This lesson explores the concept of probability within a well loved picture book. Ākonga will have opportunities to use the language of chance, possible, impossible, will happen, won’t happen or might not happen.

This activity explores the following key ideas:��

• Engage with a story�� that involves chance-based situations and:

– decide if something will happen, won’t happen, or might happen

– identify possible and impossible outcomes (e.g., what might happen next).

Resources

• Y1 Who probably sank the boat teaching notes
• A copy of the book ‘Who Sank the Boat’ by Pamela Allen or a screen to watch this of the book being read aloud
• Large vocabulary cards with the words chance, possible, impossible,�� will happen, won’t happen, might not happen.
• Plastic containers, plastic lids or paper to make a paper boat
• of how to make a paper boat
• Various small items to represent different ‘animals’ to place into the boat
• A tuff tray filled with water, water play trough or the school swimming pool

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This activity explores the following key ideas:

• Engage in chance-based investigations with equally likely outcomes by:
  – posing an investigative question
  – anticipate and then identify possible outcomes for the investigative question
  – generating all possible ways to get each outcome (a theoretical approach), or undertaking a probability experiment and recording the occurrences of each outcome
  – creating data visualisations for possible outcomes
  – describe what these data visualisations show
  – finding probabilities as fractions
  – answering the investigative question
  – reflecting on anticipated outcomes��
• Agree or disagree with others’ conclusions about chance based investigations

Resources

• Y4 teaching notes
• Year 4 Probability
• Coins, enough for three coins for each group
• Large paper or whiteboard
• Whiteboard markers, pens
• Post it notes
• The Great Coin Toss Challenge�� MM1 – for listing outcomes for various numbers of coins
• The Great Coin Toss Challenge MM2 – table to record outcomes from a probability experiment for tossing two coins
• The Great Coin Toss Challenge MM3 – bar graph blank to record results of the probability experiment
• Optional – Digital modelling tool with a bar graph generator such as Google Sheets or Microsoft Excel.

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This activity explores the following key ideas:

• Engage in chance-based investigations with equally likely outcomes by:
  – posing an investigative question
  – anticipate and then identify possible outcomes for the investigative question
  – generating all possible ways to get each outcome (a theoretical approach), or undertaking a probability experiment and recording the occurrences of each outcome
  – creating data visualisations for possible outcomes
  – describe what these data visualisations show
  – answering the investigative question
  – reflecting on anticipated outcomes��
• Agree or disagree with others’ conclusions about chance based investigations

Resources

• Y4 teaching notes
• Year 4 Probability
• Lucky Seven – Lesson 1 probability experiment – table to record results of probability experiment
• Paper, markers or something for each group to draw and record with
• Lucky Seven – sums of dice graph grids
• Lucky Seven chart – red & blue dice or Lucky Seven chart – colour according to your dice
• Lucky Seven – dice squares
• Optional virtual
• Optional
• Optional

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Ākonga will explore the relationship between theoretical outcomes and experimental outcomes within the context of a multiplication game. This two part lesson is for Year 4 ākonga.����

This activity explores the following key ideas:

• Engage in chance-based investigations with equally likely outcomes by:
  – posing an investigative question
  – anticipate and then identify possible outcomes for the investigative question
  – generating all possible ways to get each outcome (a theoretical approach), or undertaking a probability experiment and recording the occurrences of each outcome
  – creating data visualisations for possible outcomes
  – describe what these data visualisations show
  – finding probabilities as fractions
  – answering the investigative question
  – reflecting on anticipated outcomes��
• Agree or disagree with others’ conclusions about chance based investigations

Resources

• Y4 teaching notes
• Year 4 Probability
• Last One Standing gameboards��enough for your class to play in 2’s or 4’s.
• Paper clips to use as spinners, two for each gameboard
• Coloured counters
• Post It notes
• Last One Standing MM1 | Listing all possible outcomes chart
• Last One Standing MM2 |�� Frequency table
• Last One Standing MM3 | Theoretical probability table
• Last One Standing MM4 | Experimental probability table
• Optional – Digital spinner tool such as

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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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Ākonga will take turns playing this chance-based traditional Māori game, incorporating key vocabulary while anticipating outcomes. They need to play the game several times before undertaking statistical thinking. This game has potential for inclusion in everyday class interactions to build fitness, whakawhanaungatanga and to strengthen mental dexterity.��

