enVision Mathematics Topic 7
7th Grade; April – May (7 weeks); 4th Quarter
Embedded Files
Topic Title(s):
Probability
Prepared Graduates:
MP4. Model with mathematics.
MP5. Use appropriate tools strategically.
Standard(s):
3. Data, Statistics, and Probability
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
7.SP.C. Statistics & Probability: Investigate chance processes and develop, use, and evaluate probability models.
Explain 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 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. (CCSS: 7.SP.C.5)
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. (CCSS: 7.SP.C.6)
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. (CCSS: 7.SP.C.7)
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. (CCSS: 7.SP.C.7.a)
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? (CCSS: 7.SP.C.7.b)
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. (CCSS: 7.SP.C.8)
Explain that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. (CCSS: 7.SP.C.8.a)
Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. (CCSS: 7.SP.C.8.b)
Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? (CCSS: 7.SP.C.8.c)
Be innovative when designing simulations to generate frequencies of compound events by using random digits, dice, coins, or other chance objects to represent the probabilities of real-world events. (Entrepreneurial Skills: Creativity/Innovation)
Use probability models and simulations to predict outcomes of real-world chance events both theoretically and experimentally. (MP4)
Use technology, manipulatives, and simulations to determine probabilities and understand chance events. (MP5)
Inquiry Questions
Since the probability of getting heads on the toss of a fair coin is 1/2, does that mean for every one hundred tosses of a coin exactly fifty of them will be heads? Why or why not?
What might a discrepancy in the predicted outcome and the actual outcome of a chance event tell us?
Coherence Connections
This expectation supports the major work of the grade.
In prior grades, students study rational numbers and operations with rational numbers.
In Grade 7, probability concepts support the major work of understanding rational numbers. This expectation connects with analyzing proportional relationships, using them to solve real-world and mathematical problems, and using random sampling to draw inferences about a population.
In high school, students understand and evaluate random processes underlying statistical experiments, understand independence and conditional probability and use them to interpret data, and use the rules of probability to compute probabilities of compound events in a uniform probability model.
Academic Vocabulary & Language Expectations:
Outcomes, probability, event, theoretical probability, experimental probability, relative frequency, sample space, probability model, compound event, simulation
Assessments:
Instructional Resources & Notes:
enVision Mathematics Topic 7
Let's Investigate! Tasks
Let's Investigate! Take a Spin (TE) (relates to Lesson 7-2)
Let's Investigate! Roll With It (TE) (relates to Lesson 7-6)
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention: None since this Unit Plan supports the major work of the grade
Coherence Map/Concept Progressions: 7.SP.C.5, 7.SP.C.6, 7.SP.C.8.b
enVision Mathematics 6-8 & Number Worlds Connections (for SVVSD Special Education teachers only)
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