Fair Game Review. Chapter 6 A B C D E Complete the number sentence with <, >, or =
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1 Name Date Chapter 6 Fair Game Review Complete the number entence with <, >, or = Find three decimal that make the number entence true > < 9. The table how the time of a 100-meter dah. Order the runner from firt place to fifth place. Runner Time (econd) A 1.60 B 1.55 C 1.49 D 1.6 E Copyright Big Idea Learning, LLC Big Idea Math Blue 115
2 Name Date Chapter 6 Evaluate the expreion. Fair Game Review (continued) ( ) The table how the number of tudent in 4 clae. The teacher are combining the clae and dividing the tudent in half to form two group for a project. Write an expreion to repreent thi ituation. How many tudent are in each group? Cla Student Big Idea Math Blue Copyright Big Idea Learning, LLC
3 Name Date 6.1 Finding Square Root For ue with Activity 6.1 Eential Quetion How can you find the ide length of a quare when you are given the area of the quare? When you multiply a number by itelf, you quare the number. Symbol for quaring i nd power. 4 = 4 4 = 16 4 quared i 16. To undo thi, take the quare root of the number. Symbol for quare root i a radical ign. 16 = 4 = 4 The quare root of 16 i 4. 1 ACTIVITY: Finding Square Root Work with a partner. Ue a quare root ymbol to write the ide length of the quare. Then find the quare root. Check your anwer by multiplying. a. Sample: = 11 = Check: Area = 11 ft The length of each ide of the quare i. b. Area = 81 yd c. Area = 4 cm d. Area = 61 mi Copyright Big Idea Learning, LLC Big Idea Math Blue 117
4 Name Date 6.1 Finding Square Root (continued) e. Area =.89 in. f. Area = 4.41 m g. Area = ft 4 9 ACTIVITY: The Period of a Pendulum Work with a partner. The period of a pendulum i the time (in econd) it take the pendulum to wing back and forth. The period T i repreented by T = 1.1 L, where L i the length of the pendulum (in feet). L Complete the table. Then graph the function on the next page. I the function linear? L T 118 Big Idea Math Blue Copyright Big Idea Learning, LLC
5 Name Date 6.1 Finding Square Root (continued) T 8 Period of a Pendulum 7 6 Period (econd) L Length (feet) What I Your Anwer?. IN YOUR OWN WORDS How can you find the ide length of a quare when you are given the area of a quare? Give an example. How can you check your anwer? Copyright Big Idea Learning, LLC Big Idea Math Blue 119
6 Name Date 6.1 Practice For ue after Leon 6.1 Find the two quare root of the number Find the quare root() Evaluate the expreion A trampoline ha an area of 49π quare feet. What i the diameter of the trampoline? 11. The volume of a cylinder i 75π cubic inche. The cylinder ha a height of inche. What i the radiu of the bae of the cylinder? 10 Big Idea Math Blue Copyright Big Idea Learning, LLC
7 Name Date 6. The Pythagorean Theorem For ue with Activity 6. Eential Quetion How are the length of the ide of a right triangle related? Pythagora wa a Greek mathematician and philoopher who dicovered one of the mot famou rule in mathematic. In mathematic, a rule i called a theorem. So, the rule that Pythagora dicovered i called the Pythagorean Theorem. Pythagora (c. 570 B.C. c. 490 B.C.) 1 ACTIVITY: Dicovering the Pythagorean Theorem Work with a partner. a. On grid paper, draw any right triangle. Label the length of the two horter ide (the leg) a and b. c b. Label the length of the longet ide (the hypotenue) c. c b a a c. Draw quare along each of the three ide. Label the area of the three quare a, b, and c. b d. Cut out the three quare. Make eight copie of the right triangle and cut them out. Arrange the figure to form two identical larger quare. a e. What doe thi tell you about the relationhip among a, b, and c? c b Copyright Big Idea Learning, LLC Big Idea Math Blue 11
8 Name Date 6. The Pythagorean Theorem (continued) ACTIVITY: Finding the Length of the Hypotenue Work with a partner. Ue the reult of Activity 1 to find the length of the hypotenue of each right triangle. a. b. c 10 c 4 4 c. d. c 0.6 c Big Idea Math Blue Copyright Big Idea Learning, LLC
9 Name Date 6. The Pythagorean Theorem (continued) ACTIVITY: Finding the Length of a Leg Work with a partner. Ue the reult of Activity 1 to find the length of the leg of each right triangle. a. b. a b What I Your Anwer? 4. IN YOUR OWN WORDS How are the length of the ide of a right triangle related? Give an example uing whole number. Copyright Big Idea Learning, LLC Big Idea Math Blue 1
