Session 1: Balloons investigation

Today we will make a pictograph of our favourite balloon shapes. We are going to answer the investigative question “What different balloon shapes do the ākonga in our class like?”

1. Take a bag of balloons and spread out. Discuss shapes. Suggest the investigative question “What shape balloons do the ākonga in our class like?”
2. Ākonga choose favourite shape (or colour if different shaped balloons are not available) and draw it on a piece of paper (one eighth of an A4).
3. Ākonga work together to discuss ways to display the data. If matching pictures in 1:1 lines (pictograph) is not suggested, direct them to this.
4. Ākonga attach their drawing to the class chart.
5. Ask the ākonga what they notice about the information shown on the pictograph. Use the prompt “I notice…” to start the discussion. These “noticings” could be recorded as "speech" bubbles or on post it notes around the chart.
6. Talk about the need to label the axes and give the chart a title so that others could make sense of the display. The investigative question could be written as the chart title.
7. Ask analysis questions to extend the noticing about the results that require ākonga to combine sets:
   How many ākonga liked long wiggly balloons?
   How many ākonga liked long straight balloons?
   How many ākonga liked long balloons altogether?
   How can you add the numbers together?
   How many ākonga liked balloons that were not long?
   How many more ākonga liked long wiggly balloons than long straight balloons? All ākonga counting methods should be valused in this activity. However, it may be appropriate for you to (model and reinforce the use of subtraction or addition, rather than counting on or back.)
   Try to find analysis questions that will allow ākonga to use strategies such as near doubles and adding to make 10s.

Session 2: Birthday Party investigation

This birthday party investigation is described in full as a possible model for teaching and developing ideas for each of the stages of the statistical enquiry cycle at Level 2.  In New Zealand we use the PPDAC cycle (problem, plan, data, analysis, conclusion) for the statistical enquiry cycle.  You can find out more about the PPDAC cycle at Census At School New Zealand.

If the birthday party context is not suitable for your ākonga, choose another context (e.g. Diwali, matariki). The process described here will work for other contexts.

PROBLEM: Generating ideas for statistical investigation and developing investigative questions

1. Ask ākonga to think about the topic of birthday parties.  Explain that we are collecting some information to answer different investigative questions about birthday parties that we are going to pose.
   Using the starter “I wonder…” Ask the ākonga what they wonder about birthday parties.  Record their ideas. For example:
   I wonder…
   1. What are our favourite types of kai to eat at birthday parties?
   2. What games do we like to play at birthday parties?
   3. How many birthday parties have ākonga gone to? Consider whether this question might be inappropriate or emotionally distressing for your ākonga.
   4. Where do ākonga like to have their birthday parties?
   5. What birthday presents we want?
   6. What types of people go to birthday parties or school events?
   7. Using the “I wonder” prompt helps with generating investigative questions, questions we ask of the data. Record all questions and ideas on a brainstorming document (e.g. large chart, PowerPoint). 
       

2. The amount of work needed to tidy up the investigative questions will depend on the responses of your ākonga in the brainstorming session. New Zealand based research has identified six criteria to support the development of and/or critiquing of investigative questions. These criteria are used in the example below.  The teacher asks questions of ākonga to identify the information needed e.g. variable, group and with this information develops the investigative question. 

   • The intent of the investigative question is clear – we need to pose summary investigative questions (about category or whole number data)
   • The variable of interest is clear e.g. favourite kai, number of birthday parties/school events ākonga have been to already.
   • The group we are interested in is clear e.g. our class, Room 30, Kauri class
   • We can collect data to answer our investigative question
   • The investigative question considers the whole group e.g. What is Room 30's favourite kai to have at a celebration? – considers the whole group; whereas 'What is the most popular kai that ākonga in Room 30 like to eat at a birthday party – does not and is not an investigative question (it is an example of an analysis question and asks about an individual)
   • The investigative question is interesting and/or purposeful – in this case if the ideas are generated by ākonga then we would expect them to be interesting to ākonga.
      

   For the favourite kai at a birthday party example some possible questions are:

   • What will we want to find out about? (Favourite kai at a birthday party)
   • Who are we going to ask? (Our class)
   • Do you think we could find this out by asking our class? (Yes)
   • Are you interested in knowing about people's favourite kai at a birthday party? (Yes (if no, then change the question).)
      

