Parabolas in Life

Curriculum Detail

Subject: Mathematics
Year Level: 11 (NZ Curriculum Level 6)
Strand: Patterns and Relationships
Achievement Objective:

• Form and solve quadratic equations.
• Use graphs of quadratic functions to model and solve problems.

Achievement Standard (aligned with NCEA Level 1):

• AS91028 (1.2): Investigate relationships between tables, equations and graphs.

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Focus of Lesson

Topic: Quadratic Equations and Their Real-World Applications
Duration: 60 minutes
Class Size: 30 Students
Special Considerations: High number of dyslexic learners – visual, hands-on, and verbal strategies will be explicitly incorporated.

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Learning Intentions

By the end of this lesson, students will:

• Understand what a quadratic equation is and what its graph looks like.
• Identify key features of a quadratic graph (vertex, axis of symmetry, x-intercepts).
• Apply quadratic equations to a real-world context involving projectile motion in Aotearoa.
• Use calculators or online graphing tools for support, promoting multi-sensory learning styles.

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Success Criteria

• I can describe the shape of a quadratic graph and identify key features.
• I can solve a contextual quadratic equation (e.g., for height or time).
• I can explain how quadratic equations relate to real-life situations in New Zealand.
• I can work with my peers, express my ideas clearly, and use visuals to support understanding.

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Materials Needed

• Mini whiteboards & markers
• Large printed visuals of parabolas with key parts labelled (laminated for reuse)
• Printed coloured overlays for dyslexic students
• Graphing calculators or laptops with Desmos preloaded
• Pre-cut cards with matching real-world problems and equation components
• Printed “Parabolas in Aotearoa” scenario sheets
• Blu-Tack or magnets for the whiteboard

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Lesson Breakdown

⏰ 0–10 minutes: Hook & Prior Knowledge Check

Purpose: Connect to existing knowledge and excite interest
Activity: “Pass the Parabola!” – A soft projectile is thrown between students (wētā toy or rugby ball).

Teacher prompts:

• “What path did that take?”
• “If we caught it mid-air, can we predict how high it went?”
• “We're going to connect that shape to today's math!”

How it supports dyslexic students:

• Physically engaging
• Multisensory introduction
• No pressure to write yet

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⏰ 10–25 minutes: Concept Building - Visual and Physical Fluency

Activity 1: Interactive Model Drawing

• On the board (large parabola shape), the teacher labels key parts: vertex, axis of symmetry, x-intercepts.
• Call up student volunteers to place labels printed on colour-coded cards with magnetic strips/blu-tack.

Activity 2: Terminology Match

• Distribute card sets: Words (e.g., vertex) and Definitions (e.g., highest/lowest point).
• Students match words and definitions in pairs.

Dyslexia support:

• Use of visual matching
• Colour coding
• Hands-on manipulation
• Terms read aloud using peer support

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⏰ 25–40 minutes: Real-Life Application – Projectiles in Aotearoa

Contextual Scenario:
Tama launches a water balloon at a camp on the outskirts of Rotorua. The trajectory of the balloon is modelled by the equation:
h(t) = -5t² + 20t + 2, where h is height in metres and t is time in seconds.

Activity:

• Group-based breakout (5–6 students)
• Printed scenario sheet provided
• Tasks:
  • Use Desmos or calculators to graph the function
  • Identify how high the balloon goes
  • Determine when it hits the ground
  • Sketch or trace the graph and label key features
  • Discuss why this model is useful in real life (sports, engineering, etc.)

Extension prompt: “Why does gravity make this a parabola in NZ, or anywhere else?”

Role variation for dyslexic learners:

• Reader (reads questions aloud)
• Scribe (draws graph – visual focus)
• Researcher (uses tools)
• Reporter (shares group findings to class)

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⏰ 40–50 minutes: Creative Reflection – Make Your Moment

Activity: Students imagine a moment in NZ where a parabola appears (e.g., gumboot toss, fishing line cast, mountain biking jump) and create a mini “Parabola Poster”:

• Name of their event
• Estimated quadratic equation (teacher or app-assisted)
• Graph (hand-drawn or computer-generated)
• One sentence about the utility of predicting motion

Display posters for a ‘Maths Around Us’ wall over time.

Supports creativity, personal connection, and key competencies like thinking and relating to others.

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⏰ 50–60 minutes: Review and Reflect

Activity: Rapid-Fire Carousel

• Students move in small groups around 4 stations:
  • “Name That Part” (label features of a given graph)
  • “Sort the Equations” (linear vs quadratic)
  • “Solve It!” (quick graph interpretation question)
  • “Why Parabola?” (real-life relevance prompt)

Teacher circulates as a facilitator, assessing informally and giving feedback.

Exit Question:
Write down or verbally record on a class pad:
“One way I saw a parabola in today’s lesson…”

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Assessment for Learning

✔ Informal checks throughout group work and carousel
✔ Review of posters
✔ Observing group conversations and peer explanations
✔ Collect exit slips or verbal dictation

Students struggling with written output can draw, use a voice recorder, or use assistive tech.

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Differentiation Strategies

• Dyslexic Students:

  • Visuals, colour overlays, oral instructions, low-stakes writing
  • Allows audio/written/video/partner-based expression
  • Paired instructions, timers, and clear formatting

• High Achievers:

  • Extension task: Invent your own equation, explain how changes like “+5” or “-2t²” affect the graph.

• ESOL learners:

  • Visual aids, buddy support, gesture-rich explanations
  • Key terms in glossary with translated cards if available

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Key Competencies Addressed

• Thinking – making connections between algebra and life
• Using language, symbols, and texts – manipulating mathematical representations
• Relating to others – collaborative scenarios
• Participating and contributing – group problem solving and creativity

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Teacher Reflection Prompt (Post-Lesson)

• What evidence did I see that students grasped the link between the real world and quadratics?
• How did my dyslexic learners respond to the multisensory and group elements?
• What parts had high engagement or confusion?

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Suggested Follow-Up Activities

• Modify the equation and re-analyse: what if the launch height was 10m not 2m?
• Transition into solving quadratic equations algebraically (factoring, using the quadratic formula)
• Analyse graphs with less obvious intercepts to explore irrational solutions

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Ka pai tō mahi – you’ve given math meaning!