10 Name Date 6. Practice For ue after Leon 6. Find the miing length of the triangle c b 7. 1 a 4.8 Find the value of x x x 1 m 6 cm 16 cm 5 m 5 m 6. In wood hop, you make a bookend that i in the hape of a right triangle. What i the bae b of the bookend? 8 in. 10 in. b 14 Big Idea Math Blue Copyright Big Idea Learning, LLC
11 Name Date 6. Approximating Square Root For ue with Activity 6. Eential Quetion How can you find decimal approximation of quare root that are irrational? You already know that a rational number i a number that can be written a the ratio of two integer. Number that cannot be written a the ratio of two integer are called irrational. Real Number Rational Integer Natural Irrational π π 1 ACTIVITY: Approximating Square Root Work with a partner. Archimede wa a Greek mathematician, phyicit, engineer, inventor, and atronomer. a. Archimede tried to find a rational number whoe quare i. Here are two that he tried and Are either of thee number equal to? How can you tell? b. Ue a calculator with a quare root key to approximate. Write the number on a piece of paper. Then enter it into the calculator and quare it. Then ubtract. Do you get 0? Explain. Copyright Big Idea Learning, LLC Big Idea Math Blue 15
12 Name Date 6. Approximating Square Root (continued) c. Calculator did not exit in the time of Archimede. How do you think he might have approximated? ACTIVITY: Approximating Square Root Geometrically Work with a partner. a. Ue grid paper and the given cale to draw a horizontal line egment 1 unit in length. Draw your egment near the bottom of the grid. Label thi egment AC. b. Draw a vertical line egment unit in length. Draw your egment near the left edge of the grid. Label thi egment DC. c. Set the point of a compa on A. d. Ue the Pythagorean Theorem to Set the compa to unit. Swing how that the length of egment the compa to interect egment BC i unit. DC. Label thi interection a B. Scale: 1 of a unit 10 e. Ue the grid paper to approximate. 16 Big Idea Math Blue Copyright Big Idea Learning, LLC
13 Name Date 6. Approximating Square Root (continued) What I Your Anwer?. Repeat Activity for a triangle in which egment CA i unit and egment BA i unit. Ue the Pythagorean Theorem to how that egment BC i 5 unit. Ue the grid paper to approximate 5. Scale: 1 of a unit IN YOUR OWN WORDS How can you find decimal approximation of quare root that are irrational? Copyright Big Idea Learning, LLC Big Idea Math Blue 17
14 Name Date 6. Practice For ue after Leon 6. Tell whether the number i rational or irrational. Explain Etimate to the nearet integer Which number i greater? Explain , , , The velocity in meter per econd of a ball that i dropped from a window at a height of 10.5 meter i repreented by the equation v = ( )( ) Etimate the velocity of the ball. Round your anwer to the nearet tenth. 11. The area of a quare table cloth i 0 quare feet. Etimate the length of one ide of the tablecloth. Round your anwer to the nearet tenth. 18 Big Idea Math Blue Copyright Big Idea Learning, LLC
15 Name Date 6.b Practice For ue after Leon 6.b Find the cube root of the number Find the urface area of the cube. 7. Volume = 8 m 8. Volume = 4 cm 9. Volume = 7 in. 10. Volume = 1000 ft Copyright Big Idea Learning, LLC Big Idea Math Blue 18A
16 Name Date 6.b Practice (continued) Etimate the quare root to the nearet tenth Complete the tatement with < or > π B Big Idea Math Blue Copyright Big Idea Learning, LLC
17 Name Date 6.4 Simplifying Square Root For ue with Activity 6.4 Eential Quetion How can you ue a quare root to decribe the golden ratio? Two quantitie are in the golden ratio if the ratio between the um of the quantitie and the greater quantity i the ame a the ratio between the greater quantity and the leer quantity. x 1 x + 1 x + x 1 = x 1 In a future algebra coure, you will be able to prove that the golden ratio i ACTIVITY: Contructing a Golden Ratio Work with a partner.. a. Ue grid paper and the given cale to draw a quare that i 1 unit by 1 unit. Label the midpoint of the right ide of the quare C. Label the bottom left corner of the quare A, the bottom right corner B, and the top left corner D. b. Draw a line from midpoint C of one ide of the quare to the oppoite corner D. c. Ue the Pythagorean Theorem to find the length of egment CD. d. Set the point of a compa on C. Set the compa radiu to the length of egment CD. Swing the compa to interect line BC. Label the point of interection E. Form rectangle ABEF. Scale: 1 of a unit 10 e. The rectangle ABEF i called the golden rectangle becaue the ratio of it ide length i the golden ratio. Copyright Big Idea Learning, LLC Big Idea Math Blue 19
