Teaching pack: Acquiring and Representing Data (Year 4)

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Teaching pack · Year 4 Statisticsseegongsik /au

Acquiring and Representing Data: 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, a survey sheet, a mini-check and every answer.

AC9M4ST01

acquire data for categorical and discrete numerical variables to address a question of interest or purpose, using digital tools; represent data using many-to-one pictographs, column graphs and other displays or visualisations; interpret and discuss the information that has been created

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 question cards once, and print a survey sheet per pair for Day 2.
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. A data investigation starts with a question. Categorical data sorts answers into named groups, such as ways of getting to school; discrete numerical data is whole-number counts, such as numbers of pets. Children collect data with tallies, show it in pictographs and column graphs, and say what it tells them.

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.

Digital tools

The descriptor asks for digital tools. The interactive unit tallies and graphs on the board, and Day 4 shows how to make the same column graph in a spreadsheet: type the categories and totals in two columns and insert a column chart. Everything also works on paper.

On the board

This pack is the printable half of a free interactive unit. The on-screen half has six interactive pictures (choosing the kind of data, collecting with tallies, a many-to-one pictograph, building a column graph, reading the display, and a frequency table) plus a self-check quiz you can run as a class game on Day 5.

seegongsik.com/au/y4/statistics/AC9M4ST01

Aligned to the Australian Curriculum V9 (AC9M4ST01). This pack is original material from seegongsik, independently produced and not endorsed by ACARA. Curriculum content descriptors are (c) ACARA, licensed under CC BY 4.0. Free to print and use in class.

The week at a glance5 lessons

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	Questions and data	Sort questions by the data they give, named groups or counts, and choose a question to investigate	What kind of data?
2	Collect with tallies	Tally survey responses into frequency tables, then survey the class	Collecting data with tallies; A frequency table
3	Many-to-one pictographs	Read and draw pictographs where one symbol stands for 2, with half symbols	Many-to-one pictograph
4	Column graphs	Draw column graphs with a scale, a title and axis labels, from a table and from the class survey	Building a column graph
5	Read and discuss	Read a column graph, say what it shows and what it cannot, and choose a display	Reading the display; Self-check quiz

How the week builds

The week follows one investigation from question to answer. Day 1 chooses the question and the kind of data it needs, Day 2 collects the data, Days 3 and 4 show it as a pictograph and a column graph, and Day 5 reads the display and discusses what it shows. It builds on recording data in Year 3 (AC9M3ST01) and showing it in graphs (AC9M3ST02).

Materials for the week (one trip)

From the classroom: rulers, coloured pencils, scissors and this pack printed.
Optional: a computer or tablet with a spreadsheet for Day 4, and a clipboard per pair for the survey.
Cut out once: the question cards. Print one survey sheet per pair.

Words for the word wall

data, question, survey, categorical, numerical, category, tally, total, frequency table, pictograph, key, symbol, column graph, scale, axis, title, most, least

A note homeHome practice

Dear families

This week in maths, Year 4 runs a data investigation: asking a question, collecting answers with tally marks, and showing them in pictographs and column graphs.

Try this at home

Ask everyone at home a question, such as their favourite meal, and tally the answers.
Count something over a few days: cars passing, birds in the garden, or minutes of reading.
Look for graphs in newspapers, websites or cereal boxes. What does each one tell you?
Ask: is the answer a group, like a colour, or a count, like the number of pets?

Data I collected this week

Fill one row a day. Write a question you asked or counted, and what you found.

Day	Question	What I found
Monday
Tuesday
Wednesday
Thursday
Friday

Printed from the free seegongsik Acquiring and Representing Data teaching pack · seegongsik.com/au/y4/statistics/AC9M4ST01/pack

Day 1 · Teacher planDay 1 of 5

Questions and data

A data investigation starts with a question someone wants answered. The question decides the data: categorical data sorts answers into named groups, such as ways of getting to school, and discrete numerical data is whole-number counts, such as numbers of pets. Children sort question cards by the data each one gives, then choose a question for the class survey.

