Mathematics 7
Items to Support Formative Assessment
Unit 5: Statistics and Probability
7.SP.C.7 Develop a probability model and use it to find probabilities of events; compare
probabilities from a model to observed frequencies; and if the agreement is not good,
explain possible sources of the discrepancy.
a. Develop a uniform probability model by assigning equal probability to all outcomes, and
use the model to determine probabilities of events. For example, if a student is selected at
random from a class, find the probability that Jane will be selected and the probability that
a girl will be selected.
7.SP.C.7a
a. Create a uniform probability model (a model with equally likely outcomes) using the empty
spinner below.
b. Write a statement of probability for the spinner to land on one section of your spinner.
Possible Solution:
P(2)= 1/8
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7.SP.C.7a
Miss Sparks asks her students to create a uniform probability model using 10 playing cards.
What must be true about the cards? Create a possible example using the cards and describe how
those characteristics demonstrate such a model.
Solution:
All of the cards should have an equal chance of being chosen. They all need to be different or if
some of them are the same, then the number of items in each category must be the same.
Potential card arrangement:
This is an example of cards that have uniform probability. There are five items in the sample
space and two of each item.
P(A) = P(B) = P(C) = P(D) = P(E) = 2/10 = ⅕
7.SP.C.7a
A typical Bingo game utilizes the numbers 1 through 75. The five columns of the card are
labeled 'B', 'I', 'N', 'G', and 'O' from left to right. The center space is usually marked "Free" or
"Free Space", and is considered automatically filled. The range of printed numbers that can
appear on the card is normally restricted by column, with the 'B' column only containing
numbers between 1 and 15 inclusive, the 'I' column containing only 16 through 30, 'N' containing
31 through 45, 'G' containing 46 through 60, and 'O' containing 61 through 75.
(from http://en.wikipedia.org/wiki/Bingo_(U.S.)
Belinda’s grandmother takes her to Bingo at Town Hall every other Friday. Last Friday she got
the Bingo card below.
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Determine which of the following statements are true. Select all that apply
There is an equal chance of each number being called
There is an equal chance of getting BINGO diagonally, vertically, or horizontally
The P(12) < P(41)
The probability of BINGO in the “B” column is equal to the probability of the “O”
column
Solution:
There is an equal chance of each number being called. There is not an equal chance however of
getting BINGO diagonally, vertically, or horizontally because of there are only four numbers that
they need for diagonal, and if they get BINGO through the Free Space then the likelihood is
much greater. The P(12) is equal to P(41). The probability of a “B” Bingo is equivalent to the
probability of an “O” Bingo
7.SP.C.7a Group Activity
There are 20 cans of soda in the cooler at the end of the year picnic.
a. Make a list of the soda that could be in the cooler if there is an equal probability of each type
of can being chosen as you reach for one.
Fill in the blanks for the question below and determine the probability.
b. You reach in for a soda without looking in the cooler. Find the P (_____________).
c. Your friend Alex gets a soda after you do. What is the P(_______________)
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Possible Solution:
a. 5 Coke, 5 Diet Coke, 5 Dr. Pepper, 5 Sprite
5
1
b. You reach in for a soda. Find the P(Sprite)= 20or 4
5
c. Your friend Alex gets a drink after you do. What is the P(Diet Coke)= 19
7.SP.C.7a
In the game of Clue, you try to discover who committed a crime, with what weapon, and in which
room.
Suspects
Professor Plum, Mrs. Peacock, Colonel Mustard, Mrs. White,
Mr. Green, Ms. Scarlett
Weapons wrench, lead pipe, candlestick, knife, rope, revolver
Rooms
ballroom, hall, lounge, dining room, kitchen, conservatory,
billiard room, library, study
1. How many different combinations of suspect, weapon, and room are there?
2. What is the probability Mrs. Peacock committed the crime?
3. What is the probability Colonel Mustard committed the crime with the wrench?
4. What is the probability the crime was committed in the kitchen with the candlestick?
5. What is the probability the crime was committed in the lounge or the ballroom?
6. What is the probability Ms. Scarlett committed the crime with the lead pipe in the billiard
room?
Solution:
1. There are 324 different combinations. Students can use the counting principle to calculate
(6)(6)(9) or they may interpret their answer from #5 to mean that every combination has a 1/324
chance of occurring so there must be 324 possibilities.
