The materials were developed in conjunction with and trialled by Auckland Girls’ Grammar School, Lynfield College, and Northcote College mathematics and statistics departments.����

The summary investigation lessons are based on students undertaking a statistical enquiry to find out about the class or year level.�� Lessons 1, 2, 5, 6, 9, 10, 11 broadly follow a statistical enquiry using the PPDAC cycle; this is noted in each lesson.�� Lessons 3, 4, 7, and 8 are concept development lessons, timed to allow for data collection and data entry across a year level cohort for the statistical enquiry.

This teaching sequence covers the following statistical concepts:��

1. 1. investigate multivariate data situations for observational studies by
      
      1. exploring areas of interest (Lesson 1)
      2. posing summary investigative questions (Lesson 7, 9)
      3. make conjectures or assertions about expected findings (Lesson 4, 7, 9)
   2. plan how to collect or source data to answer investigative questions, including��
      
      1. identifying the variables needed to answer the investigative question�� (Lesson 2)
      2. planning how to make valid and reliable measures for the variables (when collecting) or finding out how they were collected (when sourcing) (Lesson 2, 7)
      3. identifying the group of interest or who the data was collected from (Lesson 2, 7, 9)
      4. using a set of interrogative questions that check the different ethical practices that should be considered through the entire statistical enquiry cycle, including checking data collection and survey questions before testing with peers (Lesson 2)
   3. collect or source data including (Lesson 6)
      1. making decisions about the validity of data and making simple edits (cleaning data) if appropriate (Lesson 5)
      2. creating a data dictionary (collected data) or finding the metadata (sourced data) (Lesson 2, 5, 7)
   4. create, describe and reason from data visualisations to support answering the investigative question, including
      1. using multiple visualisations to provide global and local views of the data (Lesson 3, 4, 6, 7, 9, 10)
      2. identifying relevant features in distributions (Lesson 3, 4, 6, 7, 8, 9, 10) – interweaving the context in the description of the distribution��
   5. communicate findings, using evidence from analysis, provide possible explanations for findings, reflect on�� conjectures or assertions, and evaluate the approach for the different phases of the statistical enquiry (Lesson 11)
   6. examine the data-collection methods and findings of others’ statistical investigations to see if their claims are reasonable, and critically consider data visualisations to see if they support or misrepresent the data (Lesson 12)

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Students use the PPDAC cycle to undertake statistical and probability investigations. This unit of work explicitly looks at making valid and reliable measurements and considers the different sources of variation that are present in data, and students design and explore probability distributions for real data about themselves.

Session 1: In this session, students explore real variation and apply the��statistical enquiry cycle (PPDAC)��to a summary situation using measurement data, sourcing data from the latest CensusAtSchool database, and collect some data from themselves.

Session 2: ��In this session students explore induced variation due to measurement and accident and dig deep into planning what to measure and how (PLAN).

Session 3: In this session, students explore induced variation from sampling, developing the concept of sampling variability using samples of size 30 (ANALYSIS).

Session 4: In this session, students design and explore probability distributions for real data about themselves. In this session they pose a chance-based investigative question (PROBLEM), PLAN to collect data (experimental estimates of probabilities) and then collect and record the DATA by undertaking the probability experiment.

Session 5: In this session, students design and explore probability distributions for real data about themselves. In this session they ANALYSE the data, answer the chance-based investigative question and communicate their findings (CONCLUSION). This session continues work carried out in session four.

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The��New Zealand Garden��Bird��Survey is underway until July 6, 2025. A great data-gathering activity for your students.

