Session 1

1. Frame the context for the investigation in a way that is relevant and engaging for your students (e.g. we need to decide what new sports equipment we will buy for next term - so we need to find out what the most popular winter sport is for each syndicate in our school). Tell students that they will be spending the week doing a statistics project on a sport of their choice. They will gather information from the internet, from their class and from the rest of the school, and present the data on graphs created using computers. 
2. Brainstorm as a class what sports could be investigated. Minority sports or sports which generate few statistics are best avoided.
3. Split the class into groups to investigate each sport. Groups of three or four are probably best. It doe not matter if two or three groups study the same sport.
4. Give the groups time to brainstorm what things they might want to find out about their sport. It is very important to emphasise at this point that they must think of ideas that they have a way to obtain some data on. For example, they could explore who watches their sport and who plays it, because this information can be obtained by surveying the school. They could also find information related to international sporting fixtures as the results of these are often easily accessible on the internet. Circulate and provide support, steering students towards ideas that are able to be investigated.
5. Ask students to interrogate the ideas they have come up with and pose investigative questions to explore about their given sport. Investigative questions are the questions we ask of the data. Support students to develop effective investigative questions by questioning, modelling, and working with the students. 

Arnold’s (2013) research identified six criteria for what makes a good investigative question.  At curriculum level 4, students should be introduced to the criteria, potentially through “discovering” them.  See for example, the following lesson on CensusAtSchool New Zealand: https://new.censusatschool.org.nz/resource/posing-summary-investigative-questions/ 

The six criteria are:

• The variable(s) of interest is/are clear and available or can be collected
• The group of interest is clear
• The intent is clear (e.g. summary, comparison, relationship, time series)
• The investigative question can be answered with the data (e.g. question is specific, data can be collected, ethics)
• The investigative question is one that is worth investigating, that it is interesting, that there is a purpose
• The investigative question allows for analysis to be made of the whole group.

See Travel to school for further information on developing investigative questions, including interrogating ideas for exploration.

6. As a class, discuss the investigative questions each group has come up with and ways to answer them. Focus the discussion on whether data are obtainable and how the data could be presented.

Session 2

1. Get each group to refer to their list of investigative questions and decide which are best answered by surveying the school.
2. Have each group generate a draft of a questionnaire for surveying the school  (i.e. develop data collection or survey questions - questions we ask to get the data). See How much bullying and Travel to school for ideas on this.
3. As a class discuss each group’s questionnaire and provide feedback on possible improvements. Focus the discussion on whether the survey questions will provide enough information, that is sufficiently detailed,  to answer the investigative questions posed.
4. Provide time for groups to create a final copy of their questionnaire for use in the next session.
5. It may be useful to create an online questionnaire and to potentially combine the different groups questionnaires (this would depend on how many survey questions they have).  Paper questionnaires may also be needed for classes that do not have access to computers and the internet.

Session 3

1. Provide time for groups to go to each class (that have agreed to be involved) and explain what they are doing and why they are doing it (purpose). They can take their questionnaires (paper copies) if required, or give the link to their online survey form.
2. On return to class paper questionnaires need to be entered into the online survey form.
3. The data needs to be downloaded into a spreadsheet and then imported in CODAP or similar software.  CODAP works with raw data where each respondent’s data is in a single row, online survey software downloads the data in this format. Ensure that you model the use of the software.
4. Have each group display their data using appropriate graphs.
5. Have each group describe their graphs, making statements that help to answer their investigative questions.
6. Bring all the groups together to share what they have done. Other students and the teacher can provide feedback on which graphs are best to represent each set of data. Focus discussion on strengths and weaknesses of different types of graph.
7. Have each group select their best graph(s) to keep and display.

Session 4

1. Direct the groups to refer back to their initial list of investigative questions and see which ones are best answered either from the internet or from books.
2. The bulk of this session is allocated to the students for researching statistics, some websites which may be helpful are listed below;
   • http://stats.espncricinfo.com/ci/engine/records/index.html (cricket)
   • http://stats.espnscrum.com/statsguru/rugby/stats/index.html (rugby)
   • https://www.worldathletics.org/records/by-category/world-records (athletics)
3. At the end of the session come back together as a class and discuss the data obtained by each group.
   Have you found information to answer your investigative questions?
   Can you put the information into graphs?
   What kind of graphs will you use?

