Putting information in a table makes it much easier to notice the patterns that the numbers form. That is why tables are very often used to arrange information. You will see many cases where tables are used in mathematics. Use a table whenever you think that it will be helpful when you are working on a problem.
ACTIVITY 2
To investigate relationships between variables
[LO 2.1, 2.6]
Mr and Mrs Peters want to hire a caravan for their holiday. They made enquiries about the cost from three caravan hire firms. Now they need to decide which caravan to hire, and for how long. We will help them decide. Here are the verbal descriptions of the details they obtained from the firms:
- Away–van: Their caravans cost R750 per day.
- Best Caravans charge a rental fee of R1 200, with a daily charge of R360.
- Car-a-holiday: They rent out a caravan for R950, with a R540 daily charge.
1. Arranging data: Complete the following table from the descriptions above.
| Number of days: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| Away-van: | R750 | ||||||||||
| Best Caravans: | R1560 | R1920 | |||||||||
| Car-a-holiday: | R1490 | R2030 |
2. Can you tell from the table which option will be the best depending on the length of the holiday?
Write a short summary of your conclusions.
3. This is a flow diagram for the Car-a-holiday prices. Calculate the missing values for the blocks:
4. Make flow diagrams for the other two options.
5. Bradley is holidaying in America. He would like to hire a cell phone. He has investigated three different offers. Below are the following: A description in words of offer 1, A table of values for offer 2 and A flow diagram for offer 3.
There are spaces for you to complete the other two offers in each case. After you have completed the six, do the next e x ercise.
Verbal descriptions:
Offer 1: “ADVANCED MOBILE! Lowest call cost! Popular handset! $20 when you sign, plus 60 cents per call!”
Offer 2: “GENIE RENTALS
Offer 3: “HI–PRO
Tables:
| Number of calls: | 10 | 20 | 30 | 40 | 50 | 60 |
| Advanced mobile: | ||||||
| Genie rentals: | $24 | $38 | $52 | $66 | $80 | $940 |
| Hi–Pro: |
Flow diagrams:
7. Now write down which one of the three representations was the most useful to you when you answered question 6. Give complete reasons for your statements.
ACTIVITY 3
To create a model to explain relationships
[LO 2.2, 2.3]
Olga likes chocolate-covered raisins. She has been making a list of the contents of the packets that she has been buying. She always buys from the same shop, but sometimes she buys small packets (50g), sometimes medium (100g) and sometimes large (200g) packets.
She has made a table of the facts she has discovered.
| Packet size | 50g | 100g | 200g |
| Average number of raisins | 78 | 153 | 304 |
| Cost per packet | R3,80 | R7,40 | R14,50 |
Olga contacted the manufacturers and found out from them that part of the price is for the packaging and the other part is for the contents. The packet cost is very similar for the three sizes, and the greatest part of the price is for the raisins. The unit cost of the contents stays the same regardless of the size of the packet.