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.
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 data is presented. This data-literacy is key to operating successfully in our data-rich world.
At Level 3 students refine their ability to pose investigative questions that can be explored using the PPDAC cycle. They learn to plan how they will gather the appropriate data and how to sort the data to be able to answer their investigative questions. Students become 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. The templates used work with partitions of 100.
As students work with data they need to understand the relationship between fractions, decimals and percentages and 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 with equipment. 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 investigative questions begin to arise as the connections between the data sets become apparent. Note: comparison and relationship situations are at level 4. However, it is not unreasonable to start to explore them within this context if your students are capable.
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 develop a wider awareness of the group, they develop the important understanding that data vary. Recognition of group dynamics and the relationships between data, are fundamental to developing an understanding of variation.
As students are developing questions within the investigation cycle, they must be supported to clearly see and understand the difference between investigative questions (questions we ask of the data) and the survey questions (questions we ask to get the data) 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. CODAP and 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.
Investigative questions
At Level 3, students should be generating broad ideas to investigate and then refining their ideas into an investigative question that can be answered with data. Investigative summary, simple comparison and time series questions are posed, where the entire data set can be collected or provided. The variables are categorical or whole numbers. Investigative questions are the questions we ask of the data.
Students are starting to pose their own investigative questions. The teacher is supporting this through questioning and modelling, working with the students to improve their investigative questions. Checking the variable of interest and the group of interest is key. Students are learning that the investigative question is the question we ask of the data. Data collection or survey questions are questions we ask to get the data.
Data collection or survey questions
Data collection or survey questions are the questions we ask to collect the data to answer the investigative question. For example, if our investigative question was “What ice cream flavours do the students in our class like?” a corresponding survey question might be “What is your favourite ice cream flavour?” As with the investigative question, survey question development is done by the students with teacher support to improve them so that suitable survey questions are developed.
Analysis questions
Analysis questions are questions we ask of displays of data as we start to describe it. The teacher can model this through asking students about what they see in their displays. A series of analysis questions can be developed in conjunction with the students. Analysis questions include questions about the features of the display. Questions such as: what is the most common? the least common? how many of a certain category? what is the highest value (for numerical data)? lowest value (for numerical data)? are analysis questions.
Dot plots
Dot plots are used to display the distribution of a numerical variable in which each dot represents a value of the variable. If a value occurs more than once, the dots are placed one above the other so that the height of the column of dots represents the frequency for that value. Sometimes the dot plot is drawn using crosses instead of dots. Dot plots can be used for categorical data as well.
Bar graphs
In a bar graph equal-width rectangles (bars) represent each category or value for the variable. The height of these bars tells how many of that object there are. The bars can be vertical, as shown in the example, or horizontal.
The example above shows the types of shoes worn in the class on a particular day. There are three types of shoes: jandals, sneakers, and boots. The height of the corresponding bars shows that there are six lots of jandals, 15 lots of sneakers and three lots of boots. It should be noted that the numbers label the points on the vertical axis, not the spaces between them. Notice too, in a convention used for discrete data (category and whole number data), there are gaps between the bars.
Strip graphs
A strip graph represents frequencies as a proportion of a rectangular strip. For example, the strip graph below shows that the students saw five light blue cars, seven yellow cars, 11 maroon cars and two grey ones. The strip graph can be readily developed from a bar graph. Instead of arranging the bars beside one another join them end to end. (Alternatively, you can easily get a bar graph from a strip graph by reversing the process.)
Tally charts
A tally chart provides a quick method of recording data as events happen. If the students are counting different coloured cars as they pass the school, a tally chart would be an appropriate means of recording the data. Note that it is usual to put down vertical strokes until there are four. Then the fifth stroke is drawn across the previous four. This process is continued until all the required data has been collected. The advantage of this method of tallying is that it enables the number of objects to be counted quickly and easily at the end.
In the example above, in the time that we were recording cars, there were 11 red cars, four yellow cars, 18 white cars and five black ones and 22 cars of other colours.
Using software for statistical displays
Microsoft Excel or Google Sheets can be used to summarise and graph data.
Other online statistical tools that are good for graphing data, for example CODAP – Common Online Data Analysis Platform, work with raw data and allow a more flexible approach to data analysis. Support videos for students and teachers in New Zealand on using CODAP can be found here.