Session 5

1. Bring all the students together with all their data obtained in the previous session when they were researching on the internet.
   What kinds of graph are best for which kinds of information?
   What are the important things to remember about each type of graph? 
2. Give students time to enter their data into spreadsheets and produce a range of graphs. Students describe the graphs, answering their investigative questions.  
3. Bring the graphs together and share with the class.
4. All of the graphs produced by each group could be made into a wall display or presentation with commentary added. Utilise the presentation formats that your students are confident using, and that allow them to express their mathematical understanding and ideas (e.g. verbal presentation, video, digital work, diagram, PowerPoint, poster etc.) 

This unit is set out to cover the topic of statistical investigations in depth will likely take 1-2 weeks. Some of the sessions may take more than one classroom session to complete. There is an introduction session followed by five sessions that follow the statistical enquiry cycle (PPDAC cycle) as described in the New Zealand Curriculum. Data detective posters showing the PPDAC (problem, plan, data, analysis, conclusion) cycle are available to download from Census At School in English and te reo Māori.

While this unit plan uses the five phases of the PPDAC cycle as a step by step process, in reality when using the PPDAC cycle one often moves between the different phases. For example, students might need to revisit the investigative question (problem) as a result of the planning phase. 

Session 1: Introduction

This session provides an introduction and purpose to statistical investigations. The teacher will need to provide the students with plenty of magazines, newspapers and websites that have some good examples of how data can be presented effectively and perhaps some examples of poorly displayed data. This could be collated into a chart or slideshow. Prior to the session, ask the students to spend some time at home looking through magazines and newspapers to find examples of statistics to bring in for the session.

1. Start the session with a class discussion to get the students thinking about whether or not we have a need for statistical investigations, and who uses the information?
   What is a statistical investigation?
   Can you think of an example when we might need to carry out a statistical investigation?
2. Organise the students into groups of two or three. Give out magazines, newspapers and website links and ask the students to find some examples of statistics.
3. Ask the students to look closely at the examples they have selected. Ask them to consider the following questions;
   Who has done the research for/carried out this investigation?
   Who will benefit from the results of this investigation?
   Is it clear to you what the purpose of the investigation is?
   What do you like about the way that the information is presented?
   Does it help you in any way to understand the information better?
   Do you think the information could have been presented in a different way to help the audience understand the findings? If so, what would have made it better?
4. Use a class discussion to share ideas from each group. Have the students all come up with the same ideas? Try and steer the students towards the conclusion that the best way to present the information depends on the information itself. They might notice that category data is displayed differently to numerical data.

Session 2: PROBLEM (Generating ideas for statistical investigation and developing investigative questions)

This session is ultimately about choosing an appropriate topic to investigate. You will need to discuss what data is actually measurable within your context and realistic topics that can be investigated in the given time frame. It would be a good idea to provide the students with a list of topics (perhaps relating to a current school issue, relevant curriculum area, or your students' cultural backgrounds and interests). Encourage students to come up with something original where possible.

1. Set the scene by recapping the discussion from the previous day about the purpose of a statistical investigation. The purpose of a statistical investigation is to identify a problem or issue that can be explored using data. The process includes “designing investigations, collecting data, exploring and using patterns and relationships in data, solving problems and communicating findings” (New Zealand Curriculum, 2007, p.26).
2. Set the students up to decide on a broad, relevant topic to investigate. This could include an initial brainstorming session in small groups and then the sharing of ideas as a class. Make sure the students know to choose a topic that will have some benefit or serve a purpose. Ideas to help include:
   • An issue across the school e.g. litter, uniform, parking, traffic, drop off/pick up zones
   • About the class e.g. pets, favourites, number of…, use of devices,
   • Something specific to the community e.g. options for a gala, market stall, Matariki celebration, best time for whānau to visit and see what is happening in class
   • Finding information about a particular activity e.g. sport involvement; hobbies and interests
   • Behaviours e.g. fridge pickers, tv watching, online learning
3. Once the initial brainstorming of ideas is done, interrogate the topics with the following questions:
   • Is this an area that the students in our class would be happy to share information with everyone? Or is it an area that our target group (e.g. whānau) would be happy to share information with us. If not reject the idea [ethics].
   • Can we collect data to answer an investigative question based on this topic or issue? If not reject the idea [ability to gather data to answer the investigative question].
   • Would you be able to collect the data to answer the investigative question in the timeframe we have specified? If not reject the idea [ability to gather data to answer the investigative question].
   • What would be the purpose of asking about this topic or issue? If it is not purposeful then reject the idea [purposeful or interesting].
   • Would the investigative question we pose involve everyone in the group (e.g. the class or another defined group)? If not reject the idea [does not involve the whole group].
4. Organise students into groups and have them select a topic or issue to focus on.
5. Support students to develop an investigative question(s) based on their topic or issue. If necessary, you could develop a few investigative questions as a class, before asking students to do this in their groups.
   These are the questions we ask of the data; it will be the question(s) we explore using the PPDAC cycle. 
   • Prompts to help with posing investigative questions are:
     • What is the variable that you want to ask about?
     • Describe the group that you are asking about?
     • Do you want to describe something (summary) or compare something (comparison)?
       • Summary questions have one variable and one group e.g. How much litter is around the school after lunch? [litter after lunch, around the school]; What pets do the students in our class have [pets, our class]?
       • Comparison questions have one variable and two or more groups e.g. How does the amount of litter that is around the school compare between after recess and after lunch? Does the traffic outside the school in the afternoon tend to be more than the traffic outside the school in the morning?
6. Check the investigative questions that students have posed. Collate them (e.g. write them on the board, type into a google doc or write on sticky notes to be pinned up). As a class check each investigative question for the variable and the group to be asked, against the remaining criteria:
   • Is the question purposeful? This should have been sorted in the generating topics for investigation stage.
   • Is the question about the whole group? Check that it is not just finding an individual or smaller group of the whole group. This too should have been sorted in the generating topics for investigation stage.
   • Is the question one that we can collect data for? This again should have been sorted in the generating topics for investigation stage. 
   • Is it clear that the question is a summary or comparison question?
7. Collect in the final investigative questions. Label who posed them in preparation for the next session. Double check the investigative questions before the next session as poorly posed investigative questions can hinder the subsequent phases.

