Neft Teacher Unit 8

🏀

Mean Absolute Deviation

6.SP.5c Lesson 8-3

My Math Notebook

Name:

Date:

Period:

I Can…

I can find the mean absolute deviation (MAD) to describe how spread out data is.

Reveal Math Grade 6 How to Use 6.SP.5c

🏀 SPORTS ANALYTICS

How to Use This Deck

▶Present

Click Present or press F11 for fullscreen. Use arrow keys to advance.

👩‍🏫Teacher cues

Blue boxes show exactly what to say, ask, and how long to spend.

👨‍🎓Student work

Text boxes, polls, and drag-sort save automatically in the browser.

📝Notes

Press N or click 📝 in the toolbar for pacing tips and answers.

🎮Activity link

Launch the full HTML activity for independent practice.

🖨️Print

File → Print or the print button for handout copies.

⏱️ Time: 30 sec — read aloud, then advance

Reveal Math Grade 6 Learning Targets 6.SP.5c

🎯 Content Objective / Objetivo de contenido

I can find the mean absolute deviation (MAD) to describe how spread out data is.

Reveal Math Grade 6 Agenda 6.SP.5c

🏀 SPORTS ANALYTICS

Today's Flow

1 Warm-Up 5m

2 Vocabulary 8m

3 I Do 5m

4 We Do 5m

5 Explore 8m

6 Practice 10m

7 Connect 5m

8 Exit Ticket 5m

Total pacing: ~45 min · Progress bar at top tracks your place

🏀

Lesson Phase

LAUNCH

⏱ ~10 min

Reveal Math Grade 6 Warm-Up Hook 6.SP.5c

⏱️ 3 MIN · THINK-PAIR-SHARE

Player A scored 18, 22, 20, 24, 16 and Player B scored 10, 30, 25, 12, 23. Both average 20. Which player would you count on to score close to 20 every night, and why?

mean absolute deviationdeviationspreadconsistentmean

Reveal Math Grade 6 CFU 1 6.SP.5c

🏀 SPORTS ANALYTICS

Check for Understanding #1

✋ CFU · THUMBS

❓ Ask: Can you restate the warm-up question in your own words?

⏱️ Time: 30 sec

Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.

Reveal Math Grade 6 Be Curious 6.SP.5c

Visual Prompt

Player Consistency Report

Coach wants to know which basketball player is more consistent: Player A scored 18, 22, 20, 24, 16 points in the last 5 games. Player B scored 10, 30, 25, 12, 23 points. Both players average 20 points per game. Which player would you count on to score close to 20 every night?

👁 I Notice...

🔹 Both players have the same mean. Looking at the listed scores, what is different about them?

🔹 Using the dot plot and the scores in the story, which player's scores stay closer to 20?

🔹 Which player has the biggest single-game difference from 20?

💭 I Wonder...

🔹 How can we measure how spread out each player's scores are?

🔹 Is there a number that tells us which player is more consistent?

Reveal Math Grade 6 Concept Launch 6.SP.5c

🎯 I can find the mean absolute deviation (MAD) to describe how spread out data is.

🏀 SPORTS ANALYTICS

Concept Launch

💡 What is the mean absolute deviation (MAD)?

👩‍🏫 Say: This is the big idea for today. Students should be able to repeat it by the end.

The mean absolute deviation, or MAD, is the average distance of each value from the mean. It tells you how spread out the data is: a small MAD means the data is close together, and a large MAD means it is spread out.

Key Idea:

MAD = the average of how far each number is from the mean (always a positive distance).

Reveal Math Grade 6 I Do — Watch Me 6.SP.5c

Reveal Math Grade 6 I Do — Key Step 6.SP.5c

Reveal Math Grade 6 We Do — Together 6.SP.5c

Reveal Math Grade 6 CFU 2 6.SP.5c

🏀 SPORTS ANALYTICS

Check for Understanding #2

✋ CFU · THUMBS

❓ Ask: Can you explain what we did in the We Do example?

⏱️ Time: 30 sec

Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.

Reveal Math Grade 6 You Do — Your Turn 6.SP.5c

🎯 I can find the mean absolute deviation (MAD) to describe how spread out data is.

🏀 SPORTS ANALYTICS

Now it's your turn

👨‍🎓 Students: Work independently first, then check with a partner.

⏱️ Time: 5 min

1Next, you will find the MAD for Player A's scores step by step in the table.

2Remember: deviation first, then absolute value, then average.

🎮

Open the interactive HTML activity for full practice.

