Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 66781
Number Cube
Students are asked to determine probabilities based on observed outcomes and to determine if the outcomes appear to be equally likely.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, frequency, outcome, probability, equally likely
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_NumberCube_Worksheet.docx
MFAS_NumberCube_Worksheet.pdf
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Number Cube worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to determine the probability of each outcome.
Examples of Student Work at this Level
The student does not know how to represent or calculate probabilities. The student:
Divides the total number of outcomes by the number of favorable outcomes (e.g.,
).
page 1 of 3 Divides the total number of outcomes by the number of favorable outcomes and appends a percent sign to the result (e.g.,
).
Writes the frequency as the probability.
Questions Eliciting Thinking
How is probability determined?
How can you represent probability in fraction form? Should the total number of outcomes be in the numerator or denominator? Why?
If each outcome is equally likely, how should the frequencies of each outcome compare? How should the probabilities compare?
Instructional Implications
Review the meaning of probability and how it is calculated. Explain that the probability of an event is the number of outcomes favorable to that event compared to the total
number of outcomes. Use a variety of manipulatives (e.g., coins, number cubes, and spinners) to demonstrate how probabilities are calculated. Clearly describe each possible
outcome, the total number of outcomes, outcomes favorable to a particular event, and the number of outcomes favorable to that event. Guide the student to calculate
specific probabilities and to write the probabilities in multiple forms: fraction, decimal, and percent. Remind the student that the probability of an event is a number between
zero and one (or 0% and 100%). Consider implementing CPALMS Lesson Plan A Roll of the Dice (ID 34343) or Marble Mania (ID 4732), to help students understand
probability of simple events.
Making Progress
Misconception/Error
The student is unable to determine whether the outcomes appear to be equally likely.
Examples of Student Work at this Level
The student correctly records the probability of each outcome but:
Thinks the outcomes must be exactly the same to be considered equally likely.
Does not provide an explanation.
Questions Eliciting Thinking
What does likely mean? What does equally likely mean?
Are all numbers on the number cube equally likely? Are the frequencies of the outcomes close to what you expected?
Would you expect each number to occur exactly the same number of times? Why or why not?
Instructional Implications
Make explicit that equally likely does not mean that the outcomes will occur with precisely the same frequency in an experiment. Guide the student to compare the
theoretical probabilities of getting each number on a “fair” number cube to the experimental probabilities and to determine if they are reasonably close. Explain to the
student that some deviation from the theoretical probabilities will occur even when the number cube is fair, but in the long run, the frequency of each outcome should be
nearly the same. Consider implementing CPALMS Lesson Plan M & M Candy: I Want Green (ID 7021), a lesson in which theoretical and experimental probabilities are
compared.
Have the student consider an experiment in which a coin is tossed. First, have the student calculate the theoretical probability of getting a heads and a tails [e.g., P(heads)
= 0.5 and P(tails) = 0.5]. Then suggest that a coin was tossed twice and landed on heads both times. Have the student calculate the experimental probabilities [e.g.,
P(heads) = 1 and P(tails) = 0]. Ask the student to consider if this is enough evidence to conclude that the coin is not fair and that the outcomes are not equally likely.
Emphasize that if the coin were tossed many times, the number of times that heads occurs should be very close to the number of times that tails occurs (if the coin is fair).
page 2 of 3 Simulate tossing a coin using a graphing calculator. Determine the experimental probability of getting a heads after 1, 2, 3, 4, 5, 10, 50, and 100 trials. Guide the student to
observe how the probabilities get closer and closer to 0.5.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student accurately calculates the probability of each outcome in either fraction, decimal, or percent form.
The student says that outcomes appear to be equally likely because all the probabilities are between 15% and 18%, which is very close together.
Questions Eliciting Thinking
What would you expect to happen if the number cube had been tossed 600 times? Do you think the probabilities would be the same?
Instructional Implications
Ask the student to consider how different the probabilities would need to be in order for the student to confidently conclude that the number cube is not “fair.”
Consider implementing MFAS task Marble Probability (7.SP.3.7) to further assess the student’s understanding.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Number Cube worksheet
Calculator (optional)
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.7.SP.3.7:
Description
Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed
frequencies; 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.
b. 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?
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