Graphing Parabolas

ACARA Syllabus Indicators:

• Graph simple non-linear relations, with and without the use of digital technologies (ACMNA296)
  • Complete tables of values to graph simple non-linear relationships and compare these with graphs drawn using digital technologies.

Learning Goals:

• Find coordinates using table of values
• Plot points and connect to sketch simple parabolic relationships
• Recognise the general equations of parabolas as y = ax^2.
• Use Desmos as a 'guess and check' tool

Working Mathematically Skills:

• Represent a quadratic relationship using spatial patterns, tables, graphs and equations (Communication) (NZMaths)

Resources:

• Mathematics for Cabbages activity, which is just 'Session One': https://nzmaths.co.nz/content/marys-garden
• Counters
• Desmos: https://www.desmos.com/

Description of Lesson:

Introduction: (10 min)

Collect verbal responses of homework from the previous lesson, and determine with the class whether they are appropriate examples or not. Tell students that today we will be learning how to draw parabolic relationships through a story of a gardener named Mary. Some examples of parabolic shapes which students may have shared might be:

• throwing a ball in the air
• a smile
• a half-pipe skateboard ramp

Body:

• Activity One: Mathematics for Cabbages (30 min)
  • Students complete in pairs.
  • This activity is taken from the unit of work entitled Mary's Garden from NZMaths. The teacher would follow the description provided on the link to progressively deliver the content to students.
• Reinforcement Activity: (10 min) [AFL]
  • In the first activity students only explored the parabola y = x² for positive values of x. To reinforce the skills practiced in the this activity, have students complete a sketch of the parabola, including negative values of x^. They can then attempt to sketch the following relationships using the same approach:
    • y = 2x²
    • y = 3x²
• Relate these equations and the one developed from Mary's Cabbages to the general formula y = ax². Class checks attempts together by inputing equations into Desmos.

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:

Create a new sequence for planting your favourite fruit or vegetable. Model it with either images or a table, and plot the growth on a set of axes.