You will learn
- Use data to answer a question.
- Say which category is most popular.
- Make a statement supported by the data.
- Say what the data cannot tell us.
Version 0.2 · expanded edition · expert review pending Standards alignment: pending verification. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Use the data to answer a question.
- Find the most popular category.
- Make a statement supported by the data.
- Say what the data cannot tell us.
Words to know
What the data tells us.
Numbers that support a statement.
Chosen by many.
Not unfairly favouring anyone.
1. Discover: favourite colour
A teacher asked 30 pupils for their favourite colour: blue 12, red 9, green 6, yellow 3. What can she say about the class?
2. Understand: drawing conclusions
A conclusion is a statement that the data supports. Always give evidence from the numbers.
- Blue is the most popular colour: 12 pupils chose it.
- Blue was chosen by 12 − 6 = 6 more pupils than green.
- Red and green together: 9 + 6 = 15, which is half of 30.
- Blue was chosen 4 times as often as yellow: 3 × 4 = 12.
The data tells us about these 30 pupils only. It does not tell us about every child in the school.
Idea 1: Most popular
Blue 12, red 9, green 6, yellow 3. The most popular is blue and the least popular is yellow.
Idea 2: Evidence
Total asked: 12 + 9 + 6 + 3 = 30. Blue minus yellow: 12 − 3 = 9. A good conclusion has evidence.
Idea 3: Limits
The data does not tell us why pupils chose a colour.
Why limits? A conclusion should not say more than the data shows.
3. Worked examples
Example 1 (I show you): Most
Which colour is the most popular?
- Biggest number.
Answer: blue
Example 2 (We do it together): Total
How many pupils were asked?
- 12 + 9 + 6 + 3.
Answer: 30
Example 3 (You try): Difference
Blue minus yellow
Show the steps and answer
- 12 − 3.
Answer: 9
Did you know?
A fair survey asks everyone the same question.
Why this matters
Conclusions from data help us decide what to do.
4. Explore: write conclusions
You need a frequency table.
- Find the most and fewest.
- Find one difference.
- Write a conclusion with evidence.
- Say one thing the data cannot tell.
Think about it: what did you notice?
Use numbers in every sentence.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The most popular is ___.
- The evidence is ___.
- My conclusion is ___.
- The data cannot tell us ___.
Guided practice
Question 1. Most popular colour?
Blue.
Question 2. Red and green together?
15.
Question 3. How many more chose blue than green?
6.
Independent practice
Level 1: Start
- Total pupils asked: 12, 9, 6, 3
- Fewest chose which colour?
- Blue minus yellow
- Red plus yellow
- Is 15 half of 30? (yes/no)
Level 2: Grow
- Green plus yellow
- Blue minus green
- Which colour is the most popular?
Level 3: Stretch
- Which two colours together make 21?
- Is “blue is the best colour in the world” a good conclusion from the data?
- Ali says yellow is the most popular because it is last in the list. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A shop sells 20 red caps, 12 blue and 8 green. Which colour should it order most of?
Show a sample answer
Red.
Another one. Write a conclusion from the colour data and give evidence.
Show a sample answer
Blue is the most popular because 12 pupils chose it.
7. Common mistakes
Fix: Use evidence from the data.
Fix: Only say what the numbers support.
Fix: Use the numbers.
8. Lesson summary and revision card
- I can use data to answer a question.
- I can say which category is the most popular.
- I can make a statement supported by the data.
- I can say what the data cannot tell us.
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
- Conclusions need evidence.
- Use numbers in statements.
- Data speaks only for those asked.
11. Next lesson
You have finished Grade 3 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.
- Blue 12, red 9, green 6, yellow 3. Which colour is the most popular? [1 mark]
- How many pupils were asked in total? [2 marks]
- Find blue minus green. [2 marks]
- What does a conclusion need? [1 mark]
- A shop sells 20 red caps, 12 blue and 8 green. Which should it order most? Explain. [3 marks]
Total: 9 marks.
Marking guide and model answers
- Blue [1]
- 12 + 9 + 6 + 3 [1] = 30 [1]
- 12 − 6 [1] = 6 [1]
- Evidence from the data [1]
- Red caps [1]. 20 is the highest [1]. It sells the most [1].
Score guide: 8 to 9 = secure. 6 to 7 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- Total of 12, 9, 6, 3
- Fewest chose which colour
- Blue minus yellow
- Red plus yellow
- Is 15 half of 30? (yes/no)
- Blue 12, red 9, green 6, yellow 3. Most popular: ___
- Total pupils asked: ___
- Blue minus green: ___
- Red and green together: ___
- A conclusion needs ___ from the data.
Homework
Survey 10 people, make a table and write two conclusions with evidence.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Total of 12, 9, 6, 3 | 30 | 2 |
| Fewest chose which colour | yellow | 2 |
| Blue minus yellow | 9 | 2 |
| Red plus yellow | 12 | 2 |
| Is 15 half of 30? (yes/no) | yes | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 30; 2 yellow; 3 9; 4 12; 5 yes.
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 blue; 7 30; 8 6; 9 15; 10 evidence.
Independent practice answers. Level 1: 1 30; 2 yellow; 3 9; 4 12; 5 yes. Level 2: 1 9; 2 6; 3 blue. Level 3: 1 blue and red; 2 No, the data shows only what these pupils chose; 3 Yellow has only 3 votes. Use the numbers..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Use data to answer a question | 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 category is most popular | 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 Make a statement supported by the 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 |
| O4 Say what the data cannot tell us | 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 8 of 12 core questions correct; Silver = all 12; Gold = all 12 plus both challenge questions. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Making a claim the numbers do not show. Use evidence from the data.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise reading tables and answering one question at a time.
- 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 uses data to draw conclusions. You do not need to be good at mathematics to help.
- Make a family survey and draw a conclusion.
- Ask: what is your evidence?
- Talk about what a survey cannot tell us.
- 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: use data to answer a question; say which category is most popular; make a statement supported by the data; say what the data cannot tell us.
Prerequisite knowledge. Lessons 1 to 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. 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 a frequency table. 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? What is the evidence? What can it not tell us?
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. Making a claim the numbers do not show. Use evidence from the data.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 9-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. Practise reading tables and answering one question at a time. 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.
Research used to shape this lesson. Common Core 3.MD.B.3 and 2.MD.D.10; Cambridge Primary Mathematics Stage 3 (interpreting data). These sources informed the lesson; no official alignment is claimed.