In this activity, students get more familiar with irrational solutions to quadratic equations. First, they use a concrete example of using the Pythagorean Theorem with right triangles to find side irrational side lengths. Then, students solve equations of the form \((x-a)^2 = b\) and approximate the irrational solutions in comparison to nearby integers. In the associated Algebra 1 lesson, students solve quadratic equations with irrational solutions using completing the square. The work of this lesson supports students to be more comfortable using irrational numbers. Students must look for and make use of structure (MP7) to find the nearest integers to irrational numbers.
Lesson overview
- 15.1 Warm-up: Finding a Home for Irrational Numbers (5 minutes)
- 15.2 Activity: Solving for Missing Sides (20 minutes)
- 15.3 Activity: Solving with Square Roots (15 minutes)
Learning goals:
- Recall how to use the Pythagorean Theorem to find the length of a side given two sides of a right triangle.
- Solve equations of the form \((x-a)^2 = b\) with irrational solutions.
Learning goals (student facing):
- Let’s explore irrational numbers.
Standards:
- This lesson builds towards the standards: CCSS.HSA-REI.B.4.aMS.A-REI.4aCCSS.HSN-RN.BMS.N-RNMO.A1.REI.A.2aMO.A1.REI.A.2b
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