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A teaching plan covering�� statistics and probability learning outcomes

Activity 1: Introduction to data science, statistics & Dollar Street

Lesson 1: Introduction to data science and statistics

• Introduction to data science and statistics
• Finding out about Dollar Street, New Zealand Census, and CensusAtSchool websites

Lesson 2: Introducing the Dollar Street website to the class

• Introduction to Dollar Street
• Finding out about the $ values
• Finding out what variables Dollar Street collects
• Learning about attributing photographs from the internet

Activity 2: Dollar Street Investigation

Lesson 1 – Identifying our investigative focus

• Make a connection to the Social Studies big idea of people seeing the world differently depending on their values, traditions, and experiences. Diversity: looking between and within cultures.
• Students are introduced to the PPDAC statistical enquiry cycle for data investigations.
• Students decide on an investigative purpose to gather data from Dollar Street – what will they detect?
• Students make a conjecture about what they expect to find.

Lesson 2 – Planning to collect data from Dollar Street

• Students identify the variables that they want to collect for their investigative focus.
• This will include defining the variables and possible outcomes to consider.
• Students develop data collection questions.
• Students test out their data collection ideas to see that they will work. They update data collection tools.
• Students design a way to record the data they will collect.

Lesson 3 – Collecting data from Dollar Street

• Students are collecting data from photographs on Dollar Street.
• Students are recording data in an electronic spreadsheet..��
• Students are checking data for errors.

Lesson 4 – Analysing our data from Dollar Street

• Students import their data into CODAP and create data visualisations for their data.
• Students make summary statements about the data, connecting it to the group that was investigated.

Lesson 5 – Communicating findings about Dollar Street

• Students are learning to choose the best descriptive statements to answer the investigative question.
• Students prepare their own evidence of undertaking a statistical enquiry to share with others.
• Students can reflect on their findings relative to initial conjectures they have made.��

Activity 3: Using CODAP

• Students learn how to use CODAP
• Exploring datasets using CODAP
• Saving and sharing CODAP documents

Activity 4: Probability activities

• pose investigative questions for a chance-based situation with equally likely outcomes, listing all possible outcomes for the situation
• plan, conduct, and record data for a probability experiment
• create and describe data visualisations for the distribution of observed outcomes from a probability experiment, using them to answer the investigative question
• compare my findings with those of others when undertaking probability experiments
• agree or disagree with others’ conclusions about chance-based investigations, with justification

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Students can explore and ask investigative questions about stickland people.

The data cards are virtual within the stickland environment.�� For a physical copy of the stickland data cards click here.

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Students are introduced to using scatter plots through the context of foot lengths. They use data from CensusAtSchool and interrogate this to see if they think the data is valid and reliable. Students then collect their own data and offer recommendations to the CensusAtSchool team to support improved validity and reliability of the data.��

This activity explores the following key ideas:

• Investigate relationship situations for paired numerical data (where the relationship is approximately y = x).
• Use provided data for observational studies and interrogate the dataset (describe information about the variables using data dictionaries).
• Plan for and collect data.
• Create data visualisations for relationship investigations.
• Describe features of data visualisations in context.
• Answer the investigative question(s) and communicate findings.
• Reflect on and evaluate investigations.

Resources

• Y8 Fabulous feet – Teaching notes with student worksheets

Connection to a previous activity

This classroom activity has its roots in an old favourite Scatter It. The original activity explored age versus height or age versus arm span, whereas this activity explores foot lengths (connecting to exploring paired numerical variables where the relationship is approximately y = x). The teaching and learning notes are more extensive, supporting teachers with ideas of questions to ask students to develop deeper understanding of working with paired numerical data. The data is linked to the latest CensusAtSchool database (2023), future databases are likely to include the variables (foot length) used in the activity, so the latest database can be used.

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This resource compiles a list of datasets for use by New Zealand teachers and students, fostering statistical and mathematical thinking. Just as the media coverage conceals layers of statistics and maths, this compilation connects you to key local and international sources. These include the New Zealand Statistical Association, the International Statistical Institute, and global hubs. Dive into a plethora of datasets, complemented by vivid graphics and encompassing health, economic, and social data.

