Odds Lab Teacher Guide ODDS AND DATA LAB
Facilitator Guide
Grade 7 MATH
Lesson Objectives
TEKS 7.6A-I: Represent sample spaces, compare experimental and theoretical probability, and make predictions using proportional reasoning.TEKS 7.12A: Compare two groups of numeric data using dot plots, box plots, and histograms.STAAR Focus: Master Reporting Category 4 questions involving data analysis and probability predictions.
Lab Materials
• Standard 6-sided dice (1 per pair)
• Standard deck of cards (1 per group)
• 4-color spinners (can be printed)
• Coins for flipping
• Colored paper clips (for spinners)
Lab Rotations: Hands-On Simulations
Station 1: The Die is Cast (Theoretical vs. Experimental)
Students roll a die 30 times. They compare the theoretical probability of rolling a prime number (2, 3, 5) which is \(3/6\) or \(1/2\), to their experimental results .
Facilitator Note:
Encourage students to combine class data to show how experimental probability approaches theoretical probability as the number of trials increases (Law of Large Numbers).
Station 2: Deck of Dreams (Sample Space)
Using a standard deck of 52 cards, students calculate the probability of picking a "Red Queen" or a "Heart." They must account for overlapping events (the Queen of Hearts).
Key Question:
"If you pick 100 times with replacement, how many times would you predict a Spade?" (Use \(x/100 = 13/52\)).
Master Data Displays
Box Plot Reminders
• Five-Number Summary: Min, Q1, Median, Q3, Max.
• IQR: Distance between Q3 and Q1.
• Interpretation: Each section represents exactly 25% of the data, regardless of length.
Histogram Reminders
• Intervals: Must be equal size (e.g., 0-9, 10-19).
• Frequency: Height represents count.
• STAAR Tip: Students often confuse histograms with bar graphs. Remind them histograms show ranges, not categories.
STAAR Readiness Checklist
Ensure students can set up proportions for predictions: \(\frac{\text{part}}{\text{total}} = \frac{x}{\text{new total}}\).
Practice identifying complementary events (e.g., "Not rolling a 4").
Differentiate between with and without replacement in compound events.
Analyze skewness in data displays (Left-skewed vs. Right-skewed).
Suggested Pacing (90 Min Block)
Time Activity Material 00-15 Direct Instruction: Probability Basics Odds Lab Slides 15-45 Hands-On Simulations (Rotations) Simulations Worksheet 45-70 Data Analysis & Display Creation Data Displays Worksheet 70-90 STAAR Showdown Quiz & Review Showdown Quiz
Odds Lab Simulations Worksheet ODDS LAB: SIMULATIONS
Experimental vs. Theoretical Probability
Name:
Date:
Station 1: Rolling Odds
Theoretical Probability:
What is the probability of rolling a prime number (2, 3, or 5) on a standard 6-sided die?
P(Prime) =
Trial Directions:
Roll the die 30 times . Record each prime number roll in the tally chart below.
Category Tally (30 rolls) Experimental Frequency Prime Number (2, 3, 5) Not Prime (1, 4, 6)
Compare: Was your experimental result higher, lower, or equal to the theoretical probability? Explain.
Station 2: The Red Suit Draw
Theoretical Probability:
In a deck of 52 cards, what is the probability of drawing a Red Suit (Hearts or Diamonds)?
P(Red) =
Trial Directions:
Shuffle the deck. Draw a card, record it, and replace it . Repeat 20 times .
Category Tally (20 draws) Experimental Frequency Red Card Black Card
Prediction: Based on your experimental results, how many red cards would you expect to draw in 100 trials? Show your proportion.
Station 3: Spin to Win
Spin the 4-color spinner 40 times . Compare the experimental probability of landing on Blue to the theoretical probability.
Theoretical P(Blue)
Experimental P(Blue)
If you land on Blue 12 times out of 40, is that better or worse than theoretical? Why?
Odds Data Displays Worksheet LAB DATA DISPLAYS
Mastering Box Plots & Histograms
Name:
Mission 1: The Box Plot Blueprint
Data Set: Lab Reaction Times (Seconds)
0.42 0.45 0.48 0.50 0.52 0.55 0.58 0.60 0.62 0.65 0.70 0.85
Minimum
Q1
Median
Q3
Maximum
Construct the Box Plot below using the 5-number summary above:
0.40
0.50
0.60
0.70
0.85
1. What is the Interquartile Range (IQR) of this data?
2. What percentage of the lab trials were between 0.50s and 0.62s?
Mission 2: Histogram Heart Rate
The histogram below shows the resting heart rates (BPM) of 40 lab participants. Analyze the distribution to answer the questions.
4
12
16
6
2
60-69
70-79
80-89
90-99
100-109
Heart Rate (BPM)
3. In which interval does the median heart rate fall?
4. How many participants had a heart rate of at least 80 BPM?
Mission 3: Global Predictions
If this lab was expanded to include 500 participants , based on the histogram data above, how many would you predict to have a heart rate between 70-89 BPM ? Show your proportional reasoning.
Odds Lab STAAR Quiz ODDS LAB: STAAR SHOWDOWN
Grade 7 Probability & Statistics Assessment
Student Name:
1
A bag contains 5 red marbles, 8 blue marbles, and 7 green marbles. If a marble is chosen at random, replaced, and the process is repeated 120 times, how many times would you predict a red marble will be chosen?
A 30
B 48
C 25
D 42
2
The box plots below show the scores of two different math classes on a recent test.
Class A
Class B
60708090100
Which statement is best supported by the information in the box plots?
F The median score for Class A is greater than the median score for Class B.
G The range of scores for Class A is less than the range of scores for Class B.
H The interquartile range (IQR) for Class B is greater than the IQR for Class A.
J The maximum score for Class A is equal to the maximum score for Class B.
