Activity Involves Skills Covered in Lessons 1–6

1i) Simplify -4 + 5 + 3 - 12 + 6. Check the box next to the correct answer.

a. -2b. +2c. -4

1g) Work with a friend. Use parentheses to enclose each number or expression and its sign, insert plus signs between the parentheses, and add to get a sum. Have your friend do the same. Compare answers and methods. (Hint: Watch for subtraction.)

-4 + 6 - |-3 | - (-5)

Activity Involves Skills Covered in Lessons 7–12

2i) Simplify 6 - 3 x 2. Check the box next to the correct answer.

a. +6b. -6c. 0

2g) Work with a friend. Simplify: 12 - 8 ÷ 4 x 2 - (-2) x (-1). Have your friend do the same. Compare answers and methods.

Activity Involves Skills Covered in Lessons 13–18

3i) Find the total surface area of a box (right rectangular prism) whose edges have lengths of 3 ft, 5 ft, and 6 ft. Check the box next to the correct answer.

a. 138 ft²
b. 126 ft²
c. 144 ft²

3g) Work with a group to solve the following: A rectangular box whose edges have lengths of 12 cm, 15 cm, and 20 cm is made out of a rectangular piece of cardboard that measures 50 cm by 60 cm. What is the area of the cardboard left over? (Assume no waste.) Compare answers and methods.

Activity Involves Skills Covered in Lessons 19–24

4i) Simplify . Check the box next to the correct answer.

a. 25b. 20c. 15

4g) Work with a friend. Evaluate x³y ²z if x = -1, y = -2, and z = -1. Have your friend do the same. Compare answers and methods.

Activity Involves Skills Covered in Lessons 25–30

5i) Simplify . Check the box next to the correct answer.

a. 1/8b. 1/6c. -1/6

5g) Work with a group to solve the following: If a = -1 and b = -2, which of the following shows the value of Compare answers and methods. Check the box next to the answer you all agree is correct.

a. -1b. 0
c. 1d. 2

Activity Involves Skills Covered in Lessons 31–36

6i) Simplify: . Check the box next to the correct answer.

a.
b.
c.

6g) Work with a friend. Simplify: . Have your friend do the same. Compare answers and methods. Check the box next to the answer you both agree is correct.

a.
b.
c.

Activity Involves Skills Covered in Lessons 37–42

7i) A white Christmas occurs in the city of Columbus, Ohio, in 2 out of every 5 years. If Christmas 1948 and Christmas 1999 are excluded, how many white Christmases did Columbus have between 1948 and 1999? Check the box next to the correct answer.

a. 20 white Christmases
b. 15 white Christmases
c. 10 white Christmases

7g) Work with a friend to solve the following: The ratio of teachers to students in a school is 1 to 25. If there are 675 students in the school, how many teachers are there? Set up the equation and have your friend solve it.

Activity Involves Skills Covered in Lessons 43–48

8i) Joe is 13. He has a brother who is 17 and a sister who is 12. What is the mean of these three ages? Check the box next to the correct answer.

a. 16 b. 14c. 12

8g) Work with a group to solve the following: Suppose you have a set of numbers and you add the same number to each number in the set. Which of the following does NOT change? Compare answers and methods. Check the box next to the answer you all agree is correct.

a. mean b. median
c. moded. range

Activity Involves Skills Covered in Lessons 49–54

9i) Find three ordered pairs of x and y that satisfy the equation y = 3x - 2. Graph the equation on a rectangular coordinate system.

9g) Work with a friend. Graph the equations y = -x + 3 and y = 4 on a rectangular coordinate system, and have your friend do the same on another rectangular coordinate system. Do the lines for the equations intersect? If so, what are the coordinates of the point of intersection? Compare answers and graphs.

Activity Involves Skills Covered in Lessons 55–60

10i) A store owner gave a 25 percent discount on shoes that regularly sell for $60. What is the reduced price? Check the box next to the correct answer.

a. $25b. $35 c. $45

10g) Work with a group to solve the following: One year Ohio State University had an enrollment of 57,750 students. If this was a 5% increase over the previous year, what was the enrollment the previous year?

