Whakataukī | Proverb
"Kia whakatōmuri te haere whakamua"
I walk backwards into the future with my eyes fixed on my past.
Our tīpuna understood that to move forward wisely, we must learn from what has come before. Line graphs help us see patterns across time - like tracking the seasons, watching the tides, or understanding growth. By studying trends from the past, we make smarter decisions for tomorrow.
📈 Line Graph Analysis - Trends Over Time
📋 Level 4 Achievement Objectives:
- Read and interpret line graphs showing change over time
- Identify trends (increasing, decreasing, stable)
- Make predictions based on patterns in data
- Compare multiple data sets on the same graph
- Analyse relationships between variables
🌡️ Graph 1: Average Monthly Temperature in Wellington (sample data)
Sample data built for graphing practice — a realistic Wellington seasonal shape, not a measured record. NIWA publishes the real monthly figures if you want to graph the genuine article.
| Month | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Temp (°C) | 17 | 18 | 19 | 16 | 13 | 11 | 10 | 11 | 13 | 14 | 15 | 17 |
1. What was the warmest month in Wellington? What temperature?
2. What was the coldest month? How much colder than the warmest?
3. Between which two months did the temperature drop the most? Careful — two drops are the same size. Find both, and say how big the drop was.
4. PREDICT: If this seasonal pattern continues, what temperature would you expect the following January? Explain how you decided.
🌧️ Graph 2: Rainfall in Auckland vs Wellington (mm per month, sample data)
Sample data built for graphing practice. It is realistic in shape but it is not a measured record, so do not use it to settle which city is really wetter — the two are closer than most people expect. For the real figures, look up NIWA's climate normals for each city.
| Month | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Auckland (mm) | 75 | 90 | 85 | 110 | 125 | 140 | 145 | 130 | 100 | 85 | 80 | 70 |
| Wellington (mm) | 65 | 70 | 80 | 100 | 120 | 135 | 140 | 125 | 95 | 75 | 70 | 65 |
1. Which city had more rainfall in June? How much more?
2. In this dataset Auckland is above Wellington in every single month — check that for yourself. What is the smallest gap between the two lines, and in which months does that smallest gap happen? (There is more than one.)
3. Which city had the wettest single month? Name the month and amount.
4. Overall, which city gets more rain in this dataset? Back your answer with a calculation, not just a look at the graph.
📚 Graph 3: Student Test Scores Across a 10-Week Term (sample data)
Made-up scores for an imaginary class. Aroha and Tāne are invented students — these are not any real school's results.
| Week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| Aroha (%) | 45 | 50 | 55 | 58 | 62 | 68 | 72 | 75 | 78 | 82 |
| Tāne (%) | 62 | 64 | 63 | 65 | 68 | 70 | 73 | 74 | 76 | 78 |
| Class average (%) | 60 | 61 | 62 | 63 | 65 | 66 | 68 | 70 | 71 | 72 |
1. Who made the most progress from Week 1 to Week 10? Give the exact improvement in marks.
2. At what week did Aroha overtake the class average?
3. Calculate Tāne's improvement from Week 1 to Week 10 as a percentage change. Show your working.
4. If Aroha's trend continues, predict her score at Week 15. Show your thinking — then check your answer. Is that score even possible on a test marked out of 100? What does that tell you about stretching a trend too far?
🌟 Extension Challenge
Track Your Own Data: Choose something to measure daily for 2 weeks (sleep hours, screen time, exercise minutes, pages read, etc.). Plot it on the grid below!
What I'm tracking: _________________________________
Unit of measurement: _________________________________
Plot your data points and connect them with lines. What trends do you notice?
💡 Reading Line Graphs - Quick Tips
Line goes UP from left to right
Line goes DOWN from left to right
Line stays LEVEL (no change)
RAPID change (fast increase/decrease)
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
Students will engage with this resource to develop statistical investigation skills — planning inquiries, collecting and analysing data, interpreting distributions, and communicating findings. Tūhuratanga (investigation) is framed as a tool for understanding our communities and environment in Aotearoa New Zealand.
Ngā Paearu Angitū — Success Criteria
- ✅ Students can identify an investigative question, collect relevant data, and display it clearly.
- ✅ Students can interpret statistical findings and discuss what they might mean for a real-world community or environmental context.
Differentiation & Inclusion
Scaffold support: Provide structured investigation frameworks (PPDAC cycle templates) for entry-level access. Offer partially completed data tables for students who need additional support. Extend capable learners by asking them to critique a statistical claim from a news article, or to design their own community data investigation.
ELL / ESOL: Pre-teach statistical vocabulary (median, mode, range, distribution, sample, population). Pair visual representations (graphs, tables) with plain-language explanations. Allow students to discuss statistical ideas orally before writing. Encourage use of home language for initial sensemaking.
Inclusion: Statistical investigation offers natural differentiation — all students can engage with the same real-world question at different levels of mathematical complexity. Neurodiverse learners benefit from structured, step-by-step investigation processes. Use collaborative group investigation formats that distribute roles (data collector, recorder, analyst, presenter).
Mātauranga Māori lens: Tūhuratanga — the practice of careful investigation — resonates deeply with mātauranga Māori. The maramataka is a sophisticated data system: tracking environmental patterns, seasonal cycles, and ecological indicators over generations. Iwi environmental monitoring — counting kaimoana populations, tracking water quality, observing bird migrations — is applied statistical thinking. Framing statistics within community and environmental inquiry connects data to mana whenua responsibilities.
Prior knowledge: Students should have basic familiarity with data displays (bar graphs, dot plots). No prior statistical investigation experience required — the PPDAC inquiry cycle provides accessible scaffolding for first-time investigators.
Curriculum alignment
- Statistics — Statistical Investigation: Plan and conduct investigations using the statistical enquiry cycle — determining appropriate variables and data collection methods; gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends; comparing distributions visually; communicating findings, using appropriate display.
- Statistics — Probability: Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging uncertainty.