Statistical Investigations: a week of ready-to-teach maths
Five days of lessons for Year 5 Statistics. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus question cards and display cards to sort, a worked survey from another class, a mini-check and every answer. Alongside it, your class runs an investigation of its own, from question to findings.
Start here: five minutes to Monday
- Skim the week at a glance on the next page.
- Print the five days. Each day is two A4 sheets: a plan and a worksheet.
- Print the two card sheets once per pair. Have 1 cm grid paper and sticky notes ready.
- Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
- Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.
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: a statistical investigation answers a question with data, in a cycle. Pose a question whose answers vary, collect data that fits it, choose a display that suits the data, interpret what it shows, and communicate the findings in the context of the question.
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.
The week at a glance
One lesson a day for a week. Each day stands on the day before, so run them in order.
| Day | Lesson | Children learn and do | On screen |
|---|---|---|---|
| 1 | Pose a question | Sort questions into statistical and not, make vague questions clear, and choose a question for a class investigation | What a statistical investigation is |
| 2 | Plan and collect | Plan who to ask, what to ask and how to record, then collect and check the class’s own data | Posing a question and collecting data |
| 3 | Choose a display | Match kinds of data to column graphs, dot plots and line graphs, and graph Class 5B’s survey and our own | Choosing a display |
| 4 | Interpret | Read Class 5B’s graph and our own, compare the answers, and say what the data does and does not show | Interpreting the data |
| 5 | Communicate | Judge two findings, write our findings for someone who did not see the data, and play the unit quiz | Communicating the findings |
How the week builds
Each day is one stage of the investigation cycle, practised on Class 5B’s survey and then done for real with the class’s own question. It brings together this year’s data work (AC9M5ST01 and AC9M5ST02), and it leads to Year 6, where investigations refine their questions and analyse the data further (AC9M6ST03).
Materials for the week (one trip)
- From the classroom: sticky notes for voting, clipboards for collecting, rulers, 1 cm grid paper, poster paper for Day 5, this pack printed.
- Print once per pair: the question cards (Day 1) and the display cards (Day 3).
Words for the word wall
investigation, statistical question, data, survey, tally, display, column graph, dot plot, line graph, interpret, finding, conclusion
Dear families
This week in maths, Year 5 runs a statistical investigation: the class chooses a question, collects data to answer it, shows the data in a graph, and reports what it found. A statistical question is one whose answers vary, such as ‘Which games do students in our class play at lunch?’
Try this at home
- Ask your child about the class question. Who did they ask, and what did they find?
- Think of a question you could answer by asking the family, such as favourite meals. What answers might you get?
- Spot a survey or a poll in the news. Who was asked? Does the headline say more than the data shows?
Our investigation, day by day
Fill one row a day. Write what the class did and one thing you learned.
| Day | What we did | What I learned |
|---|---|---|
| Monday | ||
| Tuesday | ||
| Wednesday | ||
| Thursday | ||
| Friday |
Printed from the free seegongsik Statistical Investigations teaching pack · seegongsik.com/au/y5/statistics/AC9M5ST03/pack
Pose a question
A statistical question expects answers that vary, so it takes data to answer: ‘How many pets does each student in our class have?’ A question with one fixed answer is not statistical. A good investigation question also says who it is about and what exactly to answer, so that everyone answers the same thing. This is the first stage of the cycle: pose, collect, display, interpret, communicate.
We are learning to
- tell statistical questions from questions with one fixed answer,
- make a vague question clear by saying who and what,
- choose a question for our own class investigation.
Success criteria
- I can explain why a question is or is not statistical.
- I can write a clear question that says who is asked and what they answer.
You need
The question cards (cut-out sheet 1), one set per pair, cut out. Sticky notes for the class vote. The worksheet.
Lesson flow (about 50 minutes)
| 10 min | The cycle Show the board (see the box). Children name what happens at each stage before you press. Ask: “Which stage do you think matters most? Why?” |
| 20 min | Sort the questions Model sharpening ‘Do people like lunch?’ into ‘Which lunch on the canteen menu do students in our class like best?’. Pairs sort the cards and do Parts A and B. Ask: “What makes ‘How tall am I?’ different from ‘How tall are the students in our class?’” |
| 20 min | Our question Children do Part C. Each pair posts its best question; the class votes with sticky notes for the question to investigate this week. Ask: “Could everyone answer this question the same way? Could anyone misunderstand it?” |
Two half-sessions instead? Split after Part A; start Session B by sharpening the questions in Part B.
