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Math 8Square Roots and the Pythagorean TheoremStudent Notes BookletName: ___________________________________Class: ________________Investigate: You will need a partner and 20 square tiles.Make as many different rectangles as you can with each area. Then draw your rectangles on the grid paper provided.4 square units6 square units8 square units9 square units12 square units16 square units20 square unitsFor how many were you able to make squares?What is the side length of each square you made?How is the side length related to the area?Find 2 areas greater than 20 that make a square.How do you know you could make a square for these areas?When we multiply a number by itself, we call it a ____________________________Example: Show that 49 is a square number.-34290111931500878518112134400496751160617147501351609835172575392A=169 cm2A=169 cm2Example: Find the perimeter of the picture: Homework Questions:Pg 8: 4, 5, 7, 10, 11, 14, 16, Extension Questions: 19, 20, 21Investigate: 68434232527211111111123456789101112131415161718192021222324252627282930Complete the factors for 9-30.Which numbers only have 2 factors?Which numbers have an even number of factors?Which numbers have an odd number of factors?Which numbers are square numbers? How do you know?Example:Find the square of each number:5b) 15Find the square root of 64. Draw a square with an area of 64 on the grid paper.Homework Questions:Pg 15: 6, 7, 10, 11 ac, 13 aceg, 17, 18, 19Extension Questions: 20, 21, 22Investigate: Do the investigation on page 17.How many squares did you draw?Describe any patterns in your measurements.How did you find the area and side length in each?Example:641350173668S00S-396240198120R00R1268730580390Q00Q125334150640001358904445P00PHomework Questions:Pg 20: 3, 4, 5, 7, 9, 10Extension Questions: 11, 12, 14Investigate:Place each square root on the number line to show approximate value.2 5 11 18 24 Check your estimates with a partner and then using your calculator.Example:Which whole number is 96 closer to? How do you know?Homework Questions:Pg 25: 4, 5, 6, 8, 9, 11, 14, 16, 23Extension Questions: 18, 20, 21Discover a relationship among the side lengths of a right triangle. Who is this Pythagorean guy? Who is this Pythagorean guy? Pythagoras was born on the island of Samos, and may have travelled widely in his youth, visiting Egypt and other places seeking knowledge. Around 530 BC, he moved to Croton, a Greek colony in southern Italy. He is often revered as a great mathematician, mystic and scientist, and he is best known for the Pythagorean theorem which bears his name. Label the sides. Hypotenuse, Leg A, Leg B383502111492600Pythagoras noticed a connection between the hypotenuse and the 2 other legs.This relationship is called: _____________________________________41070288687400Example:Find the length of the hypotenuse. 34404682104694 cm004 cm453390020964005322266183964 cm004 cmExample:30456497506565 cm005 cm496971828636610 cm0010 cm37861921259840003807725148021Find the length of leg A. Homework Questions:Pg 34: 3, 5, 6, 7, 9, 10, Extension Questions: 12, 13, 15, 16, 17Investigate:Draw an obtuse, a right angle, and an acute triangle.Draw squares on each side. Find area of all squares. Does the Pythagorean Theorem work for all? Why or why not?Example:Is this a right triangle? How do you know?Homework Questions:Pg 43: 3, 4, 5, 6 aceg, 7bdf, 9, 12, Extension Questions: 11, 13, 15, 17Investigate:A doorway is 2.0 m high and 1.0 m wide. A square piece of plywood has a side length of 2.2 m.Can the plywood fit through the door?How do you know? Show your work.3616543-24927 3575713-27296 h hExample: 357473739306500400083269609356cm0056cm29748801117533cm0033cmFind the length of the hypotenuse. Homework Questions:Pg 49: 2, 3, 4, 5, 6, 8, 9, 11, 15, 16Extension Questions: 14, 17, 19, 20, 22Unit Test Date: _______________________________________________Complete pages 54-59 for review.-226586400985000center263left000228600528764500 ................
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