Math lesson plan · 6th grade (Year 7 in England) · 60 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 · 6 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 (kg of recycling collected each week): 52, 60, 20, 55, 56. Find the mean. → 48.6Prompt: Add all the values.
- Four runners' 100 m times in seconds: 15.8, 12.4, 14.4, 14.3. Find the mean time. → 14.225Prompt: Add the four times carefully, lining up decimal points.
- Data (text messages sent in a day): 33, 57, 55, 57, 52. Find the mean. → 50.8Prompt: Add all the values.
Hook · 6 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 · 12 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 · 12 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 15, 16, 13, 12 is 14. Find the mean absolute deviation. → 1.5Prompt: Find how far each value is from the mean (ignore signs).
- Jamal's scores: 16, 18, 20, 18. Diego's scores: 14, 22, 18, 18. Both have mean 18. Whose scores are more consistent (smaller MAD)? (Jamal / Diego) → JamalPrompt: MAD measures how spread out the data is around the mean.
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Hiro's scores: 26, 29, 32, 29. Ana's scores: 21, 37, 29, 29. Both have mean 29. Whose scores are more consistent (smaller MAD)? (Hiro / Ana) → HiroPrompt: MAD measures how spread out the data is around the mean.
- The mean of 3, 4, 1, 16 is 6. Find the mean absolute deviation. → 5Prompt: 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