options: Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.
problem_activity: Activity
In this activity, each group is assigned a situation for which they will design and perform a simulation to estimate the probability. Students will give a short presentation on the methods and results of their simulation for the class after they have designed and run the simulation. Students will need to attend to precision (MP6) as well as present arguments (MP3) for the simulation method they chose. At this stage, students have experienced a large number of simulation methods and should be able to design their own to represent the situations using the appropriate tools (MP5).
Launch
Arrange students in groups of 3. Assign each group a question slip from the blackline master. Provide access to number cubes, compasses, protractors, rulers, paper bags, colored snap cubes, scissors, and coins. Give students 15 minutes for group work followed by a whole-class discussion.
Student Facing
Your teacher will give your group a paper describing a situation.
Design a simulation that you could use to estimate a probability. Show your thinking. Organize it so it can be followed by others.
Explain how you used the simulation to answer the questions posed in the situation.
Student Response
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Activity Synthesis
Ask each group to share their situation, their method of simulating the situation, and their results. Students should explain why their chosen method works to simulate the situation they were given. In particular, all important outcomes should be represented with the same probability as stated in the situation.
If all groups that have the same situation use the same simulation method, ask for ideas from the class about alternate methods that could be used for the situation.
For reference, the computed probabilities for each situation are:
\(\frac{5}{32} \approx 0.16\)
\(\frac{1}{64} \approx 0.02\)
\(\frac{59049}{100000} \approx 0.59\)
\(\frac{2072}{3125} \approx 0.66\)
\(\frac{181}{3125} \approx 0.06\)
Representation: Internalize Comprehension.
Use color and annotations to illustrate student thinking. As students show their representations of simulations and explain their reasoning, use color and annotations to scribe their thinking on a display of each problem so that it is visible for all students.
Supports accessibility for: Visual-spatial processing; Conceptual processing
Listening, Speaking: MLR8 Discussion Supports.
To help students explain why their chosen method works, provide sentence frames such as: “This simulation was designed so that . . .” and “The simulation and the actual event have the same probabilities because . . . .” As partners are sharing, encourage the listener to press for more explanation by asking: “Can you explain why the probabilities of the simulation and actual event match?” or “Is there another simulation that could provide the same probability?” This will help students practice justifying their simulation from their interpretation of the situation.
Design Principle(s): Maximize meta-awareness; Cultivate conversation


correct_option_index: 5