Unit 8, Lesson 6
Reasoning about Square Roots
Grade 8
Preparation
Lesson Narrative
This lesson continues the transition of student understanding from a geometric characterization of square roots as side lengths, to an algebraic characterization of square roots as specific points on the number line.
Students begin by considering whether statements such as are true, requiring students to make sense of what square root notation means. Next, students reason about the value of a square root by finding the two whole numbers it is closest to in order to more accurately plot the point on a number line and to help justify their placement (MP3). Finally, students think about as the solution to equations of the form and plot these points on a number line.
- Comprehend that $\text-\sqrt{n}$ represents the opposite of $\sqrt{n}$.
- Determine a solution to an equation of the form $x^2=n$ and represent the solution as a point on the number line.
- Identify the two whole number values that a square root is between and explain (orally) the reasoning.
Let’s approximate square roots.
Required Preparation
None