Display Data: Box Plots
I can make and read a box plot to summarize a data set.
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🎯 Content Objective / Objetivo de contenido
I can make and read a box plot to summarize a data set.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
The Wildcats' scores are 4, 6, 8, 10, 12, 14, 15, 18, 22, 24, 28. To build a box plot you need a five-number summary. What five numbers will you need?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Team Scoring Breakdown
The basketball league wants to compare scoring across teams. Here are the points scored by each player on the Wildcats in their last game: 4, 6, 8, 10, 12, 14, 15, 18, 22, 24, 28. The league needs a quick visual that shows the spread, the middle 50%, and any high or low scorers. Time to build a box plot!
Concept Launch
💡 What is a box plot?
A box plot is a simple picture that shows how a set of data is spread out, using just five key numbers: the lowest value, the first quartile (Q1), the median (middle), the third quartile (Q3), and the highest value.
The box always holds the middle 50% of the data, and the line inside the box is the median.
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 |
|---|---|---|---|
| Box Plot Diagrama de caja |
A graph that shows how data is spread using five key numbers. Una gráfica que muestra cómo se reparten los datos con cinco números clave. |
A box from Q1 to Q3 with a line at the median, and whiskers from min to max | |
| Median Mediana |
The middle number that splits the data in half. El número del medio que divide los datos en dos mitades. |
Data: 10, 15, 20, 25, 30 → median is 20 (the 3rd value) | |
| Quartile Cuartil |
Numbers that split the data into four equal parts. Números que dividen los datos en cuatro partes iguales. |
Data: 2, 4, 6, 8, 10, 12, 14 → Q1 = 4 (median of lower half), Q3 = 12 (median of upper half) | |
| Interquartile Range Rango intercuartílico |
The spread of the middle half of the data (Q3 − Q1). La extensión de la mitad central de los datos (Q3 − Q1). |
If Q1 = 12 and Q3 = 20, then IQR = 20 − 12 = 8 — the middle 50% spans 8 units | |
| Data distribution Distribución de datos |
How the data looks: where it sits and how spread out it is. Cómo se ven los datos: dónde están y qué tan separados están. |
A box plot where the median is centered in the box shows symmetric distribution | |
| Variability Variabilidad |
How spread out the numbers are. Qué tan separados están los números. |
Small IQR = low variability in the middle 50%. Large IQR = high variability |
Which Word Fits?
A graph that shows data with a box and whiskers based on the five-number summary 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
The Wildcats' scores are 4, 6, 8, 10, 12, 14, 15, 18, 22, 24, 28. To build a box plot you need a five-number summary. What five numbers will you need?
👂 Listen For
Students name the five-number summary (min, Q1, median, Q3, max) and find the median (14) for the 11 ordered scores.
Extend: Justify: explain how to find Q1 and Q3 for this data set and what they represent.
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
Find the five-number summary for the Wildcats' scoring data: 4, 6, 8, 10, 12, 14, 15, 18, 22, 24, 28. Place each value on the number line.
✍️ Explore Discourse
The IQR is Q3 − Q1 = 22 − 8 = 14. What does this tell you about the middle 50% of scorers?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
As you draw the box from Q1 to Q3, what does the length of the box tell you about the players' scores?
👂 Listen For
A strong answer explains the box covers the middle 50% (Q1 to Q3), its length is the IQR, and a longer box means greater spread.
Extend: Compare: how would the box plot change if the highest score were 50 instead of 28? Which part changes, the box or the whisker?
Practice Check A
Two box plots show: Team A has IQR = 8, Team B has IQR = 22. What does this tell you?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
A box plot shows: Min = 10, Q1 = 15, Median = 20, Q3 = 28, Max = 35. What is the interquartile range (IQR)?
✍️ 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
Each card describes a part of the stadium box plot. Sort each card under the matching box plot part.
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: "The box always holds the middle 50% of the data, and the line inside the box is the median." — and it works because ___.
Because Box Plot means ___, but a tricky part is ___, so I have to ___.
A common mistake with Box Plot is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Median to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
The box always holds the middle 50% of the data, and the line inside the box is the median. because ___
The box always holds the middle 50% of the data, and the line inside the box is the median. but ___
The box always holds the middle 50% of the data, and the line inside the box is the median. 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.
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
A box plot shows: Min = 10, Q1 = 15, Median = 20, Q3 = 28, Max = 35. What is the interquartile range (IQR)?
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
Two basketball teams' scoring data are displayed as box plots. Team A: Min=40, Q1=52, Median=60, Q3=68, Max=75. Team B: Min=35, Q1=55, Median=61, Q3=65, Max=80. A fan says Team B is better because they scored 80 points once.
✍️ Connection Reasoning
Which team is more consistently scoring high? Use the box plot values to support your answer.
Team A's IQR is ___ and Team B's IQR is ___. Team B's middle 50% scores between ___ and ___. The fan is wrong because ___. The box plot shows that Team B is more consistent because its Q1 and median are higher and its IQR (10) is smaller, while ___.
Turn & Talk — Connect
Team A: Min=40, Q1=52, Med=60, Q3=68, Max=75. Team B: Min=35, Q1=55, Med=61, Q3=65, Max=80. A fan says Team B is better because they scored 80 once. Which team scores high more consistently?
👂 Listen For
Students compare medians and Q1/Q3 (Team B has a higher Q1 and median) and explain the single max of 80 doesn't make a team consistently better.
Extend: Critique: the fan focuses only on the maximum. What two box-plot features give a fairer comparison? Defend your choice.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
A box plot has Q1 = 20 and Q3 = 36. What is the IQR and what does it represent?
Bonus Exit Check
On a box plot, what does the line inside the box represent?
✍️ 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 name the five-number summary (min, Q1, median, Q3, max) and find the median (14) for the 11 ordered scores.
• A strong answer explains the box covers the middle 50% (Q1 to Q3), its length is the IQR, and a longer box means greater spread.
• Students compare medians and Q1/Q3 (Team B has a higher Q1 and median) and explain the single max of 80 doesn't make a team consistently better.
• Students compute IQR = 36 - 20 = 16 and explain it is the range of the middle 50% of the data.
Common mistake: A common mistake in Display Data: Box Plots is skipping the key idea: "The box always holds the middle 50% of the data, and the line inside the box is the median." — 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: Team A's middle 50% is more consistent; Team B's is more spread out — A smaller IQR means the middle 50% of data is more tightly clustered. Team A's scoring is more consistent in the middle range.
✓ Practice 2: 13 — IQR = Q3 − Q1 = 28 − 15 = 13.
✓ Practice 3: The median — The line inside the box of a box plot always represents the median.
✓ Practice 4: 50% — The box in a box plot contains the middle 50% of the data (from Q1 to Q3).
✓ Exit ticket: IQR = 16; it is the spread of the middle 50% of the data — IQR = Q3 − Q1 = 36 − 20 = 16. The IQR tells you the range of the middle 50% of the data.