A Data Investigation: a week of ready-to-teach maths
Five days of lessons for Year 3 Statistics. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus stage cards, question cards, a mini-check and every answer. Across the week, the class runs one investigation of its own, from question to answer.
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.
- Cut out the stage cards and the question cards once; they are reused all week.
- 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. A statistical investigation has four stages, always in this order: ask a question that data can answer, collect the data, represent it in a table or graph, and interpret it to answer the question. The data can be categorical (favourite game) or discrete numerical (how many pets). The week practises each stage on printed data while the class runs its own investigation.
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 | The investigation cycle | Name the four stages, ask, collect, represent and interpret, and put them in order | The investigation cycle |
| 2 | A good question | Tell a question data can answer from an opinion, and plan the class investigation | A good question |
| 3 | Collect and tally | Collect the class data with tallies, and tally numerical data by its values | Collect and tally |
| 4 | Represent it | Draw column graphs of the class data and of numerical data, with a title and labels | Represent it |
| 5 | Interpret and answer | Read a graph to answer the question in a sentence, and report the class investigation | Interpret and answer; Put the cycle in order |
How the week builds
Day 1 meets the whole cycle. Day 2 chooses the class question, Day 3 collects the data, Day 4 represents it, and Day 5 interprets it and reports the answer: each day is one stage of the class’s own investigation. It leans on Collecting and Recording Data (AC9M3ST01) and Making and Reading Graphs (AC9M3ST02).
Materials for the week (one trip)
- From the classroom: scissors, rulers, coloured pencils, clipboards, this pack printed.
- Permission to survey another class, if the class question needs more people (Day 3).
- A large sheet of paper for the class graph and its answer (Days 4 and 5).
- Cut out once, use all week: the stage cards and the question cards.
Words for the word wall
investigation, question, ask, collect, represent, interpret, data, survey, tally, frequency, column graph, categorical, numerical, most, least, answer, conclusion
Dear families
This week in maths, Year 3 is running a data investigation: asking a question, collecting answers, drawing a graph and using it to answer the question.
Try this at home
- Choose a family question together, such as “What is our favourite dinner?”
- Ask everyone at home and tally the answers.
- Draw a quick column graph, then say the answer in a sentence.
- Ask: is that a question we could answer by counting? Why?
Our family investigation
Fill one row a day as you work through the four stages.
| Day | Stage | What we did |
|---|---|---|
| Monday | ||
| Tuesday | ||
| Wednesday | ||
| Thursday | ||
| Friday |
Printed from the free seegongsik A Data Investigation teaching pack · seegongsik.com/au/y3/statistics/AC9M3ST03/pack
The investigation cycle
A statistical investigation has four stages, always in the same order: ask a question, collect the data, represent it in a table or graph, and interpret it to answer the question. The stages make a loop, because an answer often starts a new question. This week the class runs its own investigation, one stage a day.
We are learning to
- name the four stages of an investigation,
- put the stages in order, and say why the order matters,
- match a step to its stage.
Success criteria
- I can name the four stages in order.
- I can say which stage a step belongs to.
You need
The stage cards and step cards (cut-out sheet 1). The worksheet. A sheet of paper for the class wonderings.
Lesson flow (about 50 minutes)
| 10 min | What did they do? Tell the story: a Year 3 class wondered which playground game was the favourite, asked everyone, tallied, drew a graph and found it was soccer. Children retell it in four steps. Ask: “What did the class do first? What did they do last?” |
| 25 min | Name the stage Go round the cycle on the board (see the box). Pairs sort the step cards under the four stage cards, then children sort the worksheet steps and number the stages. Ask: “Can you draw the graph before you collect the data? Why not?” |
| 15 min | Our wonderings The class lists things it wonders about the class or the school, ready to choose a question tomorrow. Ask: “Which of these could we find out by asking and counting?” |
Two half-sessions instead? Split after the card sort; start Session B with the worksheet.
Watch for these ideas
- Thinking the graph is the end. The end is the answer to the question.
