⭐ DATA DETECTIVE XP
☆☆☆ 0 / 100
🏅
GRADE 6
MATH
📊 Data Detectives: Case File #3
THE 5K
MYSTERY
Who ran the fastest? The histogram knows...
MAYA 📊 DATA DATA-BOT COACH
🔍
Mission Briefing
Solve the data mystery using histograms and frequency tables!
⭐
Learning Targets
Display data in a histogram · Describe data by shape · Compare to dot plots
CH.1
🏃 The Race Begins — Setting the Scene
City Park — Race Day Morning
Coach Rivera Fifty middle school students just finished a 5K race. I recorded everyone's pace — the time to run one kilometer.
The raw data (first 20 runners):
RunnerPace (min)RunnerPace (min)
15.1114.8
24.7125.3
35.2135.0
46.1144.6
55.4155.1
65.0165.2
74.9176.3
85.5185.0
95.1194.5
105.6205.3
...and 30 more runners!
Be Curious!
Maya Whoa... 50 numbers! How are we supposed to make sense of all this? 🤔
Data-Bot BEEP BOOP! I notice the numbers are between 4 and 7. I wonder... what's the most common time range?
"When data sets get large, we need a smarter way to organize them..."
📚 Key Words — Hover to Reveal Definitions!
PACE
noun
hover to see →
INTERVAL
noun
hover to see →
FREQUENCY
noun
hover to see →
HISTOGRAM
noun
hover to see →
CH.2
📦 Operation: Group the Data!
CLICK!
Data-Bot We group the data into intervals! Each interval covers 0.5 minutes. Let me show you the rules...
⚠️ INTERVAL RULES:
✅ All intervals are the same size
✅ Intervals never overlap
✅ Every data value fits in exactly one interval
✅ Intervals are continuous — no gaps!
Which interval does 5.2 minutes belong in?
A 4.5 – 4.9 minutes
B 4.5 – 5.0 minutes (overlapping!)
C 5.0 – 5.4 minutes ✓
D 5.5 – 5.9 minutes
Think about it: Where else have you seen the word "interval"?
🗂️ Building the Frequency Table
Coach Rivera I counted all 50 runners. Here's what I found — but some cells are missing! Can you complete the table?
Interval (min)TallyFrequency
4.0 – 4.4 ||
4.5 – 4.9 |||| |||| ||| 13
5.0 – 5.4 |||| |||| |||| |||| 20
5.5 – 5.9 |||| |||| ||
6.0 – 6.4 ||||
TOTAL 50
CH.3
📊 The Histogram Rises!
Data-Bot Explains
Data-Bot A histogram is like a bar graph, BUT the bars touch — because the intervals are continuous. No gaps between bars!
HISTOGRAM vs DOT PLOT
HISTOGRAM ✅
• Large data sets
• Shows intervals
• Bars always touch
• Great for shape!
DOT PLOT
• Small data sets
• Shows every value
• Individual dots
• Can get crowded
🔨 Build the Histogram! Click bars to set heights.
Use your frequency table! Click each bar to set it to the correct height.
2520151050
Pace (minutes per km)
🔍 Reading the Histogram — Connecting Representations!
RUNNING PACE HISTOGRAM
0 5 10 15 20 4.0–4.4 4.5–4.9 5.0–5.4 5.5–5.9 6.0–6.4 TALLEST! Pace (minutes/km) Frequency
Answer these questions about the histogram!
Q1: Which interval has the tallest bar?
A 4.5–4.9 minutes
B 5.0–5.4 minutes
C 4.0–4.4 minutes
Q2: How many students ran at a pace of 5.0–5.4 minutes? students
Q3: In context: What does the tallest bar tell us about the runners?
CH.4
🌱 New Case: The Growing Plants!
Science Lab — 2 Weeks Later
Maya New mission! 25 students grew bean plants. They measured the height (cm) after 2 weeks. Something interesting about the shape...
Plant Heights (cm)
9.210.111.412.313.0
9.810.611.712.813.5
10.011.012.013.014.0
10.311.212.113.214.5
10.511.512.513.715.1
Plant Height Histogram
0 2 4 6 8 9–9.9 10–10.9 11–11.9 12–12.9 13–13.9 14–14.9 15–15.9
↑ Notice the dashed curve shape!
🔔 The Bell Shape!
Data-Bot This histogram has a SYMMETRIC shape — like a bell! The bars on either side of the middle are about the same height.
SYMMETRIC DATA
📐 The middle bar is the tallest
↔️ Left side ≈ Right side in height
🔔 Looks like a bell curve
📊 Common in natural measurements!
The plant histogram is symmetric. Which statement is TRUE?
A Only the tallest bar matters
B About the same # of plants on each side of the middle
C All bars are the same height
CH.5
🎬 Apply: Making Moves — The Movie Mystery!
🎬 Cinema Studios
Maya A group of friends want to make a movie! They researched running times of popular films.
BEEP!
DATA-BOT REPORTS:
The histogram shows running times of 50 popular movies.
Movie Running Times
75–89
min
90–104
min
105–119
min ★
120–134
min
135–149
min
150+
min
🎬 How long should the movie be?
Read the histogram. Then write your recommendation with evidence.
Step 1: What does the tallest bar show?
A Most movies are 90–104 minutes
B Most movies are 105–119 minutes
C Most movies are 150+ minutes
Step 2: Write your recommendation!
Use this TWR frame: "Based on the histogram, I recommend the movie run ________ minutes because the data shows ________________________."
CH.6
🏁 Case Closed — Summary & Exit Ticket
📋 Case Summary
CASE CLOSED!
WHAT WE SOLVED:
📊 Histogram = bar graph showing intervals + frequencies
📋 Frequency table = organizes data into intervals
🔔 Symmetric shape = bars balance on either side
🏆 Tallest bar = most common interval
📏 Intervals = same size, no overlap, no gaps!
🎯 Exit Ticket — Mission Complete?
T1: A histogram always shows _____________ on the horizontal axis.
A Individual data values
B Intervals (ranges)
C Category names
T2: Why is a histogram better than a dot plot for 50 runners? Write 2–3 sentences.
T3 (Challenge): The bars in a histogram always touch. Why? Connect to what you know about intervals.
🎉 MISSION COMPLETE! 🎉
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