Data collection: a week of ready-to-teach maths

Five lessons for Year 8 Statistics. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet with practice and a stretch section, plus twelve scene cards, a population of 100 students with a random number list to sample from, a reaction-time experiment, a mini-check and every answer with its working.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Print the two cut-out sheets, one copy per pair: the scene cards (Day 1) and the population of 100 with its random numbers (Day 2).
4. Open the free interactive unit on the board. Every plan says which picture to show and which buttons to press.
5. Teach straight from the plan. Timings, talk prompts, misconceptions and worked answers are all on the one page.

The idea in plain words

The population is the whole group we want to know about. A census collects data from every member; a sample collects it from some of them and uses it to estimate the whole. A census is complete but can be slow, costly or impossible; a sample is quicker and cheaper, and a random sample tends to represent the population, while a convenient one can mislead. Observation watches and records without changing anything; an experiment changes one thing on purpose and compares with a group that was not changed. Each choice has practical costs and consequences, including fairness, privacy and consent.

One day, one lesson

The five lessons fill a week of maths, one lesson of about 60 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point for two shorter sessions, and every worksheet ends with a stretch section for students who finish early.

Collecting data from students

The class data this week are anonymous and harmless: reaction times and travel times, with no names. If students collect data from others, they ask first, explain what it is for, and record no names.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Days 1 and 2 decide who to collect data from: everyone, or a sample, and how to choose it. Day 3 decides how: by watching or by changing something. Day 4 weighs the practical costs and the consequences, and Day 5 puts the choices together. It builds on collecting and displaying data in Year 7, and prepares sampling methods and statistical investigations later in Year 8.

Materials for the week (one trip)

• From the classroom: pencils, calculators, scissors, this pack printed.
• Cut-out sheet 1, one per pair: 12 scene cards (Day 1).
• Cut-out sheet 2, one per pair: the population of 100 and the random number list (Day 2).
• A 30 cm ruler per pair for the reaction-time experiment (Day 3).

Words for the word wall

population, sample, census, random sample, convenience sample, representative, bias, estimate, observation, experiment, control group, fair test, variable, cost, privacy, consent, ethical

Dear families

This week in maths, Year 8 is learning how data are collected: asking everyone (a census), asking some (a sample), watching (observation) or testing a change (an experiment), and what each costs and risks.

Try this at home

• When you see a survey result in the news, ask: who was asked, and how were they chosen?
• Taste a spoonful of soup to check the salt: that is a sample. Why does it work if the soup is stirred?
• Ask: why is the Australian Census held only every five years?
• Spot an online poll. Who is likely to answer it, and who is not?

Data I noticed this week

Fill one row a day. Name some data you saw or collected, how it was collected, and one problem it might have.

Printed from the free seegongsik Data collection teaching pack · seegongsik.com/au/y8/statistics/AC9M8ST01/pack

Census or sample?

The population is the whole group we want to know about. Students tell a population from a sample, sort twelve situations into census or sample, and give a practical reason for each choice.

We are learning to

• name the population for a question,
• say whether a census or a sample suits a situation,
• give a practical reason: size, cost, time, or that testing destroys what it tests.

Success criteria

• I can name the population and explain why the light globe test must use a sample.
• I can explain why a census suits a club of seven.

You need

Cut-out sheet 1 (the scene cards) and scissors, one set per pair; the worksheet each.

Lesson flow (about 60 minutes)

Two shorter sessions instead? Split after Part A; start the second with the reasons.

Watch for these ideas

• Thinking a sample is a separate group, rather than part of the population.
• Calling every survey a census.
• Forgetting that some tests destroy what they measure.

Answers

• Part A: census 1, 4, 6, 7, 10; sample 2, 3, 5, 8, 9, 11, 12.
• Part B: card 2: testing destroys the globes; card 3: millions of people: too many to ask; card 7: seven people: ask them all; card 12: a spoonful tells you about the pot.
• Part C: 1. all the Year 8 students at our school; 2. all Australians; 3. all the fish in the lake.
• Part D: it costs a great deal and takes a long time to collect and process the answers from every household.

Census or sample?

A. Sort the scenes

A census collects data from every member of the population; a sample collects it from some. Sort the twelve cards, and record the card numbers.

B. Why?

C. Name the population

1. To find the average height of Year 8 students at our school, the population is ________________________________
2. To find how many hours Australians spend online each week, the population is ________________________________
3. To find the average length of fish in a large lake, the population is ________________________________

D. Stretch: the national Census

Australia’s Census asks every household, but it is held only every five years. Give two practical reasons for the gap.

Sampling in practice

A sample is only as good as the way it is chosen. Students take random samples of 10 from a list of 100 students’ travel times, compare the sample means with the census mean, and see what happens when they take the first 10 on the list instead.

