Session 1: Measuring the class

PROBLEM: Generating ideas for statistical investigation and developing investigative questions

1. Tell the students that school uniform manufacturers may be interested in information about different body sizes. Introduce differences in sizes by asking for volunteers and standing two students up to discuss what about them could be measured to inform clothing or footwear producers.
   Research online information about sizing guides as well.
2. Brainstorm things that could be measured and compared (height, head circumference, arm span, handspan, foot length). Ideas from this prompt should mostly be numerical (measured) variables.
   Note: that some students may be sensitive about being measured. It is not appropriate to measure weight. Ideas around the ethics of data collection are attended to in 4. Students who do not want to be measured could become the measurer for a measurement station.
3. Ask what other things school uniform or sportswear manufacturers may be interested in to help with their creation of clothing or footwear. Brainstorm additional ideas to explore.  Ideas from this prompt may tend to be more categorical variables.
4. Once the initial brainstorming of ideas is done interrogate the ideas by checking them using the following questions:
   • Is this a measurement/idea that the students in our class would be happy to share information with everyone? If not reject the idea [ethics].
   • Can we collect data to answer an investigative question based on this measurement/idea? 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 (specify)? If not reject the idea [ability to gather data to answer the investigative question].
   • What would be the purpose of asking about the measurement/idea that you have? 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)? If not reject the idea [does not involve the whole group].
5. Students to form small groups and select one attribute to measure (each group to select a different attribute). Ensure that one group selects height. Support the students to develop an appropriate investigative question to ask of the data. They should identify the variable of interest (e.g. height, arm length) and the group of interest (the class). Some groups might want to explore a categorical variable. This is ok as later they will have to do a measurement variable.

PLAN: Planning to collect data to answer our investigative question

6. Discuss ways to collect and record the data considering that every group will have data they want to collect. Get students to develop a survey question with instructions to collect their measure (numerical and categorical).
   • Exploring the guide on how to make measures for the CensusAtSchool questionnaire. The guide provides ideas on how to measure numerical data.
   • See session 2 in Crunch the Coach and particularly the data collection stations for additional ideas.
7. Measurement stations could be set up around the room for students to make their measures for the different survey questions designed. A recording card can be used to record individual student responses. See for example the data cards used in the 2019 CensusAtSchool survey. For categorical variables, the station will include the survey question with any response options.
8. A suggested option for the class is to develop an online questionnaire where students can input their responses to all the groups different survey questions (from their individual data card), for example, using Google Forms. This reduces the amount of time needed to collate data and the data can be downloaded into a .csv file for analysis. It is good to think about any demographic data that would be useful as well, e.g. gender (be aware of sensitivity around this also). Names are not needed to be recorded, nor should any identifying demographic data be collected. The teacher needs to be aware of the overall survey and if there are any potential ethical issues. See more about ethics in How much bullying? activity.

Session 2: DATA: Collecting and organising data

1. Students work around the different stations for the collective class survey questions and record the data onto their individual data cards. As the students gather data, the teacher should circulate and provide advice or assistance as required. Ensure that accuracy of measurements is maintained. Any students who were really not keen to be measured could be supervising a measurement station to ensure consistent and valid measures are made at it. For example, they could measure everyone’s height.
2. Students to check in with one another about the measurements they have made. They are checking for errors in recording their results, errors in making measurements or errors in reading measurements. They should share and discuss their thinking.
3. Once they have checked all their measurements and recorded results to any categorical survey questions get the students to input their responses into the class Google Form (or similar).

ANALYSIS introduction: Using an online tool to make data displays

In the remaining time for the 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 is written with CODAP as the online tool and is assuming students have not used CODAP before. If your students are familiar with CODAP then they can move straight into analysing the data from the class survey.

If you do not want to use an online tool then head to the making displays part and progress with paper versions of bar graphs, dot plots and histograms.

Learning how to use CODAP

4. 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.
5. Note for teachers: Students will use the data collected in this session to make their displays in the next session. Between sessions download the survey data into a .csv file and set up the CODAP document with the 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 3: ANALYSIS: Displaying and describing the data

Students use data from the previous session to produce graphs in CODAP or similar statistical analysis software.

1. Discuss the data collected in the previous session and explain that the students will be using CODAP or similar software to produce graphs of the data to answer their investigative question(s).
2. Share the link to the CODAP document that has all the class data.
3. Students should first look at the data that is given and decide which variable(s) they need to graph to answer their investigative question.
4. Initially students should be given freedom to experiment with what type of graph they feel best shows the information.
5. Once groups have produced a graph or graphs to answer their investigative question, bring the class together and discuss the graphs produced. Most will have produced a dot plot (default graph for numerical and categorical data). CODAP allows us to look at this data in different ways.
   Example of a categorical graph in CODAP:
   
   
   Example of a numerical graph in CODAP:
   
   We might explore what is missing from the height graph (units) and show students how to include the units in the graph.
   
