Patterns Over Time

Curriculum Context

Subject Area: Mathematics and Statistics
Curriculum Level: Level 8 (Year 13)
NCEA Achievement Standard: 3.8 (AS91580) – "Investigate time series data"

This lesson supports students in developing the skills needed to meet the requirements of Achievement Standard AS91580, which assesses the ability to select and use appropriate time series methods to make a forecast and support a conclusion.

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Lesson Title

Time Series Practice Assessment – Lesson 1 of 2

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Learning Outcomes

By the end of this lesson, students will be able to:

• Identify and describe components of a time series (trend, seasonality, irregularity)
• Interpret a contextualised time series graph relevant to Aotearoa New Zealand or the Pacific
• Begin independent investigation and planning for the practice time series assessment task
• Develop a justified forecast comment using contextual data
• Collaborate briefly to brainstorm ideas but work independently on their report

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Success Criteria

• Students can clearly explain the components of a time series using appropriate terminology
• Students choose suitable data relevant to life in Aotearoa or the Pacific and outline how it will be analysed
• Students create a concise and feasible plan for processing and graphing their data using statistical software
• Students demonstrate readiness to begin written analysis in the next session

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Resources Needed

For Teachers:

• Whiteboard and markers
• Printed practice assessment brief outlining context options (e.g., airline passenger numbers, temperature trends in NZ cities, salmon catch numbers in West Coast rivers)
• Broad checklist aligned to the relevant Achievement Standard (AS91580)

For Students:

• Laptops with spreadsheet software (Google Sheets / Excel)
• Access to Stats NZ website and other approved datasets
• Practice write-up template (digital or printed)
• Draft planning sheet
• Graph paper (optional for sketch planning before digital work)

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Learning Sequence (50 Minutes)

Time	Activity	Purpose
0–5 min	Mihi and Settle: Welcome the class, reaffirm the purpose of today’s session.	Settle students and create a focused learning environment.
5–15 min	Connect & Contextualise: Brief presentation of two relatable NZ time series contexts. Use a local example – e.g., average temperature changes in Christchurch over 10 years. Identify trend/seasonality/irregular components as a class. Students suggest other contexts they are interested in.	Connect topic to students’ lives and interests. Activate prior knowledge.
15–25 min	Explore the Brief: Hand out and explain the practice assessment brief. Clarify expectations and the fact that nothing is to be submitted this lesson. Emphasise completion across two lessons.	Allow students to understand structure, criteria and scope of the assessment.
25–30 min	Peer Brainstorm (Paired): Students in pairs discuss which time series topic they’ll explore. They can help each other find a dataset but must ultimately choose and analyse it individually. Teacher circulates to guide selection.	Brief collaboration for idea generation; encourages ownership and diversity in topics.
30–40 min	Planning Time (Independent): Students begin their own individual planning. They complete a data sourcing and analysis plan: - What data? - What’s the likely trend/seasonality? - Tools they’ll use? - What challenges might they face?	Gives students a pathway and structure as they begin. Encourages self-management.
40–45 min	Mini Check-in (1-on-1 or Groups of 3): Teacher checks students’ direction is manageable and suitable for the assessment. Prompt feedback about viability and appropriateness of mathematical methods.	Formative diagnostics and alignment with curriculum level.
45–50 min	Wrap Up & Confirm Next Steps: Recap what has been done well so far. Remind students that next session is fully for working on analysis/reporting.	Frame learning continuity and reassure students that the process is valued.

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Assessment and Feedback Strategy

Formative (in this session):

• Informal checking of planning and dataset choice during individual conferences
• Observation during pair brainstorming: are students grasping components of time series?
• Confirmation that students’ planning includes a pathway for analysis using technology
• Teacher records notes about students’ readiness level to guide targeted support in the next session

Summative (Next Lesson):

Performance will be assessed at the end of Lesson 2 based on the completed report submitted, aligned with AS91580 criteria.

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Cultural and Local Responsiveness

• Students are encouraged to explore contexts relevant to their whānau, iwi, or regions (e.g., rainfall data for their local area, tourism data in the Pacific).
• Assessment can be submitted in English, te reo Māori, or New Zealand Sign Language, in accordance with NCEA guidelines.
• Acknowledge Māori and Pacific worldviews where relevant in forecasting (e.g., discussing the environmental and social impacts of seasonal trends).

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Teacher Reflection Prompt (Post-Lesson)

• Did most students select appropriate and rich time series data?
• Was the mix of individual and collaborative time successful in supporting topic choice?
• Did all students independently produce a viable analysis plan by the end of the session?
• What extra support might students need next lesson (e.g., help with software/table manipulation)?

Let this lesson be a spark—where students don’t just analyse data, they see the story in the statistics of the land and life around them.