Courseversity

Collecting data

Primary EducationGrade 6MathematicsCV-PRI-G06-MATH-DAT-U01-L0245–60 min

You will learn

  • Choose a method.
  • Choose a sample.
  • Spot bias.
  • Record accurately.

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

The lesson in 60 seconds

  1. A census asks everyone; a sample asks part of the group.
  2. Bias gives an unfair picture.
  3. Random samples are fairer.
  4. Record data carefully as you go.

Words to know

survey
Asking questions.
sample
A part of the population.
bias
Unfair slant.
census
Data from everyone.

1. Discover: asking whom?

To find how pupils get to school you ask only those who live near. Is that fair?

2. Understand: collecting data

  • A census asks everyone; a sample asks a part.
  • A good sample is random and large enough.
  • Asking only nearby pupils is biased.
  • Record answers with tallies or a table as you go.

Idea 1: Sample

Asking 10 of 100 pupils is a sample. Asking everyone is a census.

Idea 2: Bias

Asking only the football team about favourite sport is biased. Choosing pupils by lottery is random and fair.

Idea 3: Methods

Heights are collected by measuring. Record as you go to avoid forgetting.

Why random? Everyone has an equal chance.

Remember: Fair, random, large enough.

3. Worked examples

Example 1 (I show you): Type

10 of 100 pupils

  1. Part of the group.

Answer: sample

Example 2 (We do it together): Bias

Only the football team

  1. They favour football.

Answer: biased

Example 3 (You try): Method

Heights

Show the steps and answer
  1. Use a ruler.

Answer: measuring

Did you know?

A larger random sample is usually more reliable than a small one.

Why this matters

Fair data collection leads to trustworthy conclusions.

4. Explore: plan

You need paper.

  1. Write the question.
  2. Choose a sample.
  3. Collect.
  4. Record.
Think about it: what did you notice?

A fair survey.

5. Practise

Say it in a sentence

Use these starters when you talk about the lesson. Say them out loud.

  • The group is ___ and the sample is ___.
  • It is biased because ___.
  • I will collect data by ___.
  • I will record ___.

Guided practice

Question 1. Asking everyone?

census.

Question 2. Asking only nearby pupils?

biased.

Question 3. A good sample is?

random.

Independent practice

Level 1: Start

  1. Census or sample: asking 10 of 100 pupils
  2. Biased? Asking only the football team about favourite sport
  3. Biased? Asking pupils chosen by lottery
  4. Method for heights
  5. Why record as you go?

Level 2: Grow

  1. Asking all 200 pupils
  2. Asking 20 of 200 pupils
  3. Names drawn from a hat

Level 3: Stretch

  1. To find siblings per pupil, use
  2. Asking only the choir about favourite music is
  3. Ben says record results at the end. What is wrong?

Answers are in the answer key below. Try first, then check.

6. Apply: everyday mathematics

You ask only the football team about favourite sport. Problem?

Show a sample answer

Biased.

Another one. You want to know the favourite lunch of all pupils. Describe a fair sample.

Show a sample answer

Choose pupils at random from every class

7. Common mistakes

Mistake: Asking only friends.
Fix: Choose randomly.
Another mistake: Asking only friends.
Fix: Choose a random sample.
Another mistake: Recording from memory.
Fix: Record as you go.

8. Lesson summary and revision card

I can…

  • I can choose a method.
  • I can choose a sample.
  • I can spot bias.
  • I can record accurately.

9. Check and master

Answer all 14 questions. You will see feedback after each one.

1. Asking 10 of 100 pupils:

2. Asking only the football team about favourite sport:

3. Choosing pupils by lottery:

4. Heights are collected by:

5. Record as you go to:

6. Asking all 200 pupils is a

7. Asking 20 pupils out of 200 is a

8. Asking only the choir about favourite music is

9. Names drawn from a hat give a

10. To find how many siblings pupils have, use

11. To find jump lengths, use

12. A bigger random sample is usually

Challenge 1. Asking everyone is a:

Challenge 2. Asking pupils leaving the library about their favourite hobby will probably be biased because

Your result appears here after you answer every question.

10. Key takeaways

  • Sample or census.
  • Random is fair.
  • Avoid bias.

11. Next lesson

Next lesson: Organising data. Keep going with the next idea in this course.

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.

  1. Asking 10 of 100 pupils is a census or a sample? Explain. [2 marks]
  2. Is asking only the football team about favourite sport biased? Explain. [2 marks]
  3. Is choosing pupils by lottery fair? Explain. [2 marks]
  4. How are heights collected? [1 mark]
  5. Ali says there is no need to record as you go. Is he right? Explain. [3 marks]

Total: 10 marks.

Marking guide and model answers
  1. Only part of the group is asked [1]; sample [1]
  2. They are more likely to choose football [1]; biased [1]
  3. Everyone has an equal chance [1]; random and fair [1]
  4. Measuring [1]
  5. No [1]. You may forget or mix up results [1]. Record as you go to avoid forgetting [1].

Score guide: 9 to 10 = secure. 6 to 8 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.

Printable worksheet

  1. 10 of 100 pupils
  2. Football team only
  3. Lottery selection
  4. Heights by
  5. Asking everyone
  6. Asking 10 of 100 pupils
  7. Asking only the football team
  8. Choosing pupils by lottery
  9. Heights are collected by
  10. Record as you go to

Homework

Plan a survey about favourite subjects.

Answer key and marking scheme

Question Expected response Marks
10 of 100 pupils sample 2
Football team only biased 2
Lottery selection fair 2
Heights by measuring 2
Asking everyone census 2
Total 10

Practice answers: Worksheet: 1 sample; 2 biased; 3 fair; 4 measuring; 5 census.

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 a sample; 7 biased; 8 random and fair; 9 measuring; 10 avoid forgetting.

Independent practice answers. Level 1: 1 a sample; 2 yes, biased; 3 no, random and fair; 4 measuring; 5 to avoid forgetting. Level 2: 1 census; 2 sample; 3 random sample. Level 3: 1 a survey; 2 biased; 3 You may forget or mix them up; record as you go..

Mastery and remediation

Objective Bronze (Developing) Silver (Proficient) Gold (Advanced)
O1 Choose a method 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 Choose a sample 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 Spot bias 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 Record accurately 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

  1. Find the misconception: Asking only friends. Choose randomly.
  2. Explain another way: use real objects first, then pictures.
  3. Show a simpler example: Tally marks.
  4. Guided practice: work through one example together and let the learner try the next one.
  5. Reassess: use the quiz again or the worksheet.
  6. Move on when the learner shows Silver-level evidence independently.

For parents and guardians

In this lesson your child learns how to collect data fairly. You do not need to be good at mathematics to help.

  • Run a small family survey.
  • Ask: is everyone included fairly?
  • Record results as you go.
  • 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: choose a method; choose a sample; spot bias; record accurately.

Prerequisite knowledge. Lesson 1.

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 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.

Key questions. Who is asked? Could the sample be unfair?

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. Asking only friends. Choose randomly.

13–15. Assessment questions, answer keys, marking scheme

Use the quiz and worksheet on this page. The 10-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. Tally marks. 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 6 » Statistics & Probability. 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.A.2 and 7.SP.A.1; Cambridge Primary Mathematics Stage 6 (collecting data). These sources informed the lesson.

Keep learning

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