18 Name Date 6.4 Simplifying Square Root (continued) f. Ue a calculator to find a decimal approximation of the golden ratio. Round your anwer to two decimal place. ACTIVITY: The Golden Ratio and the Human Body Work with a partner. Leonardo da Vinci wa one of the firt to notice that there are everal ratio in the human body that approximate the golden ratio. b a. Ue a tape meaure or two yardtick to meaure the length hown in the diagram for both you and your partner. (Take your hoe off before meauring.) f g c Navel b. Record your reult in the firt two column of the table on the next page. e h c. Calculate the ratio hown in the table. d. Leonardo da Vinci tated that for many people, the ratio are cloe to the golden ratio. How cloe are your ratio? d a 10 Big Idea Math Blue Copyright Big Idea Learning, LLC
19 Name Date 6.4 Simplifying Square Root (continued) You a a = b = = b a = b = Partner a b = c = d = c d = c = d = c d = e = f = e f = e = f = e f = g = h = g h = g = h = g h = What I Your Anwer?. IN YOUR OWN WORDS How can you ue a quare root to decribe the golden ratio? Ue the Internet or ome other reference to find example of the golden ratio in art and architecture. Copyright Big Idea Learning, LLC Big Idea Math Blue 11
20 Name Date 6.4 Practice For ue after Leon 6.4 Simplify the expreion a You build a hed in your backyard. a. What i the perimeter of the hed? 48 ft 108 ft 19 ft b. What i the volume of the hed? 1 Big Idea Math Blue Copyright Big Idea Learning, LLC
21 Name Date 6.5 Uing the Pythagorean Theorem For ue with Activity 6.5 Eential Quetion How can you ue the Pythagorean Theorem to olve real-life problem? 1 ACTIVITY: Uing the Pythagorean Theorem Work with a partner. a. A baeball player throw a ball from econd bae to home plate. How far doe the player throw the ball? Include a diagram howing how you got your anwer. Decide how many decimal point of accuracy are reaonable. Explain your reaoning. 90 ft 90 ft b. The ditance from the pitcher mound to home plate i 60.5 feet. Doe thi form a right triangle with firt bae? Explain your reaoning. Copyright Big Idea Learning, LLC Big Idea Math Blue 1
22 Name Date 6.5 Uing the Pythagorean Theorem (continued) ACTIVITY: Firefighting and Ladder Work with a partner. The recommended angle for a firefighting ladder i 75. When a 110-foot ladder i put up againt a building at thi angle, the bae of the ladder i about 8 feet from the building. The bae of the ladder i 8 feet above the ground. How high on the building will the ladder reach? Round your anwer to the nearet tenth. 110 ft x 8 ft 8 ft ACTIVITY: Finding Perimeter Work with a partner. Find the perimeter of each figure. Round your anwer to the nearet tenth. Did you ue the Pythagorean Theorem? If o, explain. a. Right triangle b. Trapezoid c. Parallelogram in. cm cm 6 ft 4 in. cm in. 4 ft 14 Big Idea Math Blue Copyright Big Idea Learning, LLC
23 Name Date 6.5 Uing the Pythagorean Theorem (continued) 4 ACTIVITY: Writing a Formula Work with a partner. a. Write a formula for the area of an equilateral triangle with ide length. b. Ue your formula to find the area of an equilateral triangle with a ide length of 10 inche. What I Your Anwer? 5. IN YOUR OWN WORDS How can you ue the Pythagorean Theorem to olve real-life problem? 6. Decribe a ituation in which you could ue the Pythagorean Theorem to help make deciion. Give an example of a real-life problem. Copyright Big Idea Learning, LLC Big Idea Math Blue 15
24 Name Date 6.5 Practice For ue after Leon 6.5 Find the ditance d. Round your anwer to the nearet tenth. 1. y. y d x d x y d x Find the height x. Round your anwer to the nearet tenth ft 5. x 16.4 ft x 5 ft 5 ft Tell whether the triangle with the given ide length i a right triangle cm 7 cm 1 m 0 m 15 cm 9 m 8. You et up a badminton net in your backyard. About how long i the rope ued to ecure the net? 1.55 m 0.5 m 16 Big Idea Math Blue Copyright Big Idea Learning, LLC
Fair Game Review. Chapter 7 A B C D E Name Date. Complete the number sentence with <, >, or =
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