• plan a probability investigation with kaiako support, to establish advice to create a bingo card that has the best chance of winning
• use lists, tables, and digital tools to systematically record data from repeated trials of probability experiments, and then determine the probabilities
• create data visualisations for findings in probability experiments and identify similarities and differences between the findings and corresponding theoretical probabilities
• use their knowledge of equally likely outcomes to find the probability for the different products in the game of Multo
• learn how to use patterns in data to establish advice on how to create a bingo card that has the best chance of winning��
• use their knowledge of probability to inform decision-making in games of chance��

Resources

• Y8 Multo teaching materials
• ��

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• plan and conduct probability experiments for chance-based situations, including undertaking a large number of trials using digital tools, by:

– posing an investigative question

– anticipating what outcomes are possible and which of them are more or less likely to occur

– identifying and systematically listing all possible outcomes to the investigative question

– collecting and recording data

– creating data visualisations for the distribution of observed outcomes

– describing what these visualisations show

– finding the probability estimates for the different outcomes

– answering the investigative question

– identifying similarities and differences between their findings and those of others

– reflecting on anticipated outcomes

This activity could be extended to use with a year 8 class, or used with a mixed year 7-8 class.

Resources

• Y7 Drawing pins teaching materials��
• ��

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This workshop has a focus on getting ready to do the 91���� questionnaire with students, and then working with the class and school data provided. Workshop participants get to engage in the PPDAC cycle as they explore teaching the statistics strand of the NZC.��

This activity explores the following key ideas:

• Preparing to Take Part in the current 91���� survey
• Working with secondary data – data cards
  • Interrogating the variables available to use
  • Posing investigative questions
  • Making data visualisations using data cards and CODAP (Common Online 91���� Analysis Platform)
  • Describing data visualisations
  • Answering investigative questions

Resources

• CODAP ����

91���� materials

Related teaching and learning activities

• Take part in 91������
• ��
• Exploring Our Class 91����: Years 7-8 – 91������
• Posing summary investigative questions – 91������
• Using data cards – 91������
• Y8 Fabulous Feet – PPDAC cycle – 91������
• Describing distributions – 91������

Related information for teachers

• Interrogating secondary data – 91������

Tāhūrangi materials

Related teaching and learning activities

• ��

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In this workshop participants use CODAP (Common Online 91���� Analysis Platform) to develop ideas for two statistical concepts.�� The median and box plots.����

This activity explores the following key ideas:

• Finding the middle of a dataset and connecting this to the median.
• Finding the middle 50% of a dataset, describing this.
• Using the middle 50% and median to build a box plot.
• Recognising the quarters within the box plot.

Resources

CODAP

Related teaching and learning activities on 91������

• – Finding the middle��

Related teaching and learning activities on Tāhūrangi

• ��

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In this workshop participants get to engage in the PPDAC cycle as they explore teaching the statistics strand of the NZC. The workshop uses the data cards based on the 2025/2026 91���� questionnaire. Links to previous data cards based on the 2023/2024 questionnaire are also given.

If planning to use the workshop in the future, it could be adapted to suit the current 91���� data cards.�� Check under the 91���� tab and find the 91���� Cards link.����

This activity explores the following key ideas:��

• Working with secondary data
• Interrogating the dataset
• Making data visualisations to answer the investigative question
• Describing data visualisations
• Answering the investigative question

Resources

Workshop materials

• 91���� detective poster
• 91���� cards: Years 1-3: Set A Set B Set C
• 91���� cards:
• CODAP
  • CODAP document
  • CODAP document

Teaching and learning activities on 91���� using the data cards

• 2025/2026 91���� card page
• 2023/2024 91���� card page

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Document with all three year plans

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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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Three sets of data cards with 7 or 8 variables. The 25 “students/children” are from the 91���� 2023 database. They are a random selection of year 3-6 students/children from across Aotearoa New Zealand, and the same students/children are used in the three sets of data cards.

Teaching and learning activities associated with the year 1-3 data cards are .

Year 4-6 data cards

The year have 14 variables. The 74 “students/children” are from the 91���� 2025-2026 database. They are a random selection of year 4-6 students/children from across Aotearoa New Zealand.

Variables included:

• Height
• Gender �� �� �� �� �� �� �� �� �� �� ��
• Hair colour�� �� �� �� �� �� �� �� ��
• Eye colour
• Languages spoken
• Favourite colour��
• Year level
• Plays a musical instrument
• Has pets
• Has broken a bone
• Travel method to school
• Time taken to get to school
• Left foot length
• Right foot length

Teaching and learning activities associated with the Year 4-6 data cards are .

