Sports figures

Purpose

In this unit students investigate the sport and recreation dispositions and habits of the students in their school, and present data using a display they have evaluated and identified as effective. 

Specific Learning Outcomes
  • Understand and calculate percentages.
  • Write summary statements from data presented in a table.
  • Use and compare the effectiveness of strip and pie graphs.
  • Pose a question for investigation, plan and carry this out.
  • Present findings, making sensible statements about the information, with supporting evidence.
  • Collate school-wide category data.
  • Critique the investigation process.
  • Pose further questions for investigation.
Description of Mathematics

Students are regularly exposed to statistical information in their daily lives. It is important that they develop statistical skills that involve interpreting and critiquing data, and evaluating the ways in which these data are presented. This literacy is key to the life skills that students need to acquire to operate successfully in our data-rich world.

At Level Three, students are refining their ability to pose questions that they want to investigate. They are learning to plan how they will gather the appropriate data, and how to sort the data in order to be able to answer their questions. Students are becoming more familiar with a range of data displays, as they use tally charts, tables, and bar graphs, (familiar from level 2). They learn to understand and work with strip graphs, and pie graphs that show proportions or percentages as part of a strip and circle respectively.

In these sessions, as students work with data, they need to understand the relationship between fractions decimals and percentages and to apply proportional reasoning skills. They learn that decimals and percentages are special cases of equivalent fractions in which the denominators are powers of ten. By explaining the percentage notation to students, they come to understand that a percentage expresses a fraction of 100 and that the symbol % is made up of the ‘out of’ or ‘per’ symbol (/) and two zeros from 100. Students should learn to show percentages physically with equipment in order to better understand the percentage concept as they calculate and work with them. Over time students develop an understanding of the role of percentages in making the comparison of data ‘easier.’

At this level the data should be multivariate. This gives the students the opportunity to identify patterns in data, and to explore the relationships between several variables. As they work with the multivariate data they have collected, they identify features of a single variable and are naturally prompted to ask summary questions of that variable. As the students then work between variables, comparison and relationship questions begin to arise as the connections between the data sets become apparent.

The nature of questions in the investigation cycle, need to be well understood. Summary questions are usually answered by a single data set, while comparison questions compare two or more data sets. As students broaden their view of the world from an individual perspective to a wider awareness of the group, they begin to develop the important understanding that data vary. Recognition of group dynamics and the relationships between data, are fundamental to developing a real understanding of variation.

As students are developing questions within the investigation cycle, they must be supported to clearly see and understand the difference between questions for investigation and the survey questions that will generate the data to answer the investigation question(s). The purpose of each question type should be made explicit within the context of their investigation.

As students manipulate data, they should be able to use computer technology to create displays to find patterns in data, including trends over time, as well as to communicate their findings to others. Tinkerplots™ and MS Excel™ allow students to define variables and to sort efficiently. Students should be required to justify their choice of display/s with reference to the information or patterns they wish to highlight.

Associated Achievement Objectives

Health and Physical Education Personal
Health and Physical Development

  • Identify factors that effect personal, physical, social and emotional growth and develop skills to manage changes.
  • Maintain regular participation in enjoyable physical activities in a range of environments and describe how these assist in the promotion of wellbeing.

Healthy Communities and Environments

  • Research and describe current health (and safety guidelines and) practices in their school and take action to enhance their effectiveness.
Required Resource Materials
Sport and recreation in the lives of young New Zealanders (2011)
available from: http://www.sportnz.org.nz/Documents/Research/yps/YPS%20Complete.pdf (extra copies of pages 18, 22, 23, 61 will be useful)

Hundreds boards and counters

Slavonic abacus

Pegboards and pegs

Number line to 100 and clothes pegs

Data squares (Attachment 1)

Paper

Pencils and erasers

Activity

Learning activities
Whilst this unit is presented as sequence of five sessions, more sessions than this may be required. It is also expected that any session may extend beyond one teaching period.

