Lesson 2

Side Lengths and Areas

Lesson Narrative

In this lesson, students learn about square roots. The warm-up helps them see a single line segment as it relates to two different figures: as a side length of a triangle and as a radius of a circle. In the next activity, they use this insight to estimate the side length of a square via a geometric construction that relates the side length of the square to a point on the number line, and verify their estimate using techniques from the previous lesson. Once students locate the side length of the square as a point on the number line, they are formally introduced to square roots and square root notation:

\(\sqrt{a}\) is the length of a side of a square whose area is \(a\) square units.

In the final activity, students use the graph of the function \(y = x^2\) to estimate side lengths of squares with integer areas but non-integer side lengths.


Learning Goals

Teacher Facing

  • Comprehend the term “square root of $a$” (in spoken language) and the notation $\sqrt{a}$ (in written language) to mean the side length of a square whose area is $a$ square units.
  • Create a table and graph that represents the relationship between side length and area of a square, and use the graph to estimate the side lengths of squares with non-integer side lengths.
  • Determine the exact side length of a square and express it (in writing) using square root notation.

Student Facing

Let’s investigate some more squares.

Learning Targets

Student Facing

  • I can explain what a square root is.
  • If I know the area of a square, I can express its side length using square root notation.
  • I understand the meaning of expressions like $\sqrt{25}$ and $\sqrt{3}$.

CCSS Standards

Building On

Addressing

Building Towards

Glossary Entries

  • square root

    The square root of a positive number \(n\) is the positive number whose square is \(n\). It is also the the side length of a square whose area is \(n\). We write the square root of \(n\) as \(\sqrt{n}\).

    For example, the square root of 16, written as \(\sqrt{16}\), is 4 because \(4^2\) is 16.  

    \(\sqrt{16}\) is also the side length of a square that has an area of 16. 

Print Formatted Materials

Teachers with a valid work email address can click here to register or sign in for free access to Cool Down, Teacher Guide, and PowerPoint materials.

Student Task Statements pdf docx
Cumulative Practice Problem Set pdf docx
Cool Down Log In
Teacher Guide Log In
Teacher Presentation Materials pdf docx

Additional Resources

Google Slides Log In
PowerPoint Slides Log In