Session 3: PLAN (Planning to collect data to answer our investigative question)

Data collection is a vital part of the investigation process. The teacher will need to stress to the students, once again, the importance of being consistent in the collection of their data. There will also need to be sufficient discussion around efficient methods for data collection and recording.

1. We need to plan to collect the data. Explain to the students that all the data will be collected using one of the following methods, depending on what data they need to collect. They might use an online survey form (e.g. google forms), and/or a paper survey, or tables (online or hard copy). Consider the skills and knowledge already developed by your students, and which method will best, in reflection of this. Ultimately, the class should move towards collecting individual data in individual rows of a spreadsheet or table. 
2. To answer our investigative questions, we need to collect specific information or data using data collection/survey questions. In this phase of the cycle we are planning to collect our data. This means we need to pose data collection/survey questions. 
   Fundamentally, data collection and survey questions are the same – they are both questions we ask to get the data. 
   • Survey questions are those we pose for a questionnaire to survey people e.g. What is your favourite colour? How did you travel to school today? Do you like eggs? People answering the questionnaire record their own responses and we collate these once all the questionnaires are complete
   • Data collection questions as those we pose for other data collection situations e.g. if we are going to collect data about the make and colour of cars passing the school then we might pose the data collection questions – what is the make of the car; what is the colour of the car and record these in a table.
3. Ask students what they think would be useful to consider when they pose their data collection/survey question(s). Gather a few key ideas to help them with this. For example:
   • The question needs to be specific
   • Keep wording simple and short
   • Avoid questions that ask about more than one thing
4. Support students to pose their data collection/survey questions. They should also think about any specific instructions, e.g. if they were going to collect information the amount of litter around the school they may need to define what they consider to be litter, what are the different areas they will collect from, how they will count the litter e.g. by number of pieces of litter, by weight, by plastic bags full.

Managing surveys: depending on the target groups and how you plan to manage the survey process there are a few options here to choose from.

Option 1: an online questionnaire is developed for each group that will be surveyed. This following should be considered:

• What is the group? E.g., the class; the parents of the class; teachers in the school; students in another class (e.g. another year level)
• Does the questionnaire contains all the survey questions from across the class that pertain to that group?
• How will the questionnaire link be sent to participants and collected by students?
• Is any identifying information collected? All responses should be anonymous – teachers will need to manage this carefully.

Option 2: a paper questionnaire is developed for each group that will be surveyed. Similar considerations to the online questionnaire are needed, except that a paper copy will need to be printed for each person to fill out. These should be collected up and brought back to the class if the people who have filled them out are not in the class

Other data collection methods

Depending on the topics, students might be collecting data about litter, cars, pedestrian traffic. These are not things that we would use a questionnaire for so the students will need to think about a plan to collect the data. They may decide to use a pre-prepared table or grid to do this. The table should be set up so that the information for each of their data collection questions for a single object can be recorded in a single row. For example:

Collecting information about vehicle make and colour – students might also think to collect the vehicle type too.

