Identifying Non-Linear Relationships

ACARA Syllabus Indicators:

• Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technologies as appropriate (ACMNA239)

Learning Goals:

• Explain the difference between non-linear and linear relationships
• Identify and recognise examples of parabolas in everyday life.

Working Mathematically Skills:

• Distinguish between different forms of linear and non-linear relationships (Reasoning)

Resources:

• Orientation Activity
• Mr Squiggle worksheet
• Frayer's Model Template, such as the one here.

Description of Lesson:

Orientation: (10 min) [TECH]

Have students follow the resource link and respond to the first prompt on Desmos Student:

As shown in the example response above, students can annotate and draw on the axes, or submit a comment.

Display student responses on the projector and using a Think-Pair-Share ( referred to as TPS from now on), have students identify:

• What are the similarities between these submissions?
• What skills are involved?

Once students arrive at the term 'linear' or 'straight', have them complete the second prompt:

Discuss responses as before.

Introduction: (15 min)

• Activity One: Mr Squiggle's Rollercoaster
  • Students complete Mr Squiggle worksheet to design their own rollercoaster. Students annotate their work to identify the different lines composing their rollercoasters as linear or non-linear, leading to a discussion of non-linear relationships. [Teacher explains that today we will just focus on parabolas].
  • Class discusses to ascertain the difference between linear and non-linear relationships. They discuss examples of parabolas in the real world, e.g. the path of a thrown ball. Teacher provides examples and students decide what kind of relationship it represents.

Body:

• Activity Two: Digital Frayer's Model [LIT & TECH] (15 min)
  • Students individually create a Flayer's model for "Non-Linear Relationships" using Microsoft Word. They can search for images online to use as examples and non-examples.
• Activity Three: Present Frayer's Models (10 min) [AFL]
  • Students pair up and present their Frayer's Models to one another student.
  • Pairs work through these questions in response to each other's models:
    • What information is new to you?
    • What part is interesting to you?
    • Is there anything you don't understand?

Conclusion: (5 min)

Reiterate the key learning ideas for the lesson.

Lesson Evaluation Questions:

• Did all of your students understand and meet the learning goals?
• Were all students engaged and participating?
• Were the activities appropriate and relevant for the stage of my learners?
• What would you change about the activities next time?

Homework/Enrichment Activities:

Students need to find 5 examples of non-linear curves which weren't discussed in class to bring to the next lesson. They can explore places such as their home, the internet or after school activities.

Variations:

• This lesson could be done in a computer lab to ensure students have ready access to computers for the second activity. Alternatively, students can complete their Flayer's model on paper.
• The orientation of this activity could be delivered on the whiteboard if technology isn't available.