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

Five days of lessons for Year 4 Statistics. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out question cards, an investigation planner for each pair, 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 question cards and step cards once for Day 1, and print one investigation planner per pair.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. 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. A statistical investigation answers a question with data in four steps: ask a clear question, collect the data, record and display it, then interpret the data and communicate the result. Each day of the week is one of those steps.

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 class investigation

The worksheets practise each step with data that is given. Alongside them, each pair keeps an investigation planner for one class question, from asking it on Day 1 to reporting the answer on Day 5, so by Friday the class has run a whole investigation of its own. On Day 3 the class records its data in a spreadsheet, the digital tool the curriculum names: one device on the board is enough.

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

The week follows the investigation cycle from start to finish. Each day children practise one step on the worksheet, then carry it out on the class question in their planner: on Day 1 they ask it, on Day 2 they collect the answers, on Day 3 they display them, on Day 4 they say what the display shows, and on Day 5 they report the result. It builds on collecting data and making column graphs (AC9M4ST01) and on judging displays (AC9M4ST02).

Materials for the week (one trip)

• From the classroom: rulers, coloured pencils, scissors, a timer or clock with a second hand, and this pack printed.
• For Day 3: one device with a spreadsheet program on the board, or one per pair if you have them.
• Cut out once: the question cards and step cards. Print once for each pair: the investigation planner.

Words for the word wall

investigation, question, data, survey, response, observe, measure, collect, tally, frequency table, column graph, dot plot, spreadsheet, cell, interpret, communicate, result

Dear families

This week in maths, Year 4 carries out a statistical investigation: asking a clear question, collecting data, displaying it and saying what it shows.

Try this at home

• Ask a family question with clear answers, such as “What is our favourite meal?”, and record everyone’s answer.
• Count something on a walk, such as dogs or red cars, with tally marks.
• Look for a graph in a newspaper or on a website. What question does it answer?
• Ask: what does the data tell us? What does it not tell us?

Our family investigation

Printed from the free seegongsik Statistical Investigations teaching pack · seegongsik.com/au/y4/statistics/AC9M4ST03/pack

Ask a question

A statistical investigation answers a question with data in four steps: ask a question, collect the data, record and display it, then interpret it and communicate the result. A good question says clearly what to count or measure; words such as nice or best mean different things to different people, so no data can answer them. Children sort question cards, make vague questions clear, and choose a class question for the week.

We are learning to

• tell a clear investigation question from a vague one,
• make a vague question clear,
• name the four steps of a statistical investigation.

Success criteria

• I can say why a question is clear or too vague.
• I can rewrite a vague question so that data can answer it.

You need

The question cards and step cards (cut-out sheet 1), one set per pair. The investigation planner (cut-out sheet 2), one per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the card sort; start Session B with the step cards.

Watch for these ideas

• Thinking any question about the class is a good question.
• Asking two things at once, such as “Do you like apples and pears?”
• Choosing a question whose answer everyone already knows.

Answers

• Card sort and Part A: good questions A, D, F, G; too vague B, C, E, H. Card B: nice means different things to different people.
• Part B: answers vary, for example “Which sport do Year 4 students play most often?”
• Part C: Record and display 3, Ask a question 1, Interpret and communicate 4, Collect the data 2. Part D: answers vary.

Ask a question

A. After your card sort, write the letters of the cards in each group.

B. Make each question clear, so that data can answer it.

C. Number the steps of an investigation in order, from 1 to 4.

D. Our class question

Collect the data

The question decides how to collect the data. A survey asks people and records their responses; observing watches and counts what happens; measuring uses a tool such as a ruler, scales or a timer. Children match questions to the method that suits them, record a set of star-jump measurements on a dot plot, then plan and start collecting the data for the class question.

We are learning to

• choose a survey, observing or measuring to suit a question,
• collect data fairly, counting everyone once,
• record measurements so they can be read.

Success criteria

• I can say how I would collect data for a question, and why.
• I can plan how our class will collect its data.

You need

A timer or a clock with a second hand. The investigation planners from Day 1. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part B; start Session B with Part C.

Watch for these ideas

• Thinking every investigation is a survey.
• Counting some people twice or leaving some out.
• Measuring unfairly, such as timing some children for longer than others.

Answers

• Part A: 1 observe, 2 survey, 3 measure, 4 survey, 5 observe, 6 measure.
• Part B: 18: 2, 19: 1, 20: 3, 21: 2, 22: 4, 23: 1, 24: 1, 25: 1 dots; the most common is 22 star jumps (4 children); the fewest 18, the most 25.
• Part C: answers vary.

Collect the data

A. How would you collect the data? Ring survey, observe or measure.

B. Fifteen children counted their star jumps in 30 seconds. Draw one dot for each child.

C. Plan how our class will collect the data for our question.

Record and display

Collected data has to be recorded before it can be counted, and displayed before it can be read. A class asked “What is the most common litter in our playground?” (so the school knows which bins would help most). Two groups walked the playground after lunch and wrote down every piece of litter they found. Children tally the list into a frequency table and draw a column graph. A spreadsheet is a digital tool that does the same job: type the kinds of litter in one column and the totals in the next, and it draws the graph.

We are learning to

• record collected data in a tally and a frequency table,
• display data in a column graph with a title, labels and an even scale,
• record and display data in a spreadsheet.

Success criteria

• I can tally a list of data and check that the totals add up.
• I can draw a column graph from a frequency table, or make one in a spreadsheet.

You need

Rulers. A device with a spreadsheet program on the board. The investigation planners. The worksheet, one per child.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Missing or double-counting items in the list; the totals then do not add up to 38.
• Drawing an uneven scale, or bars of different widths.
• Thinking a spreadsheet chooses the question or checks that the data is right.