• Set up a table with four columns: 

  Number plate	Vehicle type	Vehicle make	Vehicle colour
  AAA123	Car	Audi	Blue
  BBB456	Ute	Ford	Gold
  CCC789	Car	Holden	Red
  DDD111	Truck	Isuzu	White
  123AA	Motorcycle	Suzuki	Red

• Record in a single row the information about one car
• They should also consider in their planning how long they will collect the data for and where (this will form the “group” – data about the vehicles driving past the school from 1-2pm on 24 September).

Students need to check with the teacher before commencing data collection to ensure that their method of collection is the most appropriate and will result in data that is useful for analysis.

Session 4: DATA (Collecting and organising data)

1. Provide time for students to collect and record their data, according to their plan. Regardless of the method of collection our end aim is for students to have their data tabulated with the data from a single person or object in a single row. 
2. Provide modelling and support for students as they enter their data into a spreadsheet. This should be tabulated with the variables across the top and the data listed in rows below, the table in the example about vehicle make and colour shows the structure. Consider the following:
   • If data is in an online questionnaire, give the students only the data pertaining to their investigative questions
   • For paper questionnaires the data should be collected into a spreadsheet for their questions only
   • If a paper copy of a table was used this should be transferred into a spreadsheet
3. Check for any data input errors
4. Save as a .csv file

Note for teachers: 
Students will use their .csv file to make their displays in the next session. If it is not possible for them to save as a .csv then the teacher may need to do this and share with them or set up the CODAP document with their data and share a link to this. See the video or written instructions on how to do this. Note the video and the instructions include getting started with CODAP too.

Session 5: ANALYSIS part 1 (Using an online tool to make data displays)

In this session the students will be introduced to using an online tool for data analysis. One suggested free online tool is CODAP. Feel free to use other tools you are familiar with. This session is written with CODAP as the online tool and assumes students have not used CODAP before.

If you do not want to use an online tool, then continue to Making Displays, and construct paper versions of bar graphs and dot plots.

Learning how to use CODAP

1. Allow the students some time to get familiar with CODAP. Using the Getting started with CODAP example is a good starting point. This has a built-in video that shows the basic features of CODAP and gets you started using the tool. Other support videos can be found here. 
   
   The main features that students need to be familiar with are how to draw a graph and how to import their data. More on importing data into CODAP can be found here.
   
   Bar graphs for categorical data
   
   CODAP by default makes a dot plot for both categorical and numerical data. If the data is categorical the bar graph icon (configuration icon) can be selected to fuse the dots into bars, shown in the two pictures below. The graphs are showing the habitats of mammals.
      
   Students should be encouraged to try different things out with the data to get further insights as to what the data might show them. For example, for the above data about mammals students might want to see what happens to the diet for different habitats. They can drag the diet attribute onto the top axis of the graph (and to get different colours they can drag the diet attribute into the middle of the graph to make a legend) and the following display will result.
    
   This gives a deeper insight into the data. You will find that students at this age are comfortable with using CODAP once they have had a little time to play with the software.
   
   Dot plots for numerical data
   
   When using CODAP for numerical data a dot plot is the default setting. For example, sleep in hours for mammals shown below.
   
   The data can be split into groups by dragging a categorical attribute to the vertical axis. To explore the sleep by the different habitats, drag habitat to the vertical axis, or to explore sleep by the different diets, drag diet to the vertical axis. The following graphs result.
    
    

Making displays for the data they have collected to answer their investigative question

1. Now that the students are familiar with CODAP they can make displays with their own data to help them to answer their investigative questions. Have students label their graphs using their investigative question.
2. Graphs can be exported by using the camera icon or students can take a screen grab of the graph to put into another document. Alternatively, students can use the text feature in CODAP and write their descriptions in there. As we are heading towards a presentation it is most likely that they will use their graphs in another document for the presentation.

Session 6: ANALYSIS part 2 (Describing data displays)

1. To describe the display, encourage students to write “I notice…” statements about their displays. Initially accept all statements as encouraging the idea of noticing is valuable for both statistics and other aspects of the mathematics curriculum. If students are not sure what to notice the teacher can prompt further statements by asking questions such as:
   • What do you notice about the most common number of…?
   • What do you notice about the largest number… the smallest number…?
   • What do you notice about where most of the data lies…?
   • What do you notice about the most popular… least popular…?
   • What do you notice about how the data for the litter after lunch is different to the data for the litter after recess (more specific example for a comparison) …?
2. Check the “I notice…” statements for the variable and reference to the group. For example: “I notice that the more than half the vehicles that went past our school from 1-2pm on 24 September were cars.” This statement includes the variable (types of vehicles) and the group (past our school 1-2pm on 24 September). Support students to write statements that include the variable and the group.