Launch Activity ↗

📚

Lesson Phase

VOCABULARY

⏱ ~8 min

Reveal Math Grade 6 Vocabulary 6.SP.5c

Term / Término	Meaning / Significado	Visual
Mean Absolute Deviation Desviación media absoluta	The average distance of each number from the mean. La distancia promedio de cada número a la media.	Data: 8, 10, 12. Mean = 10. Distances from mean: 2, 0, 2. MAD = (2+0+2) ÷ 3 = 1.33
Deviation Desviación	How far a number is from the mean. Qué tan lejos está un número de la media.	If mean = 20 and value = 17, deviation = 17 − 20 = −3 (3 below the mean)
Absolute Value Valor absoluto	How far a number is from zero. It is always positive. Qué tan lejos está un número de cero. Siempre es positivo.	\|−3\| = 3 and \|3\| = 3 — both are 3 units from zero
Spread Dispersión	How far apart the numbers are. Qué tan separados están los números.	Low spread: 8, 9, 10, 11 (close together). High spread: 2, 9, 10, 25 (far apart)
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 set clustered tightly around the mean has low MAD; a set spread far from the mean has high MAD
Variability Variabilidad	How spread out the numbers are. Qué tan separados están los números.	Low variability (MAD = 1): very consistent. High variability (MAD = 8): very spread out

Absolute Value: example vs. non-example

✓ The absolute value of −4 is 4−4 is 4 units from zero.

✗ The absolute value of −4 is −4Absolute value is never negative.

Reveal Math Grade 6 Which Word? 6.SP.5c

🎯 I can find the mean absolute deviation (MAD) to describe how spread out data is.

🏀 SPORTS ANALYTICS

Which Word Fits?

❓ CLOZE POLL

❓ Ask: Vote A B C D — then defend your choice.

The average distance of each value from the mean is the ___.

Use It In a Sentence

Reveal Math Grade 6 CFU 3 6.SP.5c

🏀 SPORTS ANALYTICS

Check for Understanding #3

✋ CFU · THUMBS

❓ Ask: Use one vocabulary word in a sentence about today's topic.

⏱️ Time: 30 sec

Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.

Reveal Math Grade 6 Turn & Talk 6.SP.5c

🎯 I can find the mean absolute deviation (MAD) to describe how spread out data is.

🏀 SPORTS ANALYTICS

Turn & Talk — Launch

🗣️ TURN & TALK

👩‍🏫 Say: Partner A shares first for 45 seconds, then Partner B.

👨‍🎓 Students: Turn to your elbow partner. Use the sentence stems.

⏱️ Time: 90 sec

Player A scored 18, 22, 20, 24, 16 and Player B scored 10, 30, 25, 12, 23. Both average 20. Which player would you count on to score close to 20 every night, and why?

Sentence starters (tap to use):

✍️ I would count on Player ___ because their scores are ___.Contaría con el Jugador ___ porque sus puntajes están ___.

✍️ Even with the same mean, the players differ in ___.Aunque tengan la misma media, los jugadores difieren en ___.

Stretch further:

➕ Player ___ will have the larger MAD because ___.

➕ A larger MAD means the scores are ___, so the player is ___.

WORD BANK:

mean absolute deviationdeviationspreadconsistentmean

90s

👂 Listen For

Students choose Player A as more consistent and recognize that equal means hide different spreads.

Extend: Predict: which player will have the larger MAD, and what does a larger MAD say about consistency?

🔍

Lesson Phase

EXPLORE & PRACTICE

⏱ ~18 min

Reveal Math Grade 6 Visual Model 6.SP.5c

🎯 I can find the mean absolute deviation (MAD) to describe how spread out data is.

🏀 SPORTS ANALYTICS

Visual Modeling Workspace

Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.

Reveal Math Grade 6 Explore 6.SP.5c

🏀 SPORTS ANALYTICS

Explore Activity

Calculate the Mean Absolute Deviation (MAD) for Player A's scores: 18, 22, 20, 24, 16. Follow each step.

lowerhighercloserfartherconsistentspreadPlayer A

✍️ Explore Discourse

Player A's MAD is 2.4 points. If Player B's MAD is 7.2 points, what does that tell you about their consistency?

Player A has a ___ MAD, which means their scores are ___ to the mean. Player B has a ___ MAD, which means their scores are ___ from the mean. The more consistent player is ___ because ___.

Reveal Math Grade 6 Whiteboard CFU 6.SP.5c

🎯 I can find the mean absolute deviation (MAD) to describe how spread out data is.

