Math lesson plan · 6th grade (Year 7 in England) · 45 minutes
Problems with the mean
Statistics and probability
CCSS 6.SP.B.5.CEngland: KS3 StatisticsEngland: GCSE Foundation StatisticsEngland: 11+ Statistics
Objective and success criteria
Students will: Problems with the mean.
- 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: Mean, median, mode and range
Leads to: the next skill in this area.
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 (Mean, median, mode and range). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Find the mean of: 5, 6, 3, 10, 7, 11 → 7Prompt: Add all the numbers.
- Find the median of: 21, 6, 22, 16, 2 → 16Prompt: Put the numbers in order first.
- Find the range of: 14, 9, 19, 15, 14, 13 → 10Prompt: Range = largest − smallest.
Hook · 5 min
- Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
- Share the objective: Problems with the mean. 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: Hiro has taken 3 tests. The scores of the first 2 are 96, 86. The mean of all 3 is 90. What did Hiro score on the last test?
- Step 1: 90 × 3 = 270
- Step 2: 96 + 86 = 182
- Step 3: 270 − 182 = 88
- Answer: 88
- 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.
- Amara has taken 6 tests. The scores of the first 5 are 85, 70, 71, 83, 71. The mean of all 6 is 78. What did Amara score on the last test? → 88Prompt: Mean × number of tests = total of all scores.
- The mean of 5 numbers is 15. A new number, 18, is added. What is the new mean? Round to 1 decimal place if needed. → 15.5Prompt: Find the total of the original numbers.
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.
- The mean of 4 numbers is 18. A new number, 23, is added. What is the new mean? Round to 1 decimal place if needed. → 19Prompt: Find the total of the original numbers.
- Ines has taken 5 tests. The scores of the first 4 are 62, 76, 62, 58. The mean of all 5 is 68. What did Ines score on the last test? → 82Prompt: Mean × number of tests = total of all scores.
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: Mean, median, mode and range.
- 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
- 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