The purpose of this unit is to integrate student learning in the mathematics and the health and physical education learning areas. Students will be evaluating data and statistical interpretations from research into interpersonal skills.

Students develop their skills and knowledge on the mathematics learning progression; interpreting statistical and chance situations, in the context of health and physical education, interpersonal skills.

Students will evaluate data and statistical reports, drawing on their own interpersonal skills and processes that help them to make safe choices for themselves and others. The rich discussion that will arise over the statistics in this context can be used as a springboard or as scaffolding for further discussion in line with the health and physical education learning area.

**Introductory session**

This session is intended to motivate students towards the context/integrated learning area and to inform teachers of students' location on the learning progressions)

Sport NZ surveyed school students in New Zealand and produced the following infographic.

- What questions could they have posed to form these conclusions?
- Which statements are reporting calculated statistics and which are not?

In this activity, the teacher(s) will be able to locate their students on the interpreting statistical and chance situations learning progression by observing how students respond…

The activity itself has a health and physical education focus, with mathematical skill and knowledge needed to evaluate statistical reports. Mathematical discussion around this activity can assist in the delivery of the health and physical education learning area achievement objectives:

- 5.A3 Investigate and practise safety procedures and strategies to manage risk situations.
- 5.C3 Demonstrate a range of interpersonal skills and processes that help them to make safe choices for themselves and other people in a variety of settings.

**Session two**

Focussing on NZ school student sports participation statistical reports.

**Focus activity**

The infographic states “11-14 year old boys do the most”.

Is this a clear statement of statistics or could it be misleading?

Give at least two different sports related statistical questions that could have lead to this conclusion.

Discussion arising from activity:

- What is being implied in by ‘the most’? Is it the most time, the most number of sports, the most training…?
- What data could have been collected to substantiate such claims? What questions could have been asked in the survey?
- Was there any statement in the survey that is unambiguous and can be supported with statistics?

**Building ideas**

A claim is often made that rugby is more popular than football. Is this the same for boys and girls? Use the data in the table below to support your conclusion.

**Reinforcing ideas**

The data in the table above gives the most popular secondary school sports by gender.

What trends can you identify in these data? (consider indoor vs outdoor, team sports vs individual)

**Extending ideas**

- What are the limitations to any of the conclusions that you can draw from the data in the table above?
- What more do you need to know about the survey in order to be able to make substantiated conclusions from the data?

### Session three

Focussing on comparisons made from NZ school student sporting activity levels data.

**Activity**

The results of a survey on the health and wellbeing of NZ secondary school students was carried out in 2012 included this extract on nutrition:

Source: https://www.fmhs.auckland.ac.nz/assets/fmhs/faculty/ahrg/docs/2012-overview.pdf

Interpersonal skills are often defined as the ability for an individual to make safe choices for themselves and others. What are the safe nutritional choices suggested by this report?

Discussion arising from acivity:

What pattern of eating exemplifies a ‘safe choice’;

- breakfast or not,
- brought lunch or bought lunch,
- diet or not dieting,
- sufficient fruit and vegetables?

What are the proportions of NZ secondary school students exemplifying safe nutrition choices in each case?

**Building ideas**

The survey on health and wellbeing of NZ secondary school students, 2012, found that 50% of students in high-deprivation areas were overweight/obese, and 29% of students in low-deprivation areas were overweight/obese. What does this suggest about the relationship between weight and wealth?

**Reinforcing ideas**

The survey on health and wellbeing of NZ secondary school students targeted 10 000 students. The physical health of the students was recorded including their BMI (body mass index).

Source: https://www.fmhs.auckland.ac.nz/assets/fmhs/faculty/ahrg/docs/2012-overview.pdf

- What links, if any, are shown in the analysis of the BMI and neighbourhood deprivation data?
- Was the sample size sufficient to draw such conclusions?

**Extending ideas**

- Comment on the validity of the conclusions drawn in the discussion around BMI and the neighbourhood deprivation data.
- Is there evidence of a causal relationship?
- Could there be other contributing factors?
- Were the measures of obesity (BMI) and neighbourhood deprivation reliable for this purpose?

### Session four

Focussing on substances; alcohol and smoking and marijuana.

**Focus activity**

The graph below shows responses to the “Youth2000” survey that questioned NZ secondary students in 2001, 2007 and 2012.