- Mixing up collecting and representing. Collecting gathers answers; representing organises them.
- Starting with data, not a question. The question comes first and decides what to collect.
Answers
- Steps: 1 Represent, 2 Ask, 3 Collect, 4 Interpret, 5 Collect, 6 Ask, 7 Represent, 8 Interpret.
- Order: Ask, Collect, Represent, Interpret. The question comes first because it decides what to collect and who to ask.
The investigation cycle
Which stage?
Write Ask, Collect, Represent or Interpret for each step.
| What they did | Stage | |
|---|---|---|
| 1 | We drew a column graph of the answers. | |
| 2 | We wondered which game our class likes best. | |
| 3 | We asked everyone in Year 3. | |
| 4 | We wrote: more children walk than come by car. | |
| 5 | We tallied each child’s answer. | |
| 6 | We chose the question: How many pets do you have? | |
| 7 | We made a frequency table of the counts. | |
| 8 | We found that soccer is our favourite game. |
Put the stages in order
Write the four stages in the boxes, first to last.
Why must the question come first? __________________________________________________
A good question
A good investigation question can be answered by collecting and counting data from people we can ask: “Which fruit does our class like best?” An opinion (“Is chocolate the best food?”) or a why question cannot be settled by counting. A good question also says who will be asked, and gives one kind of data, categorical or numerical.
We are learning to
- tell a question data can answer from an opinion or a why question,
- name the kind of data a question gives,
- plan the class investigation: the question, who to ask, how to collect and show it.
Success criteria
- I can say if a question can be answered by collecting data.
- I can help plan our class investigation.
You need
The question cards (cut-out sheet 2). The class wonderings from Day 1. The worksheet.
Lesson flow (about 50 minutes)
| 10 min | Good or not? Judge questions on the board (see the box). Ask: “Could we settle ‘What is the best game ever made?’ by asking our class? Why not?” |
| 20 min | Sort and fix Pairs sort the question cards into good questions and not, and rewrite one that is not as one that is. Children then do the worksheet sort. Ask: “How could we change ‘Is chocolate the best food?’ into a question we can count?” |
| 20 min | Plan ours The class chooses its question from the wonderings and fills in the plan together; each child copies it onto the worksheet. Ask: “Who do we need to ask so that our answer is fair?” |
Two half-sessions instead? Split after the sort; start Session B with planning our investigation.
Watch for these ideas
- Choosing an opinion question. Ask: could counting answers settle it?
- A question too big to ask everyone, such as “What do Australians eat?”. Keep it to people we can ask.
- Asking two things at once. One question gives one kind of data.
Answers
- Sort: 1 good, categorical; 2 not good (an opinion); 3 good, numerical; 4 not good (a why question, for discussion); 5 good, categorical; 6 not good (about the future: it cannot be collected yet).
- Rewrite: such as “Which of these foods does our class like best?”
- Our plan: any question data can answer, with who to ask, how to collect it and a display.
A good question
Can data answer it?
Tick good or not. For a good one, write categorical or numerical.
| The question | Good | Not | Kind |
|---|---|---|---|
| Which fruit do the children in our class like best? | |||
| Is chocolate the best food in the world? | |||
| How many books did each child read last week? | |||
| Why do people like dogs? | |||
| Which day of the week does our class like best? | |||
| What will the weather be like next year? |
Our investigation plan
| Our question | |
| Kind of data | categorical □ numerical □ |
| Who we will ask | |
| How we will collect it | |
| How we will show it |
Collect and tally
Collecting is the second stage: ask everyone the question and record each answer as it comes, with a tally mark beside its category. Numerical data is tallied the same way, with one row for each number (2 people, 3 people and so on). The tallies become frequencies, and the frequencies must add up to the number of people asked.
We are learning to
- collect the answers to the class question,
- tally categorical and numerical data,
- check that the total matches the number of people asked.
Success criteria
- I can tally answers as I collect them.
- I can check that my total is right.