Session 1

This session is about students understanding and using simple percentages and displaying information on a strip graph.

SLOs:

  • Understand and explain percentage.
  • Calculate percentages.
  • Write summary statements from data presented in a table.
  • Present data on a strip graph.

Activity 1

  1. Begin the session by discussing a recent sporting event.
    Have students say their one favourite sportsman or sportswoman (‘sports figure’).
    List the names of five very popular sports figures. Explain that each student will choose which of the five they like best.
    Read the names one at a time and use tally marks beside each name to indicate the number of people for whom this person is their personal favourite.
    Have the students total the tally marks to ensure that no one voted twice.
    Write beside each sports figure, the fraction of the class that likes this person best.
    For example in a class of 27 students:
    Sports figure A||||4/27
    Sports figure B|||| |||| |11/27
    Sports figure C|||3/27
    Sports figure D|||| ||7/27
    Sports figure E|| 2/27
    Total 27/27
  2. Have students suggest how these data could be displayed. For example: bar graph or strip graph. By estimating the size of the fraction, roughly draw each one of these displays on the class chart, with input from the students, reviewing the features of both graph types.
     
  3. Suggest that successful sports figures are likely to have begun their sporting career at an early age.
    Explain that the focus of the next few sessions is on finding out more about the way in which young people of their age engage in sport.

Activity 2

Have students work in pairs. Make available copies of Attachment 1, pencils and paper.

  1. Introduce Sport and recreation in the lives of young New Zealanders, and point out that New Zealanders aged 5 to 18 years old took part in the survey.
     
  2. Have student pairs together read page 18 of Sport and recreation in the lives of young New Zealanders, Views about playing sport, discuss the figures for girls and boys in their age group, and write down three statements beginning “We notice that:……”

Activity 3

Make available hundreds boards and counters, Slavonic abacus, pegboards and pegs, a number line to 100. Ensure that each student pair has at least one of these pieces of equipment.

  1. Write the symbol % on the class chart and have student pairs discuss its meaning.
    Explain that this symbols means ‘out of 100’. It comes from the ‘out of’ or ‘per’ symbol (/) and the two zeros from 100.
     
  2. Have students take turns to model the sets of figures given for their age group (for example 5-10 years) on their equipment. This will require students to round the percentages to the nearest whole number. For example: 77% (77.4%), 20% (19.8%) and 3% (2.8%).
     
  3. Have student pairs total the sets of percentages in each of the six columns on page 18, adding each set of three decimal figures to equal 100%.
    Have them recognise that in each case the total is 100% and recognise that this is the same as all of the students in this sample.

Activity 4

  1. Ask, “When and why do we use percentages?”
    Record the student’s ideas on the class chart.
    Highlight these points:
    Percentages are an important part of our everyday lives.
    Percentage is a useful way of writing a fraction.
    Percentages can be compared more easily than some fractions.
    Decimals and fractions are special kinds of equivalent fractions in which the denominators are powers of 10.
    Percentages are used to express how large or small one quantity is relative to another quantity.
    Percentage difference is used when both values refer to the same kinds of things. (for example: How many boys, compared with girls, like playing sport).
     
  2. Ask, “Does this mean that there always has to be 100 people in a sample?” (No. Point out that the number in the class is not 100)
    Have students suggest why the percentage figures given are in decimal amounts. (Some may suggest that you can’t have parts of people.)
     
  3. Make calculators available and explain that the class will calculate percentages for their class.
    Refer to class data gathered in Activity 1, Step 1 above (favourite sports figures).
    Sports figure A 4/27 (4 of the 27 people in the class like figure A best.)
    Sports figure B 11/27
    Sports figure C 3/27
    Sports figure D 7/27
    Sports figure E 2/27
    Look at each fraction. Highlight that a fraction is also a division statement.
    Model and have students explain why this is so.
    For example 1/2 is one thing divided by 2, 1/4 is one (thing) divided by 4, 3/4 is 3 divided by 4, 4/27 is 4 divided by 27.
    Have students enter the smaller number into the calculator and divide this by the larger number. For example 4 ÷ 27 = 0.1481.
    Have students read the decimal number.
    Explain that to calculate the percentage, this figure is multiplied by one hundred: 14.81%
    Write beside each of the sports figures: For example:
    Sports figure A is liked best by 4/27 or 0.1481 or 14.81% (rounded to 15%) of the class.
     
