1 Concept of Variable A Page Jon said, “m – 1 is always greater than 1 – m.” Do you agree with Jon?
a. Yes, Jon is correct because m is a positive number. b. Yes, Jon is correct because you cannot substitute a negative number for m. c. No, Jon is not correct because 1 – m is greater than m – 1 when m is negative integer. d. No, Jon is not correct because these expressions are equivalent.
Answer ______What can you say about d if d = t + w and t + w = 40? Explain.
The equation below is true when x = 6: x3 + x = 222
What value of x will make the following equation true? (2x)3 + 2x = 222
x = ______If d – 243 = 542, what does d – 245 equal?
Answer ______The solution to the equation 11 – x = 2(13 – 2x) is 5. What is the solution to the equation? 11 –x2 = 2(13 – 2x2)
Answer ______If b – 878 = 915, what does b – 880 equal?
Answer ______Dan challenged Amy to write an equation that has a solution of 3. Which equation could Amy have written?
a. x + 2 = 3 b. –2x = 6 c. 4 – x = 10 – 3x d. 3 + x = –(x + 3)
IES Award# R324A110262 © 2012 ASPM, Iowa State University, University of Missouri 22 2
Answer ______
Carl simplified 9h – h. He said an equivalent expression was 8h. Do you agree with Carl?
a. Yes, because 9h and h are like terms so the coefficients of 9 and 1 can be combined. b. No, because h is a common term in both so h – h is 0, that leaves 9. c. It is not possible to determine if Carl is correct because you do not know the value of h. d. Carl is only correct if h is a positive number. Answer ______Bart said, “t + 3 is less than 5 + t.” Circle one: Always true Sometimes true Never true Explain your answer.
If h + m = 7, what does h + m + 7 equal?
Answer ______y – x = –(–x – y)
Circle one: Always true Sometimes true Never true Explain your answer.
Sharon wrote the equation c = 3h + 1. If the value of h is increased by 2, the value of c will …
a. Increase by 1. b. Increase by 2. c. Increase by 3. d. Increase by 6. Answer ______
Show on the number line where you would expect to find n – 3.
Cathy added 7x + 8y and got the sum 15xy. What would you say to Cathy?
a. You are correct because 8 + 7 is 15 and x + y is xy. b. You are correct because 7 and x are being multiplied and 8 and y are being multiplied. The Associative Property lets you combine these terms. c. You are not correct because unlike terms cannot be combined. d. It is not possible to know if Cathy is correct because you do not know the value of x and y.
IES Award# R324A110262 © 2012 ASPM, Iowa State University, University of Missouri 3 Concept of Variable A Page
Answer ______
B + E + M = B + R + S Circle one: Always true Sometimes true Never true Explain your answer.
Jess said, “g3 is equivalent to 3g.” What would you say to Jess?
a. Yes, it’s true because the exponent means to multiply by 3. b. Yes, it’s true because the exponent means to use g as an addend 3 times. c. No, it’s not true because the exponent means to use g as a factor 3 times. d. No, it’s not true if g is a fraction. It is true for whole numbers. Answer ______Sam said, “2n + 1 represents a greater quantity than 2(n + 1).” Do you agree with Sam? Why or why not?
Write an equation whose solutions are –3 and 7.
Cupcakes cost c cents each and doughnuts cost d cents each. I buy 4 cupcakes and 3 doughnuts. What does 4c + 3d stand for or represent?
a. The cupcakes and doughnuts b. The number of cupcakes and the number of doughnuts I buy c. The weight of the cupcakes and doughnuts d. The total cost of the cupcakes and doughnuts Answer ______
IES Award# R324A110262 © 2012 ASPM, Iowa State University, University of Missouri