Statistical Investigations: a week of ready-to-teach maths

Five days of lessons for Year 6 Statistics. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus thirty survey slips and investigation cycle cards, a mini-check and every answer.

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. Cut out the survey slips for Day 3 and the investigation cycle cards for Day 1, one set of each for each pair.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. Decide whether your class will also collect its own data on Day 2; the worksheets work either way.

No maths background needed

This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week: an investigation is a cycle (question, collect, analyse, interpret, communicate), and every stage serves the question. The week follows one investigation all the way round: the school wants fewer cars at the gate in the morning, so the class asks: “How do the students in our class travel to school, and could more of them walk or ride?”

One day, one lesson

The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.

Words to watch

A statistical question expects answers that vary across a group. A variable is the thing you record about each person, such as how they travel. A frequency table counts each category; a two-way table counts two things at once, such as how students travel and how far away they live. Findings are what the data shows; limitations are the reasons to be careful with them.

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

Each day is one stage of the same investigation, so by Friday the class has a finished report. It builds on comparing data sets (AC9M6ST01) and critiquing other people’s claims (AC9M6ST02): this time the children make the claims, and test them the same way. It leads to investigations with numerical data and summary statistics in Year 7 (AC9M7ST03).

Materials for the week (one trip)

• All week: grid paper, rulers and coloured pencils.
• For Day 1: the investigation cycle cards, one set for each pair.
• For Day 2: a copy of the class survey for each child, if your class collects its own data.
• For Day 3: the thirty survey slips, one set for each pair. For Day 5: paper for a report or a poster.

Words for the word wall

investigation, statistical question, refine, problem, variable, survey, tally, frequency table, two-way table, column graph, analyse, interpret, finding, limitation, report

Dear families

This week in maths, Year 6 runs a statistical investigation from start to finish: posing a question, collecting data, organising it, deciding what it shows and reporting it.

Try this at home

• Think of a question about your household with answers that vary, such as how many minutes each person takes to get ready in the morning.
• Collect the answers in a tally for a few days.
• Decide together what the data shows, and what it cannot tell you.
• Ask: what question would we ask next?

Our home investigation

Fill one row a day: the question you are investigating, the data you collected, and what you noticed.

Printed from the free seegongsik Statistical Investigations teaching pack · seegongsik.com/au/y6/statistics/AC9M6ST03/pack

Pose a question

An investigation starts with a question or a problem. A statistical question expects answers that vary across a group (how far from school do the students in our class live?), unlike a question with one fixed answer (what time does school start?). A good question is refined until it says who exactly, what exactly and when, so that everyone collecting data would collect the same thing. Children sort questions, refine vague ones, and turn a school problem into the class’s question for the week.

We are learning to

• tell a statistical question from one with a single fixed answer,
• refine a vague question so that it says who, what and when,
• turn a problem into a question that data can answer.

Success criteria

• I can explain why ‘How tall is the school flagpole?’ is not a statistical question.
• I can rewrite a vague question so that everyone would collect the same data.

You need

The worksheet, one per child, and the investigation cycle cards (cut-outs), one set for each pair.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the vague questions in Part B.

Watch for these ideas

• Thinking any question with a number for its answer is statistical.
• Questions too vague to collect data for, such as ‘Is our canteen good?’
• Asking about everyone in the world when the class can only ask the class.

Answers

• Part A: (1) S, (2) N, (3) N, (4) S, (5) S, (6) N.
• Part B, for example: (1) Which sport do Year 6 students at our school most like to play at lunch? (2) How do Year 6 students rate this term’s canteen lunches, from 1 (poor) to 5 (great)? (3) How many minutes did each student in our class spend on a screen for fun yesterday?
• Part C, for example: How do the students in our class travel to school, and could more of them walk or ride?

Pose a question

A. Statistical or not?

Write S if the answers would vary across a group, or N if there is one fixed answer.

B. Make it clearer

Rewrite each question so that it says who exactly, what exactly and when.

C. From a problem to a question

Write a statistical question our class could investigate to help.

________________________________________________________________________________

Our class question for the week: ________________________________________________

Plan and collect

Before collecting, plan: what to record about each person (the variables), what kind of data each is, how to collect it (a survey, an observation or a measurement) and from whom. A survey question needs boxes that fit every answer exactly once, no push toward one answer, and nothing private that the question does not need. Children plan the class investigation, fix a faulty survey, and collect the class’s answers in a tally.

We are learning to

• plan what data to collect, and how, to answer a question,
• write survey questions with boxes that fit every answer once,
• collect data accurately in a tally.

