Chapter 1: Square Roots and the Pythagorean Theorem

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Presentation transcript:

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 units2 5 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 2 14 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