Describe Data Using the Mean
I can determine the mean of a data set, use a target mean to find a missing value, and explain the mean as the fair share and the balance point of the data.
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🎯 Content Objective / Objetivo de contenido
I can determine the mean of a data set, use a target mean to find a missing value, and explain the mean as the fair share and the balance point of the data.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
Miguel earned $60 walking dogs over 4 days. What does the question mean when it asks what he earns on a 'typical day'?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Fair Share Analyst
Every week, Miguel walks dogs after school to earn money, and he keeps his earnings in a notebook. Across 4 days he earned $60 in all — but not the same amount each day. Later this lesson you'll help Sofia, who tracks her points every basketball game and wants to finish the season averaging 15 points per game.
Concept Launch
💡 What is the mean?
The mean, or average, is a measure of center that describes a whole data set with one number. It is what every value would be if the total were leveled out and shared equally.
Measures of Center: Mean. Formula: Mean = (Sum of all values) ÷ (Total number of values). 1. Add all data values together to find the total sum. 2. Divide the sum by the count of data values. 3. Concept: The mean represents the fair share or balance point of the data
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 |
|---|---|---|---|
| Mean Media |
The average of a data set. Add all the values, then divide by how many values there are. El promedio de un conjunto de datos. Suma todos los valores y divide entre cuántos valores hay. |
Miguel earned $60 in 4 days: 60 ÷ 4 = 15, so the mean is $15 per day. | |
| Average Promedio |
Another word for the mean — the amount each value would be if the total were shared equally. Otra palabra para la media: la cantidad que tendría cada valor si el total se repartiera en partes iguales. |
A player averages 15 points per game, so over 10 games she scores 15 × 10 = 150 points in all. | |
| Measure of center Medida de centro |
A single number used to describe the middle, or typical value, of a whole data set. Un solo número que se usa para describir el centro, o valor típico, de todo un conjunto de datos. |
The mean, $15, is one measure of center that describes all four of Miguel's days at once. | |
| Balance point Punto de equilibrio |
The value where the total distance of the data above it equals the total distance below it. The mean is the balance point. El valor donde la distancia total de los datos por encima es igual a la distancia total por debajo. La media es el punto de equilibrio. |
With a target mean of 15, points totaling 13 below must be matched by points totaling 13 above. | |
| Data set Conjunto de datos |
The whole collection of values that were gathered or measured. Toda la colección de valores que se recopilaron o midieron. |
Sofia's points in games 1–9 — 12, 20, 16, 11, 17, 14, 15, 10, 18 — form one data set. |
Which Word Fits?
The value found by adding all the data and dividing by how many values there are is the ___.
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
Miguel earned $60 walking dogs over 4 days. What does the question mean when it asks what he earns on a 'typical day'?
👂 Listen For
Students say a typical day is the equal-share amount, and that sharing $60 across 4 days means dividing.
Extend: Predict: before dividing, is a typical day closer to $10 or closer to $20? Explain your estimate.
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
Sofia's target mean is 15 points per game. Sort each of her first 9 game scores by how it compares to that target.
✍️ Explore Discourse
Four games are below 15 and four games are above 15. Does that already mean the data balances at 15? What else would you have to measure?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
We piled all 60 counters together and then redistributed them equally into 4 bins. How is that the same as arithmetic?
👂 Listen For
Students connect combining to addition and equal redistribution to division by the number of days, landing on 60 ÷ 4 = 15.
Extend: Generalize: write the rule for finding a mean using the words total and number of values.
Practice Check A
Sofia wants to average 15 points per game over 10 games. How many points does she need in all 10 games combined?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
Sofia's points in games 1 through 9 were 12, 20, 16, 11, 17, 14, 15, 10, and 18. How many points has she scored so far?
✍️ 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
Sort each step into the correct order for finding the mean of a data set.
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: "Measures of Center: Mean. Formula: Mean = (Sum of all values) ÷ (Total number of values). 1. Add all data values together to find the total sum. 2. Divide the sum by the count of data values. 3. Concept: The mean represents the fair share or balance point of the data" — and it works because ___.
Because Mean means ___, but a tricky part is ___, so I have to ___.