Success criteria

• I can explain why boxes of 1–2 km and 2–5 km trouble someone who lives exactly 2 km away.
• I can say whom our data comes from, and what that means for our findings.

You need

The worksheet, one per child, and, if your class collects its own data, a copy of the class survey for each child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part B; start Session B by collecting the class’s data in Part C.

Watch for these ideas

• Boxes that overlap, or that leave someone with nothing to tick.
• Collecting names or addresses that the question does not need.
• Losing count: tally in fives, then check the total against the number of children.

Answers

• Part A: travel, categorical (nominal); distance, ordinal categories (bands of a distance); both by a survey question with tick boxes; ask every student in the class once, on one morning.
• Part B: (1) there is no box for a bike, a scooter, a bus or anything else; add Bike or scooter, Bus and Other. (2) 1 km and 2 km each fit two boxes, and there is no box over 5 km; use under 1 km, 1 to under 2 km, 2 to under 5 km and 5 km or more. (3) it pushes people toward one answer; ask how they travel, without saying which way is better. (4) it asks for private details the question does not need; leave it out; the survey needs no names.
• Part C: the class’s own counts; every row and column total should add to the number of children asked.

Plan and collect

A. Plan the investigation

Whom do we ask? ______________________ When? ______________________

B. Fix the survey

Each question has a fault. Say what is wrong, then fix it.

C. Our class’s answers

Tally each student once, in the row for how they travel and the column for how far away they live.

Organise the data

Raw answers say little until they are organised. A frequency table counts each category; a column graph shows the counts as heights on a scale that starts at 0; and a two-way table counts two things at once, so each response sits in exactly one cell and the row and column totals check the counting. Children sort 30 survey slips into all three.

We are learning to

• organise survey responses in a frequency table,
• draw a column graph with a title, labels and a scale from 0,
• record two variables at once in a two-way table, and check it with totals.

Success criteria

• I can check my table: the counts add up to the number of responses.
• I can read one cell of the two-way table, such as how many come by car from under 1 km away.

You need

The worksheet, one per child, and the survey slips (cut-outs), one set for each pair.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the graph in Part B.

Watch for these ideas

• Counting a slip twice or missing one: the total should be 30.
• Starting the graph’s scale above 0, or leaving off the title and labels.
• Mixing up the rows and the columns of the two-way table.

Answers

• Part A: Walk 7, Bike or scooter 5, Car 14, Bus 4; total 30.
• Part B: columns of those heights on a scale from 0 to 16.
• Part C (rows: distances in order, then the total): Walk 5, 2, 0, 0 (7); Bike or scooter 1, 3, 1, 0 (5); Car 4, 3, 5, 2 (14); Bus 0, 0, 2, 2 (4); column totals 10, 8, 8, 4 (30).

Organise the data

A. The survey responses

How each student travels to school, and how far away they live.

C. Two things at once

Split each pile by distance. Write the counts, then the totals.

Analyse and interpret

Analysing is reading the organised data: the biggest and smallest counts, the totals, and particular cells. Interpreting is saying what that means for the question, in its context: who the data came from, when, and what it cannot show. A finding should match the size of the data: car is the most common way here, but ‘most students come by car’ is false, because 14 of 30 is less than half. Children answer the class question, judge statements and name the data’s limits.

We are learning to

• answer questions from a frequency table and a two-way table,
• interpret the findings in the context of the question,
• name the limits of the data, and what to ask next.

Success criteria

• I can find how many car travellers live close enough to walk or ride.
• I can explain why ‘most students come by car’ is not a fair finding here.

You need

The worksheet, one per child, and yesterday’s tables and graph.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the statements in Part B.

Watch for these ideas

• Calling the most common answer ‘most’ when it is less than half.
• Forgetting the context: the data comes from one class on one morning.
• Reading the two-way table along the wrong row or column.

Answers

• Part A: (1) car, 14 of 30, less than half; (2) 12; (3) 4; 7; (4) 19 of 30, more than half; (5) 12, of whom 11 come by car or bus.
• Part B: (1) U: car is the most common way, but it is less than half the class; (2) U: some of them come by car or ride; (3) F: car has the biggest count; (4) F: nearly all of them do; (5) U: the data cannot tell us that; some students live too far away to walk.
• Part C, for example: one class on one morning; distances were guesses; the table cannot say whether the way is safe. Next: ask the 7 car travellers who live under 2 km away what stops them walking or riding.

Analyse and interpret

A. Answer the question

How the 30 students travel, and how far away they live.

