3.1 Understanding what graphs tell us  (Page 2/5)

• Steepness (also called slope ) is measured as the vertical distance divided by the horizontal distance, namely: $\frac{\text{vertical}\text{change}}{\text{horizontal}\text{change}}$ or $\frac{\text{rise}}{\text{run}}$ in engineer-speak. As you will see, this is exactly how one measures the gradient of a graph.

3.1 What is the height above sea level of the spot exactly halfway between the two hills?

3.2 What is the difference in height of the two hills?

3.3 What is the lowest spot, according to the graph?

4 Look for graphs to study. You can look in newspapers, magazines (car, sports and financial magazines) and textbooks in other subjects. If you have an atlas, you will usually see graphs there. If possible, bring these graphs to school to discuss in class. If the graph is about something that you find interesting, then you can ask yourself some questions like the ones in the e x ercises above.

• When you learn about statistics in a later module, you will study more (and different) graphs.
• ACTIVITY 2

To be able to understand, construct and use the Cartesian system of coordinates

[LO 1.4, 1.7, 2.3, 3.7]

1. Arranging seats in the school hall:

The diagram shows a small school hall. The blocks are chairs for the audience. There are three doors (marked X) – one at the back and two in the middle of the sides. From the stage you can see the Left half of the chairs and the Right half of the chairs on either side of the passage. The other passage separates the front chairs (with Soft seats) from the back chairs (with Hard seats).

The rows are numbered from the centre of the hall 1 to 6 to the front, 1 to 6 to the back, 1 to 6 to the right and 1 to 6 to the left, as viewed from the stage.

• The four tickets belonging to the four white blocks in the diagram are labelled L4S1, L5H4, R2S2 and R4H2. As you can see, the first letter tells us whether the seats are to the left or to the right. The number after this letter tells how far from the centre passage the seat is. The next letter tells us whether the seat is a soft seat in the front half or a hard seat in the back, and the last number says how far it is from the passage that runs across the hall.

1.1 How many people can be seated in the hall?

1.2 If you have to show the guests to their seats, you must know which one of the white blocks goes with which ticket. Fill the correct labels in on the diagram.

1.3 In the same way, find and label these seats: R6S6; R5H1; L1S1; L6S1; L2S5; L3H3; R1H1.

1.4 If the school needed to put 25 more chairs into the hall, they could be put in the passage. Without changing the numbers already on the chairs, how would you number the 25 extra chairs? Can you use the letters now? What about the numbers?

2. Numbering the points on graph paper:

This diagram is called the Cartesian plane.

The numbers refer to the places where the lines cross, NOT the spaces in between.

The horizontal dark line is called the x–axis and the vertical dark line is the y–axis. The place where they cross is called the origin. Its coordinates are (0 ; 0). Coordinates are always written as two numbers separated by a semi–colon, in brackets