Display Data: Histograms
I can make and read a histogram to display data in intervals.
How to Use This Deck
Click Present or press F11 for fullscreen. Use arrow keys to advance.
Blue boxes show exactly what to say, ask, and how long to spend.
Text boxes, polls, and drag-sort save automatically in the browser.
Press N or click 📝 in the toolbar for pacing tips and answers.
Launch the full HTML activity for independent practice.
File → Print or the print button for handout copies.
🎯 Content Objective / Objetivo de contenido
I can make and read a histogram to display data in intervals.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
You have 30 players' points-per-game averages. Why is it easier to display them in a histogram with intervals than to list all 30 numbers?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
League Stats Organizer
The basketball league has 30 players and wants to display everyone's points-per-game average in a way that shows how the data is distributed. The raw averages are: 2, 5, 7, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 18, 18, 19, 20, 21, 22, 23, 24, 25, 28, 30, 32. Listing all 30 numbers is hard to read — a histogram will reveal the pattern!
Concept Launch
💡 What is a histogram?
A histogram is a bar graph that groups numbers into equal ranges called intervals. The height of each bar is the frequency: how many values fall in that interval. The bars touch because the intervals are continuous.
Each bar's height shows how many data values land inside that interval.
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Now it's your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Histogram Histograma |
A bar graph that groups data into equal ranges. The bars touch. Una gráfica de barras que agrupa datos en rangos iguales. Las barras se tocan. |
Bars side by side: 0-9 pts (3 players), 10-19 pts (8 players), 20-29 pts (4 players) | |
| Frequency Frecuencia |
How many times a value shows up. Cuántas veces aparece un valor. |
If 5 players scored 10-19 points, the frequency for that interval is 5 | |
| Interval Intervalo |
A range of numbers used to group data. Un rango de números para agrupar datos. |
0-9, 10-19, 20-29 are intervals of width 10 — each covers 10 values | |
| Distribution Distribución |
How the data is spread out. Cómo están repartidos los datos. |
Most data in the middle with fewer at the ends = bell-shaped; most on one side with a tail = skewed | |
| Variability Variabilidad |
How spread out the numbers are. Qué tan separados están los números. |
Data in just 2 intervals = low variability. Data across 6 intervals = high variability |
Which Word Fits?
A bar graph that shows how often data falls into equal intervals is a ___.
Use It In a Sentence
Check for Understanding #3
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Turn & Talk — Launch
You have 30 players' points-per-game averages. Why is it easier to display them in a histogram with intervals than to list all 30 numbers?
👂 Listen For
Students explain grouping into intervals makes 30 values readable and that each bar's height is the frequency for that interval.
Extend: Predict: how would the histogram change if you used intervals of 5 instead of 10? Justify the trade-off.
EXPLORE & PRACTICE
⏱ ~18 min
Visual Modeling Workspace
Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.
Explore Activity
Create a frequency table for the league scoring data using intervals of 10. Then describe the histogram shape.
✍️ Explore Discourse
The tallest bar is the 10–19 interval with 16 players. What does the shape of this histogram tell you about scoring in the league?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
As you build the frequency table with intervals of 10, what does the height of each bar in the histogram represent?
👂 Listen For
A strong answer states the bar height equals how many players' averages fall in that interval (the frequency) and locates the tallest bar.
Extend: Why can't you tell a single player's exact average just from the histogram? Justify using the intervals.
Practice Check A
A histogram of test scores shows: 50–59: 2, 60–69: 5, 70–79: 10, 80–89: 8, 90–99: 3. Which interval has the most students?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
A histogram of goals-per-game shows: 0–1: 9 players, 2–3: 6, 4–5: 3, 6–7: 1. What shape is this distribution?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Statistical vs Not Sort
Drag each question into the correct column.
✍️ Justify Your Thinking
Based on the histogram frequencies below, sort the intervals from most players to fewest: 0–9: 4, 10–19: 11, 20–29: 7, 30–39: 2.
A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.
Choose ONE option to show what you know — then do it in the workspace below.