You need
Clipboards. A class list, to tick off who has answered. The class plan from Day 2. The worksheet.
Lesson flow (about 50 minutes)
| 10 min | Collect on the board Collect favourite games on the board (see the box), one child at a time. Ask: “How do we know when everyone has answered?” |
| 15 min | Tally numbers Children tally the printed answers to “How many people live in your home?” by the number, crossing out each one, and write the frequencies. Ask: “Why does each number get its own row?” |
| 25 min | Collect ours Children ask the class question (around the room, or of another class) and tally on the worksheet; the class checks the total against the class list. Ask: “Our total is 24, but 25 children are here today. What happened?” |
Two half-sessions instead? Split after the number tally; start Session B with collecting ours.
Watch for these ideas
- Asking some people twice and missing others. Tick names off a class list.
- Writing each number down again every time it comes up. Each number has one row; add a mark.
- A total that does not match the people asked. Count again before drawing a graph.
Answers
- People at home: 2 people 2, 3 people 5, 4 people 8, 5 people 3, 6 people 2; total 20.
- Our data: the frequencies add up to the number of children asked.
Collect and tally
Tally numerical data
“How many people live in your home?” 20 children answered. Tally each answer by its number, then write the frequencies.
| People at home | Tally | Frequency |
|---|---|---|
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 |
Collect our class data
Our question: ____________________________________________
| Answer | Tally | Frequency |
|---|---|---|
| total |
Represent it
Representing is the third stage: the frequencies become a table and a graph that show the answer at a glance. A column graph needs a title, a label under each column, an even scale and one baseline. Numerical data is graphed the same way, with its numbers in order along the bottom: 2, 3, 4, 5, 6 people.
We are learning to
- draw a column graph of our class data,
- draw a column graph of numerical data, with the numbers in order,
- give a graph a title and labels.
Success criteria
- I can draw a column graph of data I collected.
- I can label it so others can read it.
You need
Rulers and coloured pencils. The Day 3 tallies. A large sheet of paper for the class graph. The worksheet.
Lesson flow (about 50 minutes)
| 10 min | Represent it Draw the graph on the board (see the box). Ask: “What does the graph show that the tally did not?” |
| 25 min | Draw two graphs Children graph the people-at-home data from Day 3, then their class data, with a title and labels. Ask: “Why do the numbers 2, 3, 4, 5 and 6 go in order along the bottom?” |
| 15 min | Class graph A group draws the class graph large for the wall while others check each column against the frequencies. Ask: “How can someone who was not here tell what this graph is about?” |
Two half-sessions instead? Split after the first graph; start Session B with the class graph.
Watch for these ideas
- Numbers out of order along the bottom (4, 2, 6 ...). Put them in order.
- Columns that do not match the frequencies. Check each one against the table.
- A graph with no title. The title says which question it answers.
Answers
- People at home: columns to 2 for 2, 5 for 3, 8 for 4, 3 for 5, 2 for 6; a title such as “How many people live in our homes?”.
- Our graph: one column for each answer, each matching its frequency, with a title and labels.
Represent it
Graph the numbers
Use your Day 3 frequencies. The bottom shows how many people live in a home.
Title: ______________________________________
Graph our class data
Write a label under each column you need, then draw the columns.
Title: ______________________________________
Interpret and answer
Interpreting is the last stage: read the graph and answer the question that started it, in a sentence about the people counted: “Soccer is our class’s favourite game; 9 of the 24 children chose it.” A good answer uses the numbers, and it often starts a new question to investigate.
We are learning to
- read a graph to answer the question it was made for,
- write the answer as a sentence, with numbers,
- report our class investigation and ask a new question.
Success criteria
- I can answer the question from a graph, in a sentence.
- I can explain our investigation, stage by stage.
You need
The class graph from Day 4. The worksheet. The unit’s self-check quiz.
