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# Math 7 Experimental vs. Theoretical Probability Lab

Product Description
Probability Lab:

Package Includes:
Teacher Instructions/ Standards the Lab Targets.
Student Copy of the Lab.
Excel Spreadsheet Template to Input the Data (shown in the thumbnails)

This is a lab I created for 7th grade Math students aligned to the common core probability standards. The students will flip coins and roll dice in order to determine various experimental and theoretical probabilities. The following day, the class will pool together their results using an Excel spreadsheet that auto calculates the data (due to the formulas I have input) as you type it in. There are enough columns on the spreadsheet for up to 12 different groups.

Pre-requisite Knowledge:
•Ability to convert between different forms of numbers (ie. decimals, fractions, percents)
•Prior knowledge of computing both experimental and theoretical probability.
•The ability to compute the probability of compound events. This can be through the use of probability rules, a factor tree, or sample space.

Materials:
•2 Number Cubes (Dice) per group. However you can give them more so that they can be faster with the rolling process. Up to your discretion.
•1 coin (penny, nickel, etc.). However you can give them more so that they can be faster with the flipping process. Up to your discretion.
•Computer with Microsoft Excel. (Hopefully a projector or Promethean/ SMART Board to display results, add ease to copying results)

Directions (Suggested):

Day 1:
1.Give each student (or group) a probability lab.
2.Give a brief explanation at the beginning of the lesson that for activity 2, they can use probability rules if they know them or draw a factor tree or sample space to figure out the theoretical probability.
3.Have the students spend the day recording the data. I tell them to fill out the tables the first day because they can answer the questions either day. This makes it much easier, in that we can fill out the attached excel sheet at the beginning of class day two. If they finished filling out both tables, I recommend they start answering the questions afterwards.

Day 2:
1.Have the group's report their data to you and you can record them into the pre-made excel sheet (which has formulas I created already set to compute the "Total Flips" and Percentages, decimals, etc.). All you have to type in is what each group had at each number of flips/ rolls, along with the number of groups for each activity in the box that says "Type # of Groups Here". The sheet will start to fill itself in based on the formulas I have created. I included a sample filled out one so that you can see as you change numbers, the sheet itself adapts.
2.Have Students Record Data on their chart.
3.Give them the rest of the class to answer the questions they still need along with the discussion questions. I usually count this a s a quiz/ project grade.

•7.NS.2c: Convert a rational number to a decimal using long division;
•7.SP.2: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
•7.SP.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 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
•7.SP.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.7: 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?
•7.SP.8: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
a. Understand 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.
b. 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.
c. 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?

Total Pages
N/A
Does not apply
Teaching Duration
2 days
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