Marble Mayhem Lesson Plan Marble Mayhem
9th Grade Geometry & Statistics | Compound Probability
Duration
50m
Learning Objective
Students will analyze compound events without replacement, distinguishing between ordered outcomes (Part E) and unordered outcomes (Part F) using visual tree diagrams and algebraic calculation.
Materials Needed
Marble Mayhem Slide Deck
Tree Diagram Workshop Worksheet
Colored Pencils (Red, Green, Blue, Yellow)
Probability Explained! Video
Lesson Procedure
5 min
Warm-up: The Prediction
Display the prompt: "Is it harder to pick Red then Blue, or just a Red and a Blue in any order?" Have students discuss with a partner. Encourage them to guess the ratio (e.g., "It's twice as likely to get any order").
15 min
Video & Discussion
Watch the "Probability Explained!" video. Focus specifically on 11:26 to the end. Pause after Part E and before Part F.
Key Question: Why did the narrator add two different scenarios for "Red and Blue"? How does the word "then" change the math?
20 min
Tree Diagram Workshop
Distribute the Workshop Worksheet. Students will use colored pencils to draw a partial tree diagram representing the marble jar (7R, 6G, 5B, 2Y).
Constraint: They must trace the paths for R → B and B → R to visually prove why P(Red and Blue) includes two branches.
5 min
Closure: Bridge to Algebra
Discuss: "How did the tree diagram help you see the addition of 7/76 + 7/76?" Ask students how they could represent "at least one red marble" using the same diagram.
Instructional Insights
Common Pitfall
Students often forget to decrease the total denominator to 19 for the second pick. Remind them: "One marble is in your pocket, not in the jar!"
The "OR" Rule
Reinforce that "OR" means "more ways to win." More ways to win = bigger probability = addition.
Marble Mayhem Presentation MARBLE MAYHEM
Compound Probability & The Power of Order
The Prediction
"Is it harder to pick Red then Blue, or just a Red and a Blue in any order?"
Option A
Red Pick 1 → Blue Pick 2
Option B
Red & Blue (Any Order)
Watch & Analyze
Part E vs Part F
Embedded media
Pay close attention to how "AND" transitions into "ADDITION"
The Big Reveal
Part E: "THEN"
Specific Order. Only one path on the tree diagram works.
\( P(R) \times P(B) \)
Part F: "AND"
General Outcome. Multiple paths work. We ADD them.
\( P(RB) + P(BR) \)
Tree Diagram Workshop
1
Draw the starting node (the Jar).
2
Branch out for the 1st Pick (7R, 6G, 5B, 2Y).
3
Draw the 2nd Pick branches (Careful! One marble is gone).
WORKSHOP TIME
Grab your colored pencils!
Tree Diagram Workshop Worksheet TREE DIAGRAM WORKSHOP
Compound Events: The Marble Problem
Name:
Date:
The Scenario
A jar contains 7 Red , 6 Green , 5 Blue , and 2 Yellow marbles (Total: 20). You are selecting two marbles WITHOUT replacement .
Part 1: The Tree Diagram
USE COLORED PENCILS
Draw a partial tree diagram starting from the center left. Only draw the branches necessary to find the probability of selecting a Red and a Blue marble in any order.
Pick 1
Pick 2
Outcome & Probability
Part 2: Algebraic Verification
Scenario A: Red THEN Blue
__ / __ × __ / __ = ______
Scenario B: Blue THEN Red
__ / __ × __ / __ = ______
Final Probability: P(Red AND Blue)
Combine your scenarios above to find the total probability for picking one of each color in any order.
Tree Diagram Workshop © Marble Mayhem Lesson Series
Workshop Master Key MASTER ANSWER KEY
Tree Diagram Workshop: Marble Problem
TEACHER USE ONLY
Part 1: Tree Diagram Visualization
7/20 (Red)
5/19 (Blue)
→ RB (7/76)
5/20 (Blue)
7/19 (Red)
→ BR (7/76)
What to look for:
Denominator Shift: Check if students changed Pick 2 denominators to 19 .Branch Colors: Use of red and blue pencils to distinguish the two paths.Path Sum: Identification that there are two valid paths (RB and BR).
Part 2: Algebraic Verification
Scenario A: Red then Blue
\[ \frac{7}{20} \times \frac{5}{19} = \frac{35}{380} = \frac{7}{76} \]
Approximately 9.2%
Scenario B: Blue then Red
\[ \frac{5}{20} \times \frac{7}{19} = \frac{35}{380} = \frac{7}{76} \]
Approximately 9.2%
Final Total Probability
Add both branches because order does not matter:
\[ \frac{7}{76} + \frac{7}{76} = \frac{14}{76} = \mathbf{\frac{7}{38}} \]
\( \approx 18.4\% \)
Discussion Prompt Guide
The "Denominator Trap": Ask "Why is it /19 and not /20?" Ensure they articulate that one marble has been physically removed from the jar.
The Multiplication vs Addition: Ask "Why did we multiply horizontally but add vertically?" Multiplication = AND (Step 1 then Step 2). Addition = OR (Path 1 or Path 2).