Session 7: CONCLUSION (Answering the investigative question and reporting findings)

This last session will focus on the final presentation of the data each group has found out. Encourage the students to be constantly evaluating what they are doing. Explain that it is fine to discover that a particular way of presentation is not working, and that it is a good idea to adjust.

1. Use this time to finish presenting information in graphs, tables, or any other format.
2. Present information in a way that includes the important parts of their investigation. Provide time and opportunity for your students to present this information using tools that are relevant and engaging for different students (e.g. as a video, poster, digital animation, speech).
   • Topic chosen
   • Investigative question(s)
   • Survey/Questionnaire/Data collection method/questions
   • Group data was collected from
   • Results – tables/graphs and descriptions of the data
   • Conclusion – answer to their investigative question
   • Call to action?
3. Have groups of students share their finished presentations with the class.
4. Evaluation: (Peer and Teacher)
   • Give feedback, including constructive criticism.
   • Is the information easy to understand?
   • Could we make it any clearer?
5. Talk about who could use the information that has been presented. Can we send it to anyone outside school? For example, investigations related to a road safety issue could be forwarded to the local council.

Session One

Part One – Introducing Data Set One

1. Organise the students into pairs, hand out a set of data cards to each pair, Data Set One Master, and get them to cut out all the data cards. Students should collect the cards together and select one of the data cards each to have a look at. Consider how you can encourage tuakana-teina by pairing more students who are more confident in maths, with students who might benefit from additional support.
2. Tell the students that this is a data card. A data card is a piece of paper containing information or data about a person. The data for these data cards has been collected by asking four survey questions. What do you think the survey questions were? Seek ideas from the class. They may just give you the variable description which is fine, such as "that is whether they are the oldest or youngest in their family".
3. Confirm that the information on these data cards comes from the following four survey questions:
   • Do more students have odd or even birthdates? Gives the top variable in the data card
   • Can you whistle? Gives the left variable in the data card
   • Are you the oldest, youngest or a middle child in your family? (Only children are classified as oldest) gives the bottom variable in the data card
   • Which hand do you write with to produce your neatest work? Gives the right variable in the data card.
4. Get the students to put the data set to one side, we will come back and use it again soon.

Part Two – Making Class Data Cards

1. Show the data card below.
   
2. Ask the class to tell you something about this student.
   • Does anyone in the class fit this data card?
   • Do you know someone that fits this data card that is not in this class?
   • How many people could this data card be correct for?
3. Discuss the importance of knowing exactly what each piece of data is about, i.e. the importance of specific survey questions. Discuss how some students could answer the same survey question differently, e.g. "Are you right handed or left handed?" could give two different answers for the person who throws a ball with one hand and writes with the other. Survey questions need to be specific, with no ambiguous answers. Hence the survey question about handedness specifically asked about which hand your write with to produce your neatest work and not just "Are you left-handed or right-handed?"
4. Ask: What would a data card about you look like for these same four survey questions?
5. Hand out a blank data card for each student to fill out. Once completed collect all data cards.
6. After this session the teacher needs to photocopy all the data cards onto a piece of paper, one set for each pair of students in the class. Photocopying onto coloured paper is suggested to make it easy to recognise the class’s data set. This data set will be used during the next session.

Part Three – Working with data set one

1. Ask the students to get the set of data cards they cut out. Have the students sort and organise the data cards to find out things about this group of students.
2. Encourage the students to look for multi-dimensional interesting things. This means looking for interesting things within different categories rather than simply counting the number in categories. For example, rather than seeing if there are more odd birthdates than even birthdates or more whistlers than non-whistlers, look to see if more odd birthdates than even birthdates are left handed or if there is a link between place in family and the ability to whistle.
3. Arranging the data cards like below, is one way to help see different patterns in the data.
   
4. Move around getting the students to explain and show what they have found out. Encourage students to add detail to their observations. This could include thinking proportionally. For example, rather than "One more even date is right handed than odd date", "A larger fraction of even date are right handed, 8 out of 12 even date in comparison to 7 out of 12 odd date are right handed." More able students are to be encouraged to think proportionally when the number in comparing groups is not the same, e.g. 8 out of 20 is a smaller proportion than 7 out of 9.
5. The following questions could be asked to encourage thinking:
   • Are there more whistling right-handers or whistling left-handers?
   • Is there anything interesting when comparing place in the family and whistling?
   • All the odd dates in this group who are the youngest can whistle, does this mean every odd date who is the youngest in their family can whistle?
6. On a large piece of paper write up what the students discover or get each pair of students to write down what they found out about this group. Keep this information, as it can be used in the next session to compare with the class data set.

