Task Teacher Guide
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In This Task…
Intentionality…
- When side lengths of a rectangle change linearly, the area can be modelled with a quadratic model;
- Multiplying two linear models together creates a quadratic model.
- The maximum value of a quadratic model occurs at the vertex of the parabola.
- A quadratic function can have multiple algebraic forms;
- Algebraic forms of a quadratic function can be manipulated using algebra;
- Area models can be helpful when manipulating algebraic forms of quadratic functions.
Spark
What Do You Notice? What Do You Wonder?
What do you notice? What do you wonder?

- A rectangle.
- A square at the start.
- Is the perimeter the same the whole time?
- When is the rectangle covering the most area?
- Why are we doing this?
- And many others…
Estimation: Prompt
Which rectangle shows the largest area?

While Students Are Estimating…
Sense Making
Crafting A Productive Struggle: Prompt
How many increases will produce the rectangle with the largest area?

During Moves
While Students Are Productively Struggling…
Student Approach #1: Additively Creating a Table of Values / Ratio Table
Student Approach #2: Building a Quadratic Model & Graphing With Technology
Student Approach #3: Building a Quadratic Model & Completing The Square
Next Moves
Consolidation: Making Connections
Reveal

Reflect
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Resources and Downloads
Lesson Tip Sheet

Videos & Images

Keynote Slides

PowerPoint Slides

Printable Handout

Explore The Entire Unit of Study
This Make Math Moments Task was designed to spark curiosity for a multi-day unit of study with built in purposeful practice, and extensions to elicit and emerge mathematical models and strategies. Click the links at the top of this task to head to the other related lessons created for this unit of study.
Consolidation Prompt #1
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Consolidation Prompt #2
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Consolidation Prompt #3
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Consolidation Prompt #4
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Download Editable/Printable Handout
Become a member to access purposeful practice to display via your projector/TV, download the PDF to upload to your LMS and/or print for students to have a physical copy