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

Memorandum

Discussion

Basic graphical literacy

The first part serves only to familiarise learners with the general appearance of a graph. Help them understand that the legends to the left and bottom of the graph contain meaningful information.

In this section the importance of correct and adequate labelling of graphs has not been emphasized in the learner’s module. This is mainly to keep the graphs legible. The teacher should point out that titles and other explanatory labels are necessary, and at appropriate times discuss the value of and need for annotation of graphs. Learners should always label their own graphs properly.

It will be difficult, as it often is with graphs, to be completely accurate in readings taken from the graph. The main idea is that they learn where and how readings can be taken, and not to want perfectly accurate answers. It is important that they be encouraged to motivate their answers – this will lead them to try and make logical sense of the work, and not to only guess.

1.1 South Asia 1.2 East Asia 1.3 East Asia 1.4 No

1.5 Roughly speaking, the increase was about in the same ratio – each increased by about 50% of what it had been.

1.6 SA started from a very low base (almost no TV sets) and increased fast. The US started with many TV sets and could therefore not increase so much.

• In question 1.6 learners should get some input from the educator, as they might not be old enough to have the necessary experience.

2.1 (a) 50 000 – 60 000 (b) about 125 000 (c) nearly a million

2.2 more than 2.3 (see below) 2.4 About thirty years

2.5 Less than ten years 2.6 Yes – the graph goes up to the right.

Question 2.3 – think Second World War!

Question 2.7: The main idea is that it is impossible for the graph to keep on going upwards forever.

Question 3 uses a graph from an area in the Western Cape – maybe it will be possible to find something close to the home range of the learners.

3.1 Between 100 m and 110 m

3.2 About 215 m

3.3 Nearly 3 000 m from Papegaaiberg

• The teacher can help a great deal to make learners more graphically literate by looking for graphs to show and discuss, and to encourage learners to do the same. An atlas usually has graphs of various kinds. Later in the module when other graphical methods are discussed, atlases can once again be used for additional examples.

Cartesian planes

• Graph paper is very expensive. Two sheets of squared paper is included at the end of this section, instead of in the learner’s module. The teacher can make photocopies of them whenever necessary
• Most learners understand coordinate systems well after a bit of practice. The hardest thing to grasp can be that the integers refer to where the lines are, and not to the space in between. This is essential to knowing how to deal with fractions of a unit. It is effort well-repaid to make sure they get this point mastered. Point out that it works like a ruler.

1. 4 × 36 = 144

2. R4H2 ; L5H4 ; L4S1 ; R2S2 (Please check these answers with the learner’s module)

3. Answer not included – left as an exercise for the teacher.

4. The letters are less useful – but this is the opportunity to bring in zero (for the chairs in the passages) and negative numbers for the seats to the left and to the front.

There is a great deal of terminology coming in at this stage – the more the educator uses the correct terms, the more familiar the learners will become with them.

1. A ( –5 ; 6) B (–4 ; –2) C (5 ; –5) D (2 ; 3)

E (6 ; 0) F (0 ; 8) G (–6 ; –6)

2. Something looking like a dog should emerge.

Tables and graphs

• When working with tables, it is important to take note of the order and pattern of the top row when trying to determine a pattern for the bottom row.

1.1 (The formula is 5 x + 12) a = 57; b = 72; c = 13

1.2 (1 ; 17) (2 ; 22) (3 ; 27) (4 ; 32) (5 ; 37) (6 ; 42) (7 ; 47) (9 ; 57) (12 ; 72) (13 ; 77)

2. This situation illustrates a stepped graph

2.1 1,5 hours is part of two hours and 2,5 hours is part of 3 hours.

2.2 Plot only dots, and don’t join them.

2.4 R245

Homework