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: 12, 12, 4, 8, 4 → 8Prompt: Add all the numbers.
- Find the median of: 30, 29, 15, 3, 18, 13, 18, 27 → 18Prompt: Put the numbers in order first.
- Find the mode of: 12, 17, 3, 12, 1, 8 → 12Prompt: The mode is the value that appears most often.
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.
- Diego has taken 4 tests. The scores of the first 3 are 60, 67, 59. The mean of all 4 is 64. What did Diego score on the last test? → 70Prompt: Mean × number of tests = total of all scores.
- The mean of 8 numbers is 9. A new number, 8, is added. What is the new mean? Round to 1 decimal place if needed. → 8.9Prompt: 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.
- Diego has taken 6 tests. The scores of the first 5 are 70, 66, 69, 75, 66. The mean of all 6 is 67. What did Diego score on the last test? → 56Prompt: Mean × number of tests = total of all scores.
- The mean of 4 numbers is 6. A new number, 29, is added. What is the new mean? Round to 1 decimal place if needed. → 10.6Prompt: Find the total of the original numbers.
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