   Click on the variable in the table or case card view.  This gives a pop-up menu.
   
   
   Select edit attribute properties, and in the pop-up window type in the unit (cm), and click apply.
   This updates the graph to show the units.
   
   Students can update all the measurement variables in the table to include the units of measure.
6. Students will now learn about bar graphs (for categorical data) and histograms (for numerical data) as alternative displays. 
7. Making bar graphs in CODAP for categorical data: If they chose a numerical variable for their investigative question, get them to choose a categorical variable to practice this with. They should display the categorical variable they have chosen.
   Click on the graph to bring up the tool bar. Select the graph icon and then select 'Fuse Dots into Bars' to make a bar graph.
        
8. Making histograms in CODAP for numerical data: If they chose a categorical variable for their investigative question, get them to choose the height to practice this with. They should make a display of the height first.
   Click on the graph to bring up the tool bar. Select the graph icon and then select 'Group into Bins' (note the different option when numerical data is recognised).
   
   This action groups the dots into bins. Click on the graph icon again and now the options for 'Bin width', 'Alignment' and 'Fuse Dots into Bars' comes up. Generally, go with the default settings for bin width and alignment; then select 'Fuse Dots into Bars'.
   
   The resulting graph is:
   
   Students can explore changing the bin width and the alignment. What happens when the alignment is changed?
   Students can compare the dot plot with the histogram and have a korero about what is similar and what is different. What are the advantages of the dot plot? What are the advantages of the histogram?
   Remind them that they can use multiple displays to show different features of the data to answer their investigative questions.

9. Students describe their data displays. A good starter is using “I notice…” as students start to notice features of their displays. For numerical data they might notice:

   • The largest value
   • The smallest value
   • Where most of the values lie e.g. between X and Y
   • Where the data peaks
   • Gaps or clusters
   • Unusual values

   For categorical data they might notice:

   • The most common
   • The least common
   • The majority
   • Combinations of categories
   • Any patterns (depending on the categories)

   All statements in the descriptions need to include the name of the variable and the group, and for numerical data, the value and the units as well.

CONCLUSION: Answering the investigative question and reporting findings

10. Students answer their investigative question using evidence from their analysis. Ensure students support each other and have opportunities to experience both tuakana and teina roles as they do this. 
11. Students can present their findings using a PowerPoint or similar presentation. Restrict to 3-4 slides
    • Their investigative question
    • Display(s) with descriptions (1-2)
    • Answer to their investigative question – linking to the school uniform or sportswear manufacturer purpose

Session 4: Comparing to students like us in New Zealand

The class will use data from CensusAtSchool to compare to their class results.

1. Students from around New Zealand have engaged in the CensusAtSchool questionnaire and measurement data has been collected, some like what we collected. This data is available on the CensusAtSchool site.
2. In this session students will get their own sample of students their age from the CensusAtSchool database to compare with the class data from the previous sessions for measurement variables. The measurements you have taken will determine which variables you can compare. If students do not have an appropriate measurement variable get them to compare heights.
3. Show students the CensusAtSchool random sampler, remembering to accept the conditions of use. Once in there familiarise the students with the tool. There are five parts to the tool.
   • Select database – here we can choose any database from 2005 onwards.  Recommend they use the 2015 or 2017 database as these have a larger range of body measurements.
   • Select subpopulation – because we want to compare with other New Zealander students our age, we want to select specific years. When we select specific years, we get a drop-down list that allows us to select the same year level as the students. Select the year level. The example shows year 8 selected, but you could select any year group.
     