2. ⅙
3.
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4.
5. 2/9
6.
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7.SP.C.7 Develop a probability model and use it to find probabilities of events; compare
probabilities from a model to observed frequencies; and if the agreement is not good,
explain possible sources of the discrepancy.
7b. Develop a probability model (which may not be uniform) by observing frequencies in
data generated from a chance process. For example, find the approximate probability that
a spinning penny will land heads up or that a tossed paper cup will land open-end down.
Do the outcomes for the spinning penny appear to be equally likely based on the observed
frequencies?
7.NS.C.7b
Jonathan, Mariana, and Bruce each rolled one number cube and recorded the results in the charts
below.
Select all the statements below that are valid given the results from the trials done by the three
students.
 Jonathan’s results do not match the predicted because his number cube might
have more twos on it.
 Marianna’s results differ greatly from the theoretical probability because she did
too few trials.
 Bruce’s observed frequencies are all very similar because there’s a 50-50 chance
of landing on each side of the number cube.
 Combining all three students’ results would yield outcomes much closer to the
predicted probability.
 The frequency of rolling a number should equal 6 because there are six sides on
the number cube.
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Solution:
Jonathan’s results do not match the predicted because his number cube might
have more twos on it.
Marianna’s results differ greatly from the theoretical probability because she
did too few trials.
Bruce’s observed frequencies are all very similar because there’s a 50-50
chance of landing on each side of the number cube.
Combining all three students’ results would yield outcomes much closer to the
predicted probability.
The frequency of rolling a number should equal 6 because there are six sides
on the number cube.
7.SP.C.7b
Jackie spun a spinner 10 times and recorded the following results:
Blue, Red, Blue, Blue, Green, Red, Yellow, Yellow, Blue, Red
Which of the two spinners below do you think she used? Explain your answer.
Solution:
If Jackie’s results are recorded in percents, blue was spun 40% of the time, red: 30%, green: 10%,
and yellow: 20%.
Spinner B’s sections are divided in a way that represents the results of the data the best.
Although spinner A could possibly give the same results, spinner B is a more likely choice.
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7.SP.C.7b: Partner Activity: Are you psychic?
**Option: Give each pair a deck of cards. Have students use the Jack, Queen, King and
Ace cards giving them a total of 16 to work with**
Each set of partners should receive a set of 40 cards. (4 different shapes, 10 of each card) For
example:
The students should be aware of what the cards look like.
Directions for students: Shuffle the set of cards and sit back to back with your partner. Pick a
card and concentrate on it. Have your partner guess the shape on the card. Record whether their
answer is correct or incorrect in the chart, but do not tell your partner whether they are correct or
incorrect. Do this for each card in the deck. Then switch places and complete the activity again.
Tally
Total
Right Answer
Wrong Answer
Using the chart you filled out, answer the questions below:
1. What is the probability of guessing the correct card?
2. Based on the chart, what was the probability of your partner guessing the correct card?
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3. Do you think it’s valid if your partner claims to be psychic? Justify your answer
mathematically.
4. If this experiment was repeated for 100 cards, how many cards do you predict your partner
would get correct?
Solution:
1. ¼ = 25%
2. Answers may vary: # of correct responses/40
3. Answers may vary. If the student answered more than 25% correctly, they did better than the
theoretical probability would suggest.
4. Answer from #2 as a decimal x 100
7.SP.C.7b Item
Flip Your Lid
Your homework was to bring in a lid from home. You brought in a top to a water bottle. The
activity had you toss the lid in the air and record how it landed given 20 trials. Below are your
results.
Result
Frequency
Lid landing right side up
6
Lid landing upside down
14
Lid landing on its side
0
a. What is the experimental probability of each outcome?
b. Based on your experiment, does this model show equally likely outcomes? How do you
know?
c. Do you think the other students in your class had similar results? Explain.
Possible Solutions:
a.
Lid landing right side up
6/20 = 3/10= 0.3= 30%
Lid landing upside down
14/20=7/10= 0.7= 70%
Lid landing on its side
0
b. I don’t think the outcomes are equally likely, because the outcomes don’t have probabilities
that are close to one another. The theoretical probability would be around 33% for each outcome.
While one is 30%, the other two are significantly lower and higher.
c. I think it depends on what the other students used for the experiment. If they used a lid that
doesn’t have even weight, I think their results would be similar to mine.
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