Voting vitality

Purpose

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

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
  • Pose investigative questions
  • Design data collection methods
  • Collect and collate data.
  • Display collected data in an appropriate format and make statements about the displays of data.
  • Make conclusions based on a statistical investigation.
Description of Mathematics

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

  • Pose investigative questions.
  • Design data collection methods.
  • Collect and collate data.
  • Display collected data in an appropriate format and make statements about the displays of data.
  • Make conclusions by answering the investigative question based on a statistical investigation.

These five 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 students to be posing (with teacher support) a greater range of questions, including investigative questions and survey 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 pictographs, tally charts and bar charts. More emphasis here will also be placed on describing the data and the making of sensible statements from both the student’s own displays and the displays of others.

Investigative questions

At Level 2 students should be generating broad ideas to investigate and the teacher works with the students to refine their ideas into an investigative question that can be answered with data.  Investigative summary questions are about the class or other whole group.  The variables are categorical or whole numbers. Investigative questions are the questions we ask of the data.

The investigative question development is led by the teacher, and through questioning of the students identifies the variable of interest and the group the investigative question is about.  The teacher still forms the investigative question but with student input.

Associated Achievement Objective

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

Opportunities for Adaptation and Differentiation

The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:

  • giving students summarised data to graph rather than them having to collect it and collate it
  • giving students a graph of the display and asking them to “notice” from the graph rather than having them draw the graph.

The context for this unit can be adapted to suit the interests and experiences of your students. For example, instead of class captains you could vote on a game to play at the end of the week, or a class treat for the end of term. The favourite example can be adapted to explore any favourites.

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 five 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 will be the class captains for our class?" (our investigative question). How might we collect data to answer our investigative question?
  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 two 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 bar graph.

  1. 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.
  2. Ask the following questions:
    What would be an appropriate title for our graph?
    What labels could you use for this graph and where would you write them?
  3. Label the axes and give the bar graph a title so that others could make sense of the display. A good idea is to write the investigative question as the graph title.
  4. Ask the following questions:
    Is this a helpful way of presenting this information?  
    It is easier to make statements from a bar graph or from a strip graph?
    Which completed graph shows our results most clearly? 

    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.
  5. Summarise the responses and make recommendations about when each graph might be a useful way of presenting information
    Ask the students what they notice about the information shown on the bar graph. Use the prompt “I notice…” to start the discussion. These “noticings” could be recorded as "speech" bubbles around the bar graph.
  6. Conclude by revisiting the original investigative question posed: Who will be the class captains for our class?  Make statements from the results to answer the original investigative question. 

Session 4

  1. Talk about the types of things that are worth investigating. It is important that possible investigations are relevant to what is happening in the students’ lives and what is happening at school at the time.  Possible investigative questions 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 investigative question?
    2. How will we collect the data to answer our investigative question?
    3. Who are we going to ask? How many people are we going to ask?
    4. How are we going to display our results? In tables? What is the best graph to use?  
    5. What is the answer to our investigative question based on the results of our investigation?
  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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Level Two