1. Chapter 1: Square Roots and the Pythagorean Theorem
1.1 Square Numbers and Area Models

2. Activating Prior Knowledge
Refresh area: the amount of surface a shape covers. It is measured in square units.
Area of a rectangle: A = b x h
Area of a triangle: A = b x h 2
Complete “Check” #1 a) – d) on your own.

3. Refresher…
Reminder: What is the difference between rectangles and squares?
Is every square a rectangle?
Yes!
Is every rectangle a square?
No!

4. Investigate, pg. 6
Draw as many rectangles as you can of the following areas: (on grid paper)
4 square units
6 square units
8 square units
9 square units
10 square units
12 square units
16 square units

5. For how many areas above were you able to make a square?
4, 9, and 16 square units
What is the side length of each square you made?
4 square units: side length = 2
9 square units: side length = 3
16 square units: side length = 4

6. How is the side length of a square related to its area?
**The side length of a square multiplied by itself equals the area. **
side length = 5 units
area = 5 x 5 = 25 units2
5 units
5 units

7. Connect, pg. 7
When we multiply a number by itself, we square the number.
eg: the square of 4 is 4 x 4 = 16
We write, 4 x 4 = 42
So, 42 = 4 x 4 = 16
We say four squared is sixteen.
16 is a square number or perfect square
One way to model a square number is to draw a square whose area is equal to the square number.

8. Example 1, pg. 7
To show that 49 is a square number, use a diagram, symbols, and words.
Draw a square with area 49 square units. The side length of the square is 7 units.
Then, 49 = 7 x 7 = 72
We say: Forty-nine is seven squared.
side length = 7 units
area = 7 x 7 = 49 units2
7 units
7 units

9. On your own…
Using a diagram, show that 14 is not a square number.

10. On your own… Show that 14 is not a square number.
Can you make a square with 14 square units?
No, just two rectangles.
Try example 2 on pg. 7 1 2 14 7

11. Consecutive Squares
Consecutive squares: squares of consecutive numbers.
Eg. 12 = 1, 22 = 4, 32 = 9, are the first 3 consecutive squares.
Are there any squares between consecutive numbers?
No, square are always products of whole numbers and consecutive squares are the squares of consecutive numbers.
Hint: Think of a number line.

12. Common Misconceptions
52 does not equal 5 x 2 = 10
52 is five multiplied by itself: 5 x 5 = 25
Likewise, if you see 53, it is not
5 x 3 = 15, rather, it is 5 x 5 x 5 = 125
What does 59 look like?
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5

13. On a sheet of loose leaf, complete the following…
Put your name, date, and assignment title at the top (1.1: Square Numbers and Area Models).
#4 on pg. 8 in textbook
Extra Practice Sheet 1 #1 – 6
Due date: next class, Friday, Sept. 17