Activity Involves Skills Covered in Lessons 61–66

11i) Simplify .

11g) Work with a friend. Simplify and have your friend do the same. Compare answers and methods.

Activity Involves Skills Covered in Lessons 67–72

12i) Factor x² + 4x + 3. Check the box next to the correct answer.

a. (x + 3) (x + 1)
b. x²(+2) (x² + 1)
c. (x² + 4) (2x + 1)

12g) Work with a friend. Factor x² + (a - 1)x - a and have your friend do the same. Compare answers and methods. Check the box next to the answer you both agree is correct.

a. x(a - 1) (x - a)
b. (x² - 1) (x + a)
c. (x + a) (x - 1)

Activity Involves Skills Covered in Lessons 73–78

13i) Which of the following equals 1019² - 619²? (Hint: Try factoring.) Check the box next to the correct answer.

a. 600 x 619 b. 400 x 1019
c. 1019² x 619² d. 400 x 1638

13g) Work with a group to solve the following: An urn contains 10 yellow marbles and 5 marbles that are red or blue. A marble is drawn at random and not replaced. Then a second marble is drawn. What is the probability that the first marble is yellow and the second marble is either red or blue?

Activity Involves Skills Covered in Lessons 79–84

14i) If f (x) = what is f (-1)? Check the box next to the correct answer.

a. f (-1) = 4
b. f (-1) = 2
c. f (-1) = 3

14g) Work with a friend to solve the following: If f (x) = -3x + 10, what is f (x² + 2)? Compare answers and methods.

Activity Involves Skills Covered in Lessons 85–90

15i) The number of diagonals d in a polygon with n sides is given by the formula d = . If a polygon has 20 diagonals, how many sides does it have? (Solve by factoring.) Check the box next to the correct answer.

a. n = 12; 12 sides
b. n = 10; 10 sides
c. n = 8; 8 sides

15g) Work with a group to solve the following: The number of robins in an aviary is 3 more than twice the number of wrens in the aviary. The total number of robins and wrens in the aviary is 78. How many robins are in the aviary? How many wrens are in the aviary?

Activity Involves Skills Covered in Lessons 91–96

16i) Find the simplest factored form of the complex fraction below.

16g) Work with a group to simplify . Explain each step in the procedure. Compare answers and methods.

Activity Involves Skills Covered in Lessons 97–102

17i) Find the length of one side of a square whose diagonal is 8 cm long.

17g) Work with a friend. An airplane is flying at an altitude of 5000 ft. Its slanted, direct-line distance from the airport is 13,000 ft. How far is the airplane horizontally from the airport? Draw a diagram of the problem, and then solve the problem. Have your friend do the same. Compare answers and methods.

Activity Involves Skills Covered in Lessons 103–108

18i) Find the equation of the line that passes through the origin and the point (-3, 4).

18g) Work with a friend. Find the equation of the line that passes through the point (-¹/₂, ¹/₃) and is parallel to the line whose equation is y -6x - 5 = 0. Have your friend do the same. Compare answers and methods.

Activity Involves Skills Covered in Lessons 109–114

19i) a and b are directly proportional (a varies directly with b).When a = 4, b = 5. What is b when a = 2? Check the box next to the correct answer.

a. b = ⁵/₂
b. b= ⁴/₅
c. b = ²/₅

19g) Work with a group to solve the following: A job takes 12 hours with 5 machines. How long does it take with 6 machines? (Hint: The number of hours required is inversely proportional to the number of machines used.)

Activity Involves Skills Covered in Lessons 115–120

20i) Use the quadratic formula to solve 4x² - x + 5 = 0.

20g) Work with a friend to solve the following: The hypotenuse of a right triangle is 26 cm long. One of the other two sides is 14 cm shorter than the other. What is the length of each side? Compare answers and methods.