Watch for these ideas
- Thinking any question about numbers is statistical, such as a sum with one answer.
- A question about ‘people’ with no group named, so nobody knows who to ask.
- Choices that overlap or leave answers out, such as no ‘other’.
Answers
- Part A: answers vary (statistical) 1, 4, 5, 7, 10, 11; one fixed answer 2, 3, 6, 8, 9, 12.
- Part B: versions vary, for example ‘Which sport do students in our class like best: soccer, netball, cricket or swimming?’; ‘How many hours of screen time did each student in our class have yesterday?’; ‘Which pet would students in Year 5 most like to have: dog, cat, fish, bird or another?’. Part C: the class’s own questions.
Pose a question
A. Sort the question cards. Write the card numbers.
| Answers vary: a statistical question | One fixed answer |
|---|---|
B. Make each question clear. Say who is asked and what they answer.
1. ‘Do kids like sport?’
2. ‘How much screen time?’
3. ‘What is the best pet?’
C. Our class investigation
A question I would like our class to investigate:
Who would we ask? ______________________________________________
What answers might we get? ______________________________________
Plan and collect
Before collecting, plan three things: who will be asked (everyone the question is about, or a fair group of them, not only friends); exactly what they will be asked, with choices that cover every answer once; and how the answers will be recorded, so that none are lost or counted twice. Then collect, and check the data as it comes in.
We are learning to
- plan who to ask, what to ask and how to record,
- collect data for our class question,
- check the data as it is collected.
Success criteria
- I can explain who we asked and why that is fair.
- I can record answers so that none are missed or counted twice.
You need
The class question chosen on Day 1. A class list and clipboards for collecting. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | A good question Show the board (see the box). Children choose before you press. Ask: “Which answer choices does our own question need? Is anyone left out?” |
| 20 min | Plan Model a plan for the canteen question from Day 1: everyone in the class, once each; the menu items plus ‘another’; a tally beside a class list. Pairs fill Part A, then the class agrees one plan. Ask: “If we asked only the people at our table, what might go wrong?” |
| 20 min | Collect and check Each pair asks its share of the class and records in Part B; then the class combines the tallies and does Part C. Ask: “Two pairs asked the same person. What happens to our data, and how do we fix it?” |
Two half-sessions instead? Split after the plan; collect in Session B.
Watch for these ideas
- Asking only friends or one group, so the data does not stand for everyone the question is about.
- Choices that overlap, such as ‘sport’ and ‘soccer’, or that leave some people out.
- Tallying without a list of who has answered, so people are missed or counted twice.
Answers
- Parts A and B: the class’s own plan and data.
- Part C: all three checks should be yes; any answer that does not fit is checked with the person or set aside, and the reason noted.
Plan and collect
A. Our plan
B. Collect: our tally
| Answer | Tally | Frequency |
|---|---|---|
| Total |
C. Check the data
What will we do with an answer that does not fit?
Choose a display
The kind of data decides the display. Answers in categories, nominal or ordinal, suit a column graph; counted numbers, such as how many pets, suit a dot plot; one thing measured again and again over time suits a line graph. Whatever the display, it needs a title, labels, and a scale from 0 in equal steps.
We are learning to
- choose a display that suits the kind of data,
- draw a column graph with a title, labels and a scale,
- choose and draw the display for our own data.
Success criteria
- I can say which display suits some data, and why.
- I can draw a display that someone else can read exactly.
You need
The display cards (cut-out sheet 2), one set per pair, cut out. Rulers and 1 cm grid paper. The class tally from Day 2.
Lesson flow (about 50 minutes)
| 10 min | Which display? Show the board (see the box). Children choose before you press. Ask: “Why would a line graph of favourite sports make no sense?” |
| 20 min | Sort and draw Model choosing a display for the canteen question: its answers are categories, so a column graph. Pairs sort the display cards (Part A), then draw Class 5B’s graph (Part B). Ask: “Which card could go in two piles? What would decide it?” |
| 20 min | Our display Children do Part C and draw the class’s own display on 1 cm grid paper. Ask: “Does your display answer our question at a glance? What would make it clearer?” |
Two half-sessions instead? Split after Part A; start Session B by drawing Class 5B’s graph.
