# Stage 4 - data representation

Stage 4 -Data – Data Representation

## Strategy

Students can

- read and interpret data in tables
- construct, read and interpret histograms, column graphs, line graphs and stem and leaf plots.

## Activities to support the strategy

### Activity 1

1. Show students examples of tables with data from newspapers and the Internet. As a class, discuss:

- What is the title of the table?
- What does the table compare or show?
- What are the different column or row headings?
- What unit of measurement is used or implied?
- What is the highest value? The lowest value?
- What trends can you see?
- Is this a convenient way to display data?
- What are the advantages of displaying data in a table? What are the disadvantages?
- Which data in tables might be better displayed as a graph?

2. Have students investigate examples of different graph types from newspapers, magazines, non-fiction books, reference books, the Internet and other sources. Divide students into groups, with each group to investigate one of the following graph types: sector / pie, conversion, divided bar, line, travel, column and step.

Students should provide examples and record any features of the graph type. Students should also determine other situations when it would be appropriate to use the graph type.

Each group should then report back to the class and share their findings on:

- The features of the type of graph
- Situations when this graph type is appropriate / best
- What unit of measurement is used or implied?
- What is the highest value? The lowest value?
- What trends can you see?
- Is the data displayed this way misleading? Are there any errors which would not occur in another graph type?
- Is this a convenient way to display data?
- What are the advantages of displaying data in this type of graph? What are the disadvantages?
- Which data might be better displayed as a table or another graph type?

Records of each groups' findings should be displayed, to allow students to compare and contrast the different types.

### Activity 2 – drawing line graphs

In science, students are often required to extract information from different types of graphs, including line graphs, using information from first-hand investigations as well as from secondary sources such as texts. They should be able to interpret information and identify trends and patterns in the data. To determine which is the most appropriate graph to represent a particular set of data requires students to demonstrate an understanding of the type of data that they are dealing with, such as continuous data, as well as how to construct the graph using appropriate scales, plotting points etc.

Line graphs are commonly used in science to represent the relationship between two variables.

1. Give the students a graph such as Room temperature over the day. This graph shows the inside temperature of a room from sunrise to sunset.

A line graph is used in this case because the data is continuous. It provides an opportunity to model how students can determine the temperature of the room in between the times that the temperature was recorded.

In determining the temperature increase from 7 am to 8 am, students should be able to move from a given data point on the horizontal axis (Time) to the corresponding data on the vertical axis (Temperature) to determine:

- The temperature at 7 am (13°C)
- The temperature at 8 am (15°C)

Therefore the temperature increase from 7 am to 8 am

= temperature at 8 am – temperature at 7 am

= 15 – 13

= 2°C

Students determine from the graph:

- the temperature at 10 am
- the maximum temperature reached during the day.

2. Students identify trends expressed by the shape of the graph or slope of the line to determine the period of the day when the temperature did not rise or fall.

E.g. the slope of the line is zero between 10 am and 11 am. This indicates that the temperature has remained constant (the same) during this period of time.

3. Students answer these questions using the graph:

- Between which times of the day did the temperature increase the fastest?
- At what times of the day did the temperature begin to decrease? Students provide reasons for the decrease in temperature at these times.

There are many experiments that provide data for students to graph.

4. Choose a warm sunny day. Ask students to identify whether they would find it more comfortable to be in a lighter or darker coloured car of the same make, which is parked in the sun on a hot summer's day for around 20 minutes. Consider the ability of each car to heat up in the sun.

When the students have provided their prediction, give the following equipment to each group of students:

- a silver coloured can
- a black coloured can
- 2 corks with a hole in each
- 2 thermometers (these could be replaced by temperature probes and a data logger)

Ask each group to propose and design an investigation to model the situation of the dark and light coloured cars with the equipment supplied. The aim of this investigation would be to collect data to test their prediction of which car (lighter or darker coloured) would heat up the fastest and reach the highest temperature.

Students place the cans together, with the thermometers inside, in the sun for a period of about 20 minutes. Record the temperature of both thermometers every minute, including the initial temperature, using a table such as the one below. Students will need guidance in the appropriateness of their data collection and recording techniques, such as reading the thermometer, timing of readings, working in teams to ensure efficient data collection and recording etc.

