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Comparing Unit Rates: Tables, Equations and Points: Classroom Packet

Grade 8 Algebra: Comparing Unit Rates: Tables, Equations and Points

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Tables and equations through the origin

  1. 1. Which has the greater unit rate:
    A:y=3xB:x1234y481216\begin{array}{ll} \textbf{A:} & y = 3x \\[14pt] \textbf{B:} & \begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline y & 4 & 8 & 12 & 16 \end{array} \end{array}
  2. 2. Which has the greater unit rate:
    A:y=5xB:x0123y061218\begin{array}{ll} \textbf{A:} & y = 5x \\[14pt] \textbf{B:} & \begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 0 & 6 & 12 & 18 \end{array} \end{array}
  3. 3. Which has the greater unit rate:
    A:y=7xB:x1234y6121824\begin{array}{ll} \textbf{A:} & y = 7x \\[14pt] \textbf{B:} & \begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline y & 6 & 12 & 18 & 24 \end{array} \end{array}
  4. 4. Which has the greater unit rate:
    A:x2468y10203040B:y=4x\begin{array}{ll} \textbf{A:} & \begin{array}{c|cccc} x & 2 & 4 & 6 & 8 \\ \hline y & 10 & 20 & 30 & 40 \end{array} \\[14pt] \textbf{B:} & y = 4x \end{array}
  5. 5. Which has the greater unit rate:
    A:y=2xB:y=2.5x\begin{array}{ll} \textbf{A:} & y = 2x \\[14pt] \textbf{B:} & y = 2.5x \end{array}
  6. 6. Which has the greater unit rate:
    A:x1234y9182736B:y=8x\begin{array}{ll} \textbf{A:} & \begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline y & 9 & 18 & 27 & 36 \end{array} \\[14pt] \textbf{B:} & y = 8x \end{array}
  7. 7. Which has the greater unit rate:
    A:y=10xB:x2468y22446688\begin{array}{ll} \textbf{A:} & y = 10x \\[14pt] \textbf{B:} & \begin{array}{c|cccc} x & 2 & 4 & 6 & 8 \\ \hline y & 22 & 44 & 66 & 88 \end{array} \end{array}
  8. 8. Which has the greater unit rate:
    A:x36912y12243648B:x5101520y15304560\begin{array}{ll} \textbf{A:} & \begin{array}{c|cccc} x & 3 & 6 & 9 & 12 \\ \hline y & 12 & 24 & 36 & 48 \end{array} \\[14pt] \textbf{B:} & \begin{array}{c|cccc} x & 5 & 10 & 15 & 20 \\ \hline y & 15 & 30 & 45 & 60 \end{array} \end{array}

Answer Key

Level 1

  1. 1. B (4>3)B\ (4 > 3)
  2. 2. B (6>5)B\ (6 > 5)
  3. 3. A (7>6)A\ (7 > 6)
  4. 4. A (5>4)A\ (5 > 4)
  5. 5. B (2.5>2)B\ (2.5 > 2)
  6. 6. A (9>8)A\ (9 > 8)
  7. 7. B (11>10)B\ (11 > 10)
  8. 8. A (4>3)A\ (4 > 3)

Grade 8 Algebra: Comparing Unit Rates: Tables, Equations and Points

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Tables, equations and two points

  1. 1. Which has the greater rate of change:
    A:(1,4), (3,10)B:y=2x+5\begin{array}{ll} \textbf{A:} & (1, 4),\ (3, 10) \\[14pt] \textbf{B:} & y = 2x + 5 \end{array}
  2. 2. Which has the greater rate of change:
    A:(0,2), (4,22)B:x0123y171319\begin{array}{ll} \textbf{A:} & (0, 2),\ (4, 22) \\[14pt] \textbf{B:} & \begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 1 & 7 & 13 & 19 \end{array} \end{array}
  3. 3. Which has the greater rate of change:
    A:y=1.5xB:(2,4), (6,10)\begin{array}{ll} \textbf{A:} & y = 1.5x \\[14pt] \textbf{B:} & (2, 4),\ (6, 10) \end{array}
  4. 4. Which has the greater rate of change:
    A:x0246y371115B:(1,1), (4,10)\begin{array}{ll} \textbf{A:} & \begin{array}{c|cccc} x & 0 & 2 & 4 & 6 \\ \hline y & 3 & 7 & 11 & 15 \end{array} \\[14pt] \textbf{B:} & (1, 1),\ (4, 10) \end{array}
  5. 5. Which decreases faster:
    A:y=−2x+8B:(0,12), (4,0)\begin{array}{ll} \textbf{A:} & y = -2x + 8 \\[14pt] \textbf{B:} & (0, 12),\ (4, 0) \end{array}
  6. 6. Which has the greater rate of change:
    A:(2,5), (6,7)B:y=13x+4\begin{array}{ll} \textbf{A:} & (2, 5),\ (6, 7) \\[14pt] \textbf{B:} & y = \tfrac{1}{3}x + 4 \end{array}
  7. 7. Which has the greater rate of change:
    A:x1357y4101622B:(2,9), (5,21)\begin{array}{ll} \textbf{A:} & \begin{array}{c|cccc} x & 1 & 3 & 5 & 7 \\ \hline y & 4 & 10 & 16 & 22 \end{array} \\[14pt] \textbf{B:} & (2, 9),\ (5, 21) \end{array}
  8. 8. Which has the greater rate of change:
    A:(−1,2), (3,14)B:y=3x−1\begin{array}{ll} \textbf{A:} & (-1, 2),\ (3, 14) \\[14pt] \textbf{B:} & y = 3x - 1 \end{array}