This activity explores the following key ideas:��

• Engage in chance-based investigations about games and everyday situations to:
  – anticipate and then identify possible outcomes
  – collect and record data
  – create visualisations for frequencies of outcomes (e.g., lists, picture, graphs)
  – describe what these data visualisations show
  – answer chance-based investigative questions
  –�� notice variations in outcomes��

Resources

• Y3 Whano whano teaching notes
• How to play Whano whano
• If you wish to play an alternative version you can begin with two movement options only and then build up to selecting from the four moves once confident with the way to play the game.�� The full game is needed for this probability lesson.
• This Scratch Garden Mini Maths Movie shows how to record using a tally chart
• Large paper and vivids for making a class table
• Paper or something for ākonga to record their results in��
• Optional – counters to represent the different possible outcomes

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There are many forms of random name generators utilised in classrooms across the curriculum. This provides many opportunities to make use of this lesson. It is a lesson that can be as small or as large as you would like to make it. We suggest that you teach this lesson as one larger lesson early in the year, it can then be used as an ongoing classroom activity to reinforce language and key vocabulary.

This activity explores the following key ideas:

• Engage in chance-based investigations about games and everyday situations to:
  – identify possible outcomes
  – collect and record data
  – create visualisations for frequencies of outcomes (e.g., lists, picture, graphs)
  – describe what these data visualisations show
  – answer chance-based investigative questions
  –�� notice variations in outcomes��

Resources

• Y3 Random name generator teaching notes
• Two cups, one labelled ‘coming up soon’, one labelled ‘have had a go’.
• Iceblock sticks labelled with names, one for each ākonga.��
• Other cups for group work, two for each group.
• A class list of names, one for each group.
• Material Master, one copy for each group.

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This chance-based investigation explores possible combinations through an animal drawing activity. Students will draw different animal heads, bodies, and tails/legs, then experiment with various combinations to create new animals, discovering all possibilities. This activity offers the opportunity to create patterns when exploring possible outcomes and numerous opportunities for extension��

This activity explores the following key ideas:

• Engage in chance-based investigations about games and everyday situations to:
  – identify possible outcomes
  – collect and record data
  – create visualisations for frequencies of outcomes (e.g., lists, picture, graphs)
  – describe what these data visualisations show
  – answer chance-based investigative questions
  –�� notice variations in outcomes��

Resources

• Y3 Crazy animals teaching notes
• One sheet per ākonga of A4 paper folded into thirds, so that there is a top, a mid section and a lower section.
• Felt pens, scissors

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Ākonga will explore a chance-based investigation that emphasises the role of data organisation and clarifies ākonga understandings of key vocabulary. This lesson is for Year 2 ākonga.

This activity explores the following key ideas:��

• Engage in chance-based investigations about games and everyday situations to:
  – identify possible outcomes
  – collect and record data
  – create visualisations for frequencies of outcomes (e.g., lists, picture, graphs)
  – describe what these data visualisations show
  – answer chance-based investigative questions
  – notice variations in outcomes��

Resources

• Y2 Gumball Machine teaching notes
• A ‘gumball machine’. This may be homemade (see ),�� a glass jar such as a jam jar with (30 yellow, 19 blue and 1 red) beads/pom pom balls or similar inside.�� Ākonga must be able to see through the sides of the container.
• A jar for each group of ākonga.
• Beads, pompoms, or counters for each group. You may also like to use a (gumballs).��

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Data cards are a way of storing data about a person, object or non-physical entity. When using data cards each individual data card represents one person, object or non-physical entity. Data information for each person, object or non-physical entity is recorded in the same way to make future analysis more straightforward. Information from data cards can also be recorded into a spreadsheet for analysis to be made using statistical software.

Data cards can provide secondary data, as many of the examples given here show.�� They can also be used for collecting data, CensusAtSchool data collection information usually has a data card for students to record their measurements on. The data card shown here is from the 2025-2026 CensusAtSchool questionnaire primary teachers guide page 5.

Year 1-3 Data Cards

Three sets of data cards with 7 or 8 variables. The 25 “students/children” are from the CensusAtSchool 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 CensusAtSchool 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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