Unit 8, Lesson 2
Side Lengths and Areas
Grade 8
Preparation
Lesson Narrative
In this lesson students are formally introduced to square roots and square root notation where:
is the length of the side of a square whose area is square units.
To get to this definition, students find the area and side length of squares on a grid, starting with squares that have whole number side lengths. They reason that 2 squares with the same area must also have the same side length.
Next, students investigate squares whose side lengths are not whole numbers. By comparing the area of these squares to the areas of squares with known side lengths, students can make reasonable approximations for the unknown side lengths (MP7).
Finally, students work with a geometric construction of a square with one corner at the origin of a coordinate plane. Using a rotation about the origin helps students to see the side length as a point on the number line and leads to the introduction of the term "square root" and its notation.
- Comprehend the term “square root of $n$” (in spoken language) and the notation $\sqrt{n}$ (in written language) to mean the side length of a square whose area is $n$ square units.
- Estimate the side length of a square by comparing it to squares with known areas, and explain (orally) the reasoning.
Let’s investigate some more squares.
Required Preparation
Make a class display listing perfect squares up to . This display should be posted in the classroom for the remaining lessons within this unit.