  4. Have student pairs calculate percentages for each of the sports figure fractions. Have them check finally that these total 100% (or all of the class).
     
  5. Have student round the percentage to a whole number and use a different piece of equipment from that used previously to model each of the class percentage figures for the favourite sports figures.

Activity 5

Make available to each student a copy of Attachment 2.

  1. Have students write what they have each learned about percentages.
     
  2. Have students use their percentage figures from Activity 4, Step 5 and accurately create a strip graph showing the relative popularity of the five identified sports figures. Highlight the fact that the whole length of the strip is 100%, or the whole class.
    Have them write at least three summary statements about these data.

Activity 6

Have student pairs refer to page 18 of Sport and recreation in the lives of young New Zealanders and create one strip graph for boys and one for girls in their age group

Have them write at least three summary statements about one data set or comparison statements about girls and boys.

Activity 7

Conclude the session by having students consider how they would answer the questions:
How much do you like playing sport?
- A lot
- A little
- Not at all

Session 2

This session is about comparing tables of information, strip graphs and pie graphs.

SLOs:

  • Write comparison statements.
  • Interpret data presented in a pie graph.
  • Present given data in a pie graph.
  • Compare the effectiveness of data displays.

Activity 1

  1. Begin by listing sports and recreational activities that students in the class engage in.
     
  2. Write the numbers 1, 2, 3, 4, 5, >5 on the chart. Ask students to indicate which number represents the number of sports or recreational activities they are involved in.
    For example: a student may attend swimming and dance classes and do athletics (3 sports/activities).
    Record in tally marks beside each number, the number of students for whom this applies. For example:
    1|||| ||(7 students participate in one sport only)
    2|||| ||||(10 students participate in two sports or activities)
  3. Have students estimate the amount of time per week that they spend on sporting activities.
    List some of these times.

Activity 2

Make available to student pairs copies of page 61 of Sport and recreation in the lives of young New Zealanders:. Connect this to the discussion in Activity 1, Step 3 above.

  1. Allow time for students to interpret the displays.
    Discuss and list features of the pie graphs on page 61 of Sport and recreation in the lives of young New Zealanders: Time Spent Participating in Sport and Recreation – Combined Time.
    Note:
    • The time categories (≥3 hours, < 3 hours, No time) and relate these to the students’ own time indicated in Activity 1, Step 3.
    • A pie graph is circular and each sector shows the relative size of each value.
    • The sectors represent a percentage.
    • The full circle of the graph represents 100% (or all of the students surveyed in a particular category. For example: Boys 5 – 10 years.)
    • 7% is 7/100 of the pie.
    • 0.2 is 1/5 of 1% (1/100) of the pie, 0.1 is 1/10 of 1% (1/100) of the pie and these are very tiny sectors of the pie. In rounding percentages to whole numbers, these portions would not be shown.
  2. Have student pairs become familiar with the information presented and make at least three comparison statements as they look at the 6 pie graphs. Have them pair share their statements.

Activity 3

  1. Choose from pages 22 or 23 of Sport and recreation in the lives of young New Zealanders the chart in which most students in the class are represented: For example:
    If most of the students in the class are 10 years old, choose: page 22, Top 20 sport or recreation activities participated in ‘this year’ by 5 to 10-year olds.
    Have students understand that many participants in the survey are involved in more than one sport or activity so many of the students will be represented in the figures for several of the sports. (Refer to Activity 1, Step 2 above when the students listed their participation in multiple sports).
    Have them understand that the percentages given for each sport (and numbers participating) are a fraction of the total number of participants.
    Carefully examine the information together, having students together share ‘what they notice’.
     