Presented by the New Zealand Statistical Association’s Education Committee, this document empowers teachers and students to unearth statistical insights within contexts that resonate with them. The New Zealand Statistical Association’s Education Committee is providing this document, with the intention that teachers and students will find useable datasets.

Compiled by Amy Renelle, September 2023

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Student projects should engage in good, ethical practice and must meet commonly accepted ethical standards.

1. Ethics and your project

Ethics for students

• Student projects must meet commonly accepted ethical standards.
• Students must consider these before a project involving human or animal participants can be approved.
• Considering ethics is a very good learning experience for students.
• If you need animal ethics approval, you must apply for and obtain approval��before��you begin your investigation.

Animal Ethics

All animals need to be cared for and should be treated with respect at all times as they are sentient living things.

Under New Zealand law, everyone has a legal duty to provide animals in their care with all of their needs:

• food and water, shelter
• the opportunity to behave normally
• to be handled carefully by people
• ensure maintenance of good health.

When do we need to consider animal ethics?

We need to consider applying for animal ethics approval when using animals in teaching or in an investigation or experiment and the animal is being ‘manipulated’.

This means changing the animal’s normal needs, for example what it eats and drinks, where it lives/sleeps or things it does (like its type of toys) in some way.

This type of situation is when ethics approval is needed and is required under New Zealand’s law Animal Welfare Act.

For Science and Technology Fair investigations, the students are to be the applicants for the ethical approval, not their teachers, parents or caregivers.

In all of the above situations, approvals are not transferable from student to student, teacher to teacher or school to school

��Human Ethics

• If your project will involve humans in anyway, you must plan how you will incorporate the Human Ethics guidelines.

These ethical practice guidelines are for students and teachers engaged in school research and other projects that involve people (other students, family, members of the community).

Human Ethics Planning Template

Possible human consent form

Human Ethics and Your Project

Will your investigation involve yourself or other people in:

• tasting, touching or smelling different foods or other substances?
• taking any medicines, drugs or other substances?
• applying any substance to their bodies?
• undergoing any physical or medical tests?
• giving you any information of a personal, private of confidential nature?
• giving information that could identify them?

If it does, then you must think about the safety of yourself and the participants involved.

How important is research design?

People should only be asked to contribute to research that will give meaningful results. Design the research carefully and think about how you are going to use or analyse the results before you ask people to contribute to your work by being research participants.

If your project involves asking questions, you could try them first on your friends or relatives to determine whether they appear reasonable and acceptable, particularly from a stranger if that is how it will be posed.

What information do I need to give my research participants?

When you ask people to participate in your research, you need to tell them, in a language they can easily understand:

• the purpose of your research
• what will be required of them
• what risks or benefits there will be to them if they agree to work with you
• that they can withdraw from your research at any time
• if you are collecting information about people they should know beforehand whether or not the information can be linked to a particular person, what you will do with that information, who else will see it, and how you will dispose of your records when the project is over.

It is best to give this information to people in a written form and to give them a chance to think about it and to ask any questions, before they make any decisions.

What level of risk to research participants is reasonable?

Any research that involves bodily fluids or the ingesting of material (e.g., such as taking any kind of medication, ingesting substances, testing body tissue, saliva, skin scrapes, use of pain or deprivation of basic food or drink)��should only be done under the guidance of a medical person.��It is very unlikely that you will be doing such projects while still at school.

Any project should only involve minimal risk i.e., any adverse effect should be very small, and the probability of that effect occurring should be low. For instance, if one is asking people for information, it should only be the sort of information it would be safe, easily volunteered, and appropriate to ask in an ordinary conversation, or if you are asking people to exert themselves, physically it should only be to a level that that person might do in everyday life.

Who needs to give permission (or consent) for someone to participate in research?

A parent or guardian needs to give their permission for anybody under 16, as well as the young person agreeing. The parent or guardian needs to have all the information that you would give a research participant. You should keep records of who has given consent and how it has been given whenever the research involves more than observation of individuals in their normal activities.