Year 7-8 data cards – to come

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91���� card from the Primary Teacher Guide 91���� 2023, p. 38

91���� 91���� Cards

• 2025–2026
• 2023–2024

More 91���� Cards

• All Whites FIFA World Cup
• Stick Figure 91���� Cards
• New Zealand Olympic Team 2024

What are 91���� Cards?

91���� cards are a way of storing data about a specific person, object, or non-physical entity. In this system, each individual card represents a single item.

To ensure straightforward future analysis, the data for every entity is recorded using a consistent format. Information from data cards can also be transferred into a spreadsheet for deeper analysis using statistical software.

While data cards are excellent sources of secondary data, they can also be used for primary data collection. For instance, 91���� data collection materials typically feature a dedicated data card for students to record their measurements.

Using 91���� Cards

91���� cards are a good way of introducing students to using secondary data. They allow for hands-on activities such as making data visualisations to analyse the data for an investigative question. The complexity of the data cards should change depending on the year level aimed at. The 91���� 2023 database data cards are examples using secondary data.

Whether the secondary data is provided by the teacher or sourced by the students, the information required for understanding about the data collection is within the information we refer to as the contextual knowledge about the dataset. Contextual knowledge includes:

• The group or population that the data was collected from
• When, where and how the data was collected
• The original purpose for collecting the data

“Planning” for secondary datasets includes interrogative questions to help with developing a deep understanding of the data that would be available to use. The “overall for the dataset” interrogative questions in the next section help us with understanding about the data collection and align with the contextual knowledge ideas listed above. Regardless of whether the teacher provides the data or the students source the data themselves, contextual knowledge is important. The “overall for the dataset” interrogative questions also include who the data was collected from (adapted from , p. 90).

The final part of finding out about the secondary dataset, the data cards, is to identify and interrogate the variables in the dataset. To do this the “specific to the variable” interrogative questions in the next section are used.

PLAN/DATA: Interrogating secondary datasets

It is good practice to interrogate any secondary datasets that are used with students. Depending on what you are trying to achieve, it could be built into the teaching and learning sequence, or it could be background research you do before using the dataset with students.

The following interrogative questions provide a good starting point to understand the data, what was collected, how it was collected and who it was collected from.

Overall for the dataset:

1. Was the data collected using an observational study or an experiment (from year 9)? (1. Method)
2. Who was the data collected from? (2. “Who”)
3. Who collected the data? (1. Method)
4. When was the data collected? (1. Method)
5. Where was the data collected? (1. Method)
6. What was the purpose for collecting the data? (Initial investigator’s problem/purpose)

Specific to the variable (3. What and how):

7. State the variable.
8. What was the data collection or survey question asked to collect the data?
9. How was the variable measured?
10. What are the units, if any, for the variable?
11. What are the possible outcomes for the variable?
12. What type of data is it? Categorical or numerical?

(, p. 79)

The 91���� 2023 database data cards should be interrogated before they are used by students so that they become familiar with the variables that are available for each data card set.

Two useful documents to support this are the 2023 91���� questionnaire, and the 2023 variable list.

PROBLEM: Posing investigative questions

When we start with a provided dataset, for example, using the 91���� 2023 database data cards, the way we work through the PPDAC cycle is different from when we are collecting primary data.

Using the statistical enquiry cycle for a provided dataset may follow the approach shown in Figure 4.10 below.

Figure 4.10. The statistical enquiry cycle for provided datasets (, p. 159)

Investigative questions are posed once the data has been interrogated and students understand the variables which are available in the dataset, and who the data was collected from.

ANALYSIS: Creating & describing data visualisations

Early data visualisations can be made with data cards, from year 1 students can sort and order the data cards to summarise data. 91���� cards are an enactive mode (Bruner, in Graham, 2006), where students are manipulating objects and building spatial awareness. 91���� cards are foundational to dot plots, bar graphs, histograms, scatter plots and two-way tables. They can be used in summary, comparison and relationship situations. For more on the development of these types of data visualisations see Statistical investigations | Te Tūhuratanga Tauanga () analysis chapter – dot plots pp 229-237; bar graphs pp 237-243; histograms pp 254-248; scatter plots pp 275-280; two-way tables pp 266-271.

Examples below using the different data cards.

Y1-3 sorted by travel method to school

Y1-3 sorted by hair colour

Year 4-6 (year 6 only) travel method to school

Year 4-6 (year 6 only) hair colour

Year 7-8 data cards – set 1 – sorted by height (5 cm intervals)

Year 7-8 data cards – Set 2 – sorted by bed time

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Dinos of patagonia data cards

Variables:

The data is also available in a CODAP document |

You can use the blank data cards to find out information about other dinosaurs. If you want to add the new dinosaurs to the dataset, then make a copy of this and add them in.

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