Watch for these ideas
- Choosing a line graph for categories, as if the categories were times.
- A scale that does not start at 0 or jumps unevenly.
- Choosing the display that looks best rather than the one that answers the question.
Answers
- Part A: column graph A, D, H; dot plot B, F, G; line graph C, E, I.
- Part B: columns soccer 7, netball 4, cricket 3, dodgeball 9, tag 2, on a scale from 0 to 10, with a title and labels. Part C: the class’s own choice, with a reason that names its kind of data.
Choose a display
A. Sort the display cards. Write the card letters.
| column graph | dot plot | line graph |
|---|---|---|
B. Class 5B asked: ‘Which game should we play at the end-of-term fun day?’
| Game | soccer | netball | cricket | dodgeball | tag |
| Students | 7 | 4 | 3 | 9 | 2 |
Draw a column graph of the table. Write a title and label each column; the scale is drawn for you.
Title: ________________________________________________
C. Our display
Our data is ____________________ (categories, counted numbers or measured over time), so we will draw a ____________________ . Why?
Interpret
Interpreting means reading a display back and saying what it shows about the question: the most and least common answers, how big the differences are, how many took part, and anything surprising. Care is needed with words like ‘most’: the most common answer may still be chosen by fewer than half. And a conclusion is only about the people who were asked.
We are learning to
- read and compare the counts in a display,
- say what the data shows about the question,
- say what the data does not show, and why.
Success criteria
- I can find the most and least common answers and the differences between them.
- I can explain who a conclusion is about, and who it is not about.
You need
The class display from Day 3. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Read the columns Show the board (see the box). Children choose before you press. Ask: “What else could you say about this fruit graph, beyond the most popular?” |
| 25 min | Class 5B Model three statements about the canteen tally: the most common answer, one difference, and how many answered. Children do Part A. Ask: “Is the most common answer the same as what most people want? How do you check?” |
| 15 min | Our data Children do Parts B and C on the class’s own display. Ask: “Would another class have given the same answers? What could make them different?” |
Two half-sessions instead? Split after Part A; start Session B with our own display.
Watch for these ideas
- Saying ‘most people’ for the most common answer when it is fewer than half.
- Reading the tallest column but not saying how many, or how much taller.
- Stretching a conclusion to people who were never asked.
Answers
- Part A: 1. dodgeball, 9. 2. tag, 2. 3. 7 − 4 = 3. 4. 25. 5. no: 9 of 25 is less than half (12.5). 6. no: only Class 5B was asked, not the rest of Year 5.
- Parts B and C: the class’s own statements; check each against the display.
Interpret
A. Class 5B asked: ‘Which game should we play at the end-of-term fun day?’
5. Did more than half of Class 5B choose the most popular game? Explain.
6. Can we say that all of Year 5 at this school wants that game? Why or why not?
B. Our data: three things our display shows
C. Something surprising, or a new question our data raises
Communicate
A finding answers the question in its context, for someone who did not see the data: what was asked and of whom, what the data shows (with numbers), and what can be concluded, including its limits. The findings go with the display, on a poster or in a short report, so the reader can check them.
We are learning to
- tell a useful finding from a weak one,
- write findings that answer our question in context,
- check findings against the data.
Success criteria
- I can say what makes a finding useful to someone who did not see the data.
- I can write findings with the question, the people asked, numbers and limits.
You need
The class display from Day 3. Poster paper if you have it. Mini whiteboards for the quiz. The worksheet.
Lesson flow (about 50 minutes)
| 10 min | A good finding Show the board (see the box). Children choose before you press. Ask: “Who will read our findings? What do they need to know first?” |
| 25 min | Write and check Model one finding about the canteen question, naming the question, the people asked and a number. Children do Part A, write the class’s findings in Part B, then swap with a partner for Part C. Ask: “Which sentence in your findings would you cut if you had to keep only three? Why?” |
| 15 min | Quiz Run the unit’s self-check quiz as a class game, teams showing answers on mini whiteboards. Ask: “Which question split the class? Who can convince the others?” |
Two half-sessions instead? Split after Part A; start Session B by writing the findings.
Watch for these ideas
- A finding with no context, such as one word, that makes sense only to someone who saw the graph.