Associated Achievement Objectives
Health and Physical Education Personal
Health and Physical Development
Healthy Communities and Environments
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:
The context for this unit can be adapted to suit the interests and experiences of your students.
Te reo Māori vocabulary terms such as kauwhata ira (dot plot graph), kauwhata pou (bar graph), kauwhata (strip graph), tauanga (statistics), and raraunga (data) could be introduced in this unit and used throughout other mathematical learning. Numbers in te reo Māori can be used alongside numbers in English.
Learning activities
Whilst this unit is presented as a 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:
Activity 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 of those mentioned in discussion. Explain that each student will choose which of the five they like best.
Read the names one at a time. Beside each name record tally marks to indicate the number of people who voted for this person.
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 |
Activity 2
Have students work in pairs. Make available copies of the data cards (Copymaster 1), pencils and paper.
Activity 3
Make hundreds boards and counters, Slavonic abacus, pegboards and pegs, and a number line to 100 available to students. Ensure that each student pair has at least one of these pieces of equipment.
Activity 4
Activity 5
Make available to each student a copy of Copymaster 2.
Activity 6
Ask student pairs to 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. Support small groups of students as necessary.
Ask them to 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 survey questions:
How much do you like playing sports?
- A lot
- A little
- Not at all
Session 2
This session is about comparing tables of information, strip graphs and pie graphs.
SLOs:
Activity 1
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 (three sports/activities).
Record in tally marks beside each number, the number of students for whom this applies. For example:
1 | (Seven students participate in one sport only) | |
2 | (10 students participate in two sports or activities) |
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 (estimate the amount of time per week that they spend on sporting activities).
Activity 3
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 (Copymaster 3)
d) Data Tables (pages 22 and 23).
Have student pairs decide which “display” is the most ‘effective’ and justify their decision.
Emphasise 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.
Session 3
This session is about posing investigative questions and planning a survey that will gather data to answer the investigation question(s).
SLOs:
Activity 1
Activity 2
Introduce the students to data cards (Copymaster 1). Point out that about four variables can be collected and easily sorted using this tool (data squares) that is used to collect data to answer their investigative question.
NB: Highlight the difference between the investigative questions (above), and the survey questions that will generate the data to answer the investigative questions(s).
Establish that two of the four survey questions will be:
Are you a boy or a girl? (include non-binary option if appropriate)
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 investigative 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)
(Investigative questions generated in Activity 1, Step 2 may require refinement or reworking).
Explain that each student in the school will answer each of these survey questions on their own data cards.
Model and discuss an example of a participant response and together interpret the data. For example:
Ballet is the activity that this seven year-old girl does most and she spends less than three hours per on sporting/recreational activities.
Explore several other examples, keeping student interests and cultural perspectives in mind. Explain that each person in the class will soon complete their own data cards.
Activity 3
Activity 4
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:
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 Copymaster 2 and Copymaster 3.
Have students lay out the data cards, rearrange them looking for patterns in the data, and answers to the investigative question(s).
Activity 3
Direct students to 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:
Boys | Girls | Class total | |
8 | 16 | = | 24 |
33% (33.3%) | 67% (66.7%) |
For example:
Activity 4
Have students rearrange data cards to seek answers to comparison investigative questions. Have them create strip graphs (which are more easily directly compared) to present data and answer comparison investigative questions, with evidence.
Have students write class level answers to comparison investigative questions as appropriate.
NB. Some of the comparison investigative 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 investigative questions and suggesting strategies for engaging all students in the school in regular sporting/recreational activities.
SLOs:
Activity 1
Begin this session by asking students to pair-share their data displays and findings for the class/sample group they have worked with.
Have them give feedback to each other, discuss the investigation process that they have engaged in so far, discuss interesting points about the use of the data cards and identify any challenges in ‘arranging’ them to find patterns and relationships.
Activity 2
Activity 3
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 behaviour. This could form the basis for units focused on health and physical education and/or persuasive and explanation writing.
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 record 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.
Dear parents and whānau,
We have been carrying out a statistical investigation into the sporting and recreation habits of the students in our school.
We have found: Include statement of findings
You are invited on __________________________to come and learn about how we used data cards to collect our survey information, and to see our statistical displays. We look forward to seeing you and to telling you about what we have learned.
Thank you for the support and encouragement that you give us with our sporting activities.
Printed from https://nzmaths.co.nz/resource/sports-figures at 11:53am on the 29th March 2024