Session Two

During this session, students will be sorting and arranging data cards about themselves, i.e., the students’ own data cards.

1. Before the class data set is handed out, remind the students about what they found out from Data Set One in Session One and how they organised the data cards to see discover patterns and differences.
2. Briefly discuss what they expect to find out about their class:
   1. What do you expect to find out about the class?
   2. Will the things we found out about the unknown group from Data Set One, be different or similar to our class?
3. Hand out a set of class data cards to each pair of students. The pairs cut out the data cards, then sort and arrange them, and look for patterns of interest. Move around getting students to explain and show what they have found out. Ask them to leave their final sort intact.
4. Conclude the session by asking the whole class to wander around the final sorts of each group. Encourage ako by asking the displaying pair to explain the patterns and differences they found. Compare the findings to the statements the students made at the beginning of the session and share other things of interest.

Session Three

1. Hand out a set of data cards, Data Set Two, to each pair of students. The pairs are to cut out the data cards for use in class. Ask the students to select one or two of the data cards they have just cut up. Tell them it is information from students in a class like ours, then ask them the following questions:
   • What do you think the letter and numbers mean?
   • Why are letters and numbers used instead of words?
   • What specific survey questions could give the answers: O, 6, 10 or 13? Seek ideas from the class.
     
2. Explain that the four survey questions for these data cards are:
   • Is your birthday an odd or even number? – O (top)
   • What year level are you at school? – 6 (left)
   • How many years old are you? – 10 (right)
   • What is your reaction score for catching a ruler, in centimatres? – 13 (bottom)
3. The reaction score is the average length a ruler falls, before being caught, when it is dropped four times. To work out the reaction score, one student holds a ruler vertically above the test student’s first finger and thumb; the bottom of the ruler is in line with the top of the thumb. The ruler is released and the test student closes their finger and thumb as quickly as they can to catch the ruler. The number of centimetres the ruler falls through the finger and thumb is the score. This is repeated four times, with the scores averaged to give the reaction score. For example, if the ruler fell 12cm the first time, 15cm the second time, 11cm the third time and 14cm the fourth time, the average is 12 + 15 + 11 + 14 = 52, 52 ÷ 4 = 13, therefore, the reaction score is 13.
   
   Ask students to anticipate what the data may show. Examples might be:
   • Older students will have better reaction scores than younger students
   • Class level will always be five years less than age
   • There should be the same number of odd and even birthdates
      
4. Get the students to sort and arrange the data cards to look for patterns and differences of interest. Move around getting each pair of students to explain and show what they have found out. Share the patterns and differences as a class.

Data Set Three – Optional
A third data set has been included for teachers wishing to repeat the activity in this session. The data for this set was obtained from www.censusatschool.org.nz/.

Data Set Three is a data set of 24 students. The data is: top – male/female, left – arm span in cm, right – height in cm, bottom – age in years.

Session Four

Today the students, in small groups, will design and compile their own data card set. Each small group of students will design three survey questions to ask the students in the class.

1. Provide students with blank data cards and explain that each group will be collecting their own data based on four survey questions. The first survey question will be "Are you the oldest, middle or youngest child in your family?" and three new survey questions will be added by students. Discuss "issues" that are of current importance to students. For example, students might be interested in whether people think fireworks should be only used in controlled displays, whether buses should be organised to get students to school, or how many different ethnicities or languages are represented in your class. You could frame this with the context of finding out more about make-up of our class, or as learning to inform persuasive writing, speeches or community action. Take care with issues that may be sensitive, particularly those related to body image, gender identity, religion and culture. 
2. Discuss how to define position in the family? Oldest – no siblings older than you; Middle – have older and younger siblings; Youngest – you have older sibling(s), but no siblings younger than you. An only child would be the oldest; if there are two children then there is an oldest and a youngest, from three children onwards a middle child (or children) becomes possible.
3. Discuss and brainstorm suitable survey questions. Discuss, including the measurement unit, when numeric data is gathered, For example:
   • How many centimetres tall are you?
   • How many centimetres across is the span of your right hand? (thumb to pinky finger)
     Specific instructions will be needed with survey questions like this, so it is clear where to start and finish measuring.
   • How many seconds does it take you to run 100m?
   • What is your favourite...?
   • How many languages are spoken in your family?
     A list of possible favourites to select from is best with survey questions like this.
   • What time did you go to bed last night, in hours and minutes?
     When organising the data from survey questions like this, categories may be needed, e.g. before 8 pm, 8 to 9 pm, 9 to 10 pm, and later than 10 pm.
4. Students could also look at the Census At School questionnaires for ideas of survey questions they could ask. On the explore the data page the questionnaires are available on the right hand side.
5. Before starting to collect data each small group of students needs to write three anticipatory statements about what they expect to find out about the class.
6. Each small group of students needs to collect information and make data cards from students in the class. The best way to do this is for each pair to create a "station" for other students to visit. The stations can be labelled with letters of the alphabet to ensure all students visit each station, like a dance card.
    