We are learning to

tell categorical data from discrete numerical data,
write a question that gives the data we want,
choose a question of interest to investigate.

Success criteria

I can say whether a question gives categorical or numerical data, and why.
I can write a survey question with clear answers.

You need

The question cards (cut-out sheet 1), one set per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

10 min	Groups or counts? Show the board (see the box). Children vote with a hand up for groups, a fist for counts. Ask: “Can you add up favourite colours? Can you add up numbers of pets?”
30 min	Sort the cards Pairs sort the question cards under the two headings, then do Parts A and B. Ask: “‘How old are you?’ Is that a group or a count?”
10 min	Our question Children share Part C. The class votes on a question for its own survey on Day 2. Ask: “Will everyone know how to answer it? What answers could people give?”

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

On the board

In “What kind of data?” children decide, then press “Categorical” or “Numerical”. “New variable” moves from favourite colour to number of pets, goals scored and type of fruit.

seegongsik.com/au/y4/statistics/AC9M4ST01

Watch for these ideas

Thinking any answer written as a number is numerical: a house number or a team number names a group.
Writing questions with no clear answers, such as “What do you like?”
Thinking numerical data must be large numbers.

Answers

Card sort: the cards that start with “How many” are numerical; the rest are categorical. Part A: categorical 2, 4, 5; numerical 1, 3, 6.
Part B: answers vary; a categorical question names groups, a numerical one asks how many. Part C: answers vary.

Day 1 · Worksheet

Questions and data

NameClassDate

A. Does each question give categorical data (named groups) or numerical data (counts)? Tick one.

Question	Categorical	Numerical
1. How many teeth have you lost?	□	□
2. What is your favourite ice-block flavour?	□	□
3. How many glasses of water did you drink today?	□	□
4. Which planet would you visit?	□	□
5. Which is your favourite day of the week?	□	□
6. How many times can you skip in a minute?	□	□

B. Write a question of your own for each kind of data.

Categorical: ______________________________________________

Numerical: ________________________________________________

C. A question I would like to ask the class

My question: ______________________________________________

Answers people might give: _________________________________

Kind of data: categorical / numerical (ring one)

Day 2 · Teacher planDay 2 of 5

Collect with tallies

A tally chart records answers as they arrive: one mark for each answer, and every fifth mark drawn across the four before it, so the marks count in fives. The totals go in a frequency table. Children tally two surveys from their responses, one categorical and one numerical, then survey the class with the question chosen on Day 1.

We are learning to

record survey answers with tally marks in fives,
turn a tally into a frequency table of totals,
collect data from the class to answer our question.

Success criteria

I can tally answers so that the marks count in fives.
I can check my totals add up to the number of answers.

You need

The survey sheet (cut-out sheet 2), one per pair, and a clipboard if you have one. The worksheet, one per child.

Lesson flow (about 50 minutes)

10 min	Tally on the board Show the board (see the box). Ask the class the first question; a child presses a button for each answer. Ask: “Why is the fifth mark drawn across the other four?”
25 min	Tally the surveys Children do Parts A and B, crossing out each response as they tally it. Ask: “Your totals add up to 27, but there were 28 answers. What could have happened?”
15 min	Survey the class Pairs ask the class question from Day 1 and tally the answers on the survey sheet. Ask: “How will you make sure no one is asked twice?”

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

On the board

In “Collecting data with tallies” press “+ red”, “+ blue” or “+ green” for each answer; the fifth mark crosses the four before it. “Reset” starts again. Then show “A frequency table” and press “Reveal next” for each total.

seegongsik.com/au/y4/statistics/AC9M4ST01

Watch for these ideas

Drawing the fifth mark as a fifth upright line, so the marks cannot be counted in fives.
Skipping or double-counting answers: cross each one out as it is tallied.
Leaving out a value that nobody chose: a total of 0 still belongs in the table.

