Line Logic Teacher Guide Line Logic
Teacher Facilitation Guide
Topic
Geometric Probability (Length)
Objective
Students will calculate the probability of a point landing on a specific sub-segment of a larger line segment using the ratio of lengths.
Lesson Pacing
5 min Warm-up: Probability Line Activity
10 min Instruction: Video Analysis (Length Segment)
20 min Practice: Waiting for the Bus Worksheet
5 min Closure: Segment Snaps Exit Ticket
Materials needed
Masking Tape
Yardstick/Tape Measure
Student Worksheets
Exit Tickets
Projector for Video
Preparation: The Floor Tape Activity
Setup Instructions
Tape a 10-foot line on the floor.
Mark "0 ft" at one end and "10 ft" at the other.
Place specific markers (colored tape) at the 3-foot and 7-foot points.
This creates Segment AD (0-10) with sub-segments AB (0-3), BC (3-7), and CD (7-10).
Facilitation Notes
Have a student stand anywhere on the line at random.
Question: What is the probability they are standing in segment BC?Discussion: Transition from "counting positions" (discrete) to "measuring length" (continuous).
Video Discussion Guide
Timestamp Topic Discussion Prompts 4:02 - 5:49 Length Example Ask: "Why did we add 8, 4, and 6 to get the denominator?" Ask: "Why is 4/9 the better answer than 8/18?" (Simplification/Standard practice).
Answer Keys
Worksheet: Waiting for the Bus
1. Segment Length: 30 minutes (0 to 30)2. Success Interval: 1:10 to 1:15 (5 minutes)3. Calculation: \( \frac{5}{30} = \frac{1}{6} \)4. Percentage: ~16.7%
Exit Ticket: Segment Snaps
Problem: Point on XY (length 20) in segment LM (length 5).Calculation: \( \frac{5}{20} = \frac{1}{4} \)Decimal: 0.25 Linear Odds Slides Line Logic
Geometric Probability on Segments
Warm-up: The Human Line
Look at the tape on the floor. It represents a line segment from 0 ft to 10 ft.
"If you stand on the line at random, what are the odds you land on the yellow segment?"
1
Identify the Total Length
2
Identify the Favorable Segment
Discrete vs. Continuous
Discrete (Counting)
"How many marbles in the jar?"
P = count / total
Continuous (Measuring)
"How long is the segment?"
P = length / total
Geometric Probability
Watch the "Length" segment (4:02 - 5:49)
Length Example
Embedded media
The Calculation Logic
Length Formula
\[ P = \frac{\text{Length of Event}}{\text{Total Length}} \]
Step 1
Measure the total length of the target line.
Step 2
Measure the favorable length you want.
Step 3
Divide and simplify your final fraction.
Waiting for the Bus
"A bus arrives anytime between 1:00 and 1:30. You arrive at the stop at 1:10. What is the probability you wait less than 5 minutes ?"
Challenge:
Model this on a number line representing 30 minutes.
Segment Snaps
Complete the exit ticket on your desk before you leave.
Bus Stop Probability Worksheet Waiting for the Bus
Geometric Probability: Length Ratios
Name:
Date:
Key Formula
Geometric probability for lengths:
\[ P = \frac{\text{Length of Favorable Segment}}{\text{Total Length}} \]
The Situation
A city bus arrives at your stop randomly anytime between 1:00 PM and 1:30 PM. You arrive at the bus stop exactly at 1:10 PM.
Step 1: Create the Model
Draw a line segment that represents the full 30-minute interval (1:00 to 1:30). Label the start as "0" and the end as "30". Mark your arrival time at 1:10 (10 minutes in).
Step 2: Define the Success Zone
If you want to wait less than 5 minutes, what is the latest time the bus can arrive? Shade this interval on your model above.
Step 3: Calculate
Set up your ratio. What is the length of the favorable segment? What is the total length you could have chosen from?
What is the probability you wait less than 5 minutes?
(Show your final fraction and decimal rounded to hundredths)
Extension Challenge
Suppose you arrive late and get to the stop at 1:15 PM. Now, what is the probability that you wait more than 10 minutes?
Segment Snaps Exit Ticket Segment Snaps
Exit Ticket: Geometric Probability
Name:
Period:
Figure A: Segment AD
A B C D
AB = 6 units BC = 12 units CD = 2 units
1. A point is chosen at random on segment AD. What is the probability that the point is on segment BC?
Simplified Fraction
Decimal (Hundredths)
Percentage
2. Critical Thinking: Why can't we just count the 4 points (A, B, C, D) to find the probability? Explain in 1-2 sentences using the word continuous.
Geometry Unit 4 | Probability Logic
