Do the experiment results match the math?

Answer Key - Grade 7 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Ari flips a water bottle 40 times and it lands upright 14 times. Using these results as the model, how many uprights should Ari expect in 200 more flips?

   70
2. 2.

   Bo makes 18 of 50 free throws in practice. Using that as the model, how many shots should Bo expect to make in 300 more free throws?

   108
3. 3.

   Esme plants 60 bean seeds and 27 sprout. Using that as the model, how many sprouts should Esme expect from 400 seeds?

   180
4. 4.

   Jun's spinner has 4 equal sections, so gold has a 1/4 chance. Jun gets gold 14 times in 40 spins. Zee gets gold 108 times in 400 spins. Whose result is closer to the model?

   • Jun's result: the tally is 4 above the expected 10, while Zee's is 8 above the expected 100.
   • Neither is closer, since both tallies are above the expected count for their spins.
   • Zee's result: 27% is 2 points from 25%, while Jun's 35% is 10 points away.
5. 5.

   A fair coin has a 1/2 chance of heads. Ari gets 9 heads in 20 flips. Ren gets 90 heads in 200 flips. Whose result is closer to the model?

   • They are equally close: both shares are 45%, which is 5 points under 50%.
   • Ari's result: 9 is 1 under the expected 10, while Ren's 90 is 10 under the expected 100.
   • Ren's result: 200 flips is a larger sample, so it has to be closer to the model.
6. 6.

   Luz's spinner has 5 equal sections, 3 of them green, a 0.6 chance. Luz lands on green 19 times in 30 spins. Tala lands on green 135 times in 200 spins. Whose result is closer?

   • They are equally close, since both shares are above the 60% that the model gives.
   • Luz's result: 19/30 is about 63%, 3 points over 60%, while Tala's 67.5% is 7.5 over.
   • Tala's result: 200 spins is a larger sample than 30 spins, so Tala's has to be closer.
7. 7.

   Tala's spinner has red, blue and green. In 120 spins, red came up 61 times, blue 30 and green 29. Which model of the spinner is most reasonable?

   • Red 1/2, blue 1/4, green 1/4, because the tallies sit near 60, 30 and 30.
   • Red 2/3, blue 1/6, green 1/6, because red came up more times than blue and green put together.
   • Red 1/3, blue 1/3, green 1/3, because a spinner with three colors gives each one a 1/3 chance.
   • Red 1/6, blue 1/3, green 1/2, because the color with the smallest tally should get the biggest chance.
8. 8.

   Noah rolls a number cube 60 times. The counts for faces 1 to 6 are 8, 9, 11, 10, 12 and 10. A fair cube gives about 10 of each. What can Noah say?

   • The 5 came up most, so a 5 has the biggest chance and the model should say so.
   • Only the 4 and the 6 came up exactly 10 times, so the cube seems unfair.
   • The six counts add up to 60 rolls, so the fair model is right.
   • Every count is within 2 of 10, so the fair-cube model seems reasonable.
9. 9.

   Milo draws a marble from a bag of 12, records its color and puts it back. In 120 draws: red 61, blue 29, green 30. Which contents of the bag best fit these results?

   • 8 red, 2 blue and 2 green, because red came up more times than blue and green put together.
   • 6 red, 2 blue and 4 green, because green came up more than blue, so green gets twice as many marbles.
   • 6 red, 3 blue and 3 green, because those shares predict 60, 30 and 30 draws.
   • 4 red, 4 blue and 4 green, because three colors should each fill an equal share of the bag.
10. 10.

    A game spinner is designed with red 1/2, blue 1/3 and green 1/6. In 120 spins, Pia gets red 52, blue 46 and green 22. Which statement fits best?

    • The tallies miss 60, 40 and 20 by 8, 6 and 2, so the three chances in the design are wrong.
    • The tallies add up to 120 spins, so the total is what matters and the design is right.
    • The tallies are within 8 of the expected 60, 40 and 20, so the design seems reasonable.
    • Blue came up more than green, so green should have the bigger chance of the two.