In this lesson, students investigate two common forms that polynomials are written in, factored form and standard form, and how to identify information about the graph of the polynomial from each. Students compare each form to the graph of the polynomial in order to make connections using structure (MP7) and use precise language learned in earlier lessons (MP6) to describe functions and to discuss the similarities and differences between two polynomials whose expressions differ only by a constant multiple. This lesson lays the groundwork students will need in order to sketch graphs of polynomials expressed in any form and to understand the end behavior of functions.
One of the activities in this lesson works best when each student has access to devices that can run Desmos, because students will benefit from seeing the relationship in a dynamic way.
Lesson overview
 6.1 Warmup: Which One Doesn’t Belong: Small Differences (5 minutes)
 6.2 Activity: The Return of the Box (15 minutes)
 6.3 Optional Activity: Using Diagrams to Multiply (15 minutes)

6.4 Activity: Spot the Differences (15 minutes)
 Digital applet in this activity
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 6.5 Cooldown: Identifying Polynomial Features (5 minutes)
Learning goals:
 Comprehend that all polynomials can be written in standard and factored forms.
 Describe features of polynomial graphs and expressions using precise language.
 Identify properties of polynomials by representing them in equivalent forms.
Learning goals (student facing):
 Let’s use the different forms of polynomials to learn about them.
Learning targets (student facing):
 I can identify features of polynomials and their graphs using their standard and factored forms.
Required materials:
 Graphing technology
Required preparation:
 Devices that can run a Desmos applet are required for the digital version of the activity “Spot the Differences.”
 The digital version is recommended for all classes over the paper and pencil version.
Standards:
 This lesson builds on the standard: CCSS.HSASSE.B.3MS.ASSE.3MO.A1.SSE.A.3aMO.A1.SSE.A.3b
 This lesson builds towards the standards: CCSS.HSAAPR.B.3MS.AAPR.3CCSS.HSFBF.B.3MS.FBF.3MO.A2.APR.A.5MO.A2.BF.A.3
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