We are learning to

• choose a random sample with a list of random numbers,
• estimate a population mean from a sample mean,
• explain why a convenient sample can be biased.

Success criteria

• I can take a random sample of 10 from the list and find its mean.
• I can explain why the first 10 students on the list give a poor estimate.

You need

Cut-out sheet 2 (the population and the random numbers) per pair; a calculator and the worksheet each.

Lesson flow (about 60 minutes)

Two shorter sessions instead? Split after Part A; start the second with the class results.

Watch for these ideas

• Picking “random” students by choosing ones that look interesting.
• Counting a repeated number twice in one sample.
• Expecting a sample mean to equal the census mean exactly.

Answers

• Part A, for example from row 1: students 17, 80, 34, 94, 42, 95, 22, 63, 24, 59 (repeats skipped), mean 26.4 minutes.
• Part B: the census mean is 2383 ÷ 100 = 23.8 minutes. Samples taken in turn from the list give 26.4, 29.2, 25.1, 21.7: close, but none exact.
• Part C: students 00 to 09 average 3.7 minutes, far below 23.8: in street order the first ten live closest to school.
• Part D: for example, every tenth student from a random start between 00 and 09; it spreads the sample along the whole street list.

Sampling in practice

Cut-out sheet 2 lists 100 students, numbered 00 to 99, with each one’s travel time to school in minutes. The list is in order of street address, so neighbours sit together.

A. A random sample

Start at your row of the random number list. Each two-digit number is a student. Skip a number you have already used. Record 10 students and their times, then find the mean.

Mean of my sample = ______ minutes

B. Samples and the census

All 100 times add to 2383, so the census mean is ______ minutes. Four random samples of 10 taken in turn from the list had means of 26.4, 29.2, 25.1, 21.7 minutes. How close are they to the census? Is yours?

C. The first ten

Ari takes the first 10 students on the list, 00 to 09, because it is quick. Find their mean time. Why is it so far from the census mean?

D. Stretch: no random numbers

Without random numbers, how could you choose 10 students from the list fairly? Why does your method suit a list in street order?

Observation and experiment

Observation watches without changing anything; an experiment changes one thing on purpose and compares. Students sort six situations, run a reaction-time experiment with a dropped ruler, and compare a practice group with a no-practice group.

We are learning to

• tell an observation from an experiment,
• plan a fair experiment with one group changed and one not,
• compare two groups and say what the results do and do not show.

Success criteria

• I can say why counting birds at a feeder is an observation.
• I can name what is changed, what is measured and what is kept the same in the ruler experiment.

You need

A 30 cm ruler per pair; the worksheet each.

Lesson flow (about 60 minutes)

Two shorter sessions instead? Split after Part A; start the second with the ruler drop.

Watch for these ideas

• Calling any data collection an experiment.
• Changing two things at once, so the cause is unclear.
• Leaving out the group that is not changed.

Answers

• Part A: observation 1, 4, 5; experiment 2, 3, 6.
• Part B: changed: practice or none; measured: the catch distance in cm; kept the same: the ruler, the start at 0, the hand, the finger gap and how the drop is made.
• Part C: means 12.25 cm with practice and 16 cm without, about 3.75 cm sooner after practice. With eight students a group this suggests practice helps; it does not prove it for everyone.
• Part D: no: by watching alone, students who practise might differ in other ways (age, sport, sleep). Changing only the practice and comparing rules those out.

Observation and experiment

A. Watch or change?

B. The ruler drop

Does practice make you catch a falling ruler sooner? Plan the experiment, then run it.

C. A class’s results

One class’s catch distances in centimetres. Find each group’s mean and compare.

Practice: 14, 11, 13, 10, 12, 15, 11, 12. No practice: 17, 15, 19, 14, 16, 18, 13, 16. What do the results show? What do they not show?

D. Stretch: could we just watch?

Could you find out whether practice helps by observation alone? Why is an experiment better here?

Practicalities and implications

Every way of collecting data has costs and consequences. Students weigh cost, time and accuracy, then find the problem in six data-collection plans, from biased samples to privacy, and fix them.

We are learning to

• weigh the cost, time and accuracy of a census and a sample,
• recognise bias from convenient samples, volunteers and leading questions,
• explain privacy, consent and fairness in collecting data.

Success criteria

• I can name the problem in a data-collection plan and say how to fix it.
• I can explain why a representative sample is spread across the population.

You need

The worksheet each.

Lesson flow (about 60 minutes)

Two shorter sessions instead? Split after Part A; start the second with the plans.

Watch for these ideas

• Thinking a bigger sample fixes a biased way of choosing it.
• Missing a leading question because it sounds polite.
• Collecting names or details the question does not need.