5. Once students have conducted the investigation and collected the data, discuss the type of graph that is most useful in displaying data that changes continuously over time. Students should choose a line graph for their data presentation.

6. Review the features of a line graph including the horizontal and vertical axes, scales, labelling the axes, plotting the points and giving the graph an appropriate title. Guide the students to:

- identify time as the independent variable, labelled on the horizontal axis
- identify temperature as the dependent variable, labelled on the vertical axis
- choose an appropriate scale on each axis for the data gathered
- plot the values for the silver coloured can and label the line
- plot the values for the black coloured can and label the line
- label the graph with a heading such as the temperature change in a black and silver can placed in the sun for 20 minutes.

Ask students to extract information from the data in their graph and discuss:

- Which coloured can heated to the highest temperature in the time period?
- Which coloured can heated the fastest? How can you tell?
- Which coloured can's temperature increased at the fastest rate? Explain.
- Exploring deep understanding (QTF)
- Consider the concepts of radiation, absorption, conduction and reflection.

### Activity 3 – histograms

Discuss what histograms are and how they are constructed.

A good explanation is at Histograms: Construction, Analysis and Understanding which can be downloaded from quarknet.fnal.gov/toolkits/new/histograms.

### Activity 4 – stem and leaf plots

1. Show students examples of stem and leaf plots from newspapers and the Internet. As a class, discuss:

- What is the highest value? The lowest value?
- What trends can you see?
- Is this a convenient way to display data?
- Which section do you think is the 'stem'?
- Which section do you think is the 'leaf'?
- What are the advantages in displaying data in a stem and leaf plot? What are the disadvantages?
- Which data might be better displayed as a table or a line graph?

2. Divide the class into small groups and distribute the examples of stem and leaf plots. Ask each group to prepare a frequency table of the data in the stem and leaf plot and a column graph. Students then provide half a page of notes about the features they noticed in their stem and leaf plot. Groups should then share these with the class.

3. Ask small groups of students to compare these representations of data and discuss the similarities and differences. A scribe should record the group's reflections. Groups should then combine and compare reflections.

4. Have the class do the stem and leaf plot from - How to construct stem and leaf plots.

5. Students should conduct a survey and use the website How to construct stem and leaf plots. These stem and leaf plots should be printed and displayed around the room, along with each group's survey question. Students can choose from the following topics:

- The heights of students in our year
- The results for my science class in our last test
- The number of cars passing our school in one hour
- The length of each advertisement on TV in one hour
- The number of students buying different food and drink at the school canteen
- The number of students bringing a laptop each day to school over a one week period
- The number of students using a laptop in each subject over a one week period.

6. For each of the following stem and leaf plots, calculate the range, mean, median and mode:

## References

### Australian curriculum reference: ACMSP170

Construct and compare a range of data displays including stem-and-leaf plots and dot plots

### NSW syllabus reference: MA4-19SP

Collects, represents and interprets single sets of data, using appropriate statistical displays.

### NSW literacy continuum reference: VOCC13M2

Vocabulary knowledge, Cluster 13, Marker 2: Uses technical vocabulary to explain a complex concept or phenomenon.

### Other literacy continuum markers: SPEC13M5

Aspects of speaking, Cluster 13, Marker 5: Uses talk to explore understandings of new concepts, ideas and issues. SPEC13M7: Aspects of speaking, Cluster 13, Marker 7: Collaborates effectively in pair and group work when exploring subject content, concepts and ideas. SPEC13M8: Aspects of speaking, Cluster 13, Marker 8: Asks relevant clarifying questions. SPEC13M9: Aspects of speaking, Cluster 13, Marker 9: Listens critically to spoken texts to discuss and support opinions based on evidence in the text.

Links to other curriculum areas: Science

## Teacher resources

- Australian Bureau of Statistics ‘Four Graphs Story’
- Data representation and analysis Part 1- Histograms and polygons

#### Lesson plans

## Student resources

Plotting own data and calculating mean, mode, median

#### Making and ordering stem and leaf plots

- Organising data in a stem and leaf plot - part A
- Organising data in a stem and leaf plot - part A -ordering
- How to read a stem and leaf plot

## Numeracy app

Factor Race: Need to find out the mean, median or range of a set of numbers?

- add up to nine numbers
- go up to 1,000,000 Mean Median and Range Calculator.