Real Numbers Student Activity Sheet 1; use with Overview
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1 Real Numbers Student Activity Sheet 1; use with Overview 1. Complete the graphic organizer with examples of each type of number. 2. REINFORCE Give at least three examples of each type of number. Whole number: Integer, but not a whole number: Rational, but not an integer:. What types of numbers make up real numbers? Page 1 of
2 Real Numbers Student Activity Sheet 1; use with Overview 4. What are two characteristics of irrational numbers? 5. REINFORCE For each rational number, write its decimal or fraction equivalent. Then draw and label a number line. Locate each rational number on your number line. a. 2.4 b. 7 8 c. 9 d e f. 1 2 Page 2 of
3 Real Numbers Student Activity Sheet 1; use with Overview 6. REVIEW Find the areas of squares of the squares. Estimate the side length of each square. a. b. c. Page of
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5 Student Activity Sheet 2; use with Exploring Undiscovered territory on the real number line 1. Draw all possible ad spaces in the grids provided. Be sure to follow the requirements given on page 2 of the Exploring. Draw only one ad space per grid. After drawing an ad space, find its area and label the area inside the ad space. There are a total of 8 different ad spaces possible. Page 1 of 6
6 Student Activity Sheet 2; use with Exploring Undiscovered territory on the real number line 2. Use this table to record the approximate side length for each of the squares you found. Area of square (units 2 ) 1 Side length (units) What is a perfect square? 4. What is a good approximation for the side length of a square with an area of 2 units 2? Page 2 of 6
7 Student Activity Sheet 2; use with Exploring Undiscovered territory on the real number line 5. Complete the graphic organizer describing the real number system. 6. What type of number represents the side lengths of non-perfect or tilted squares? 7. REVIEW Find the areas of the following perfect squares. Side length Area Page of 6
8 Student Activity Sheet 2; use with Exploring Undiscovered territory on the real number line 8. What is a square root? Give an example and explain how the symbol is read. 9. What is the side length of a square with an area of square units? 10. What type of number is 2 and what is its the approximate value? 11. Find the area of this square with s = Does s 2 = 2? 12. What is one more example of an irrational number that you are already familiar with? Hint: it is the ratio of a circle s circumference to its diameter and it lies between and 4 on the number line. Page 4 of 6
9 Student Activity Sheet 2; use with Exploring Undiscovered territory on the real number line 1. Why does this number belong to the irrational set of numbers? What is the fraction commonly used to approximate this number? 14. REINFORCE Explain how you can find the approximate value of the square of this number? Check your thinking with a calculator. 15. Find the side lengths for thesquares with the following given areas. Area a. 1 square unit Side length b. 4 square units c. 9 square units d. 16 square units e. 25 square units f. 6 square units 16. How can you use square roots to write the solution to x 2 = 25? Page 5 of 6
10 Student Activity Sheet 2; use with Exploring Undiscovered territory on the real number line 17. REINFORCE Write the solution using the square root symbol and then solve for x. a. x 2 = 81 b. x 2 = 64 c. x 2 = REINFORCE Apply what you now know about the relationship between the area of a square and its side lengths to find the precise missing measurements. Use a calculator to verify your answers. NOTE: Squares are not drawn to scale. a. b. A = 11 sq units s = s = A = 0 sq units s = s = c. d. A= sq units A = 81 sq units s = s = Page 6 of 6
11 Student Activity Sheet ; use with Exploring Approximating the value of irrational numbers 1. REVIEW Approximate the value of What were the limitations of the strategies used to approximate 10? Which strategy came closest to finding the actual area of 10 square centimeters?. Between which two perfect squares will Hairy s logo of 10 square centimeters fall? 4. Which perfect square is the logo closest to in size, 9 square cm or 16 square cm? Explain. 5. Place the perfect square roots on the number line. Then use their locations to help estimate the locations of the irrational numbers. 1, 2, 4, 5, 9, 14, 16, 17, 21, 25, 0, 6 Page 1 of 7
12 Student Activity Sheet ; use with Exploring Approximating the value of irrational numbers 6. To summarize, a square with an area of 10 falls between the perfect squares and ; but the area is closer to the. The side length of a square with an area of 10,, is between the whole numbers and ; but is closer to. Now that you know that 10 is slightly more than, a reasonable decimal value for sqrt10 can be determined, such as,. 7. REINFORCE Approximate the value of each square root. Do not use a calculator. Is between Inequality Approximate value 0 5 and 6 25 < 0 < because 0 is about halfway between 25 and Page 2 of 7