Lesson flow (about 50 minutes)
| 10 min | Answer, not describe Interpret and order the cycle on the board (see the box). Ask: “‘Soccer has the tallest column’ or ‘Soccer is our favourite game’: which one answers the question?” |
| 25 min | Answer it Children answer the pet questions, then write the answer to the class question and a new question it raises; pairs share theirs at the class graph. Ask: “What new question does our answer make you wonder about?” |
| 15 min | Class quiz Run the self-check quiz as a team game: teams hold up one, two or three fingers for their choice. Ask: “Which picture from this week would prove that answer?” |
Two half-sessions instead? Split after the pet graph; start Session B with our answer and the quiz.
Watch for these ideas
- Describing the graph instead of answering. Answer in words about the people counted.
- Leaving out the numbers. Use them: 8 of the 22 children have one pet.
- Thinking an investigation is finished for good. An answer can start a new question.
Answers
- Pets: 1 8, 2 6, 3 1 pet, 4 22, 5 8.
- A sentence such as: the most common number of pets is 1 (8 of the 22 children), and 6 children have none.
- Our answer: the class question answered in a sentence with numbers, and a new question.
Interpret and answer
“How many pets do you have?” The bottom shows the number of pets.
- How many children have 1 pet? ______
- How many children have no pets? ______
- Which number of pets is the most common? ______
- How many children were asked altogether? ______
- How many children have more than 1 pet? ______
- Answer the question “How many pets do children in this class have?” in a sentence.
Our class investigation
Our question was: ____________________________________________
We found that: ______________________________________________
A new question we wonder about: __________________________________
Stage cards and step cards
Cut out the four stage cards and the eight step cards. On Day 1, pairs lay the stage cards in order and sort the step cards under them.
Teacher note: We drew the columns with a ruler (Represent); We said: dogs are the most common pet in our class (Interpret); We went round the class with a clipboard (Collect); We chose a question: Which pet do most of us have? (Ask); We wrote the frequencies in a table (Represent); We made a tally mark for each answer (Collect); We wondered how many books our class reads (Ask); We found that 5 children read more than 3 books (Interpret).
Question cards
Cut out the twelve cards. On Day 2, pairs sort them into questions data can answer and questions it cannot, then the class may choose one of the good ones for its own investigation.
Teacher note: data cannot answer "Is soccer the best sport?", "Why is the sky blue?", "What will we have for lunch in ten years?", "Which animal is the cutest?" (an opinion, a why question, the future). The others are good: 4 categorical and 4 numerical (the “How many” ones).
What we know: A Data Investigation
Work on your own.
- Put the stages in order: Represent, Ask, Interpret, Collect. ______________________________
- Circle the question that data can answer: Which is the best sport in the world? / Which sport do most children in our class play? / Why is sport fun?
- Is “How many teeth have you lost?” categorical or numerical? ______________
- A class makes a tally mark as each child answers. Which stage is that? ______________
“What is our class’s favourite snack?”
- Which snack is the most popular? ______________
- How many children were asked? ______
- How many more chose yoghurt than cheese? ______
- Answer the question in a sentence: ____________________________________________
Answers and marking guide
Answers
- Ask, Collect, Represent, Interpret.
- Which sport do most children in our class play?
- Numerical.
- Collect.
- Fruit.
- 20.
- 3.
- Such as: fruit is our class’s favourite snack; 7 of the 20 children chose it.
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| The cycle (Q1, Q4) | names some stages, out of order | names the four stages in order and places a step in its stage | explains how an answer can start a new question |
| Questions and data (Q2, Q3) | chooses opinion questions | chooses a question data can answer, and names the kind of data | rewrites a poor question as one data can answer |
| Representing and interpreting (Q5 to Q8) | reads the graph but does not answer the question | reads values and answers the question in a sentence with numbers | adds a comparison or a new question to the answer |
Eight questions, three ideas. A child at standard follows the four stages in order and ends with an answer in words, not just a graph.
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 | Knows the cycle | Good question | Collects | Represents | Interprets |
|---|---|---|---|---|---|
The five columns are the five days: the cycle, a good question, collecting, representing, and interpreting.