Summary
Students will learn about theoretical and experimental probability through stations and will discuss the differences between them. They will also learn how to write fractions as decimals and as percentages.
Essential Question(s)
When does probability change from theoretical to experimental?
Learning Objectives
Compare theoretical probability to experimental probability by conducting repeated trials and analyzing data.
Snapshot
Engage
Students will play the card game The 21 Challenge and attempt to beat the teacher by getting as close to 21 without going over.
Explore
Students will investigate different probability situations and hypothesize the outcomes.
Explain
Students will determine the difference between experimental and theoretical probability and calculate the probability from the previous situations.
Extend
Students will develop and solve their own word problem for experimental or theoretical probability.
Evaluate
Students will analyze scenarios for experimental or theoretical probability and summarize the differences between the two types.
Materials
Lesson Slides (attached)
Station Instructions (attached; one set per class)
Probability Stations packet (attached; print two-sided and stapled; one per student)
Probability Note Catcher handout (attached; print two-sided; one per student)
Probability Scenarios packet (attached; print two-sided and stapled; one per student)
I Notice, I Wonder handout (optional; attached; print one-sided; one per student)
Gist handout (attached; print two-sided; one per student)
2 decks of cards (two cards per student)
Skittles
Pennies
Dice
Spinners
Ball
Trashcan
Chart paper
Preparation
Preparation for Engage
Remove the jokers from the decks of card and shuffle the decks together.
Preparation for Explore
Prior to the lesson print out the Station Instructions and place them in the desired locations. Use sheet protectors or sign stands for repeated use. Place the necessary materials at each station.
Engage
Use the attached Lesson Slides to present the lesson to students. Display slide 2 and introduce students to the lesson title and topic of the lesson: Experimental vs. Theoretical Probability. Use slides 3–4 to go over the essential question and objectives.
Transition to slides 5–6 and explain to students the goal and rules of the card game: The 21 Challenge. Pass out two cards to each student from a deck of cards. Instruct students to look at their cards. Deal out two cards for the teacher and reveal one of the cards to the students. Explain to students situations in which they would want to “hit,” add another card, or “stand,” stay with the cards they have. Those with a value less than 16 should hit, and those who have more than 16 can make the decision to hit or stay. Pass out an extra card to the students that choose to hit. Once all cards are passed out, have students flip over their cards to see whether or not they stayed under 21 or “bust,” went over. The first student who reaches 21 or a number higher than the teacher but still below 21 wins.
Explore
Move to slide 7 and go over the descriptions of the stations that students will be going to:
Skittles
Coin Flip
Dice Roll
Spinner
Hoop
Pass out a copy of the Probability Stations handout to each student. Explain to students that there are instructions at each station that students need to read prior to performing the activity. Inform students that they will answer questions, perform the activity for 20 trials, and tally up their results in the first table. They should not fill out anything past the first table for each station. They will return to the rest of this handout later. Inform students that once they have completed the activity they will wait to move stations until time is called.
Explain
Pass out the Probability Note Catcher to each student. Use slides 8–9 to go over how to convert a fraction to a decimal and a decimal to a percentage.
Move to slide 10 and instruct students to complete the remaining table calculations and questions on their Probability Stations handout for each station.
Move to slide 11 and go over the difference between theoretical and experimental probability. Move to slide 12. Have students reflect on the stations they visited and determine which stations represented theoretical and experimental probability. Direct students to the backside of the Probability Note Catcher and use slides 13–14 to have students practice theoretical vs. experimental probability.
Extend
Have students form groups of three or four. Pass out the Probability Scenarios to each student and a piece of chart paper for the group. Move to slide 15 and inform students that they will create a real-world problem for theoretical or experimental probability and solve for the fraction, decimal, and percentage. Tell students that their problem needs to be reviewed before they can transfer their final word problem onto the chart paper.
Transition to slide 16 and invite students to take their handout and do a Gallery Walk to try and solve each word problem. Provide a timer to keep students on task. After rotations are completed, have each group share their scenario and see if the group correctly identified and calculated each scenario.
Evaluate
Move to slide 20 and pass out the Gist handout. Introduce students to the Gist strategy. Have students decide from the various scenarios whether they are theoretical or experimental. After completing their placement, guide students to write their gist of 28 words or less to explain the reasoning for their placement using the learned vocabulary.
Resources
K20 Center. (n.d.). Gallery walk/carousel. Strategies. https://learn.k20center.ou.edu/strategy/118
K20 Center. (n.d.). Gist. Strategies. https://learn.k20center.ou.edu/strategy/3289
K20 Center. (n.d.). I notice, I wonder. Strategies. https://learn.k20center.ou.edu/strategy/180
K20 Center. (2026). Career-focused - climatologist with Monica Maddox [Video]. YouTube. https://www.youtube.com/watch?v=Am10w_ksBQg