Probability Explorations

Overview

This 30-minute blended learning lesson engages 7th grade students in hands-on and discussion-based activities that build conceptual understanding of probability. The lesson follows the International Baccalaureate Middle Years Programme (MYP) Mathematics framework, emphasizing inquiry, communication, and reflection aligned with TEKS readiness and supporting standards. Students will collaboratively explore simple and compound events through simulations, tree diagrams, and data analysis to connect theoretical and experimental probability.

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IB MYP Objectives Addressed

• Criterion B: Investigating Patterns
  • Apply mathematical problem-solving to explore concepts of probability, make predictions, and analyze outcomes.
• Criterion C: Communicating
  • Use appropriate mathematical language and representations such as tree diagrams and sample spaces to explain probability reasoning.
• Criterion D: Applying Mathematics in Real-Life Contexts
  • Use probability theory to make informed decisions and justify predictions based on data and probability models.

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Learning Objectives

By the end of this lesson, students will be able to:

• Represent sample spaces for simple and compound events using lists and tree diagrams (TEKS 7.6A).
• Use simulations to model simple and compound probability events and compare experimental with theoretical probabilities (TEKS 7.6B, 7.7I).
• Make qualitative and quantitative predictions and compare results from simulations and theoretical calculations (TEKS 7.6H, 7.6C, 7.6D).
• Calculate the probability of events and their complements and articulate their relationship (TEKS 7.6E).
• Use data to make inferences about larger populations (TEKS 7.6F).

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Materials Needed

• Decks of playing cards (one per pair)
• Coins (one per pair)
• Dice (one per pair)
• Whiteboards/markers or paper
• Tree diagram handouts
• Laptops/tablets (optional) with probability simulation apps or websites
• Timer or stopwatch

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Lesson Timing & Activities

Time	Activity Description	Teaching Script & Tips
0-5 min	Engage: Think-Pair-Share Prompt: "What is probability? Can it be predicted? How do we know if it’s right?" - Students think individually for 30 sec. - Turn and talk to neighbor for 2 mins. - Share some quick answers aloud.	“Probability tells us how likely something will happen. Today, we test if predictions match what actually happens.” Use this to activate prior knowledge.
5-10 min	Explore: Simulation Stations (Simple Events) - Pairs simulate flipping a coin 20 times, rolling a die 20 times. Record outcomes. - Calculate experimental probability of getting heads, rolling a 4, etc. - Draw simple sample spaces as lists on whiteboards.	“As you do your trials, think: How does your experimental probability compare to what you expect theoretically?” Circulate, ask guiding questions. Encourage accuracy in recording.
10-17 min	Explain: Tree Diagrams & Compound Events - Introduce tree diagrams for flipping two coins or rolling two dice. - Model building the tree diagram step-by-step on the board. - Students create tree diagrams for own compound events on handouts. - Turn and talk: Share how the tree diagram helps list all possible outcomes.	“Tree diagrams show us every possible outcome systematically – no skips!” Emphasize organizing skill and link to sample space size.
17-23 min	Elaborate: Theoretical vs. Experimental Probability - Use students’ prior recorded data to calculate experimental probability of compound events. - Calculate theoretical probabilities using tree diagrams. - Think-Pair-Share: Discuss why probabilities may differ and how more trials reduce the differences.	“Let’s compare what actually happened to what we predict.” Discuss causes of variation.
23-27 min	Evaluate: Probability of Event & Complement - Pose problem: “If probability of rolling a 4 on one die is 1/6, what is the probability of NOT rolling a 4?” - Students write answer, explain relationship between event and complement, share aloud. - Extension: Discuss how this helps check probability calculations.	“Events and their complements always add to 1 or 100%. This is a quick way to verify answers.”
27-30 min	Reflect & Exit Ticket - Students write a brief exit ticket: “How can simulations and tree diagrams help us make better predictions in real life?” - Collect answers for assessment and reflection.	“Think about where probability shows up outside class — weather, games, decisions.”

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Assessment

• Formative: Observation and questioning during turn and talks and activities.
• Exit Ticket: Evaluation on ability to reflect on applications and mathematical representations.
• Student Work Samples: Tree diagrams, probability calculations compared with experimental data.

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Differentiation and Engagement Tips

• Provide partially completed tree diagrams for students needing support.
• Challenge honors students to create probability models with 3-stage events (e.g., flipping 3 coins).
• Incorporate technology by letting students use online probability simulators during Explore phase if available.
• Use humor and relatable examples (flipping coins, rolling dice, sports stats) to maintain engagement.

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Reflection for Teacher

• Did students effectively model sample spaces with tree diagrams?
• Were misconceptions about complement probability identified and addressed?
• How did paired discussions support conceptual understanding?
• What additional supports or extensions are needed for future lessons?

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This lesson honours the IB MYP emphasis on inquiry and conceptual thinking within the framework of TEKS standards, giving students a balanced experience between theoretical mathematical structures and real-world data applications in probability.