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Chapter 1: Square Roots and the Pythagorean Theorem

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

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Chapter 1: Square Roots and the Pythagorean Theorem

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  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

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