   For each of the ideas generated in part 1, possible investigative questions are:

   1. What are favourite kai at birthday parties for ākonga in Room 30?
   2. What are Room 30’s favourite birthday games?
   3. How many birthday parties have the children in Room 30 been to before?
   4. Where do Room 30 children want to have their birthday parties?
   5. What presents do Room 30 children want for their birthday?
   6. How many people do Room 30 children want at their birthday parties?
       

3. Each group selects one of the investigative questions to explore.

    

PLAN: Planning to collect data to answer our investigative questions

4. Explain to ākonga that they need to think about what question or questions they will ask to collect the information they need to answer their investigative question.
    

5. Explain that these questions are called survey questions and they are the questions we ask to get the data. Work with groups to generate survey questions. For example: 

   • If the investigative question is: “What are the favourite birthday cakes for children in Room 30?”, ask ākonga how they could collect the data. 
   • A possible response is to ask the other ākonga “What is your favourite birthday cake?”
   • This might lead to a discussion about whether they mean the flavour and/or the style (a possible way to extend this for some ākonga), e.g. I might respond my favourite birthday cake is a dinosaur, when they might have been meaning the flavour e.g. chocolate, banana etc.
   • This might also mean that the investigative question needs adjusting to: What are favourite birthday cake flavours for children in Room 30?
   • Also, the ākonga might want to ask, “What is your favourite birthday cake out of chocolate, banana, vanilla and carrot?” You could challenge them as to if this would really answer the investigative question and suggest that possibly they might change the survey question to allow for other answers.
      

   Possible survey questions are:

   • What is your favourite birthday cake flavour?
   • What is your favourite game to play on your birthday?
   • How many birthday parties have you been to before?
   • Where do you want to have your birthday party?
   • What presents do you want for your birthday? (this could give multiple answers, may want to change to what is the present you most want…)
   • What is your favourite kai at birthday parties?
   • How many people do you want to have at your birthday party?

    

6. In these examples you can see that the survey question and investigative question are very similar, but there are key differences that make it an investigative question (What are favourite birthday cakes for the ākonga in Room 30? – overall about the class data) rather than a survey question (What is your favourite birthday cake flavour? – asking the individual).
    
7. Ask ākonga to think about how they will record the information they get. Options may include:
   • Tally chart
   • Writing down names and choices
   • Using predetermined options
   • Using a class list to record responses
      
8. Let ākonga try any of the options they suggest.  They are likely to encounter problems, but this will provide further learning opportunities as they reflect on the difficulties and how they can improve them.

DATA: Collecting and organising data

1. Ākonga collect data from the rest of the class using their planned method. You might provide a graphic organiser for your ākonga to use to organise their data. Consider also whether your ākonga need explicit instruction in how to record tally marks. Expect a bit of chaos. Possible issues that lead to useful teaching opportunities include:

• Predetermined options
• What happens for ākonga whose choice is not in the predetermined options?
• What if nobody likes the options given and they end up with a whole lot of people choosing "other"? They only have tally marks so they cannot regroup to new categories.
• Using tally marks only
  • The discussed issue above about the “other” category
  • Have fewer tally marks than the number of ākonga in the class 
    • and they think they have surveyed everyone
    • or they do not know who they have not surveyed yet
  • Have more tally marks than the number of ākonga in the class
• Possible solutions to the above issues could be (generated by the ākonga if possible)
  • Recording the name of the ākonga and their response and then tallying from the list
  • Giving everyone a piece of paper to write their response on, then collecting all the papers in and tallying from the papers

2. Regardless of the process of data collection we are aiming for a collated summary of the results.

ANALYSIS: Making and describing displays

1. Taking their summarised information, ākonga make a pictograph to help to answer their investigative question. As for the balloon activity we want to have uniform pieces. Provide:
   • Squares of paper all of the same size for ākonga to create their own pictures
   • Chart paper
2. Ākonga give the chart a title – a good option is the investigative question.
3. Ākonga make the pictograph by glueing enough pictures to represent the data they collected. This could be done by hand, or with an online tool.
4. Teacher roams, questioning for understanding and ensuring that ākonga can correctly construct a pictograph.
5. Once ākonga have completed their pictograph they should write or share 2-3 "I notice…” statements about their pictograph. These could be written on post it notes and stuck onto the chart. This could also be filmed and presented as a mini movie or set of slides with voiceover accompaniment.
6. Teachers can prompt further statements by asking questions such:
   • What do you notice about how many ākonga liked cakes that were not chocolate?
   • What do you notice about the number of birthday parties attended? Did you notice the greatest number of birthday parties? The least number of birthday parties?
   • Emphasise questions that require ākonga to operate with the numbers in their displays.
7. Check the “I notice…” statements for the variable and reference to the class.  For example: “I notice that the most favourite birthday cake flavour for Room 30 children is chocolate cake.”This statement includes the variable (favourite birthday cake flavour) and the class (Room 30 children). Support ākonga to write statements that include the variable and the group.
    