Answers

• Part A: wrapper 14, paper 9, food scrap 7, bottle cap 5, straw 3; altogether 38.
• Part B: bars to 14, 9, 7, 5, 3 on the 0 to 16 scale; the paper, food scrap, bottle cap and straw bars end halfway between two lines.
• Part C: B3 9, B4 7, B5 5, B6 3; the number of bottle caps is in cell B5; one more straw changes cell B6.

Record and display

A. Tally the litter, then write the totals.

Interpret the data

Interpreting means reading the display to answer the question the investigation began with, and saying what the data does and does not show. Children read the litter graph from Day 3, compare its bars, answer the litter question in a sentence, and use the data to suggest what the school could do. Watch for one trap: wrappers were the most common litter, yet most of the litter was not wrappers. Pairs then interpret the display of their class data.

We are learning to

• read a display to answer the investigation question,
• compare categories and the whole data set,
• say what the data does not tell us.

Success criteria

• I can answer our question from the display and give the numbers.
• I can tell the most common from most of the data.

You need

Mini whiteboards. The investigation planners with the class displays from Day 3. The worksheet, one per child.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Reading the most common category as most of the data: wrappers were 14 of the 38 pieces, fewer than half.
• Misreading a bar that ends halfway between two lines.
• Saying what they expected instead of what the data shows.

Answers

• Part A: 1 wrappers, 2 straws, 3 9, 4 16, 5 38, 6 no: 14 of 38 is less than half, which would be 19.
• Part B: for example “Wrappers were the most common litter: 14 of the 38 pieces we found.”
• Part C: answers vary; a good answer uses the numbers, such as a rubbish bin where children eat lunch, because wrappers were the most common litter (14 of 38).
• Part D: answers vary; litter changes from day to day, so count again on other days and compare.

Interpret the data

A. Read the graph.

1. Which kind of litter was most common? __________
2. Which kind was least common? __________
3. How many more wrappers than bottle caps were found? ____
4. How many pieces of paper and food scraps were there together? ____
5. How many pieces of litter were found altogether? ____
6. Were more than half of the pieces wrappers? Yes □    No □ How do you know? ____________________

B. Answer the question in a sentence. Use numbers from the graph.

C. What could the school do? Use the data to explain your idea.

D. The litter was counted on one day. Would it be the same every day? How could you check?

Communicate the result

An investigation ends by telling others what the data showed. A clear statement says what was counted and gives the numbers, so someone who never saw the data understands the answer; a vague one, such as “The playground is messy.”, could be said without collecting any data at all. Children judge statements about the litter count, make a vague one clear, then write and share a report of the class investigation.

We are learning to

• tell a clear statement of a result from a vague one,
• use numbers from the data to communicate a result,
• report a whole investigation, from the question to the answer.

Success criteria

• I can write a statement that answers our question with numbers from the data.
• I can explain our investigation to someone who did not take part.

You need

The step cards from Day 1. The investigation planners. The worksheet, one per child.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Writing statements with no numbers, or with numbers that do not answer the question.
• Reporting what they hoped to find instead of what the data shows.
• Claiming more than the data shows, such as saying one day of counting is true of every day.

Answers

• Part A: 1 clear, 2 vague, 3 vague, 4 clear, 5 clear, 6 vague.
• Part B: answers vary, for example “We found 38 pieces of litter in the playground after lunch.”
• Part C: answers vary; a clear report gives the question, the method, what the display showed with numbers, the answer and a next step.

Communicate the result

A. These statements are about the litter count. Is each one clear or vague? Tick one.

B. Make this statement clear. Use the data from the litter count.

C. Our investigation report

Question cards

One set per pair, for Day 1. Cut out the two headings and the eight cards, then sort each question under the heading that fits it.

Step cards

Cut out the four steps and put them in order. Keep them for Day 5.

Teacher note: good questions A, D, F, G; too vague B, C, E, H. The steps in order: Ask a question, then Collect the data, then Record and display, then Interpret and communicate.

Our investigation planner

One per pair. Fill one part each day, from the question on Day 1 to the answer on Day 5.

Day 1: Our question

Day 2: Collect the data

Day 3: Our display

Day 4: What we found

Day 5: Our answer

What we know: Statistical investigations

1. Ring the two questions that data could answer clearly.

   Is it fun?

   Which pet do most Year 4 students have?

   How many books did each of us read this term?

   What is the best thing?
2. How would you collect the data? Write survey, observe or measure.

   How long are our shadows at noon? __________

   Which ice-block flavour do you like best? __________

   How many people cross at the school crossing before 9 am? __________
3. Number the steps of an investigation in order, 1 to 4.

   interpret ____collect ____question ____display ____
4. Which is the most common way to get to school? __________
5. How many children answered the survey? ____
6. Do most of these children walk? Yes □    No □ How do you know? __________________________
7. Name a digital tool that can record this data and draw the graph. __________________
8. Ring the clearer statement.

   “Lots of us get to school.”

   “More of us walk to school than come by car.”
9. Write one more clear statement about the graph. ________________________________

Answers and marking guide

Answers

1. “Which pet do most Year 4 students have?” and “How many books did each of us read this term?”
2. measure, survey, observe.
3. interpret 4, collect 2, question 1, display 3.
4. Walk.
5. 22.
6. No: 9 of the 22 children walk, fewer than half, which would be 11.
7. A spreadsheet.
8. “More of us walk to school than come by car.”
9. Answers vary, for example “6 children come by car and 3 by bike.”

A quick three-level guide

Nine questions, three ideas. A child at standard asks a question data can answer, collects and displays the data in a way that suits it, reads the display to answer the question, and reports the result with numbers.

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: asking a question, collecting, recording and displaying, interpreting, and communicating.