A common mistake with Mean is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Average to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Measures of Center: Mean. Formula: Mean = (Sum of all values) ÷ (Total number of values). 1. Add all data values together to find the total sum. 2. Divide the sum by the count of data values. 3. Concept: The mean represents the fair share or balance point of the data because ___
Measures of Center: Mean. Formula: Mean = (Sum of all values) ÷ (Total number of values). 1. Add all data values together to find the total sum. 2. Divide the sum by the count of data values. 3. Concept: The mean represents the fair share or balance point of the data but ___
Measures of Center: Mean. Formula: Mean = (Sum of all values) ÷ (Total number of values). 1. Add all data values together to find the total sum. 2. Divide the sum by the count of data values. 3. Concept: The mean represents the fair share or balance point of the data so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Sofia's target mean is 15 points per game. Sort each of her first 9 game scores by how it compares to that target.
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
Find the mean of: 4, 6, 8, 10
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
Sofia tracks the number of points she scores in each basketball game. In games 1 through 9 she scored 12, 20, 16, 11, 17, 14, 15, 10, and 18 points. She wants to end the season with a mean of 15 points per game across all 10 games. Compared with that target of 15, her nine games came in 3 below, 5 above, 1 above, 4 below, 2 above, 1 below, even, 5 below, and 3 above.
✍️ Connection Reasoning
How many points does Sofia need to score in the last game to hit her goal, and how does the balance-point view give the same answer as adding and dividing?
After 9 games Sofia has scored ___ points. To average 15 across 10 games she needs ___ points in all, so game 10 must be ___ points. Using the balance point instead, her games total ___ points below the target mean and ___ points above it, so game 10 has to land ___ the target mean.
Turn & Talk — Connect
Sofia wants a mean of 15 points over 10 games. After 9 games her points are 3 below, 5 above, 1 above, 4 below, 2 above, 1 below, even, 5 below, and 3 above the target. How does that help you find game 10?
👂 Listen For
Students total 13 below and 11 above, notice the 2-point gap, and conclude game 10 must be 2 above 15.
Extend: Justify: why does balancing above and below give the SAME answer as adding and dividing?
Summarize: Describe Data Using the Mean
Measures of Center: Mean. Formula: Mean = (Sum of all values) ÷ (Total number of values). 1. Add all data values together to find the total sum. 2. Divide the sum by the count of data values. 3. Concept: The mean represents the fair share or balance point of the data
In your own words:
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
Data set: 8, 12, 10, 14. What is the mean?
Bonus Exit Check
Sofia has 133 points after 9 games and needs 150 points in all to average 15 over 10 games. How many points must she score in game 10?
✍️ 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 say a typical day is the equal-share amount, and that sharing $60 across 4 days means dividing.
• Students connect combining to addition and equal redistribution to division by the number of days, landing on 60 ÷ 4 = 15.
• Students total 13 below and 11 above, notice the 2-point gap, and conclude game 10 must be 2 above 15.
• Students add to 44, divide by 4, and report a mean of 11 while naming why the divisor is 4.
Common mistake: The most common mistake with the mean is adding correctly and then dividing by the wrong number — or not dividing at all. Students report the total (for 8, 10, 6, 12 they say the mean is 36) or they divide by a count that does not match the data, such as dividing a 4-value total by 5, or skipping a zero when counting the values. Before you finish, do two things: count the values in the data set out loud, and check that your mean lands between the smallest and largest value. A mean of 36 for data that never goes above 12 is impossible.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: 150 points — If every one of the 10 games hit the target of 15 points, the total would be 15 × 10 = 150 points. That is the total she needs for a mean of 15.
✓ Practice 2: 133 points — 12 + 20 + 16 + 11 + 17 + 14 + 15 + 10 + 18 = 133 points after 9 games.
✓ Practice 3: 17 points — She needs 150 points in all and already has 133, so game 10 must supply 150 − 133 = 17 points.
✓ Practice 4: 7 — Add the values: 4 + 6 + 8 + 10 = 28. There are 4 values, so the mean is 28 ÷ 4 = 7.
✓ Exit ticket: 11 — Add the values: 8 + 12 + 10 + 14 = 44. There are 4 values, so the mean is 44 ÷ 4 = 11.