3
A scientist flipped a coin 50 times. The coin landed on "Heads" 22 times. Which statement correctly compares the theoretical probability of landing on "Heads" to the experimental probability in this lab?
A The theoretical probability is \(1/2\), which is less than the experimental probability of \(11/25\).
B The theoretical probability is \(1/2\), which is greater than the experimental probability of \(11/25\).
C The theoretical probability is \(22/50\), which is equal to the experimental probability.
D The theoretical probability is \(1/2\), which is equal to the experimental probability of \(25/50\).
4
The histogram shows the number of hours students spent studying for a final exam.
5
15
20
10
0-2 hrs 3-5 hrs 6-8 hrs 9-11 hrs
Based on the histogram, what is the total number of students who studied for 6 or more hours?
F 20
G 30
H 50
J 10
5
A restaurant offers a lunch special with a choice of 1 sandwich (Turkey, Ham, Veggie), 1 side (Chips, Fruit), and 1 drink (Water, Juice). Which list represents the sample space for all possible meal combinations?
A T-C-W, T-C-J, T-F-W, T-F-J, H-C-W, H-C-J, H-F-W, H-F-J, V-C-W, V-C-J, V-F-W, V-F-J
B T-C-W, T-F-J, H-C-W, H-F-J, V-C-W, V-F-J
C Turkey, Ham, Veggie, Chips, Fruit, Water, Juice
D T-C, T-F, H-C, H-F, V-C, V-F, W-J
6
A random survey of 60 seventh-graders found that 15 students preferred soccer as their favorite sport. Based on these results, how many students would you expect to prefer soccer in a school with 400 seventh-graders?
Odds Lab Answer Key ODDS LAB: ANSWER KEYS
Teacher Resource & Assessment Guide
Internal Use Only
Simulations Worksheet Key
Station 1: Dice
Theoretical P(Prime): \(3/6\) or \(1/2\) or \(50\%\)
Experimental results will vary by student, but should be near 15/30.
Station 2: Cards
Theoretical P(Red): \(26/52\) or \(1/2\) or \(50\%\)
Prediction (100 trials): If experimental was \(12/20\), then \(x = 60\).
Data Displays Worksheet Key
Mission 1: Box Plot (Reaction Times)
Sorted: 0.42, 0.45, 0.48, 0.50, 0.52, 0.55, 0.58, 0.60, 0.62, 0.65, 0.70, 0.85
Min: 0.42Q1: 0.49 (avg of 0.48/0.50)Med: 0.565 (avg of 0.55/0.58)Q3: 0.635 (avg of 0.62/0.65)Max: 0.85IQR: 0.145
Mission 2 & 3: Histogram & Prediction
Q3 (Median Interval): 80-89 BPM (Middle person is 20th/21st; 4+12 = 16, so median is in 80-89 range).
Q4 (At least 80): 16 + 6 + 2 = 24 participants.
Mission 3 Prediction: 70-89 BPM = 12 + 16 = 28/40. Proportion: \(\frac{28}{40} = \frac{x}{500}\). x = 350 participants.
STAAR Showdown Quiz Key
# Answer TEKS Rationale 1 A 7.6I \(P(\text{Red}) = 5/20 = 1/4\). \(\frac{1}{4} = \frac{x}{120}\). \(x = 30\). 2 H 7.12A IQR for B (80 to 95 = 15) is greater than Class A (70 to 85 = 15 - Wait, visual shows B is slightly wider). Correct: H. 3 B 7.6E Theo: \(25/50\). Exp: \(22/50\). Theo is greater. 4 G 7.12A Sum of bars for 6-8 hrs (20) and 9-11 hrs (10) = 30 students. 5 A 7.6A Total combinations = \(3 \times 2 \times 2 = 12\). Option A lists all 12. 6 F 7.6I \(\frac{15}{60} = \frac{1}{4}\). \(\frac{1}{4} \times 400 = 100\). 7 A 7.12A
Odds Lab Slides Final ODDS & DATA LAB
Grade 7 Probability & Statistics
Probability
Data Displays
Mission Goals
01
Crack the Code
Compare theoretical and experimental probability using hands-on simulations.
02
Predict the Future
Use proportional reasoning to make accurate predictions based on data sets.
03
Visualize Results
Master box plots, dot plots, and histograms for the STAAR "Showdown."
TEKS Focus
7.6A-I & 7.12A: Data Analysis & Personal Financial Literacy
Theory vs. Reality
Theoretical
What SHOULD happen in a perfect world.
\[ P(E) = \frac{\text{favorable outcomes}}{\text{total outcomes}} \]
Experimental
What ACTUALLY happens during trials.
\[ P(E) = \frac{\text{actual occurrences}}{\text{total trials}} \]
Pro-Tip: More trials lead to results closer to theory!
Making Predictions
We use proportions to predict outcomes for larger sample sizes.
Set up your ratio:
\[ \frac{\text{Prob}}{1} = \frac{x}{\text{New Total}} \]
Lab Case Study:
"If you flip Heads 12 times out of 20, how many Heads in 500 flips?"
\[ \frac{12}{20} = \frac{x}{500} \]
Answer: x = 300
Box Plot X-Ray
MIN
Smallest
Q1
Lower Quartile
MEDIAN
Middle
Q3
Upper Quartile
MAX
Largest
Each section holds exactly 25% of the data!
Mastering Histograms
The Rulebook
Shows ranges , not categories.
Bars touch (continuous data).
Height = Frequency (count).
STAAR Strategy:
Watch Out!
Histograms show distributions . To find the median, find the middle data point across all frequency bars!
LAB STATIONS OPEN
Grab your lab coat and worksheet. Complete each station's trial. Data is the heart of the lab—record every result!
30 Minutes
Work in Pairs
