Select some of the information and represent your

choice in a pie charti. Which representation would you chose in a

newspaper article?

Activity 12

2.Crime data bank

Activity 12

a.Draw a table and then a compound bar chart representing the four different money value categories for theft, fraud and receiving stolen property on the same set of axes.

Activity 12b. Which of the two representations that you made gives a quicker

picture of the information?c. When would the table be more valuable?d. What do the phrases “theft by false pretences” and “attempted

theft” mean?e. Explain how the author makes sure that you, the reader,

understands exactly what the terms mean. f. Which of forgery, uttering a false document or perjury is

considered the more serious offence? All are considered equalg. Put the sections 11 and 12 into wordsh. Represent the “Possession of Dagga” section – choose what you

think is the best representation?

Activity 12

3.Exchange rate graph

Activity 12a. When was the maximum reached on this broken line graph?b. What do the two arrows indicate? c. What is strange about the vertical axis? d. Why can the graph be sketched with this vertical axis – think of

the audience it was prepared for? e. Why would it make no sense to represent this data set in other

way? f. Read the maximum value and explain what it means.g. The graph is rising steeply in the first quarter of 2008. Is this

good or bad for South African citizens? h. Describe the exchange rate from 1998 to 2008.i. What do you predict for the next year?

Activity 12

3. Petrol price breakdown

Activity 12

a. In June of 2008, the price of petrol reached 9.68. Calculate the percentage increase since December 2004.

b. If the distribution of the various components of the total price remain unaltered, calculate the actual price components in 2008.

Activity 12

c. Draw up a table of the information in the legend comparing the 2004 and 2008 actual prices.

Activity 12

d. How would a pie chart of the 2008 figures look?e. Why is a pie chart the chosen method of

representation here?

Activity 13

1.Describe how the % share of total South African disposable income has changed from 1960 to the present time.

Activity 13

2.Describe the trends in the 3 series of data in these line graphs.

Activity 14• Select the most appropriate representation for data

1.    A salesman has a base salary of R2000 / month and earns a 10% commission on all goods sold.a.    What type of graph would you use to represent this data? Explain why.b.    Sketch the graph of sales versus commissionc.    Would would the salesman income be if he sold:            i.    R50 000 worth of goods            ii.    R220 000 worth of goodsd.    If the salesman wishes to earn R15000 in a month. How much must he aim to sell?

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Activity 14

2. Investigate the following information and decide on one or two good ways to represent the information

b. Complete the percentages column

c. Sketch one of your selected representations.

Summative assessment

1. Choose the correct relationship between two variables for the description given.

Constant relationship; direct proportion relationship; linear relationship; inverse proportion relationship

Summative assessment• In Case study 7 of module 1 on numbers, you set up a

table relating the total external surface area of cylindrical 1-litre cans and the change in radius.

• You used the formulae:• Volume of a cylinder = r²h• Total external surface area of cylinder = 2 r² + 2 rha. Copy your table in here or if you have not done it yet,

then complete the table by calculating the total external surface area of the cans

b. Translate this table into a graph with radius length against total external surface area of the cylinder.

Summative assessment

c. Read from the graph what the total external surface area will be for a radius of 3,5cm.

d. Predict from the graph what the total external surface area will be for a radius of 11cm.

Approx 680cm2

Approx 930 cm2

Summative assessment

3. Use the formula for the volume of a rectangular prism (a box) in the table above in Activity 11 and the formula for the total external surface area of such a box

• Take the height of the box as 16cm and the width of the base 7,5cm.

• Do a similar exercise as in number 2 above to determine length of base for the least amount of cardboard used.

• Draw up the table and an appropriate graph.• Explain how you can read values off this graph – i.e. how

can you used the graph.

Summative assessment

4.a. Label the sketches as direct proportion or inverse proportion.

b. Think of an example where each of these graphs could emerge from the relationship between two variables.