🏀 SPORTS ANALYTICS

Whiteboard Moment

🖊️ WHITEBOARD CFU

👨‍🎓 Students: On your whiteboard or paper, solve ONE quick problem using today's strategy. Hold it up when done.

⏱️ Time: 2 min

Show your work clearly. Be ready to explain your thinking to a partner.

Reveal Math Grade 6 Discuss Explore 6.SP.5c

🎯 I can find the mean absolute deviation (MAD) to describe how spread out data is.

🏀 SPORTS ANALYTICS

Turn & Talk — Explore

🗣️ TURN & TALK

👩‍🏫 Say: Partner A shares first for 45 seconds, then Partner B.

👨‍🎓 Students: Turn to your elbow partner. Use the sentence stems.

⏱️ Time: 90 sec

To find the MAD for Player A (18, 22, 20, 24, 16, mean 20), why do we take the ABSOLUTE VALUE of each deviation before averaging?

Sentence starters (tap to use):

✍️ We use absolute value so the deviations are all ___.Usamos el valor absoluto para que las desviaciones sean todas ___.

✍️ Without absolute value, the deviations would add up to ___.Sin valor absoluto, las desviaciones sumarían ___.

Stretch further:

➕ The absolute deviations are ___, which sum to ___.

➕ Dividing by 5 gives a MAD of ___, meaning ___.

WORD BANK:

mean absolute deviationdeviationabsolute valuespreadmean

90s

👂 Listen For

A strong answer explains deviations above and below the mean would cancel to zero, so absolute value keeps each as a positive distance.

Extend: Compute and justify: find the MAD of 18, 22, 20, 24, 16. Show the deviations, take absolute values, and average them.

Reveal Math Grade 6 Practice A 6.SP.5c

🎯 I can find the mean absolute deviation (MAD) to describe how spread out data is.

🏀 SPORTS ANALYTICS

Practice Check A

📝 QUICK CHECK

❓ Ask: Give students 1 minute. Cold-call one student to defend their answer.

⏱️ Time: 2 min

Two runners have the same average time of 60 seconds. Runner A's MAD is 1.2 seconds. Runner B's MAD is 5.8 seconds. Which runner is the coach more likely to pick for a relay race that needs a reliable time?

✍️ Show Your Work

Explain why your answer is correct using today's vocabulary.

Teacher reveal: Runner A's MAD of 1.2 means times are usually within 1.2 seconds of 60. Runner B's times vary more widely. For reliability, pick Runner A.

Reveal Math Grade 6 Practice B 6.SP.5c

🎯 I can find the mean absolute deviation (MAD) to describe how spread out data is.

🏀 SPORTS ANALYTICS

Practice Check B

📝 QUICK CHECK

❓ Ask: Partner discussion first, then vote.

⏱️ Time: 2 min

The mean of a data set is 15. One value is 11. What is the absolute deviation of that value from the mean?

✍️ Show Your Work

Explain why your answer is correct using today's vocabulary.

Teacher reveal: Deviation = 11 − 15 = −4. Absolute deviation = |−4| = 4.

Reveal Math Grade 6 Statistical vs Not Sort 6.SP.5c

🎯 I can find the mean absolute deviation (MAD) to describe how spread out data is.

🏀 SPORTS ANALYTICS

Statistical vs Not Sort

📈 CARD SORT

👨‍🎓 Students: Work at your own pace. Check with a partner before we discuss.

⏱️ Time: 5 min

✍️ Justify Your Thinking

Reveal Math Grade 6 Sort It Out 6.SP.5c

Sort these data sets from LEAST spread out (lowest MAD) to MOST spread out (highest MAD).

Card Bank — cut or drag these cards:

Least to most spread out

Reveal Math Grade 6 Error Analysis 6.SP.5c

⚠ Find the MAD Error

A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.

Student's work — read every step:

1 Data set 5, 10, 15, 20, 25

2 Find mean Sum = 75, Count = 5, Mean = 15

3 Find deviations −10, −5, 0, 5, 10

4 Find MAD MAD = (−10 + −5 + 0 + 5 + 10) ÷ 5 = 0

Which step has the error?

Reveal Math Grade 6 Choice Board 6.SP.5c

Choose ONE option to show what you know — then do it in the workspace below.

I chose option — my work:

Reveal Math Grade 6 Think Write 6.SP.5c

Use evidence from today's lesson to complete each frame.

Frame 1 Explain the Rule

Today's key idea is: "MAD = the average of how far each number is from the mean (always a positive distance)." — and it works because ___.

Frame 2 Because / But / So

Because Mean Absolute Deviation means ___, but a tricky part is ___, so I have to ___.