Answer Key

Level 2

  1. 1. A (3>2)A\ (3 > 2)
  2. 2. B (6>5)B\ (6 > 5)
  3. 3. Same (1.5)\text{Same } (1.5)
  4. 4. B (3>2)B\ (3 > 2)
  5. 5. B (−3 vs −2)B\ (-3\text{ vs }-2)
  6. 6. A (12>13)A\ (\tfrac{1}{2} > \tfrac{1}{3})
  7. 7. B (4>3)B\ (4 > 3)
  8. 8. Same (3)\text{Same } (3)

Grade 8 Algebra: Comparing Unit Rates: Tables, Equations and Points

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Comparing rates in context

  1. 1. Which car is faster (x = hours, y = miles):
    A:y=55xB:(2,120), (5,300)\begin{array}{ll} \textbf{A:} & y = 55x \\[14pt] \textbf{B:} & (2, 120),\ (5, 300) \end{array}
  2. 2. Which worker earns more per hour (x = hours, y = dollars):
    A:y=14x+20B:x2468y306090120\begin{array}{ll} \textbf{A:} & y = 14x + 20 \\[14pt] \textbf{B:} & \begin{array}{c|cccc} x & 2 & 4 & 6 & 8 \\ \hline y & 30 & 60 & 90 & 120 \end{array} \end{array}
  3. 3. Which plan costs less per GB (x = GB, y = dollars):
    A:(2,13), (6,25)B:y=3.5x+5\begin{array}{ll} \textbf{A:} & (2, 13),\ (6, 25) \\[14pt] \textbf{B:} & y = 3.5x + 5 \end{array}
  4. 4. Which tank drains faster (x = minutes, y = liters):
    A:y=−6x+90B:x051015y100755025\begin{array}{ll} \textbf{A:} & y = -6x + 90 \\[14pt] \textbf{B:} & \begin{array}{c|cccc} x & 0 & 5 & 10 & 15 \\ \hline y & 100 & 75 & 50 & 25 \end{array} \end{array}
  5. 5. Which printer is faster (x = minutes, y = pages):
    A:(3,45), (7,105)B:y=16x\begin{array}{ll} \textbf{A:} & (3, 45),\ (7, 105) \\[14pt] \textbf{B:} & y = 16x \end{array}
  6. 6. Which is the better buy (x = pounds, y = dollars):
    A:x2468y7142128B:(3,12), (5,20)\begin{array}{ll} \textbf{A:} & \begin{array}{c|cccc} x & 2 & 4 & 6 & 8 \\ \hline y & 7 & 14 & 21 & 28 \end{array} \\[14pt] \textbf{B:} & (3, 12),\ (5, 20) \end{array}
  7. 7. Which runner is faster (x = minutes, y = meters):
    A:x0246y04008001200B:(1,180), (4,720)\begin{array}{ll} \textbf{A:} & \begin{array}{c|cccc} x & 0 & 2 & 4 & 6 \\ \hline y & 0 & 400 & 800 & 1200 \end{array} \\[14pt] \textbf{B:} & (1, 180),\ (4, 720) \end{array}
  8. 8. Which candle burns faster (x = hours, y = cm tall):
    A:y=−1.5x+20B:(2,16), (6,8)\begin{array}{ll} \textbf{A:} & y = -1.5x + 20 \\[14pt] \textbf{B:} & (2, 16),\ (6, 8) \end{array}

Answer Key

Level 3

  1. 1. B (60>55 mph)B\ (60 > 55\text{ mph})
  2. 2. B ($15>$14)B\ (\$15 > \$14)
  3. 3. A ($3<$3.50)A\ (\$3 < \$3.50)
  4. 4. A (6>5 L/min)A\ (6 > 5\text{ L/min})
  5. 5. B (16>15)B\ (16 > 15)
  6. 6. A ($3.50<$4)A\ (\$3.50 < \$4)
  7. 7. A (200>180 m/min)A\ (200 > 180\text{ m/min})
  8. 8. B (2>1.5 cm/h)B\ (2 > 1.5\text{ cm/h})