Use evidence from today's lesson to complete each frame.
Today's key idea is: "Each bar's height shows how many data values land inside that interval." — and it works because ___.
Because Histogram means ___, but a tricky part is ___, so I have to ___.
A common mistake with Histogram is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Frequency to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Each bar's height shows how many data values land inside that interval. because ___
Each bar's height shows how many data values land inside that interval. but ___
Each bar's height shows how many data values land inside that interval. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Fill in the table using today's strategy.
| Interval (Points) | Tally / Count | Frequency |
|---|---|---|
| 0–9 | ||
| 10–19 | ||
| 20–29 | ||
| 30–39 |
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
A histogram shows these frequencies: 0–4: 3 players, 5–9: 8 players, 10–14: 12 players, 15–19: 5 players. How many players are represented in total?
Core practice aligned to the standard.
Extension with error analysis or multi-step reasoning.
Partner Activity
Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.
Check for Understanding #4
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Real-World Connection
🌍 Math in the Wild
A soccer coach looks at a histogram of shots-per-game for the team: 0–2 shots: 1 player, 3–5 shots: 8 players, 6–8 shots: 10 players, 9–11 shots: 3 players, 12–14 shots: 1 player. The coach says, 'Most of my players take a good number of shots.'
✍️ Connection Reasoning
Does the histogram support the coach's claim? What does the shape of the data tell you?
The histogram peaks at the ___ interval with ___ players. The shape is approximately ___. This ___ the coach's claim because ___.
Turn & Talk — Connect
A histogram of shots-per-game shows 0-2: 1 player, 3-5: 8, 6-8: 10, 9-11: 3, 12-14: 1. The coach says 'most players take a good number of shots.' Does the shape support that claim?
👂 Listen For
Students read the 3-5 and 6-8 intervals (18 of 23 players) as the cluster and judge whether 'a good number' fairly describes the shape.
Extend: Critique: a teammate ignores the 0-2 and 12-14 bars because they are short. Should those intervals be ignored? Defend.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
A histogram of player heights shows: 60–63 in: 2, 64–67 in: 7, 68–71 in: 9, 72–75 in: 4. Which interval has the most players?
Bonus Exit Check
A histogram shows these frequencies: 0–4: 3 players, 5–9: 8 players, 10–14: 12 players, 15–19: 5 players. How many players are represented in total?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Reflection & Self-Assessment
Continue Learning
Launch the Full Interactive Activity
Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.
Family Connection
Share tonight's family homework and discuss one vocabulary word at home.
Open Family Homework ↗Teacher Notes
⏱️ Pacing Guide
- Launch & vocab: 12 min
- I Do / We Do / You Do: 15 min
- Explore & practice: 15 min
- Connect & closure: 8 min
Total: ~45 min
🎯 Listen For · Common Errors
• Students explain grouping into intervals makes 30 values readable and that each bar's height is the frequency for that interval.
• A strong answer states the bar height equals how many players' averages fall in that interval (the frequency) and locates the tallest bar.
• Students read the 3-5 and 6-8 intervals (18 of 23 players) as the cluster and judge whether 'a good number' fairly describes the shape.
• Students identify 68-71 in (9 players) as the most-populated interval because it has the highest frequency.
Common mistake: A common mistake in Display Data: Histograms is skipping the key idea: "Each bar's height shows how many data values land inside that interval." — always check your work against this rule before you submit.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: 70–79 with 10 students — The 70–79 interval has the highest frequency of 10 students.
✓ Practice 2: Skewed right (most players low, tail toward high values) — The tallest bars are at the low end (0–1) and the bars shrink as goals increase — the tail points right, so it is skewed right.
✓ Practice 3: 28 — Add all frequencies: 3 + 8 + 12 + 5 = 28 players.
✓ Practice 4: The frequency (count) of data in that interval — Each bar's height shows the frequency — how many data values fall within that interval.
✓ Exit ticket: 68–71 inches — The 68–71 inch interval has the highest frequency of 9 players.