In this lesson, students solve quadratic equations of the form \((x-a)^2=b\) and practice a step in completing the square by adding a constant value to complete the square. In the associated Algebra 1 lesson, students solve equations by completing the square. The fluency students gain by practicing these methods will support them through the future Algebra 1 lessons. Students must look for and express regularity in repeated reasoning (MP8) when they find appropriate values to add to make a perfect square.
Lesson overview
- 13.1 Warm-up: Math Talk: Halved and Squared (5 minutes)
- 13.2 Activity: Solving Quadratics with Perfect Squares (15 minutes)
- 13.3 Activity: Make It a Perfect Square (20 minutes)
Learning goals:
- Determine a constant term that could be added to a quadratic expression in standard form to make it a perfect square.
- Solve equations of the form \((x+a)^2 = b\).
Learning goals (student facing):
- Let’s explore the constants in Quadratic Equations.
Standards:
- This lesson builds towards the standards:CCSS.HSA-REI.AMS.A-REIMO.A1.REI.ACCSS.HSA-REI.B.4.bMS.A-REI.4bMO.A1.REI.A.2c
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