Making Sense of Graphs That Tell A Story

Grade 10 Mathematics Literacy

What is a graph?A graph is a mathematical picture of the

relationship between two variables such as temperature and the day of the week.

The benefit of graphs is that you can see and understand the whole picture at a glance.

Graphs going up and going down (increasing and decreasing)

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5

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Inflation Rate over 7 years

Year

Inflati

on R

ate

%

Looking at a graph in a newspaperTessa saw the graph in a financial magazine –

What information can Tessa extract from this graph?It shows the inflation rate for each year for

seven years. Looking at the line of the graph, you can see

that inflation goes up in general. The graph is steepest in the last year.

Therefore inflation increased the most in the 7th year.

What is Inflation?The increase in the price of goods in a

country.If a graph is increasing, the slope goes up

from left to right.If a graph is decreasing, the slope goes

down from left to right.

How can you tell if one line is steeper than another line? You can see the difference by looking at the slope or gradient:

A steeper graph shows a quicker change.A gradual slope shows a slower change.

Another example…

08h00 10h00 12h00 14h00 16h00 18h00 20h005

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11

14

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20

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Range of Temperature over the course of 1 day

Time of the Day

Tem

pera

ture

(ᵒC

)

Looking at the graph of temperature over one day, answer the following questions:

1. At what time in the day is the temperature the lowest?

2. When is the temperature the highest? 3. Is there any time period during the day that

the temperature stays the same? 4. Between what hours in the day do you see the

biggest increase in temperature? 5. Is there a decrease in temperature? If so,

what time in the day and explain.

1. At 8h00, as the graph is at the lowest point.2. At 14h00, as the graph is at the highest point.3. Yes, between 18h00 and 20h00. We know this

because the line of the graph remains constant during these 2 time periods.

4. The biggest increase in temperature takes place between 10h00 and 14h00.

5. There is a decrease in temperature from 14h00 to 18h00. We know this because the graph goes down the highest point.

Continuous and Discrete graphsSome types of values can only be whole

numbers, while others, like measurements, can have decimal fraction values.

Whole numbers must be shown by points on a graph, connected by dotted lines.

These kinds of graphs are called discrete. Values which are continuous, such as length,

should be connected by solid lines, to show that the values in between the points are included too.

Looking at the graph below, it shows the number of passengers on a bus for six different trips.

And this graph shows the distance that a bus travels for one trip.

Why does the first graph have dotted lines and the second graph have a solid line?

Interpreting Graphs…Graph 1: Chantal and Sarah went on a training

run and drew this graph to show their progress:

07h00 07h15 07h30 07h45 08h00 08h15 08h300

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6Timing & Kilometres of Training Run

Time of Day

Num

ber

of

Kil

om

etr

es

run

1. What was the total distance of the training run and how many hours did it take?

2. Give the times when Chantal and Sarah were resting (where the distance stayed constant).

3. One part of the graph is steeper than the others. Identify this part.

Graph 2: Daniel's car takes 45 litres of petrol. The graph below shows the amount of petrol in the tank over one week.

1. Is there any time when his petrol tank is completely empty? How do you know?

2. Daniel was sick for two days during the week and stayed at home. Which days was he sick? Explain your answer.

3. How many times does he fill up his car with petrol? Where do you see this on the graph?

Graph 3: This graph shows the temperature in Grahamstown, measured over one week in September.

Using the graph on the previous slide, answer the following questions:

1. Is this graph continuous or discrete? Explain. 2. What was the highest temperature recorded

during the week? On what day was this? 3. What was the lowest temperature recorded

during the week? On what day was this? 4. Write down the maximum and minimum

temperatures on Wednesday. Calculate the difference between them.

Dependant and Independent Variables:Variable: The quantity you are measuring

or calculating.

Independent Variable: a variable that stands alone and isn't changed

by the other variables you are trying to measure.

Dependant Variable: depends on other factors.

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.

Touching the axesWhat does it mean when a graph touches the horizontal axis or the vertical axis?

Interpreting a graph that touches the vertical axisJane buys chocolate as a present for her dad.

Look at this graph of the price of chocolate per weight.

1. What is the price when the weight of the chocolate is 0 kg? Explain your answer.

2. Explain which is the independent and which is the dependent variable.

Interpreting a graph that touches the horizontal axisMark empties his 500 ml water bottle at a constant

rate.1. Describe what you see in the graph below.2. Explain which is the independent and which is the

dependent variable.

1. The volume of the water starts at 500 ml. It decreases steadily as Mark empties it. At 5 minutes, it reaches 0 ml. This means it has taken 5 minutes to empty the bottle completely.

2. The volume changes with time, so time is the independent variable, and volume is dependent.

One last problem to work on…

Reading graphs: Helen has a long walk to school today and takes a one litre bottle of water with her. Look at this graph carefully and then answer the questions on the next slide.

1. What are the two variables plotted on this graph?

2. Which variable is dependent and which is independent? Explain fully.

3. What happens to the amount of water in the bottle during the first two hours?

4. What happens at hour number 5? Explain.

5. Between which two hours does Helen drink her water the fastest?

6. Is there a point at which she finishes all the water in her bottle? How do you know this?

1. Time is on the horizontal axis, and the volume of water in Helen’s bottle is on the vertical axis.

2. The volume of water is dependent on time, the independent variable.

3. It remains at the same level.4. The amount of water in the bottle increases

suddenly which suggests that Helen refilled her water bottle.

5. Between the hours of 8 and 10.6. No. At no point does the graph touch the

horizontal axis - i.e. at no point is the volume of water in the bottle 0 ml.