Lesson 2Side Lengths and Areas
Learning Goal
Let’s investigate some more squares.
Learning Targets
I can explain what a square root is.
I understand the meaning of expressions like
and . If I know the area of a square, I can express its side length using square root notation.
Lesson Terms
- square root
Warm Up: Notice and Wonder: Intersecting Circles
Problem 1
What do you notice? What do you wonder?
Activity 1: One Square
Problem 1
Use the circle to estimate the area of the square shown here:
Problem 2
Use the grid to check your answer to the first problem.
Are you ready for more?
Problem 1
One vertex of the equilateral triangle is in the center of the square, and one vertex of the square is in the center of the equilateral triangle. What is
Activity 2: The Sides and Areas of Tilted Squares
Problem 1
Find the area of each square and estimate the side lengths using your geometry toolkit. Then write the exact lengths for the sides of each square.
Problem 2
Complete the tables with the missing side lengths and areas.
side length, | ||||||||
---|---|---|---|---|---|---|---|---|
area, |
side length, | ||||||||
---|---|---|---|---|---|---|---|---|
area, |
Problem 3
Plot the points,
Print Version
Plot the points,
Problem 4
Use this graph to estimate the side lengths of the squares in the first question. How do your estimates from the graph compare to the estimates you made initially using your geometry toolkit?
Problem 5
Use the graph to approximate
Lesson Summary
We saw earlier that the area of square ABCD is 73 units².
What is the side length? The area is between
We say the side length of a square with area 73 units² is
All of these statements are also true: