The Probability Scale
Impossible
0
Unlikely
Even Chance
0.5 or 1/2
Likely
Certain
1
Calculating Probability
The probability of an event is calculated with this formula:
P(event) = Number of favourable outcomes / Total number of possible outcomes
For example, the probability of rolling a 4 on a standard six-sided die is 1/6, because there is one '4' and six possible outcomes in total.
Probability Practice 🎲
1. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles.
a) What is the probability of pulling out a blue marble?
b) What is the probability of pulling out a red marble?
c) Is it more likely to pull a red or a blue marble?
2. You spin a spinner with 8 equal sections numbered 1-8.
a) What is the probability of landing on an even number?
b) What is the probability of landing on a number greater than 5?
3. Mark the following events on the probability scale below.
A) You will have homework this week.
B) A coin flip will land on heads.
C) It will snow in Auckland in July.
📚 NZ Curriculum Alignment
Mathematics & Statistics
Achievement Objective: S4-1
Plan and conduct investigations using the statistical enquiry cycle
Key Competencies
- • Thinking critically about probability concepts
- • Using mathematical language and symbols
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
Students will engage with this resource to explore the intersection of STEM disciplines and mātauranga Māori — understanding how Indigenous knowledge systems and Western science share complementary ways of knowing the world.
Ngā Paearu Angitū — Success Criteria
- ✅ Students can identify connections between mātauranga Māori and STEM concepts in this resource.
- ✅ Students can explain how dual knowledge systems strengthen understanding of natural phenomena.
Differentiation & Inclusion
Scaffold support: Provide concept maps or sentence frames to scaffold access for students at the entry level. Offer extension tasks exploring specific mātauranga Māori knowledge domains (e.g., tohu āhua rangi, rongoā, whakapapa o te taiao) in greater depth.
ELL / ESOL: Pre-teach key vocabulary in both te reo Māori and English — including domain-specific STEM terms. Bilingual glossaries and visual anchors support comprehension. Allow students to demonstrate understanding in their preferred language.
Inclusion: Tasks are designed for a range of readiness levels. Neurodiverse learners benefit from structured, chunked activities with clear success criteria. Use hands-on, inquiry-based formats where possible. Affirm the value of different ways of knowing.
Mātauranga Māori lens: Mātauranga Māori encompasses astronomy, ecology, navigation, agriculture, and medicine — systems of knowledge developed over centuries. This unit treats mātauranga Māori as epistemically equal to Western science, not supplementary. Bring kaitiakitanga as a guiding ethic: knowledge is held in relationship, not extracted.
Prior knowledge: Students benefit from baseline understanding of the relevant STEM domain. No specialist te reo Māori knowledge required — glossaries provided. Best used after introductory lessons or as a standalone exploration.
Curriculum alignment
- Nature of Science — Knowledge: Science is a way of investigating, understanding, and explaining our natural, physical world; mātauranga Māori offers complementary systems of knowledge that enrich scientific understanding.
- Identity, Culture, and Organisation: Understand how different knowledge systems — including mātauranga Māori — shape how communities relate to the natural world.