Frame 3 Catch the Mistake

A common mistake with Mean Absolute Deviation is ___. It happens because ___, and the fix is ___.

Frame 4 Prove It

I can prove my answer is correct by ___, using Deviation to check my work.

Reveal Math Grade 6 Because · But · So 6.SP.5c

✍️ TWR · WRITE 3 SENTENCES · 7 MIN

Sentence kernelMAD = the average of how far each number is from the mean (always a positive distance).

because

Give a reason

MAD = the average of how far each number is from the mean (always a positive distance). because ___

but

Name a tricky part

MAD = the average of how far each number is from the mean (always a positive distance). but ___

so

State what it means

MAD = the average of how far each number is from the mean (always a positive distance). so ___

Reveal Math Grade 6 Sentence Expansion 6.SP.5c

🌱 TWR · GROW THE KERNEL · 6 MIN

Sentence kernelToday we used Mean Absolute Deviation.

Answer these to add detail

What exactly?When?Where in real life?Why does it work?How did we use it?

Sentence starters (tap to use)

First, …For example, …This means that …In other words, …As a result, …I know this because …

Reveal Math Grade 6 Student Workspace 6.SP.5c

🎯 I can find the mean absolute deviation (MAD) to describe how spread out data is.

🏀 SPORTS ANALYTICS

Student Workspace

📊 FILL THE TABLE

👨‍🎓 Students: Complete the missing cells. Check with a partner before we discuss.

⏱️ Time: 5 min

Fill in the table using today's strategy.

Score	Deviation (Score − Mean)	Absolute Deviation
18
22
20
24
16

✏️ Sketch Your Strategy

Reveal Math Grade 6 Differentiation 6.SP.5c

🏀 SPORTS ANALYTICS

Differentiation Paths

🎯 CHOOSE YOUR LEVEL

👩‍🏫 Say: Everyone works on the same math goal — pick the level of support that fits today.

⏱️ Time: 8–10 min independent or partner

🧩 Level 0 · Most support

Step-by-step with a worked model and sentence frames.

🌱 Level 1 · Support

The mean of a data set is 15. One value is 11. What is the absolute deviation of that value from the mean?

🎯 Level 2 · Core

Core practice aligned to the standard.

🚀 Level 2+ · Enrichment

Extension with error analysis or multi-step reasoning.

Reveal Math Grade 6 Partner Activity 6.SP.5c

🎯 I can find the mean absolute deviation (MAD) to describe how spread out data is.

🏀 SPORTS ANALYTICS

Partner Activity

🤝 PARTNER WORK

📦 Materials: Whiteboards or paper, pencils, vocabulary reference cards

👨‍🎓 Students: Partner A solves, Partner B coaches. Switch roles on the next problem.

⏱️ Time: 6 min

Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.

Reveal Math Grade 6 CFU 4 6.SP.5c

🏀 SPORTS ANALYTICS

Check for Understanding #4

✋ CFU · THUMBS

❓ Ask: Thumbs up if you and your partner agree on your answer.

⏱️ Time: 30 sec

Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.

Reveal Math Grade 6 Math in the Wild 6.SP.5c

🎯 I can find the mean absolute deviation (MAD) to describe how spread out data is.

🏀 SPORTS ANALYTICS

Real-World Connection

🌍 Math in the Wild

👩‍🏫 Say: Read the scenario. Ask: where else have you seen this kind of math?

Two soccer goalkeepers track goals allowed per game over 6 games. Keeper A: 1, 2, 1, 3, 2, 1 (mean = 1.67, MAD ≈ 0.67). Keeper B: 0, 4, 1, 3, 0, 2 (mean = 1.67, MAD ≈ 1.33). The coach needs to pick a starter for the championship game.

1.67lowerhigherconsistentspreadreliableMADKeeper A

✍️ Connection Reasoning

Both keepers allow the same average goals. Which should the coach pick and why?

Both keepers have a mean of ___. Keeper A's MAD is ___, which means ___. Keeper B's MAD is ___, which means ___. The coach should pick ___ because ___.

Reveal Math Grade 6 Discuss Connect 6.SP.5c

🎯 I can find the mean absolute deviation (MAD) to describe how spread out data is.

🏀 SPORTS ANALYTICS

Turn & Talk — Connect

🗣️ TURN & TALK

👩‍🏫 Say: Partner A shares first for 45 seconds, then Partner B.

👨‍🎓 Students: Turn to your elbow partner. Use the sentence stems.