Answers

Part A: walk 8, car 10, bus 4, bike 3, scooter 3; 28 answers, and car is the most common way.
Part B: 0 pets 7, 1 pet 9, 2 pets 5, 3 pets 2, 4 pets 1; 24 answers. The class survey: answers vary.

Day 2 · Worksheet

Collect with tallies

NameClassDate

A. How do you get to school? Tally these 28 answers, then write the totals.

car, walk, bus, car, bike, walk, car, scooter, walk, car, bus, car, walk, bike, car, scooter, walk, car, bus, walk, car, bike, car, walk, scooter, bus, car, walk

Way to school	Tally	Total
walk
car
bus
bike
scooter

B. How many pets do you have? Tally these 24 answers, then write the totals.

1, 0, 2, 1, 1, 0, 3, 1, 2, 0, 1, 4, 0, 2, 1, 1, 0, 2, 1, 3, 0, 1, 2, 0

Number of pets	Tally	Total
0 pets
1 pet
2 pets
3 pets
4 pets

Check: the totals in each table should add up to the number of answers.

Day 3 · Teacher planDay 3 of 5

Many-to-one pictographs

In a many-to-one pictograph one symbol stands for several things, and the key says how many. With one book for 2 books, 12 books are 6 symbols and 9 books are 4 and a half symbols: half a symbol stands for half of 2. Children read a pictograph by counting symbols and using the key, then draw one from a table.

We are learning to

read a pictograph where one symbol stands for 2,
use half a symbol for an odd number,
draw a pictograph with a title and a key.

Success criteria

I can use the key to read any row of a pictograph.
I can draw a pictograph from a table, with half symbols where I need them.

You need

Coloured pencils and rulers. The worksheet, one per child.

Lesson flow (about 50 minutes)

10 min	Read the key Show the board (see the box). Children work out each row before you reveal it. Ask: “If each circle stood for 10, how would Wednesday’s row look?”
30 min	Read and draw Children do Part A, then draw the fruit pictograph in Part B. Ask: “Oranges are 5. How many symbols is that? How do you show the extra one?”
10 min	Why a key? Children do Part C and compare their answers. Ask: “Why not draw one book for every book?”

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

On the board

Show “Many-to-one pictograph”: each circle stands for 5, and Monday, Tuesday and Wednesday have 2, 3 and 4 circles. Children work out each total, then press “Show totals” for 10, 15 and 20. “Reset” hides them.

seegongsik.com/au/y4/statistics/AC9M4ST01

Watch for these ideas

Counting symbols and forgetting the key: 6 books instead of 12.
Reading half a symbol as 1 whole symbol, or ignoring it.
Drawing symbols of different sizes, so the rows cannot be compared by length.

Answers

Part A: 4A 12, 4B 9, 4C 15, 4D 6; the most is 4C, the fewest is 4D, 4C read 9 more than 4D, and 42 books altogether.
Part B: apples 4, bananas 3, oranges 2 and a half, grapes 1 and a half symbols. Part C: so that big numbers fit; one symbol for 1 would need 15 books in the 4C row.

Day 3 · Worksheet

Many-to-one pictographs

NameClassDate

A. Read the pictograph.

Books read this week

Key: = 2 books

How many books did 4C read? ______

Which class read the fewest books? ______

How many more books did 4C read than 4D? ______ How many books altogether? ______

B. Draw a pictograph of this table. Use one star for 2 pieces of fruit.

Fruit eaten at lunch	Total
apples	8
bananas	6
oranges	5
grapes	3

Title: ______________________________

apples

bananas

oranges

grapes

Key: = 2 pieces of fruit

C. Why does a pictograph use one symbol for more than one thing?

______________________________________________________

Day 4 · Teacher planDay 4 of 5

Column graphs

A column graph shows each category as a bar as tall as its total, read against a scale up the side. A finished graph has a title, a label on each axis, and a scale that goes up evenly. Children graph the transport survey from Day 2 on a scale in twos, then graph their own class survey, choosing the scale themselves; a spreadsheet can draw the same graph.

