Get ready before the bell rings!
 Take out homework and a pencil to prepare for the
homework quiz!
 Check the file folder for your class to pick up graded
work.
Investigation 2: Squaring Off
CHAPTER 2: LOOKING FOR PYTHAGORAS
2.1 Looking for Squares
IN PROBLEM 1.3, YOU FOUND AREAS OF
SHAPES ON A DOT GRID. WHAT SHAPES
WERE MOST HELPFUL?
Launch
 What is the smallest square area we can draw using dots
as vertices? Largest?

Smallest: 1, Largest: 16
 Do you think you can find a square area for every number
between 1 and 16?
2.2 Square Roots
Helpful Link!
https://www.youtube.com/watch?v=Ymcf14wC9Ck
2.3 Using Squares to Find
Lengths
FOCUS QUESTION: HOW CAN YOU FIND THE
DISTANCE BETWEEN ANY TWO POINTS ON A
GRID?
Launch
 During our last class (2.2), we found side lengths of the
squares below.
1
2
√(2)
√(8)
√(5)
4
3
√(10)
 Can you draw a line segment on a 5 dot-by-5 dot grid with a
length that is different from these?

Yes, I can make longer line segments.
Problem 2.3A
There are 14 different lengths that you can draw.
Can you find the value of them all?
Problem 2.3A
 Your line segments should be contained in the 5x5 dot grids
that are boxed in on Labsheet 2.3A. However, the square
you draw can extend outside of the 5x5 enclosed grid.

In the example below, the line segment is within the 5x5 grid, but the square
extends outside. This is okay. The area of the square below is 13, so the side
length is √(13)
Problem 2.3A Answers
 All of the possible answers.
Problem 2.3B
Problem 2.3B Answers
Problem 2.4: Cube Roots
WHAT DOES IT MEAN TO TAKE THE CUBE
ROOT OF A NUMBER?
Helpful Links:
•http://www.dailymotion.com/video/xxi4ed_class-viii-cubes-and-cube-roots_school
•https://www.youtube.com/watch?v=Ujp1wugVDm8
Calculator Help:
•https://www.youtube.com/watch?v=sWaiiEXg8tA
Launch
1.
If we have a length of 4 units, what is the area of the square we can
build on that length? How can we write this relationship as an
equation?
16 square units; 42 = 16
2.
If we have a square area of 25 units, what is the side length of the
square? How can we write this relationship as an equation?
5 units;
What if…
 If we have a length of 2 units, what is the volume of
the cube we can build on this?


How did you figure this out?


8 cubic units
Multiply 2 by itself 3 times.
How can we write this relationship as an equation?

23 = 8
 If we have a length of 4 units, what is the volume of
the cube we can build on this?