What Are My Chances

This is URL provides an activity that instructs students to conduct five experiments through stations to compare theoretical and experimental probability. Hands- on activity that allows students to rotate to different stations. Students find probability, build ratios and convert ratios to decimals and fractions.

Standards & Objectives

Academic standards
CCSS.Math.Content.6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams,...
CCSS.Math.Content.7.RP.A.3
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and...
CCSS.Math.Content.7.SP.C.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...
CCSS.Math.Content.7.SP.C.6
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative...
CCSS.Math.Content.7.SP.C.7
Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the...
CCSS.Math.Content.7.SP.C.8
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
GLE 0606.2.3
Understand and use ratios, rates and percents.
GLE 0606.3.6
Understand and use the Cartesian coordinate system.
GLE 0606.5.1
Understand the meaning of probability and how it is expressed.
GLE 0706.2.4
Use ratios, rates and percents to solve single- and multi-step problems in various contexts.
GLE 0706.4.2
Apply proportionality to converting among different units of measurements to solve problems involving rates such as motion at a constant speed.
GLE 0706.4.4
Understand and use ratios, derived quantities, and indirect measurements.
GLE 0706.5.5
Understand and apply basic concepts of probability.
GLE 0806.5.1
Explore probabilities for compound, independent and/or dependent events.
SPI 0606.2.6
Solve problems involving ratios, rates and percents.
SPI 0606.3.9
Graph ordered pairs of integers in all four quadrants of the Cartesian coordinate system.
SPI 0606.5.1
Determine the theoretical probability of simple and compound events in familiar contexts.
SPI 0706.2.6
Express the ratio between two quantities as a percent, and a percent as a ratio or fraction.
SPI 0706.2.7
Use ratios and proportions to solve problems.
SPI 0706.5.4
Use theoretical probability to make predictions.
SPI 0806.1.1
Solve problems involving rate/time/distance (i.e., d = rt).
SPI 0806.1.3
Calculates rates involving cost per unit to determine the best buy.
SPI 0806.4.4
Convert between and within the U.S. Customary System and the metric system.
SPI 0806.5.1
Calculate probabilities of events for simple experiments with equally probable outcomes.
SPI 0806.5.2
Use a variety of methods to compute probabilities for compound events (e.g., multiplication, organized lists, tree diagrams, area models).
TSS.Math.6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems.
TSS.Math.7.RP.A.3
Use proportional relationships to solve multi-step ratio and percent problems.
TSS.Math.7.SP.C.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...
TSS.Math.7.SP.C.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...
TSS.Math.7.SP.C.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...
TSS.Math.7.SP.D.8
Summarize numerical data sets in relation to their context.
 
Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.
 
Learning objectives: 

Students will:

  • Use probabilities to predict trends.
  • Interpret the relationship between experimental and theoretical probabilities.
  • Explore the Law of Large Numbers.
Essential and guiding questions: 
  • Is there a connection between theoretical and experimental probability?
  • How could you explain the two type of probability to someone who hasnever heard of them?
  • Why is it useful to know about probabilities?

Lesson Variations

Blooms taxonomy level: 
Applying
Extension suggestions: 
  • Ask students to make a prediction table as to what they think the results will be through 30 trials of a coin toss. Have them number 1 through 30 on a piece of paper and record H or T for what they think will come up for each trial. Most students will end with experimental probabilities around 1/2 and will not put 6 or 7 heads in a row through the table, even though it is possible that the coin will land heads up for 7 in a row. Then, have students run 30-trial experiments and compare their predictions to actual trials. Discuss the word random and what it really means. Key question: If 7 heads come up in a row, does that mean tails is due?
  • Introduce students to the Monte Carlo problem.
  • Introduce the term equally likely events to students. Give them the example of tossing a die. The chances of rolling evens or odds are equally likely. Both have a 50% chance of happening. The probability of rolling a number less than 2, equal to 2, or greater than 2 are not equally likely. Rolling a number greater than 2 is much more likely. Read a list of events to students and have them respond whether each has equally likely outcomes. You could also have them place pennies on a scale between 0 and 100% where they think each of the probabilities will be. If the coins are in the same spot, the outcomes are equally likely. For example if you ask the chance of it raining today, students should place one coin to represent the chance of it raining and another to represent the chance of it not raining. If both coins are on 50%, then the events are equally likely. You may also need to discuss with students that the probabilities have to add up to 100%.
  • Move on to the next lesson, Probably Graphing.

Helpful Hints

Materials:

  • Dice
  • Pennies or other coins
  • Several decks of Cards
  • Calculators
  • What Are My Chances? Activity Sheet 
  • Computers or tablets with internet connection (optional)

References

Contributors: