Mathematics 7
Items to Support Formative Assessment
Unit 5: Statistics and Probability
7.SP.C Investigate chance processes and develop, use, and evaluate probability models.
7.SP.C.5 Understand that the probability of a chance event is a number between 0 and 1
that expresses the likelihood of the event occurring. Larger numbers indicate greater
likelihood. A probability near 0 indicates an unlikely event, a probability around ½
indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a
likely event.
7.SP.C.5
A deck of cards contains 26 black and 26 red cards. 13 out of the 26 black are spades and 13 are
clubs. 13 out of 26 red are hearts and 13 are diamonds. The cards number 2-10, Jack, Queen,
King, Ace.
What event would have a probability that is
1.
2.
3.
4.
Impossible: P(_________________________________)
Certain: P(__________________________________)
Likely: P(_________________________________)
Unlikely: P(__________________________________)
Explain your reasoning.
Possible Solution
1.
2.
3.
4.
Impossible: P(1)
Certain: P(black or red card)
Likely: P(numbered card)
Unlikely: P(3 of hearts)
Impossible events have a probability of 0. It is impossible to pick a 1 from a deck of playing
cards. To be an impossible event it cannot happen. Certain events have a probability of 1. In
this case, black and red are the only possible colors to choose making this event certain. A likely
event would have a probability greater than ½. There are 9 numbered cards in each “suit”.
Therefore the probability of choosing a numbered card would be 36/52 or 18/25. This is greater
than ½. There is a greater chance of choosing a numbered card then not choosing a numbered
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card. Conversely, an unlikely event would have a probability less than ½. In this case there is
only one three of hearts making the probability 1/52.
7.SP.C.5
Maria was asked if the probability of spinning blue on the spinner below was very likely. She
replied yes. Do you agree with her? Explain why.
Potential solution:
I do not agree with Maria. To be likely, that would mean that the probability would need to be
nearer to 1. The probability of spinning and landing on blue on this spinner is 3/12 or ¼. It is less
likely that she will land on blue than not land on blue.
7.SP.C.5
Shade each of the spinners below so the probability of spinning a shaded section matches the
label.
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Likely
Not Likely
Equally Likely
Solution
Likely: More than half of the sections should be shaded.
Not Likely: Less than half of the sections should be shaded
Equally Likely: Half of the sections should be shaded.
7.SP.C.5
Mark the location on the number line below to estimate the probabilities of given events. Provide
a rationale.
the probability of...
A: rain today
B: rolling a one with a number cube
C: winning the megamillions
D: Ravens’ winning the Super Bowl again next season
E: flipping a coin and getting tails
F: a student in this class having PE today
Potential solutions:
A: based upon the sky, weather report etc.; likely events would be closer to one and unlikely
events close to 0
B: in the lower ¼ of the graph. The actual probability is ⅙
C: very unlikely; this should be closer to 0. There is a low probability of having those specific
balls in the machine chosen because there are so many combinations in the sample space
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D: this is more of a prediction. What you are looking for is the rationale to support the placement
on the number line. There have only been 7 teams to repeat in the history of the super bowl.
E: should be at the ½ line. Flipping and getting heads is as likely as flipping and getting tails.
F: around ½. Students have PE for half of a year every year. Therefore about ½ of the students in
a given grade would have PE in a given semester.
7.SP.C.6 Approximate the probability of a chance event by collecting data on the chance
process that produces it and observing its long-run relative frequency, and predict the
approximate relative frequency given the probability. For example, when rolling a number
cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not
exactly 200 times.
7.SP.6
You are going to toss a plastic cup into the air and determine how it lands once it reaches the
ground.
a. What are the different outcomes for the experiment?
b. Make a guess as to what the probability would be for each of the possible outcomes. If your
probabilities are different for each outcome explain why.
c. Toss the cup into the air 20 times and record the outcomes.
#1
#2
#3
#4
#5
#6
#7
#8
#9
#10
#11
#12
#13
#14
#15
#16
#17
#18
#19
#20
Top
Bottom
Side
Top
Bottom
Side
d. Determine the experimental probability of each outcome and compare it to your original guess.
Teachers Note:
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Solution:
a. The outcomes are that the cup could land on the top, bottom, or side.
b. Solutions may vary depending on the type of cup you use.
c. Solutions may vary.
d. Solutions may vary.
7.SP.C.6
If you were to spin the spinner below 200 times, how many times would you expect to land on 2?
Explain your reasoning.
Solution:
I would expect to land on 2 around 50 times because the theoretical probability of spinning 2 on
the spinner above is 1/4. If I have 200 outcomes I can determine 25% of 200 by setting up a
proportion or multiplying 200 x 0.25.
7.SP.C.6 (MP.2 and MP.3)
Megan argues that the spinner below will land on red about 100 times if it is spun 300 times in
all. Is her logic reasonable? If so, defend her thinking. If you disagree, explain where her error
lies and provide a better estimate based upon mathematical reasoning and understanding.
Solution:
Megan’s reasoning is incorrect. Her mistake was in thinking that there was an equally likely
chance of landing on each of the three colors and there is not. The probability of landing on red
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is ¼ because the portion that red makes up in the circle is ¼ of the entire circle. The probability
of blue on the other hand is ½ that makes these probabilities not equally likely. With that in
mind, if the spinner is spun 300 times, we would expect it to land on red ¼ of the 300 spins
which is equal to 75 times.
7.SP.C.6 (MP.1, MP.2, and MP.3)
Kendall drew a marble from a bag of 55 marbles and recorded the color in the chart below. He
returned the marble back to the bag each time. He did this 15 times. Using his chart determine
how many of each marble could have been in the bag.
RED
YELLOW
BLUE
GREEN
8
4
1
2
Potential Solution:
The data shows that there were 15 draws of a marble from the bag. If there are 55 marbles in the
bag, then proportionally the number of draws of each color should be somewhat close to the
number of each color in the bag. If:
8/15 = x/55, then the number of red marbles was approximately 29.
4/15 = x/55, then the number of yellow marbles was approximately 15.
1/15 = x/55, then the number of blue marbles was approximately 4.
2/15 = x/55, then the number of green marbles was approximately 7.
One prediction could be 29 red, 15 yellow, 4 blue, and 7 green. This would be a good prediction
because it totals 55 marbles.
7.SP.C.6
How many times would you expect a number cube to land on a number less than three in:
a. 10 rolls
b. 30 rolls
c. 50 rolls
Solution:
The probability of rolling a number less than 3 is 2/6�
2/6 �of 10 is 3.3
2/6 �of 30 is 10
2/6 �of 50 is 16.7
Students should round appropriately.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.