Chapter 1: Square Roots and the Pythagorean Theorem

1.1 Square Numbers and Area Models

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.

Refresher…

Reminder: What is the difference between rectangles and squares?

Is every square a rectangle? Yes! Is every rectangle a square? No!

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

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

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 units25 units

5 units

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.

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

On your own…

Using a diagram, show that 14 is not a square number.

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

142

7

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.

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

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