Looking for ongoing and discrete relatinship

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We give learners the basic tools to interpret graphs that they see in the media. This section is particularly useful for learners who have ly been intimidated by graphs and don't understand how representations work, so it is vital to keep this section informal. Do not ask learners to read points off a graph or to work with independent and dependent variables in this section. They will do this in the following sections. In Maths Literacy, almost every problem begins with a story, which then needs to be analysed and solved if possible. It is easier to understand the meaning of a picture than a list of s.

A graph is just a mathematical picture of the relationship between two quantities, such as distance and time. The advantage of a graph is that you can see and understand the whole picture at a glance. In this section we will look at the messages that graphs give us. You will develop the skill of interpreting graphs and you will learn to identify some important features of graphs.

How do we know when a line is steeper than another line? You can see the difference by looking at the slope or gradient:. The 2nd worked example in Chapter 2 deals with very important concepts in graph work, which learners need to master at the beginning of Grade increasing, decreasing, constant, gradients, maximum and minimum points.

They do not need to use the formal terminology; but they must be able to interpret these features of graphs correctly. Using realistic contexts for these graphs is a good way to check whether learners understand the meaning of the features. The following activity is a good opportunity to assess this informally. In Chapter 1 we learnt that some types of values can only be whole s, while others, like measurements, can have decimal fraction values.

This is important when drawing graphs, because whole s must be shown by points on a graph, connected by dotted lines. We call these kinds of values, and graphs, discrete. Continuous values, such as length, should be connected by solid lines, to show that the values in between the points are included too. The use of dotted lines in a discrete graph is to help us see the differences between the points and the steepness of the slope between them, rather than indicating a connection between the points.

Look at the graphs below. The first graph shows the of passengers on a bus for six different trips. The second graph shows the distance that a bus travels for one trip. Explain why the first graph has dotted lines connecting the points while the second has solid lines. The first graph has discrete variables, as both the of passengers and the of trips can only be whole s there can't be half a passenger on the bus, for example! The second graph shows measurement values, which are continuous. The solid line shows that all of the points along the graph are part of the relationship.

Any measurement of time and distance would be valid, because the bus trip took place over a continuous of minutes, and the bus drove all the way, along a continuous distance. One part of the graph is steeper than the others. Identify this part. The graph below shows the amount of petrol in the tank over one week. Pumeza was ill for two days during the week and stayed at home. Identify the two days and explain your answer. Tuesday and Wednesday - her petrol consumption did not change at all, this suggests she did not use her car, and was therefore at home.

Continuous - there are no gaps in the graph, temperature is measured all day, from Friday to Thursday. Write down the maximum and minimum temperatures on Wednesday. Calculate the difference between them. Where is the highest point on the graph? There is a dotted line to indicate that the graph is not continuous between the plotted points. The sales are discrete points because Naledi only sells a whole of necklaces each day. An independent variable is a variable that stands alone and isn't changed by the other variables you are trying to measure.

For example, someone's age might be an independent variable. Other factors such as what they eat, how they go to school, how much television they watch aren't going to change a person's age. A dependent variable depends on other factors.

For example, a test score could be a dependent variable because it could change depending on several factors such as how much you studied, how much sleep you got the night before you took the test, or even how hungry you were when you took it. An easy way to remember which is the dependent variable and which is the independent variable is to put the names of the two variables you are using in a sentence in a way that makes the most sense.

Then you can see which is the independent variable and which is the dependent variable. For example, time causes a change in distance travelled and it isn't possible that distance travelled could cause a change in time. When we plot graphs of variables, we usually put the independent variable on the horizontal axis and the dependent variable on the vertical axis.

We plot the independent variable in a relationship on this axis. We plot the dependent variable in a relationship on this axis. You will not see these features on all graphs, but they are important to look for on a graph. The following worked examples show you how to interpret this in graphs.

Nicola buys biltong in fancy packaging as a present for her dad. Look at this graph of the price of biltong per weight. By now, you have a good idea about what kinds of things to look at when you 'read' a graph. Do the following activity to put all of this information together. Tumelo has a long day at work ahead and takes a one litre bottle of water to work with him.

Look at this graph carefully and then answer the questions below. The amount of water in the bottle increases suddenly. This implies that Tulemo refilled his water bottle. Between hour and hour. At no point does the graph touch the horizontal axis - i. Jabu sees the following graph in a newspaper article: What information can Jabu extract from this graph? Answer the following questions and explain your answers by referring to the graph: On which day is the temperature the lowest during the week? When is the temperature the highest? On which day s does the temperature stay the same?

Between which days do you see the biggest increase in temperature? Which part of the graph shows a decrease in temperature? Exercise 2. What was the total distance of the hike and how many hours did it take? Give the times when Lindi and Thabang were resting where the distance stayed constant. Is there any time when her petrol tank is completely empty? How do you know?

How many times does she fill up her car with petrol? Where do you see this on the graph? The graph below shows the temperature in Bloemfontein, measured over one week in September. What was the highest temperature recorded during the week?

On what day was this? What was the lowest temperature recorded during the week? Naledi makes and sells beaded necklaces. Look at the graph below and answer the questions:. Between which two days is the biggest increase in sales? Between Thursday and Friday - the graph is constant between these two points. Describe what happens to the sales between Wednesday and Thursday. Worked example 4: Interpreting a graph that touches the vertical axis Nicola buys biltong in fancy packaging as a present for her dad.

What is the price when the weight of biltong is 0 kg Explain your answer. Explain which is the independent and which is the dependent variable. Worked example 5: Interpreting a graph that touches the horizontal axis Tumelo empties his ml water bottle at a constant rate. Describe what you see in this graph. What are the two variables plotted on this graph? Time, on the horizontal axis, and the volume of water in Tumelo's bottle, on the vertical axis.

Which variable is dependent and which is independent? Explain fully. The volume of water is dependent on time, the independent variable. What happens to the amount of water in the bottle during the first two hours? What happens at hour 5? Between which two hours does Tumelo drink his water the fastest? Does he finish all the water in his bottle at any point? How do you know this?

Looking for ongoing and discrete relatinship

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