Voting vitality

Purpose

In this unit, which explores the context of voting, students will become familiar with and apply the four keys steps of carrying out a statistical investigation.  

Specific Learning Outcomes
  • Display collected data in an appropriate format.
  • Label graphs correctly.
  • Make conclusions on the basis of statistical investigation.
Description of Mathematics

In this unit which explores the context of voting, students will become familiar with and apply the four keys steps of carrying out a statistical investigation:

  • Write questions for statistical investigations and design a method of collection of data.
  • Display collected data in an appropriate format.
  • Make statements about implications or possible actions based on the results of an investigation.
  • Make conclusions on the basis of statistical investigations.

These four are closely linked as what data is collected can dictate the way that it is displayed and the conclusions that can be reached from the investigation. On the other hand, if some restrictions have been placed on the means of display, only certain types of data collection may be relevant.

At Level 2 you can expect the students to be posing a range of questions. They will be learning some of the issues involved in conducting surveys and learn new methods for collecting data. While at Level 1 the 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.

Associated Achievement Objective

Social sciences AO2: understand that people make choices to meet their needs and wants.

Required Resource Materials
  • Paper cut into squares for voting
  • Large sheets of paper and pens for recording.
Activity

This teaching sequence is designed for teachers to take students through the four key stages of a statistical investigation. The context used is voting for the class captain, however school house captains could be an alternative context.  At the end of this unit other possible statistical investigations are provided as examples of what students might further investigate in pairs or small groups. This would then allow for the unit to be extended beyond a week.

Session 1

It’s that time again where we need to vote for the class captains.  The hunt is on to find the most suitable boy and girl to lead our class. 

  1. We need two class captains for our class, one girl and one boy.  They are going to be in charge of meeting with the school committee and representing your ideas and thoughts to the rest of the school.  If appropriate suggest a more relevant role for the class captains e.g. they may help organise the school disco or up and coming class trip.
  2. Start the discussion by asking ‘What leadership qualities do you believe a person would need for this role?  Brainstorm the qualities on a large sheet of paper.  Ask students to think about who they might like to nominate from the class.
  3. You may like students to put their hand up and nominate class members or you may like to carry out the nominations more formally by asking them to write down their nomination on a piece of paper. 
  4. Once the nominations have been made these need to be displayed.  Students are then asked how they are going to decide who should be the class captains?  How might we collect this data?
  5. Examples of tally charts, lists etc could be used to exemplify ways of collecting such data.  Organise students into groups of four to ask them how might this data best be collected?  Reminding students of the purpose of collecting the data.
  6. As a class share ideas from each group.  What ideas have each group come up with?  Come to a consensus of the method for collecting the data ready for the next day.  Students may decide one vote for a girl, one vote for a boy, or that each student gets 2 votes and they can vote for anybody.

Session 2

This session is about going through the voting process and collecting the data in a systematic way. 

  1. Recap the discussion from the previous day and encourage students to think about what we are trying to find out and why are we carrying out this investigation?
  2. Have the nominated individuals’ names written on labels.  Use the data collection method that was arrived at from the previous day’s discussion.  Further teaching on tally marks and how they work may be needed if this is knowledge students do not have.  Why do we use tally marks when collecting large amounts of data? 
  3. Students are given a square piece of paper for each vote they are allowed to make (one piece of paper for one vote, two pieces of paper each if they are going to vote twice)  they are asked to write down the name of the person they are voting for on the square of paper.
  4. Students are given 1 minute to complete their vote and then asked to sit in a circle on the mat.
  5. The teacher holds up the name of a nominated person and invites those people who voted for Sally to bring their voting square to the front. The voting squares are placed side by side as illustrated below.
    diagram.
  6. The process is then repeated for the other nominees and the voting squares are added on to make a long strip.
    diagram.
  7. Complete until all votes are represented in the strip. 
  8. Ask students to make statements about what they can see from the strip and relate this to their investigation. Be sensitive about how the information about the lowest scoring candidate is presented.

Session 3

In this session students will see how a strip graph can be transformed into a pie graph or a bar graph.

  1. Consider dyeing or colouring the strip graph to differentiate between the votes, as illustrated above. This will give greater clarity when modelling how it can be used to make a pie graph.
  2. Join the two ends of the strip graph together to make a circle.  Place this on the mat and, using chalk, find the middle of the circle and draw lines to where the colours change (voting names change). Alternatively a large piece of paper  and felt pens can be used. A pattern like this will be made.
    pattern.
  3. A large compass or piece of string can then be used to draw the circle around the outside to make the pie graph.
    diagram.
  4. Ask the following types of questions; Is this a helpful way of presenting this information?  It is easier to make statements from a pie graph or from a strip graph? 
  5. Undo the strip graph at the two ends and break the strip graph into the votes for each nominee.  Place the name labels at the bottom of the graph and place each piece of the strip graph above the appropriate name, as illustrated below.
    graph.

Session 4

In this session students will be asked to reflect on different ways of displaying data and making statements about which ways show the results most clearly.

  1. Revisit the graphs drawn over the last 2 days to show the results of the class voting.
  2. Ask the following questions;
    What would be an appropriate title for our graphs?
    What labels could you use for these graphs and where would you write them?
    Which completed graph shows our results most clearly? 
    What have we found out about who the class captains should be in our school?
  3. The questions could be asked in a whole class situation or students could complete a bus stop activity with the questions being posed on the top of a large piece of paper and students visiting each station to record their ideas.  Small groups would also be a valuable way for ideas and responses to the questions to be discussed and explored.
  4. Summarize the responses and make recommendations about when each graph might be a useful way of presenting information
  5. Conclude by revisiting the original question posed for investigation: Who will be the class captains for our room?  Make statements from the results to answer the original question.

Session 5

  1. Talk about the types of things that are worth investigating. It is important that possible investigations are relevant to what’s happening in the students’ lives and what is happening at school at the time.  Possible investigations may include:
    What are the class’s favourite pastimes?
    What should we spend the fundraising money on? 
    What class pet should we get?
  2. Encourage students to review the process they went through to decide how they were going to collect and present the voting data.  List the process as questions that students can refer back to. For example
    1. What is our investigation question?
    2. Will we pose a question or develop a survey?  
    3. Who are we going to ask? How many people are we going to ask?
    4. How are we going to collect our data?
    5. How are we going to display our results ? In tables? What is the best graph to use?  
  3. Students can now work in small groups or pairs to carry out their own investigation.  This could be completed as a homelink activity or as a follow up activity.
  4. Results should be shared and conclusions made based on the results. This investigation is likely to require at least three sessions of fairly intensive work; one session of planning and checking, one session of collecting and displaying data, and one of developing statements and conclusions and presenting these.

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