Answers

• Part A: a census costs more and takes longer, but is complete; a sample is cheaper and quicker, but only estimates. A sample is the only choice when testing destroys things or the population is too big to reach.
• Part B: 1 convenience sample; 2 leading question; 3 volunteers only; 4 no comparison; 5 too small; 6 privacy.
• Part C, for example: 1: choose students at random from the whole school roll; 2: ask “Is the school day too long, about right or too short?”; 3: ask a random sample, not whoever chooses to answer.
• Part D: answers vary; for example students may not answer honestly about their own screen time, the data are private, and asking everyone takes lesson time.

Practicalities and implications

A. Census or sample: the costs

B. Spot the problem

Each plan has one problem from this list: leading question, convenience sample, too small, privacy, no comparison, volunteers only. Write the problem beside each plan.

C. Fix three plans

Rewrite plans 1, 2 and 3 so the problem is gone.

D. Stretch: what follows from the data?

The school wants a census of every student’s screen time. Name two problems this could cause, and how to reduce them.

Choosing a technique

Choosing how to collect data comes first in any investigation. Students choose a technique for four questions, plan one, say what its data cannot show, and play the quiz as a class game.

We are learning to

• choose a census, a sample, an observation or an experiment to suit a question,
• justify the choice by its practicalities,
• say what the data will and will not be able to show.

Success criteria

• I can choose a technique for a question and give two reasons.
• I can name one thing my plan’s data could not show.

You need

The worksheet each; the self-check quiz at the bottom of the unit page for the game.

Lesson flow (about 60 minutes)

Two shorter sessions instead? Split after Part A; start the second with the plan and the quiz.

Watch for these ideas

• Choosing an experiment when nothing is being changed.
• Choosing a census for a population too big to reach.
• Forgetting to say how a sample will be chosen.

Answers

• Part A: 1 experiment: change one thing (music or none) and compare; 2 sample (or a census of a small year group): too many to ask quickly; a random sample estimates it; 3 observation: watch and count without changing anything; 4 census: only nine people: ask them all.
• Part B: plans vary; a complete plan fills every row, chooses a sample at random, and records no names.
• Part C, for example: a sample only estimates; an observation shows what happens but not why; an experiment in one class may not hold for everyone.
• Part D: for example, an experiment on a random sample of students, or an observation of a sample of times of day.

Choosing a technique

A. Which technique?

B. Plan one

Choose one question from Part A and plan how to collect its data.

C. The limits

Name one thing your data will not be able to show, and why.

D. Stretch: two at once

Describe an investigation that uses a sample and an experiment together. What does each part do?

Twelve scene cards

For Day 1, one set per pair

Cut out the cards. Would you collect data from every member of the population (a census), or from some of them (a sample)?

Teacher note: census 1, 4, 6, 7, 10; sample 2, 3, 5, 8, 9, 11, 12. No row or column of cards gives an answer away.

The population of 100

For Day 2, one per pair

Each cell gives a student’s number (00 to 99) and their travel time to school in minutes. The list is in order of street address, so neighbours sit together.

Random numbers

Each two-digit number picks a student. Start at the row your teacher gives you and read along; skip a number you have already used.

100 students in all. The numbers were made by a computer’s random number generator, so every student is equally likely to be picked.

What we know: Data collection

Work on your own. Give a reason with each answer.

1. Explain the difference between a population and a sample, with an example. ______________________
2. A factory checks whether its matches light by striking them. Should it use a census or a sample? Why? ______________________
3. Which is an experiment: (a) counting the buses that arrive late at a stop; (b) giving one group a new study app and comparing its test scores with a group that did not use it? ______________________
4. Sam asks the first 20 people leaving a gym how often Australians exercise. What is wrong with this sample? ______________________
5. Rewrite this question so it does not lead: “Isn’t recycling the most important thing we can do?” ______________________
6. Give one advantage and one disadvantage of a census. ______________________
7. A random sample of 10 Year 8 students averaged 7.1 hours of sleep, but a census of the year group averaged 8.2. Give a reason the two could differ. ______________________
8. Why should a survey about students’ habits not ask for their names? ______________________

Answers and marking guide

Answers with working

1. The population is the whole group of interest, such as all Year 8 students; a sample is a part of it, such as 30 of them.
2. A sample: striking a match uses it up, so testing every match would leave none to sell.
3. (b): it changes one thing (the app) and compares with a group that was not changed. (a) only watches.
4. It is a convenient, biased sample: people leaving a gym exercise more than most, so it overestimates.
5. For example: “How important is recycling to you: very, a little, or not at all?”
6. Advantage: it is complete, with no sampling error. Disadvantage: it costs more and takes longer, and can be impossible.
7. Ordinary variation between samples, or a sample that by chance or by its method missed part of the year group.
8. Privacy: answers can be traced to people, and students may not answer honestly; names are not needed.

A quick three-level guide

Eight questions, four ideas. A student at standard answers most questions and gives a practical reason for each choice.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: census or sample, sampling in practice, observation and experiment, implications, and choosing a technique.