1. What is the most common way to come to school? Is it most of the class? ____________________

2. How many students walk or ride? ______

3. How many car travellers live under 1 km away? ______ Under 2 km away? ______

4. If the car travellers who live under 2 km away walked or rode instead, how many would walk or ride? ______ out of 30

5. How many live 2 km or more away? ______ How many of them come by car or bus? ______

B. Fair or not?

Write F (fair) or U (unfair), and why.

C. What we cannot say

Two reasons to be careful with these findings: ____________________________________________

A question we would ask next: _____________________________________________________

Communicate the findings

A report brings the investigation together for someone who was not there: the question and why it matters, how the data was collected and from whom, a clear display, the findings in plain sentences with numbers, the limits, and what to do or ask next. It is written for its reader, here the principal, so it answers the problem it started from. Children write a report from the week’s data, or their own, and play the unit’s quiz.

We are learning to

• write a report that answers the question with the data,
• choose a display that suits the reader,
• state the limits of the findings and a next step.

Success criteria

• My report gives the question, how the data was collected, a display, two findings with numbers, a limit and a next step.
• I can explain why my display suits my reader.

You need

The worksheet, one per child, the tables and graph from Day 3, and poster paper if you prefer.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the first three parts of the report; start Session B with what it means.

Watch for these ideas

• A report that shows the graph but never says what it means.
• Findings without numbers, such as ‘lots of people’.
• Forgetting the limits, or claiming the findings speak for every school.

Answers

• A model report. Question: How do the students in our class travel to school, and could more of them walk or ride? Data: all 30 students in our class said, one morning, how they travel and how far away they live. Found: car is the most common way (14 of 30) but less than half, and 12 walk or ride; 7 car travellers live under 2 km away, and if they walked or rode, 19 of 30 would. Be careful: one class, one morning, and the distances were guesses. Next: ask those 7 what would help them walk or ride, and survey other classes.

Communicate the findings

Write a report for the principal. Use the week’s data, or your class’s own.

Survey slips

Print one set for each pair and cut along the dashed lines. Each slip is one student’s answers to the two survey questions.

Teacher note: the slips match the list on the Day 3 worksheet, numbered the same, so pairs without slips can tally from the list.

Investigation cycle cards

Print one set for each pair and cut along the dashed lines. Lay the five stage cards in order, then put each task under its stage.

Teacher note: question B and I; collect C and G; analyse A and E; interpret D and H; communicate F and J. Some tasks could argue for two stages; let pairs say why.

What we know: Statistical Investigations

Work on your own. Show your thinking if you can.

1. Circle the statistical question. (a) How old is our principal? (b) How many hours of sport do Year 6 students play each week? (c) What day is it today?
2. Make this question clearer, so it says who, what and when: “Do people like the library?” ______________________________
3. A survey asks: How many pets do you have? ☐ 0 ☐ 1–2 ☐ 2–3 ☐ 4 or more. What is wrong? Fix the boxes. ______________________________
4. To find the favourite lunch of the 420 students at a school, Sam asks 10 friends. What is the problem? What would be better? ______________________________
5. Twelve students named their favourite fruit: Apple, Banana, Apple, Grapes, Apple, Banana, Mango, Apple, Banana, Grapes, Apple, Banana. Make a frequency table on the back. Which fruit is the mode? ______
6. Lunch choices. How many Year 6 students chose hot food? ______ Which lunch was most popular overall? ______ How many students altogether? ______

   	Sandwich	Hot food	Salad
   Year 5	8	10	2
   Year 6	6	12	4

7. 9 of the 25 students in a class come by bus. Kim writes: “Most students come by bus.” Is this a fair finding? Write a fair one. ______________________________
8. List four things a report of an investigation should include. ______________________________

Answers and marking guide

Answers

1. (b): the answers vary from student to student.
2. For example: How many times did each Year 6 student borrow a library book this term?
3. Someone with 2 pets fits two boxes. For example: 0, 1 to 2, 3 to 4, 5 or more.
4. Ten friends are few, and likely to be alike. Better: ask students chosen from every class, or ask everyone.
5. Apple 5, Banana 4, Grapes 2, Mango 1; mode apple.
6. 12; hot food (22); 42.
7. No: 9 of 25 is less than half. Fair: 9 of the 25 students come by bus; the rest come other ways.
8. Any four of: the question, how the data was collected and from whom, a display, the findings with numbers, a limit, a next step.

A quick three-level guide

Eight questions, four ideas. A child at standard poses a clear statistical question, collects and organises data fairly, and reports findings with numbers and a limit.

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: posing a question, planning and collecting, organising, interpreting, and reporting.