8. Ask ākonga to leave their charts on their desks.  Hand out post-it notes to the ākonga and ask them to wander around the class and to look at all the other graphs.  Encourage them to add “I notice…” statements to the graphs of others by using post-it notes.
    

CONCLUSION: Answering the investigative question

At the end of the session get each group to share their chart. They should state their investigative question and then the answer to the investigative question. The answer should draw on the evidence from their graph and their “I notice…” statements.

For example: What are some favourite birthday cake flavours for children in Room 30?

Answer: The most popular birthday cake flavour for Room 30 is chocolate cake. 15 ākonga in our class had chocolate as their choice. The other flavours that were liked included carrot cake, banana cake and ice-cream cake.  Carrot cake was the least popular cake flavour for Room 30.

Extending: If I (the teacher) was to make a cake for the class what flavour should I make?

Session 3: Popcorn

The previous session involved the full PPDAC cycle.  In this session today we are going to look at using tally marks to record the number of pieces of popcorn in a small cup and a bar graph to display the data.  We are focusing on the data collection and analysis phases.

1. Display a small cup (or bag) of popcorn and ask ākonga to guess how many pieces of popcorn they think are in the cup.
2. Pose the investigative question: How many pieces of popcorn are in the small cups?
3. We are going to collect data to answer our investigative question by counting how many pieces of popcorn are in each of the cups I have here (count the number of pieces of popcorn in the small cup).
4. How should we do that? Elicit ideas including counting them all. Ask how we could count them and keep a track? Accept all ideas including using tally marks to keep a track.
5. Teacher models using tally marks to track how many pieces of popcorns she/he counts. Ensure hands are washed and tables are clean.
6. Distribute individual cups of popcorn to small groups. You may wish to provide one cup of popcorn per ākonga, or use the tuakana/teina model and provide one between two.
7. Ākonga count the pieces of popcorn and use tally marks to record the number of pieces of popcorn in each cup. They should add together the total of the tally marks each ākonga in the group recorded. (Record the number of pieces of popcorn in the cup, but don’t combine, later we will use each ākonga cup count as a data point).
8. Gather the total tallies on the board or a chart.
9. Using a prepared bar graph outline, the teacher constructs a bar graph with the information from the individual total tallies.
10. Discuss features of the graph and summarise the information shown.
    What was the most common number of pieces of popcorn?
    What was the least common number of pieces of popcorn?
    How many more pieces of popcorn were there in the cup with the most, than the one with the least?
11. As a class challenge, try to work out how many pieces of popcorn the class counted altogether.
    How many pieces of popcorn did each table group count?
    Discuss strategies for adding the numbers together (for example: combine the numbers that add to 'tidy' numbers; use place value; use doubles or near doubles).

Session 4. Favourites

In this session we will undertake a statistical investigation using the idea of favourites as our starting point.  The big ideas for the investigation are detailed in session 2.  Ideas to support the specific context are given here.

PROBLEM

Brainstorm with ākonga different things that they have a favourite of. You might use the starter “I wonder what are favourite _________ for our class?”

Using the ideas developed previously, identify 10-15 favourites to be explored and develop investigative questions for pairs of ākonga to explore. A tuakana/teina model could be used here.

Investigative questions might be:

• What are favourite sports that the children in our class play?
• What are our class’s favourite waiata?
• What are Room 30’s favourite kai?

PLAN

As ākonga have had some practice with planning previously, allow them some freedom, as appropriate, to plan their data collection. Check in on the survey questions they are planning to ask. Encourage ākonga to use the tuakana/teina model to support their learning journey.

DATA

Ākonga collect the data that they need to answer their investigative question. Be prepared for some potentially inefficient methods. Use any resulting errors or problems to improve their data collection methods.

ANALYSIS

Ākonga can display the data to answer their investigative question.  They may use a pictograph or a bar graph.  Remind them to label using the investigative question and to write “I notice…” statements about what the data shows.

CONCLUSION

Allow time for pairs to present their findings by giving their investigative question and then answering it using evidence from their displays and noticings.