Student projects should engage in good ethical practice so you might like to consider these general ethical principles when planning your project

Respect for your participants

• People do not have to help you with your research, and they do not have to give you a reason. If you are conducting a class survey it can’t be compulsory to participate.
• You need to understand the cultural and religious beliefs of your participants and make sure your research is not disrespectful or offensive
• All the data belongs to the respondents so it is nice to give them a summary of your final research finding at the end so they share in what you found out.

Minimise harm to the participants

• Harm can be things like pain, stress, fatigue, emotional distress, and embarrassment. Think about what you want to do in terms of the harm it could cause.�� The best way to do this is to test your ideas with your CREST group (teacher, consultant/s and assessor). That way you will get a range of opinions for you to consider.�� Once you have a plan you should ask people from your participant group how they would feel about the activities or questions you propose.
• You may need to alter your design to minimise the harm. For example, if you are doing a fitness test and collecting weight data would you do this in public or test each person on their own?

Informed and Voluntary Consent

• Participants should give signed informed consent. You should keep these safely until the end of your project
• You must give them enough information about your project and testing you want to do for them to make a good decision.
• They must not feel pressured to participate in the project.
• It is best if the information given to them in advance of the research, in written form, so they have time to think about it.
• Participants can withdraw at any time without giving you a reason and you should return any data already collected unless they say you can keep it.

Respects for Privacy and Confidentiality

• If the person could be identified, they must give their consent. If you want to use the data in a way they could be identified, use photos of them or video material you should get their written permission
• You must keep private and confidential any information you are given.
  • Where are you going to store your information = locked filing cabinet
  • What is the data going to be used for= your project
  • How will it be destroyed after the project = shredder or burnt.
  • Who else will see the raw data = you, your teacher or maybe your consultant.
  • It is good practice to tell your participants this information when they are giving their consent, by putting on your information form.

Avoidance of Unnecessary Deception

• Sometimes it is necessary to hide the true reason for the research in order to collect valid data. This is a very rare occasion but if it is necessary and the deception will not cause harm then it can be done. You should make sure that the participants are told as soon as possible what the real reason for the research was. Ideally this should be before they leave the testing room.

Social and Cultural Sensitivity

• It is very easy to only see things from our own cultural and religious perspective. Do some research and consultant with people from the group you wish to research. Be sensitive to what you are being told is important to them when you are planning your project and then check you plan with your experts.

Social and cultural��awareness��in research assumes an appreciation of those attitudes, values, beliefs, protocols, and actions which constitute the intellectual property, and cultural traditions of ethnic groups.

Social and cultural awareness��include actions which recognize and respect the cultural identities of others, and safely meet their needs.

This could involve:

• Clear, open and respectful communication to develop trust.
• Collaboration between researchers and participants engaging with others in a two-way dialogue where knowledge is shared.
• Modification of plans, where and when necessary, following discussions with participating groups; Approval and/or support by ethnic group(s) involved in the study must be sought��before��fieldwork begins.
• Where a Māori population is the focus, respect must be given to the principles of participation, partnership, and protection that are implicit in the Treaty of Waitangi.
• Research methodology reflects trust between persons, the rights, interests, cultural and intellectual property of the research participants being safeguarded.
• No exploitation of the research participants for personal gain or financial remuneration.
• The full contribution of participating population(s) should be recognised in the publication of results.

Some Other Points to Think ��Ӱֱ��

• If your school has a Human Ethics committee then you are required to submit an application if their guidelines require it.
• If you are dealing with a group that is unable to give informed consent then you need to be especially careful. If working with children (under 16) then you need to get their parents informed consent as well as that of the participant. Make sure you give age-appropriate information to the participants.
• While it is exciting to discuss your project with friends and family you should remember to respect the privacy of the participants especially if they go to your school and could be identified by others.

2. Human ethics planning template

Human Ethics Planning Template

3. Consent form

Possible human consent form

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