In this unit, using our fridge as the context, we collect data and present these as dot plots, strip graphs and pie charts.
- plan an investigation
- display data in dot plots, strip graphs and pie charts
- discuss features of data display using middle, spread, and outliers
Planning an investigation at this level is more complex than at Level 2. Here the students can begin to talk about situations they have experienced, pose questions and produce a plan for a statistical investigation. Students may be capable now of incorporating a computer into their work. In this unit the students are introduced to dot plots, strip graphs and pie charts. Depending on the nature of the questions they are posing they will find out that they need to collect and organise the data in different ways. When considering the data they now start to see and talk about distinctive features of their displays such as outliers and modes.
Dot plots:A dot plot represents data as dots on a scale. For example, in the dot plot below, we show the time students take to get to school from home. There are four students who take 8 minutes to get to school because there are four dots above the 8 minute mark. Sometimes it is more convenient to show the dots as crosses. This is because dots can be more easily missed or deleted than crosses.
Strip Graph: A strip graph represents frequencies as a proportion of a rectangular strip. For example, the strip graph below shows that the students saw 5 light blue cars, 7 yellow cars, 11 maroon cars and 2 grey ones. The strip graph can be readily developed from a bar graph. Instead of arranging the bars beside one another join them end to end. (Alternatively, you can easily get a bar graph from a strip graph by reversing the process.)
Pie Chart:(from Strip Graph) A pie graph is just like a piece of pizza pie divided up into sections. The size of the piece, that is the angle subtended at the centre of the pie, tells the relative magnitude of the object represented by that piece of pie. In the diagram, the light blue piece of pie represents 5/25 = 1/5 of the pie; the yellow section represents 7/25 of the pie; the maroon section, 11/25 of the pie; and the grey section 2/25 of the pie. Actually this pie chart is easily formed from a strip graph. Take the strip in the example above and join the two ends to form a circle. Draw a circle this size on your paper. Mark off the lengths of the different coloured parts on the edges of the circle. Join the ends of the marks to the centre of the circle. Of course reversing this process we can get a strip graph from a pie chart.
- Memo cube paper
- Strips of paper
data, pie chart, dot plot, strip graph, spreadsheet , categories, investigation, outliers, distribution, predictions, preferences, compare, survey
We begin the week collecting fridge data. We use this information to form a strip graph which we magically turn into a pie chart.
- Tell the class that this week they will be investigating Fridge Pickers.
What do you think a fridge picker is?
What types of food do you like picking from your fridge?
- List the ideas on the board and then group into 5-6 categories with one of these categories being an other category.
- Give students a small square of paper and ask them to select one of the categories to either write or draw on the paper. (The final graph is more distinctive if each category has been drawn on a different coloured square. Memo cube paper works well for this.)
- Collect and sort the squares of paper.
- Join the squares to form a strip graph. Attach the squares using tape or glue onto another strip of paper.
- What statements can you make about us as fridge pickers?
- Next take the ends of the strip and join to form a circle. Draw around the inside of the circle marking the end-points of each colour. Now draw lines from each colour to the centre of the circle to form a pie chart.
How is this display different from the strip graph? What do you notice about the pie chart?
Is it easier to make statements from? Why? Why not?
Where else have you seen pie charts?
How many people in your family do you think are fridge pickers?
What time of the day do you think people fridge pick?
How could we find out?
- Show the students the dot plot chart and highlight its features. Explain that they are to use it at home one day this week to investigate fridge pickers. Each time a person opens the fridge to pick they are to put a X beside the time. If you want to add individual detail ask each member of the family to use a different coloured pen or to write their Initial instead of a X. The dot plots are to be brought to school for the activity on session 5.
- As a class make predictions about the information.
We think that :
Our fridge’s will be opened the most before teatime.
That no one will open the fridge between midnight and 6 am.
- Ask each child to write an additional 1-2 statements about who they think will open the fridge the most in their home.
Over the next three days the students gather information around the theme of fridge’s or food. They display and share the information using strip graphs and pie charts. If you have a computer in the classroom you could take turns showing small groups of students how to enter and display their data on a spreadsheet.
The charting function of spreadsheets allows the students to readily produce a number of different graphs.
- Brainstorm ideas for other fridge or food investigations. List these on the board. Some ideas could include;
- What drinks do we keep in our fridges?
- What type of fridge do we have?
- What are our favourite frozen vegetables?
- What types of yoghurt do we like?
- What brand of margarine do we prefer?
- Let the students work in pairs to plan and then conduct an investigation. First ask the students to select a topic. If two or more pairs want to do the same investigation, let them do so. When it comes to sharing findings remember to compare results.
- Next ask the pairs to list the categories (or options) for their survey.
For example: Frozen vegetables
Categories: Peas, Carrots, Beans, Corn, Mixed Vegetables, Other
- Finally the students need to prepare instructions for their survey, ie, they need to prepare instructions to indicate how others are to respond on their squares of paper.
- To check the clarity of directions have pairs exchange directions.
Read the directions.
Are they clear to you?
Can you tell what you are supposed to do?
What do you think they need to change to make the directions clearer?
- Allow time for the directions to be modified.
- Tell the pairs to leave their directions with squares of paper at their desks. Have them rotate around the room completing the other students' surveys.
- After the surveys have been completed the pairs return to work with the data collected.
- Discuss with students the features that you want them to include in their report (or poster) of the investigation. The reports could include:
- The aim of the investigation.
- A list of predictions.
- A description of how the data was collected.
- The data displayed in strip graphs and pie charts.
-A written summary about the data.
- Display the completed investigations. Give the students a couple of minutes to look at the other investigations before discussing.
Tell some of the things you learned from the investigations. What are the preferences of students in our class?
What was the most popular choice in your survey?
How can you tell?
How many students made that choice?
Which display is most effective?
Did you have any unexpected results?
- Compare investigations completed by more than one pair.
Do these displays look alike?
Did the two surveys have the same choices for you to make?
What differences are there between the investigations?
In today’s session we use the data we have gathered at home to examine our initial predictions about fridge pickers.
- We begin this session by looking at the dot plots that the students have created at home.
What can you say about your chart?
Which times of the day are the busiest for fridge pickers? Why?
Which times of the day are the quietest? Why?
Who opens the fridge the most often in your home?
- Ask the students to make a poster displaying the results of their fridge picker investigation. List the requirements for the poster for the students to complete, for example:
- Display your data using a dot plot
- Label you dot plot
- Give your poster a title
- Make 3 statements telling things you have learned about the fridge pickers in your family.
- Discuss ideas for making a classroom display of the posters.