- Findings with no numbers, so a reader cannot check them.
- Leaving out what the data cannot tell us, such as people who were not asked.
Answers
- Part A: finding 2; it says who was asked and how many, gives numbers, answers the question and notes a limit; finding 1 gives only the game.
- Parts B and C: the class’s own findings; each item of the checklist should be there.
Communicate
A. Two findings about Class 5B’s survey. Which is better, and why?
B. Our findings
Write them for someone who did not see our data. Use the checklist below.
C. Partner check
| The findings include... | Partner’s tick |
|---|---|
| our question | |
| who we asked, and how many | |
| what the display shows, with numbers | |
| our answer to the question | |
| what our data cannot tell us |
Question cards
One set per pair (Day 1). Cut out the cards and sort them into two piles: questions whose answers vary, so data is needed, and questions with one fixed answer.
How do students in our class get to school?
What is the name of our school?
How tall is our teacher?
How many hours do students in Year 5 sleep on a school night?
How long does it take each student in our class to run 100 m?
What is 12 × 12?
Which season do the people in our street like best?
How many legs does a spider have?
What time does our school start?
How many books has each student in our class read this term?
Which fruit do students in Year 5 bring to school most often?
What is my favourite colour?
Teacher note: six of each. The sort is on the Day 1 plan.
Display cards
One set per pair (Day 3). Each card describes some data. Cut them out and sort them by the display that suits the data best: a column graph, a dot plot or a line graph.
Favourite ice-cream flavour of each student
How many brothers and sisters each student has
The temperature outside the classroom every hour
How students get to school
A puppy’s mass every week for 10 weeks
The number of goals each team scored in one round
How many letters are in each student’s first name
Which game students want at the fun day
The height of a tomato plant each day
Teacher note: three cards for each display. The sort is on the Day 3 plan.
What we know: Statistical Investigations
Work on your own.
- Circle the statistical question.a. What day is the school fair?b. How many minutes does each student in our class read each night?c. How many legs does an ant have?
- Make this question clearer: ‘Do you like music?’
- To find out how students in Years 5 and 6 get to school, who should you ask? Circle one.a. only your friendsb. students from Years 5 and 6, chosen fairlyc. the teachers
- Write the display that suits each: a column graph, a dot plot or a line graph.a. the day of the week each student was born on ________________b. the water level in a tank every morning for a month ________________c. how many teeth each student has lost ________________
- Class 5C asked: ‘How should we raise money for the school garden?’ Which idea was most popular? How many more chose it than the least popular idea? ______________
- Is this a good conclusion? ‘Everyone at our school wants a disco.’ Explain.
- Put the stages of an investigation in order.interpretpose a questioncommunicatecollect datachoose a display
- Write one finding about Class 5C’s survey, in context.
How did this week feel? Circle one: I can teach it · I am getting there · I need more help
Answers and marking guide
Answers
- b: its answers vary from student to student
- for example, ‘Which kind of music do students in our class like best: pop, rock, country or another?’
- b: the question is about all of Years 5 and 6, so a fair group of them
- a. column graph; b. line graph; c. dot plot
- disco, 11; 11 − 4 = 7 more than raffle
- no: only Class 5C (30 students) was asked, and 11 of 30 is not even half of them
- pose a question, collect data, choose a display, interpret, communicate
- for example: in Class 5C, 11 of 30 students chose a disco to raise money for the garden, more than any other idea
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Posing questions (Q1, Q2) | asks a question with one fixed answer | poses a clear question whose answers vary | refines a question so everyone answers the same thing |
| Planning and collecting (Q3, Q7) | asks whoever is nearest | plans who to ask, fairly, and the steps in order | explains how a plan avoids missed or double answers |
| Displays (Q4, Q5) | picks any graph | matches displays to kinds of data and reads them | explains why another display would mislead |
| Interpreting and communicating (Q6, Q8) | states one value with no context | writes findings in context, with numbers | notes the limits of the data |
Eight questions, four ideas. A child at standard answers most questions and can say why, by keeping the question and the people asked in view at every stage.
Weekly class record
Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.
| Name | Poses a question | Plans, collects | Chooses a display | Interprets | Communicates |
|---|---|---|---|---|---|
The five columns are the five days: posing a question, planning and collecting, displaying, interpreting and communicating.