13 Student Activity Sheet ; use with Exploring Approximating the value of irrational numbers 8. Fill in the table with information about the area and side lengths of the square logos. Ad space Area Exact length Side length Nearest whole number length Best decimal approximation Smoothies Galore Hamburger Barn Planet pizza Dirty s Car Autobody 9. Place the approximate side lengths of the logos on the number line below. Page of 7
14 Student Activity Sheet ; use with Exploring Approximating the value of irrational numbers 10. Without using a ruler and without guessing, find the best decimal approximation for the line segment AB. Page 4 of 7
15 Student Activity Sheet ; use with Exploring Approximating the value of irrational numbers 11. REINFORCE Without using a ruler, find the exact length of line segment XY. Then approximate the length as a rational number. XY = Page 5 of 7
16 Student Activity Sheet ; use with Exploring Approximating the value of irrational numbers 12. REINFORCE Without using a ruler, find the exact length of line segment QR. Then approximate the length as a rational number. QR = Page 6 of 7
17 Student Activity Sheet ; use with Exploring Approximating the value of irrational numbers 1. REINFORCE Critique the following students statements: Student A: The square root of 17 must be is larger than 4 but less than 25 because the square root of 16 is 4 but 5 is square root of 25. Student B: The square root of 101 must be 25 point something because the square root of 100 is 25 and 101 is a little bit greater than 100. Student C: The square root of 50 is in between 49 and 64 because those are the perfect squares. Page 7 of 7
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19 Student Activity Sheet 4; use with Exploring Cubes and cube roots 1. What will the cube root of the volume of a cube tell you about the cube? 2. What is the cube root symbol?. REINFORCE What is the x? How do you say that expression? Page 1 of 5
20 Student Activity Sheet 4; use with Exploring Cubes and cube roots 4. Fill out the following table. Sketch of cube Product of the dimensions of the cube Volume of cube Side length of cube expressed as a cube root Page 2 of 5
21 Student Activity Sheet 4; use with Exploring Cubes and cube roots 5. REINFORCE Which is greater, the cube root of 64 or the square root of 64? Explain. 6. REINFORCE Is there a positive number for which the square root and cube root are equivalent? 7. Complete the table of perfect cubes. x x Page of 5
22 Student Activity Sheet 4; use with Exploring Cubes and cube roots 8. REINFORCE Solve the following cube roots. a. 27 = b. 216 = c. 1 = d = 9. What value of x makes x = 216 true? 10. REINFORCE What value of x makes x = 729 true? 11. A sculptor is working with a large block of ice in the shape of a cube. He would like to cut 125 smaller cubes with side lengths of 1 foot. a. How many smaller cubes will be along each side of the larger cube? Write this solution using the cube root symbol. Explain, and draw a picture of the large ice cube split up. b. How many cuts along each side of the larger cube does the sculptor need to make? Page 4 of 5
23 Student Activity Sheet 4; use with Exploring Cubes and cube roots 12. REINFORCE You are cutting a large cube of tofu into smaller cubes. If you cut 27 smaller cubes, how many smaller cubes will be along each edge of the larger tofu cube? Write your solution using the cube root symbol. Sketch a picture of the larger cube of tofu showing the slices needed to create the smaller cubes. 1. The ice sculptor has another large block of ice that he would like to cut into smaller cubes of 1-foot side length. He knows that the larger cube has a volume of 45 cubic feet of ice. Using your table of perfect cube roots, estimate the number of smaller cubes will be along each side of the larger cube. 14. REINFORCE Find each cube root, or list the two consecutive whole numbers that the given number is between. Do not use a calculator. Cube root or estimate Explanation = between 5 and < 200 < Page 5 of 5
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25 Student Activity Sheet 5; use with Exploring Approximating the value of irrational numbers Locate each ordered pair on the coordinate plane. It may be necessary to approximate the location of the ordered pair. Connect points within each list. List A (x,y) List B (x,y) List C (x,y) List D (x,y) List E (x,y) (-1,4.5) (-1,4 1 2 ) ( 1 2, 4 ) (1,4 4 ) (5,- 4 ) (-2 1, 64 2 ) (-4.5,7.0) (0,1.5) (2.5,6.5) ( 16,-1 4 ) (-4, 1 2 ) (-5 1 2, 6 ) (-0.8,1.5) ( 25, 49 ) (5,-2.75) (-4.5,2.5) (-5,5) (-1.5,1) (5,4.25) ( (-4,1.5) (-4.5,2 1 2 ) (-1,0.5) (-,0) (0,0) (-0.5,-0.75) ( 6,0) ( 27 6,-1.75) Begin new line ( 27,4 Begin new line ) (5,-1.25) 4,5 1 2 ) (4.5,-1.75) (6,- 4 ) (,0.5) (5, 40 ) (5,-2.25) (7 1 2,0.75) (.5, 1 2 ) (5.5,-1.75) (7.7,1.25) (4,1.2) (5,-1.25) (7 7 10,2) (4,1.5) (7 1 2,2.50) (.5,1.75) (6 1 2, 1 4 ) (,1 4 ) (6,.75) (2 1, 8 2 (4.5,4.5) ( 1, 8 2 (,4.75) (1,4.75) (-1,4.5) ) ) Page 1 of 2
26 Student Activity Sheet 5; use with Exploring Approximating the value of irrational numbers List F (x,y) Draw a line by connecting (-2 1,4) to (-5,6.5) 2 Draw a line by connecting (6 1,.25) to (6.5,-0.5) 2 Draw a line by connecting (7.7,1.25) to (8,1.25) Draw a line by connecting (7.7,2) to (8, 4 ) Draw a line by connecting (8,.5) to (8,- 1 2 ) Page 2 of 2
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