Source: https://www.fmhs.auckland.ac.nz/assets/fmhs/faculty/ahrg/docs/2012-overview.pdf

Which of the following statements are valid conclusions, about NZ secondary school students, that may be drawn from the data?

- More girls than boys have tried smoking.
- Girls are more likely to be addicted to smoking.
- Students don’t smoke as much now because it is more expensive.
- The number of students who have tried smoking has reduced since 2001.

Discussion arising from activity:

- A valid conclusion states only what can be deduced from the data.
- Which of the statements are saying more than in shown in the data?
- Why might those statements not be true?

**Reinforcing ideas**

Look at the three graphs below, from the “Youth2000” survey and make at least three valid statements that describe the trends shown in the data.

Source: https://www.fmhs.auckland.ac.nz/assets/fmhs/faculty/ahrg/docs/2012-overview.pdf

**Extending ideas**

Look at the three graphs above, from the “Youth2000” survey.

- What does the data tell you about the trends in the use of each of cigarettes, alcohol and marijuana, by NZ secondary school students?
- Is there a significant difference between the behaviour of boys than of girls, shown in these results?
- Could these results be used to find the number of students who may have tried cigarettes, marijuana and binge drinking within four weeks of the survey?

### Session five

Focussing on risk taking behaviours (examples given around driving).

**Focus activity**

Look at the graph below from the “Youth2000” survey and use it to write an attention grabbing headline for a local newspaper.

Source: https://www.fmhs.auckland.ac.nz/assets/fmhs/faculty/ahrg/docs/2012-overview.pdf

Discussion arising from activity:

- What are possible factors that could have contributed to this trend?
- In the report that included this graph, students were quoted as crediting media campaigns with a greater awareness of road safety?
- To what extent do you think such use of media may have contributed to the trends shown in the graph?

**Building ideas**

Use the graph “Students involved in risky driving behaviours” to find:

- The percentage of students who have been driven by someone who has been drinking alcohol in the 2001 survey.
- The percentage of students who have been driven by someone who has been drinking alcohol in the 2012 survey.
- Describe the trend of students who have been driven by someone who has been drinking alcohol, over time.
- Use your answer above (3) to predict the shape of the graph if a survey for this year was included.

**Reinforcing ideas**

The concluding statements from the “Youth2000” survey included:

Source: https://www.fmhs.auckland.ac.nz/assets/fmhs/faculty/ahrg/docs/2012-overview.pdf

- Highlight the part(s) that relate to risky driving behaviours.
- Look at the trends shown in the two graphs and describe the trends as increasing or decreasing, and as linear or non-linear
- Extend those statements to include a mathematical description of the trends shown in the graph of ‘Students involved in risky driving behaviours’.

**Extending ideas**

Consider what the concluding remarks from the “Youth2000” report say about risky driving behaviours. The information came from students responding to survey questions.

- Are the data and trends shown likely to represent the population?
- What other ways could the trends in youth risky driving behaviours be gathered?
- Find supporting evidence from organisations such Statistics NZ and NZTA to build a stronger statement of risky driving behaviours and NZ youth.

### Session six

Focussing on 'making safe choices'

**Focus activity**

Consider the statistics about NZ secondary school students that we have been looking at in this unit:

- Participation in sports
- BMI and eating habits
- Exposure to cigarettes, alcohol and marijuana
- Risky driving behaviours

Suggest a practical method of collecting reliable data on these issues.

Discussion arising from activity:

- Which would give more representative data
- Interviews or questionnaires?
- Selected students or voluntary contributions?
- All students from selected schools or selected students from all schools?

**Building ideas**

Consider the reliability of youth data, collected from questionnaires. If your school were to investigate a sensitive issue within the school, how should reliable data be obtained?

**Reinforcing ideas**

Consider the statistics about NZ secondary school students that we have been looking at in this unit:

- Participation in sports
- BMI and eating habits
- Exposure to cigarettes, alcohol and marijuana
- Risky driving behaviours
- Why is such data useful to collect?
- The “Youth2000” project collected data in 2001, 2007 and 2012. Was this frequency sufficient to give a clear pattern?

**Extending ideas**

Considering the statistics about NZ secondary school students that we have been looking at in this unit:

- Participation in sports
- BMI and eating habits
- Exposure to cigarettes, alcohol and marijuana
- Risky driving behaviours
- To what extent are these issues interrelated?
- Could a group of youths with a high risk profile have skewed the data?
- How could the report writers have found and/or presented this?