   • Some students may want to also compare data by region. Ask if any students would like to share their iwi, hapū, marae, or location of other whānau connections with the class. They may decide to compare data from their home region with data from a region of Aotearoa they have iwi, hapū or whānau connections with. 
   • Select variables – because we want to look at measurements specifically, we only want to select specific variables. When we select specific variables, we get a drop-down list of all the variables in the survey. Suggest the following variables are selected:
     
   • Select sample type – leave as random sample
   • Enter sample size (Maximum 1000) – suggest they select 100 to give a slightly bigger group to work with.
   • Note: 100 is a good size for a later activity where we find the middle and the middle 50%, also 100 will give a bigger group (sample) size than the class and provides the opportunity to deal with comparing different size groups, something students sometimes think we cannot do.
4. Once they have made the selections in the five parts, they click on generate sample and then download sample.
5. Students save the .csv file and then import into CODAP. (The video here shows how to import data from CensusAtSchool.)
6. Once the data has been collected from the site get the students to discuss how they might make a comparison with our class data e.g. they might suggest that a histogram is easier to compare than the dot plot.
7. Students display the data for any variables we have identified that we can compare using CODAP. If they need to choose, suggest they choose height.
8. They should write “I notice” statements about what they see in their data from CensusAtSchool.
9. Focus the discussion on similarities and differences between the data sets, the class data and the CensusAtSchool sample (we are calling the group from CensusAtSchool, CensusAtSchool sample to describe the group. We are NOT doing sample to population inference – this is in curriculum level 5).
   
   Note also that the different group sizes might be a sticking point for students as they may not think they are able to compare different sized groups. Get them to focus on the summary information e.g. where is most of the data, where does the data peak, what is the biggest value, the smallest value, the middle value, how do these compare? These were the suggested features from the description of their class data.
   
   Note: If the students have all downloaded their own individual samples from CensusAtSchool the discussions each student makes could be quite different. If you want them all to have the same sample from CensusAtSchool you can download a sample yourself, import into CODAP and then share the CODAP document with your students (see this video on saving and sharing CODAP documents).

Session 5: ANALYSIS: Going deeper - investigating the middle and the middle 50% of our data using CODAP

Note that measures of centre are not introduced in The New Zealand Curriculum until level 5. At curriculum level 4 we introduce informal ideas of the middle and the middle 50%

Describing the middle

Students to work with their class data initially. The example given is for heights, but the ideas are the same for any numerical data.

Introducing the idea of the median, this is the middle of the data

1. Make the graph for height using CODAP. Stretch the graph out so that the dots are not over top of one another. This can be done by dragging the bottom corner along so that the graph is wider.
2. Select the ruler (measures) and tick 'Count' and add a movable value.
   

• Ask the students what they see on their graph now.   
• They should see a line with a number in blue with a number on the top and two values, one to the left of the line and one to the right of the line. What do the two values (left and right of the line) represent? This is the count of the number of people in the class (in the given example it is 3+27, 30 students in the class).
• Discuss where the middle value would be, e.g. for this graph it would be in the middle of 30 which is 15, that is 15 on each side of the movable line.  
• Therefore, we want to move the movable value so that the counts are about half each side.   
• The place that we settle the movable value at is the middle value or the median. The median is the technical statistics term for the middle value in a set of data when the data are placed in order from smallest to largest.
   
• Get the students to read the middle value from their graph. In this example the middle value (OR middle height) is 157.5 cm (always include the unit).
  
• They should now write a statement in a text box under their graph that says…
• The median height for students in our class is __________ cm.

Repeat the idea for the data they have from CensusAtSchool.

• Students make the graph for heights for the CensusAtSchool group.
• They click on the ruler and select 'Count' and 'Movable Value'.
• They move the line until they have about half on each side (if they have selected 100 students then there will be 50 on each side).
• They write a statement about the middle value of their graph.
• The median height for students in the CensusAtSchool sample is _________cm.

This special value, the median, can be found using the CODAP measures tool.  Click on the ruler and then select median. They should get a red line showing the 'Median'. By hovering over this red line, they can find the median value, e.g. for first height example see picture below. They can also notice how close their guess at the middle was to the actual median (the middle of the values when placed in order from smallest to largest).

Introduce the idea of the middle 50% of the data

The “signal” for the data is often where the middle 50% of the data is.

• Go back to the class height graph
• Untick 'Median'
• Tick 'Movable Value' (add) so there are two movable values on the graph
  
• Discuss with the students how many people would be in the middle 50% (in this case 15). This would leave 15 outside the middle 50% or 7/8 either side.
• Move the lines so that the counts match this or are very close to this.
  
• Read the values for the middle 50%, from the two movable values. In this case it would be 151.5 cm for the bottom value and 163.5 cm for the top value.
• We would describe this as the middle 50% of heights for students in our class is between 151.5 cm and 163.5 cm.

Repeat idea for the CensusAtSchool sample heights data.

Making comparisons between our class data and the CensusAtSchool sample data

With these two additional pieces of information – the middle (median) and the middle 50% update your discussion around the similarities and differences between the class data and the CensusAtSchool sample data. Ensure students support each other and have opportunities to experience both tuakana and teina roles as they do this. 

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.) 

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.