Math lesson plan · 6th grade (Year 7 in England) · 45 minutes
Mean absolute deviation (MAD)
Statistics and probability
CCSS 6.SP.B.5.CEngland: KS3 Statistics
Objective and success criteria
Students will: Mean absolute deviation (MAD).
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Calculate the mean, including decimal answers; Distance between two integers
Leads to: Compare two groups using centre and spread
Materials: Squared paper for charts, Class survey data, Sticky notes for a live chart, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Calculate the mean, including decimal answers; Distance between two integers). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Data (push-ups in one minute): 20, 32, 28, 13, 30. Find the mean. → 24.6Prompt: Add all the values.
- Four runners' 100 m times in seconds: 16.1, 13.4, 16.6, 13.7. Find the mean time. → 14.95Prompt: Add the four times carefully, lining up decimal points.
- Data (minutes of screen time): 37, 106, 126, 166, 146. Find the mean. → 116.2Prompt: Add all the values.
Hook · 5 min
- Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
- Share the objective: Mean absolute deviation (MAD). Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: The mean of 18, 24, 15, 21, 22 is 20. Find the mean absolute deviation.
- Step 1: Distances: 2, 4, 5, 1, 2
- Step 2: 2 + 4 + 5 + 1 + 2 = 14
- Step 3: 14 ÷ 5 = 2.8
- Answer: 2.8
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- The mean of 7, 11, 10, 0 is 7. Find the mean absolute deviation. → 3.5Prompt: Find how far each value is from the mean (ignore signs).
- Ethan's scores: 18, 21, 24, 21. Sofia's scores: 16, 26, 21, 21. Both have mean 21. Whose scores are more consistent (smaller MAD)? (Ethan / Sofia) → EthanPrompt: MAD measures how spread out the data is around the mean.
You do: independent practice · 10 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Ben's scores: 21, 24, 27, 24. Fatima's scores: 18, 30, 24, 24. Both have mean 24. Whose scores are more consistent (smaller MAD)? (Ben / Fatima) → BenPrompt: MAD measures how spread out the data is around the mean.
- The mean of 16, 15, 15, 8, 1 is 11. Find the mean absolute deviation. → 5.2Prompt: Find how far each value is from the mean (ignore signs).
Watch out for
- Forgetting to put data in order before finding the median.
- Reading a bar's height wrongly when the scale goes up in 2s or 5s.
Support and stretch
Support
- Review first: Calculate the mean, including decimal answers.
- Use concrete materials: squared paper for charts.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Move on to: Compare two groups using centre and spread.
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-6.
Free lesson plan from eurekami.com/lesson-plan-builder