You will learn
- State conclusions supported by data.
- Spot misleading graphs.
- Say what data cannot tell.
- Write evidence-based statements.
Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- A conclusion must be supported by evidence.
- Scales that start above 0 can mislead.
- Small samples may not represent everyone.
- Two things that rise together are not always cause and effect.
Words to know
What the data shows.
Data that supports a claim.
Giving a false impression.
An unfair slant.
1. Discover: is it fair?
A graph starts its scale at 90 so two bars of 95 and 100 look very different. Is that fair?
2. Understand: conclusions
- A conclusion must be supported by the data: “Class B scores are more spread out (range 8 vs 6).”
- A graph whose scale starts above 0 can exaggerate differences.
- A small sample may not represent a large group.
- Correlation is not proof of cause: ice cream sales and sunburn both rise in summer.
Idea 1: Misleading graphs
A graph starting at 90 can exaggerate differences. Asking only 3 people is not enough.
Idea 2: Cause
Ice cream sales and sunburn rise together because of summer weather, not because ice cream causes sunburn.
Idea 3: Good conclusion
“Class B scores are more spread out (range 8 vs 6).” Bias is an unfair slant.
Why evidence? Without it a conclusion is only an opinion.
3. Worked examples
Example 1 (I show you): Decide
Graph starting at 90
- Look at the scale.
Answer: misleading
Example 2 (We do it together): Decide
Ask 3 people
- Too few.
Answer: not enough
Example 3 (You try): Conclude
Range 6 vs 8
Show the steps and answer
- Compare spread.
Answer: class B more spread out
Did you know?
Correlation means two things move together; it does not prove one causes the other.
Why this matters
Careful conclusions protect us from false claims.
4. Explore: judge
You need two graphs.
- Look at the scale.
- Look at the sample size.
- Write a conclusion.
- Write one thing the data cannot show.
Think about it: what did you notice?
Fair or misleading.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The data show that ___.
- The evidence is ___.
- This could mislead because ___.
- We cannot say ___ because ___.
Guided practice
Question 1. Does starting at 90 exaggerate?
Yes.
Question 2. Does a small sample represent everyone?
Not necessarily.
Question 3. Must conclusions use evidence?
Yes.
Independent practice
Level 1: Start
- Is a graph starting at 90 misleading?
- Is asking 3 people enough?
- Write a conclusion for range 6 vs 8
- Does ice cream cause sunburn?
- What does bias mean?
Level 2: Grow
- A survey of only team members about sport. Is it biased?
- Where should a bar graph scale start?
- Do two things rising together prove cause?
Level 3: Stretch
- Write a conclusion for means of 12 and 15.
- More fire engines go to bigger fires. Do engines cause fires?
- Ben says asking 10 people tells us about the whole world. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Two bars of 95 and 100 look very different on a scale from 90. Why?
Show a sample answer
The scale starts too high.
Another one. Class A scores 5, 7, 8, 9, 11 and class B scores 4, 6, 8, 10, 12. Write one conclusion.
Show a sample answer
Both classes have a mean of 8, but class B is more spread out.
7. Common mistakes
Fix: Check the scale.
Fix: Look for another reason.
Fix: Ask more people.
8. Lesson summary and revision card
- I can state conclusions supported by data.
- I can spot misleading graphs.
- I can say what data cannot tell.
- I can write evidence-based statements.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Evidence.
- Check scale and sample.
- Beware bias.
11. Next lesson
You have finished Grade 5 Mathematics. Well done!
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- Is a graph that starts at 90 misleading? Explain. [3 marks]
- Is asking 3 people enough? Explain. [2 marks]
- Write a conclusion for two classes with ranges 6 and 8. [2 marks]
- Does ice cream cause sunburn? Explain. [3 marks]
- What does bias mean? [2 marks]
Total: 12 marks.
Marking guide and model answers
- Yes [1]. Bars look very different [1]. It exaggerates differences [1].
- No [1]. Too few to represent everyone [1].
- Class B is more spread out [1]; range 8 vs 6 [1]
- No [1]. Both rise in summer [1]. Hot weather is the real cause [1].
- An unfair slant [1]; it can make results false [1]
Score guide: 11 to 12 = secure. 8 to 10 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- Is a graph starting at 90 misleading? (yes/no)
- Is asking 3 people enough? (yes/no)
- Does ice cream cause sunburn? (yes/no)
- What does bias mean
- A conclusion needs
- A graph scale starting at 90 can…
- A conclusion needs…
- A sample of 3 people…
- Ice cream sales and sunburn both rise because…
- Bias is…
Homework
Find a graph in a newspaper and decide if it is fair.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Is a graph starting at 90 misleading? (yes/no) | yes | 2 |
| Is asking 3 people enough? (yes/no) | no | 2 |
| Does ice cream cause sunburn? (yes/no) | no | 2 |
| What does bias mean | unfair slant | 2 |
| A conclusion needs | evidence | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 yes; 2 no; 3 no; 4 unfair slant; 5 evidence.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 exaggerate differences; 7 evidence; 8 may not represent everyone; 9 of summer weather; 10 an unfair slant.
Independent practice answers. Level 1: 1 yes, it exaggerates differences; 2 no, it is too few; 3 class B scores are more spread out (range 8 vs 6); 4 no, both rise in hot weather; 5 an unfair slant. Level 2: 1 yes; 2 0; 3 no. Level 3: 1 The second group has the higher mean (15 vs 12).; 2 No. Bigger fires need more engines.; 3 10 people is too few and may not represent everyone..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 State conclusions supported by data | 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 Spot misleading graphs | 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 Say what data cannot tell | 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 evidence-based statements | 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 |
Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Believing every graph. Check the scale.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Read simple graphs.
- 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.
For parents and guardians
In this lesson your child draws careful conclusions from data. You do not need to be good at mathematics to help.
- Discuss claims in advertisements.
- Ask: what is the evidence?
- Spot graphs that start above 0.
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: state conclusions supported by data; spot misleading graphs; say what data cannot tell; write evidence-based statements.
Prerequisite knowledge. Lessons 3, 4 and 7.
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. 45–60 minutes. It can be split into two shorter sessions.
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 two graphs. 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.
Key questions. What does the data show? Could it mislead?
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. Believing every graph. Check the scale.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 12-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Read simple graphs. 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
This lesson is based on the sources below, and no official 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. Where a standard code is named, it points to the official framework.
Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 5 » Measurement & Data. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 6.SP.B.5 and MP3; Cambridge Primary Mathematics Stage 6 (drawing conclusions). These sources informed the lesson.