7. Once the data cards are completed, students are to sort and arrange them to look for things of interest. The small groups of students are to prepare a brief report of the things they have found out. Ideally the report includes some display of the data which might be the data cards organised in groups or bars.

Session Five

If a further session is required, the ideas from session 4 can be repeated, or students can make up their own set of data cards by selecting a small sample of students from Census At School. To do this they would need to go to the random sampler and agree to the terms.  Then select SPECIFIC variables and select four variables for their data cards. The first three sections are pretty good to choose from. Then enter sample size – 30 should be enough. Generate a sample, then an option to download the sample comes up – select this. Save their sample and then open the spreadsheet and use the information to make their own data cards.

Session 1

We begin the session by looking at our resting heart rate and our heart rate after we’ve done some exercise. We display this data using dot plots. Discuss with the students what they already know about dot plots graphs. Show and discuss some examples. These could be found in media (e.g. newspapers, CensusAtSchools data) or in texts. Briefly refer to the important features (e.g. title, y and x-axis, scale, regular intervals, type of data displayed - number or category). Explain that you are going to collaborate (mahi tahi) and create a dot plot. You have chosen a dot plot because you want to display number/numerical data.

1. Pose the problem: About how many times will your heart beat today?
2. Ask the students to indicate whether they think it will beat more than thousand/ more than ten thousand/ more than a million.
3. Discuss ideas that the students have for working out the answer. List these ideas on the board, for example:
   • Need to know the number of beats per minute and then the number of minutes in a day.
   • Need to consider that our heartbeat changes.
4. We want to explore heart rate, what does heart rate mean? [heart rate is measured by the number of beats of the heart per minute (bpm), another term is pulse rate].
5. Ask the students to plan a way of finding how many times their heart beats in a minute. Can they find their pulse?  Possible places include the neck (carotid artery) and wrist (radial artery).
6. Share plans, for example:
   • Work with a partner who tells you when a minute has passed (using the second hand on the class clock).
   • Work with a partner. Count the beats for 15 seconds and then multiply by 4.
7. We are first going to find our resting heart rate, exploring the investigative question (Problem): What are the resting heart rates of our class? What might we need to do before we find this? (more planning).  We need to make sure we have rested e.g. sit still for some time e.g. 5 mins or be mindful for 5 mins. Once we have “rested” everyone can find their resting heart rate using the method decided on. You could explore the patterns of numbers if the method to get the heart rate is to time for 15 seconds and then multiply by 4, or to time for 10 seconds and multiply by 6, or to time for 30 seconds and double. 
8. Draw a dot plot scale on a chart, digital display, or on the board. Note normal pulse rates at rest for children over 10 years and adults is 59-99. As we want to include the heart rate after exercise on the same dot plot suggest the plot is from 50-170 using 10s only. In the picture below you can see a faint dotted line, we will put the after-exercise heart rates above this line.
   
9. Have a student tell you their resting heart rate (76). Plot it on the graph without explaining how you positioned it. Ask another student to tell you the resting heart rate and put it on the graph. Again, do not give an explanation. (Data and analysis)
10. Then ask the students:
    Can anyone explain why I have put those numbers at that place on the graph? [Think about scale. For example,  76 is just over halfway between 70 and 80].
11. Now get the students to add their heart rates on the graph.
12. Look at the dot plot and discuss.  Ask the students “What do you notice?” (Analysis)
    Where are most of the heart rates?
    Which heart rate is near the middle? (Dot plots are great for answering this question as you can mark where you think the middle is and check that half the data is to the left and half the data is to the right)
    Which heart rates are grouped together in clusters?
    Which heart rates are lying outside the cluster?
13. Hand out the heart rate dot plot template (Copymaster 1).  Get the students to make a copy of the data collected for the class on their own dot plot.  Point out that they want to try to keep the data for resting heart rate in the bottom half of the display.
14. Discuss the factors which cause heart rates (heart beats) to vary.
15. Now send the students out for a two minute fitness run. Get them to take their pulse again and put the figures above the resting heart rate figures on the dot plot. Students can add to their graphs at the same time as you are collecting the data from the class. They should label the two groups on their dot plot: bottom group is the resting heart rate; the upper group is the heart rate after exercise. Get the students to make statements about the data they collected, what do they notice.
    Are there any surprises?
    What are the differences between the two sets of data?
    Ensure the statements include the variables (resting heart rate and heart rate after exercise) and the group (our class). As this is numerical data the statements should also include values and units (beats per minute). Use this information to answer the investigative question using evidence from our statements (conclusion). Students can share their statements with each other and provide feedback to each other. 
16. At the end of the session reflect on the initial problem about heartbeats in a day. Leave this as a problem for the students to work on during the week.

