You will learn
- Compare two datasets.
- Say which has the greater mean.
- Compare spreads using range.
- Write a comparison.
Version 0.1 · published for early use · expert review pending Standards alignment: pending verification. Not yet reviewed against the Courseversity scorecard.
Student lesson
Words to know
A group of data.
How far apart values are.
Total ÷ count.
Greatest minus least.
1. Discover: two classes
Class A scores: 5, 7, 8, 9, 11. Class B: 4, 6, 8, 10, 12. Which class did better?
2. Understand: comparing datasets
- Mean A: 40 ÷ 5 = 8. Mean B: 40 ÷ 5 = 8. Same mean.
- Median: both 8.
- Range A: 11 − 5 = 6. Range B: 12 − 4 = 8.
- Conclusion: same average, but B is more spread out.
3. Explore: compare
You need paper.
- Find each mean.
- Find each median.
- Find each range.
- Write a sentence.
Think about it: what did you notice?
Same mean, B more spread.
4. Practise
Guided practice
Question 1. Mean of A?
8.
Question 2. Range of B?
8.
Question 3. Which is more spread?
B.
Independent practice
- Range of A
- Mean of B
- Median of A
- Who has the greater range?
- Do they have the same mean?
Answers are in the answer key below. Try first, then check.
5. Apply: everyday mathematics
A has range 6 and B has range 8. Which is more spread out?
Show a sample answer
B.
6. Common mistake
Fix: Compare mean and range.
7. Check and master
Answer all questions. You will see feedback after each one.
Your result appears here after you answer every question.
8. Key takeaways
- Centre and spread.
- Use a full sentence.
- Same mean can hide differences.
9. Next lesson
Next lesson: Drawing conclusions. Keep going with the next idea in this course.
Printable worksheet
- Range of A
- Mean of B
- Median of A
- Greater range
- Same mean? (yes/no)
Homework
Compare the heights of two groups of five people.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Range of A | 6 | 2 |
| Mean of B | 8 | 2 |
| Median of A | 8 | 2 |
| Greater range | B | 2 |
| Same mean? (yes/no) | yes | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 6; 2 8; 3 8; 4 B; 5 yes.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, challenge C.
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Compare two datasets | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O2 Say which has the greater mean | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O3 Compare spreads using range | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O4 Write a comparison | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
Proposed Courseversity thresholds for this page: Bronze = at least 3 of 5 core questions correct; Silver = all 5; Gold = all 5 plus the challenge. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Comparing only one value. Compare mean and range.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Mean of small sets.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: compare two datasets; say which has the greater mean; compare spreads using range; write a comparison.
Prerequisite knowledge. Lesson 6.
Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.
Preparation. Gather the counters and draw the example pictures on the board before the lesson.
Suggested duration. 35–45 minutes.
6–9. Teaching procedure, explanation notes, guided and independent activities
Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.
Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.
Guided activity (10 min). You need paper. Learners follow the Explore steps in pairs.
Independent activity (10 min). Learners complete the independent practice and the worksheet.
Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.
Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.
10–12. Differentiation, formative assessment, common misconceptions
Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.
Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.
Misconceptions. Comparing only one value. Compare mean and range.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-mark scheme and all answers are in the answer key above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Mean of small sets. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.
Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.
Sources and standards
Alignment is pending verification and no external endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Specific standard codes will be added once checked against the official documents.