Purpose

In this unit students collect data about favourites and present them in a variety of ways, starting with tally charts, and building up to using Microsoft Excel to create bar charts.

Achievement Objectives

S2-1: Conduct investigations using the statistical enquiry cycle: posing and answering questions; gathering, sorting, and displaying category and whole-number data; communicating findings based on the data.

Specific Learning Outcomes

- Collect data on a tally chart.
- Make pictograms to represent data.
- Produce bar charts of data using Microsoft Excel.

Description of Mathematics

At Level 2 you can expect students to be posing a greater range of questions. They will also be helped to understand some of the issues involved in conducting surveys and learn new methods for collecting data. While at Level 1 students collected data and chose their own ways to display their findings, at Level 2 they will be introduced to uniform pictograms, tally charts and bar charts. More emphasis here will also be placed on the discussion of the data and the making of sensible statements from both the student’s own displays and the displays of others.

**Uniform Pictograph**

In a uniform pictograph the pictures are drawn on uniform pieces of paper. This means that the number of objects in each category now bears a direct relationship to the size of each category on the display. An example is shown in the diagram below.

In a further development the pictures can be displayed on a chart with axes and titles. The vertical axis can be numbered to match the pictures.

**Bar Chart**

In a bar chart the pictures are replaced with vertical straight lines or rectangles. The position of these rectangles indicates what they represent and the height of these rectangles tells how many of that object there are.

The example above shows the types of shoes worn in the class on a particular day. There are three types of shoes: jandals, sneakers, and boots. The height of the corresponding rectangles shows that there are 6 lots of jandals, 15 lots of sneakers and 3 boots. It should be noted that the numbers label the points on the vertical axis, not the spaces between them. Notice too, in a convention used for discrete data, there are gaps between the columns.

**Tally Chart**

A tally chart provides a quick method of recording data as events happen. So if the students are counting different coloured cars as they pass the school, a tally chart would be an appropriate means of recording the data. Note that it is usual to put down vertical strokes until there are four. Then the fifth stroke is drawn across the previous four. This process is continued until all the required data has been collected. The advantage of this method of tallying is that it enables the number of objects to be counted quickly and easily at the end.

In the example above, in the time that we were recording cars, there were 11 red cars, 4 yellow cars, 18 white cars and 5 black ones and 22 cars of other colours. Microsoft Excel is a program available on most types of computers that allows data to be entered onto a spreadsheet and then analysed and graphed very easily.

Required Resource Materials

- Paper for tally charts
- A4 paper cut into eighths for pictograms
- Computers with Microsoft Excel or similar

Activity

- Brainstorm with students things that they have a favourite of.
*My favourite colour is blue, what are your favourite colours?*Get students to suggest others (eg. animal, food, day of the week, flavour of icecream, sport, song, school subject). Make a list of suggestions. - As a class, select one of the suggestions to investigate, avoiding choosing colour as it will be used in session three.
- Make a list of the possible responses trying to keep the number of possible answers to no more than about five or six. This may require some negotiation, for example, students will come up with more than six icecream flavours, so some may have to be disallowed, or joined with other flavours to create groups such as ‘anything with chocolate’.
- Get students to come up individually and put a mark beside the answer that is their favourite.
- Once all students have made a mark, write the number beside each group of tally marks. Show how it would be easier to count the tally marks if they were grouped into fives. Explain that the usual way to do it is to draw vertical tally marks until there are four and then draw the fifth as a horizontal or diagonal line. Discuss what the chart shows.
*What is the favourite, which is the least favourite etc.*

- Select one of the suggestions from the list of class favourites, making sure it is one which could be drawn (eg. animal, food, sport)
- Make a list of the possible answers, again keeping the number of different answers allowed to no more than five or six.
- Hand out a piece of paper (one eighth of an A4) to each student.
- Get them to draw their favourite on their piece of paper.
- Ask the students for suggestions as to how the pictures could be displayed to show which is the favourite. If matching pictures in 1:1 lines (Pictogram) is not suggested, you will need to direct them to this.
- Students attach their drawing to the class chart.
- Discuss information shown on pictogram. These could be recorded as "speech bubbles” around the chart.
- Talk about the need to give the chart a title so that others could make sense of the display. Write the title on the chart.

- Tell the students that we will be making another pictogram like the previous lesson. Today we will be working on favourite colour.
- Draw up a set of axes and label with favourite colours along the x-axis and draw in a grid to allow each student to colour in one box. Note that because this is discrete data (we count it rather than measuring it) we will make a bar graph, not a histogram, so there should be gaps between the bars.

- Get students to come up one at a time and ‘draw in’ their favourite colour.
- Talk about what it shows. Discuss how we could make it clearer, look for suggestions to add a title, and put numbers up the side. Point out that the location of the numbers on the vertical axis is beside a line, not in a space.
- Explain that this is a bar graph because we have bars to represent how many students chose each colour.

- Select another from the list of possible favourites.
- Again ensure that there are no more than five or six answers allowable.
- Survey the class, summarising the results on a tally chart, add in the results from the at home survey.
- Explain that we are going to make a bar graph like in the previous session, but this time we are going to use the computer to help us.
- Enter the results onto an Excel spreadsheet and save the file.
- Show the students how to make a bar graph of the results.
- Students could work in small groups to experiment with changing sizes, colours, fonts etc. to make their own bar graph of the data. Print the graphs for later discussion. (As most classes will not have sufficient computers for the groups to do this at the same time you may need to timetable turns throughout the day.)
- Display and discuss the printed graphs. Point out important features:
*Is it clear?*

Can you tell what it is about?

Can you see all the information?

- Students work in small groups to select another topic either from the class list, or an idea which they have had approved by the teacher to survey.
- Groups to survey either the class or possibly other classes within the school, producing tally charts of their results.
- Students may require some help from the teacher entering the data onto Excel spreadsheets.
- Students produce bar graphs of data and are given time to adjust to their own preference.
- Early finishers could write a commentary of what their graph tells them.
- Time allowed to share completed graphs with the class.
- Display work on wall.

Home Link

Dear Parents and Whānau,

In mathematics this week we are doing a statistics study on favourites. Could you please help us by filling in the survey form your child has produced to get some data about favourite things?

Thank you.

Name:

Favourite |
|||||

Favourite |
|||||

Favourite |
|||||

Favourite |