  2. Make available to each student Attachment 3.
    Have students choose 5 sports/recreation activities. Have them round each % figure to a whole number and create a pie graph for boys’ participation and one for girls’ participation in each of the 5 sports, to show how they compare.
    Have students write a title for each simple pie graph, and write the participation percentage and the non-participation percentage on the appropriate of the two sectors of each graph.

Activity 4

Have students evaluate displays by first considering the displays they have worked with so far:
a) A table with graphics (Views about playing sport, page 18 of Sport and recreation in the lives of young New Zealanders)
b) The strip graphs they have made to represent these data.
c) Pie graphs (page 61) and their own (Attachment 3)
d) Data Tables (pages 22 and 23).
Have student pairs decide which “display” is the most ‘effective’ and justify their decision.
Recognise that strip graphs can be more easily ‘lined up’ and compared than pie graphs, and that numerical data tables are necessary but they do not have the visual impact that a graph has.
List student ideas related to each display type.

Session 3

This session is about posing investigation questions and planning a survey that will gather data to answer the investigation question(s).

SLOs:

  • Pose a question for investigation.
  • Plan an investigation.
  • Design effective survey questions.
  • Prepare to explain the data collection process to the sample.

Activity 1

  1. Review content and learning from Sessions 1 and 2.
    Suggest that it’s time and it would be fun to investigate the sport and recreation data of students within the school.
    Give student pairs a short time to write a question that they would like to investigate.
    (This may be initially worded as an ‘I wonder’ statement). Have students think about the information that they would need to gather from each student (in the school) to answer their question.
     
  2. As a class, list some of the ideas for investigation and together phrase these as questions.
    Focus on summary (S) questions that are answered by a single data set and comparison (C) questions that compare two or more data sets. For example:
    Which is the most popular sport or recreational activity in our school. (S)
    How many students in our school spend no time on sporting or recreational activities? (S)
    Do older boys in our school spend more time on sporting and recreational activities than younger boys? (C)
    Do ten year-old girls in our school spend more time on sporting and recreational activities than ten year-old boys? (C)
     
  3. Have students predict the answer(s) to the question(s) and record these.

Activity 2

Introduce the students to data squares (Attachment 1). Point out that 4 sets of data can be collected and easily sorted using this tool that is used to collect data to answer their investigation question.
NB: Highlight the difference between the investigation questions (above), and the survey questions that will generate the data to answer the investigation questions(s).
Establish that 2 of the four survey questions will be:
Are you a boy or a girl?
How old are you?

Recognise that in gathering consistent school-wide data, for practical reasons, the other two survey questions will be agreed upon as a class. (Pairs of students can then go to different classes, explain the survey task and format, and quickly gather the data).
Agree on two other survey questions that will generate the data necessary to answer the favoured investigation question(s).
For example:
What is the sport or recreational activity that you do most?
How many hours altogether do you spend per week, participating in sport or recreational activities? (≥3, < 3, None)

(Investigation questions generated in Activity 1, Step 2 may require refinement or reworking).
Explain that each student in the school will answer each of these questions on their own data square.
Model and discuss an example of a participant response and together interpret the data. For example:
 
Ballet is the activity that this 7 year-old girl does most and she spends less than 3 hours per on sporting/recreational activities.
Explore several other examples. Explain that each person in the class will soon complete their own data square.

Activity 3

  1. Together decide which class in the school (or cohort of students) each student pair will survey.
    Make available to each student pair a data sheet, a small plastic bag and scissors. Have them then work in pairs to cut their data squares and prepare their explanation for the participant class. (Why they are carrying out the survey, what questions they want the participants to answer and how to complete a data square).
    Recognising that 5 year-old students will require great support in completing the squares than older students.
    While Activity 3, Step 1 is being completed:
     
  2. Circulate a sheet of data squares (keep the on one sheet for quick photocopying). Have each student in the class complete their own data square on a class sheet. When this is done, make enough photocopies of the completed class sheet for each pair of students to have one copy of the class set of data. (Keep the original sheet.)