Session 2-3

In these two sessions we focus on the use of bar graphs to display results of categorical data.

Discuss with the students what they already know about bar graphs. Show and discuss some examples. These could be found in media (e.g. newspapers, CensusAtSchools data) or in texts. Briefly refer to the important features (e.g. title, y and x-axis, scale, regular intervals, type of data displayed - number or category). Explain that you are going to collaborate (mahi tahi) and create a bar graph. You have chosen a bar graph because you want to display category/categorical data

1. State the investigative question (problem): What lunchtime activities do the students in our class like? Adapt this question, if necessary, to better engage your students.
2. To answer the investigative question, we will ask the students the following survey question: Which activity do you like doing at lunchtimes? We list the possibilities on the board (plan). E.g. sport, music, coding/robotics, garden club, reading café, art
3. Discuss ideas for quickly deciding which is the favoured activity (plan and data).  We might also need to discuss if the survey question needs to change – students might like all of the activities, so we could change to What activity do you like doing the most at lunchtimes. Discuss how to collect the data from the class.  This could include:
   • standing in lines according to the activity you most like doing
   • putting a tally mark under the activity you most like doing
   • putting a post-it under the activity you most like doing.
4. Discuss ideas for making a permanent display of the data. As a class, make a bar graph with each student placing a coloured square or post-it above their preferred activity. Discuss the need for the pieces of paper to be the same size and pasted on the paper as evenly as possible. This graph could also be created digitally and displayed on a class screen.
   
5. Look at the bar graph. 
   Are there any surprises in the data we’ve collected? 
   What can you say about the information in this graph?
6. Tell the students that the principal has asked the class to find out which equipment the school should buy for lunchtime activity. (A letter from the principal or a request in person would be useful here.)
7. Get small groups of students to investigate, using the PPDAC cycle, the equipment the school has for a particular activity (cricket gear, rugby balls, board games, library books, robots, dance equipment etc) and put the information on a bar graph. The equipment can then be "matched" with the bar chart about the students’ preferred activities. Students could create graphs digitally (e.g. with Google Sheets, CODAP, or Microsoft Excel), on graphing paper, or with the use of post-it notes. Consider what will be most beneficial and engaging for your students.
8. They will then give recommendations to the school principal (write letter, give presentation, e-mail) for increasing or decreasing the equipment available to the students at lunch time (conclusion – communicating findings).

Session 4-5

Over the next two days the students gather information around the theme of sports. They use the PPDAC cycle to collect, display and share the information with others.

1. Brainstorm ideas for sports investigations. List these on the board. Some ideas could include:
   How many crunches (sit ups) can they do in a minute?
   How many breaths do they take in a minute before exercise, after exercise?
   How long does it take to run a certain distance (time in seconds)?
   How many skips can they do in a minute?
2. Look at the list of ideas and discuss the ones that would be suitable for display as a dot plot (numerical data) or a bar graph (categorical data).
3. Let the students work in pairs or small groups to identify their investigative question and plan to collect the data to answer their investigative question. Have them consider the practicalities of data collection. Once this has been checked with the teacher the students can collect their data according to their plan, make data display(s), write statements about their displays and answer the investigative question using evidence from their displays. Consider their method for creating data displays - they could use a different method from the last session, or could develop their skills with the same method. 
4. Students should present their findings as a report or presentation. Discuss with students the features that you want them to include in their report of the investigation. The reports could include:
   • The investigative question.
   • A description of how the data was collected.
   • A data display
   • A written summary about the data, including an answer to their investigative question.

Remind them to include the variable and the group in any statements they make about the data, and if the data is numerical to also include values and units. Give students the opportunity to share their learning with others within the class or as a whole class group.