⏱️ Time: 90 sec

Two keepers both allow a mean of 1.67 goals, but Keeper A's MAD is 0.67 and Keeper B's is 1.33. Which keeper should the coach start in the championship, and why?

Sentence starters (tap to use):

✍️ The coach should pick Keeper ___ because their MAD is ___.El entrenador debe elegir al Portero ___ porque su DAM es ___.

✍️ A smaller MAD means the keeper is more ___.Una DAM más pequeña significa que el portero es más ___.

Stretch further:

➕ A coach might prefer the higher-MAD keeper when ___.

➕ Higher spread could be acceptable if ___ because ___.

WORD BANK:

mean absolute deviationdeviationspreadconsistentmean

90s

👂 Listen For

Students pick Keeper A and explain a smaller MAD (0.67) means goals allowed stay close to the mean, so performance is more reliable.

Extend: Critique: when might a coach actually prefer the LESS consistent keeper (higher MAD)? Defend with a scenario.

✅

Lesson Phase

CLOSURE & REFLECT

⏱ ~8 min

Reveal Math Grade 6 Exit Ticket 6.SP.5c

Reflection

Today I learned that ___ because ___.

One thing I am still not sure about is ___.

Quick Exit Ticket

Data set: 4, 8, 6, 10, 2. The mean is 6. What is the MAD?

Reveal Math Grade 6 Goal Tracker 6.SP.5c

Reveal Math Grade 6 Bonus Check 6.SP.5c

🎯 I can find the mean absolute deviation (MAD) to describe how spread out data is.

🏀 SPORTS ANALYTICS

Bonus Exit Check

📝 QUICK CHECK

❓ Ask: Optional for early finishers.

⏱️ Time: 2 min

A data set has absolute deviations of 3, 1, 5, 2, 4. What is the MAD?

✍️ Show Your Work

Explain why your answer is correct using today's vocabulary.

Teacher reveal: Sum of absolute deviations = 3 + 1 + 5 + 2 + 4 = 15. MAD = 15 ÷ 5 = 3.

Reveal Math Grade 6 Reflection 6.SP.5c

🏀 SPORTS ANALYTICS

Reflection & Self-Assessment

3 Things I learned:

2 Connections:

1 Question:

Self-Assessment:

Reveal Math Grade 6 Digital Activity 6.SP.5c

🏀 SPORTS ANALYTICS

Continue Learning

🎮

Launch the Full Interactive Activity

Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.

Open Lesson Activity ↗ Family Homework ↗

👩‍🏫 Say: Early finishers: open the activity. Everyone else: start homework tonight.

Reveal Math Grade 6 Family Connection 6.SP.5c

🏀 SPORTS ANALYTICS

Family Connection

Share tonight's family homework and discuss one vocabulary word at home.

Open Family Homework ↗

👩‍🏫 Say: Tell families: "Ask your student to teach you one thing from today's lesson."

Reveal Math Grade 6 Teacher Notes 6.SP.5c

🏀 SPORTS ANALYTICS

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 choose Player A as more consistent and recognize that equal means hide different spreads.

• A strong answer explains deviations above and below the mean would cancel to zero, so absolute value keeps each as a positive distance.

• Students pick Keeper A and explain a smaller MAD (0.67) means goals allowed stay close to the mean, so performance is more reliable.

• Students compute absolute deviations 2, 2, 0, 4, 4 (sum 12), divide by 5, and report MAD = 2.4.

Common mistake: A common mistake in Mean Absolute Deviation is skipping the key idea: "MAD = the average of how far each number is from the mean (always a positive distance)." — always check your work against this rule before you submit.

Reveal Math Grade 6 Answer Key 6.SP.5c

🏀 SPORTS ANALYTICS

Answer Key (Teacher Appendix)

Hide this slide during presentation or move to the end of your copy.

✓ Practice 1: Runner A — lower MAD means more consistent times — Runner A's MAD of 1.2 means times are usually within 1.2 seconds of 60. Runner B's times vary more widely. For reliability, pick Runner A.

✓ Practice 2: 4 — Deviation = 11 − 15 = −4. Absolute deviation = |−4| = 4.

✓ Practice 3: 3 — Sum of absolute deviations = 3 + 1 + 5 + 2 + 4 = 15. MAD = 15 ÷ 5 = 3.

✓ Practice 4: 6 — Deviation = 26 − 20 = 6. Absolute deviation = |6| = 6.

✓ Exit ticket: 2.4 — Deviations: −2, 2, 0, 4, −4. Absolute deviations: 2, 2, 0, 4, 4. Sum = 12. MAD = 12 ÷ 5 = 2.4.