Activity 4

  1. Distribute to student pairs copies of the class data.
    Have them cut out the data squares, rearrange them, begin to look for patterns in the data, and answers to the investigation question(s) as they apply to their own class.
  2. Conclude by sharing some of the findings (summary and comparison) the students have made.

Session 4

This session is about sorting data into categories, presenting information using a bar graph, and calculating percentages and presenting data using a strip graph or a pie graph.

SLOs:

  • Sort information into categories.
  • Answer summary questions by sorting, organising and arranging information.
  • Make statistical displays of the collated data.
  • Make sensible statements about the information, with supporting evidence.

Activity 1

Have students practice the presentation they planned in Session 3, Activity 3, Step 1.
Have students go to other classes (or student groups) in the school and collect data.

Activity 2

Make available graph paper and Attachment 2 and Attachment 3.
Have students lay out the data squares, rearrange them looking for patterns in the data, and answers to the investigation question(s).

Activity 3

  1. Now have students sort their data by examining one variable (univariate) at a time recording the results (using tally marks as appropriate), calculating percentages and presenting summary data in a display.

    For example:
    Gender: 
    BoysGirls Class total
    816=24
    33% (33.3%)67% (66.7%)  



    For example:

     
  2. Students can make summary statements about each data set and answer summary investigation questions at a class level. (These can later be aggregated to answer the school summary questions.)

Activity 4

Have students rearrange data squares to seek answers to comparison questions. Have them create strip graphs (which are more easily directly compared) to present data and answer comparison questions, with evidence.
Have students write class level answers to comparison questions as appropriate.
NB. Some of the comparison questions are likely to require the aggregation of school-wide data.

Activity 5

Create a spreadsheet to collect school-wide data, and as they are ready, have student pairs enter summary data for each data set from their class investigations.

Session 5

This session is about answering comparison investigation questions and suggesting strategies for engaging all students in the school in regular sporting/recreational activities.

SLOs:

  • Collate school-wide category data.
  • Critique the investigation process.
  • Pose further questions for investigation.
  • Present findings.

Activity 1

Begin this session by having students pair-share their data displays and findings for the class/sample group they have worked with.
Have them give feedback to their partner pair, discuss the investigations process that they have engaged in so far, and interesting points about the use of the data squares and challenges in ‘arranging’ them to find patterns and relationships.

Activity 2

  1. Make available to all student pairs the school-wide data spreadsheet.
    Allow time for students to become familiar with the data table.
     
  2. Display the investigation questions.
    Allow time for students to seek (and find) answers within the data, and for each student to write answers to the investigation questions.
    Make students aware that they may have to refer to the data sets from particular classrooms to answer some questions.
     
  3. Have student refer to their predictions and compare these with their findings.

Activity 3

  1. As a class, brainstorm reflections on the investigation process.
    Critique together the investigation question(s), survey questions, use of the data square tool, the types of data displays and the findings.
     
  2. Allow a short time for student pairs to list further questions that the investigation has generated, or different survey questions that they think they should have asked or would like to ask.

Activity 4

If results show a cohort of students who are disengaged from any sport or recreational activities, have students suggest initiatives that could help to change this behavior. For example, support each student in the school to commit to x hours of sport/activity per week and maintain a diary/timesheet for a defined period of time.

Activity 5

If appropriate, make comparisons with the findings of the Sport and recreation in the lives of young New Zealanders.

Activity 6

Conclude the session by allowing time for each student to write a personal reflection about their experience of gathering and working with multivariate data, using strip and pie graphs, and what they have learned from these sessions.

Attachments

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