We are learning to

draw a column graph from a frequency table,
give a graph a title, axis labels and an even scale,
choose a scale that fits our data.

Success criteria

I can draw each bar to the right height, even between the numbers on the scale.
My graph has a title and a label on each axis.

You need

Rulers, coloured pencils, the Day 2 worksheets and survey sheets. Optional: a computer with a spreadsheet. The worksheet, one per child.

Lesson flow (about 50 minutes)

10 min	Bar by bar Show the board (see the box). Children say each height before you add the bar. Ask: “Blue is 7, but the scale only shows 6 and 8. Where does the bar stop?”
30 min	Graph two surveys Children do Part A from their Day 2 totals, then Part B from the class survey. Ask: “Your biggest total is 14. What scale fits that on the graph?”
10 min	On the computer Show Part C on a computer: type the transport totals and insert a column chart. Ask: “What did the computer do for us? What did we still have to decide?”

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

On the board

In “Building a column graph” press “Add bar” four times: red 4, blue 7, green 3 and gold 5 rise against the scale. “Reset” clears the bars.

seegongsik.com/au/y4/statistics/AC9M4ST01

Watch for these ideas

Drawing bars of different widths, or with no gaps between them.
Numbering the spaces instead of the lines, so every bar is one too high.
A scale that jumps unevenly, such as 0, 2, 5, 10.

Answers

Part A: bars walk 8, car 10, bus 4, bike 3, scooter 3; a title such as “How we get to school”, and axis labels “Way to school” and “Number of children”.
Part B: graphs vary; check the bars match the survey totals and the scale goes up evenly. Part C: the spreadsheet graph matches Part A.

Day 4 · Worksheet

Column graphs

NameClassDate

A. Graph the Day 2 survey “How do you get to school?” Add a title and axis labels.

B. Graph your class survey. Write the categories and choose the scale.

C. On a computer (optional)

Type the ways to school in one column and the totals in the next. Select both columns and insert a column chart. Does it look like your graph in Part A?

Day 5 · Teacher planDay 5 of 5

Read and discuss

A graph is made to be read. Children read a column graph to answer questions (the most, the least, how many more, how many altogether), then discuss what it tells us and what it cannot: a graph of favourite activities says how many chose each one, not why. They finish by choosing the best display for a set of data and reading their own class survey.

We are learning to

read a column graph to answer questions,
say what a graph tells us and what it cannot,
choose a display that suits the data.

Success criteria

I can answer most, least, how many more and how many altogether from a graph.
I can write something a graph shows and a question it cannot answer.

You need

The class survey graphs from Day 4. The worksheet, one per child.

Lesson flow (about 50 minutes)

10 min	Read the bars Show the board (see the box). Children answer each question on fingers first. Ask: “How did you work out how many more chose blue than green?”
30 min	What does it tell us? Children do Parts A to D, then share one thing their class survey graph tells them. Ask: “Does the graph tell us why handball is popular? How could we find out?”
10 min	Class game Run the self-check quiz as a class game. Ask: “What question would you ask the class next week?”

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

On the board

In “Reading the display” children choose an answer for which is most popular, how many chose green and how many more blue than green; “New question” moves on. Then run the self-check quiz; question 5 asks why we collect data at all.

seegongsik.com/au/y4/statistics/AC9M4ST01

Watch for these ideas

Reading the height of the bar from the wrong line, or from the top of the next bar.
Answering “how many more” with one of the two numbers instead of the difference.
Reading more into a graph than it shows, such as why children chose an activity.

Answers

Part A: handball (9); drawing (3); 5 more chose handball than reading; 28 children altogether; skipping was chosen by 5.
Part B: answers vary, such as “handball is the most popular”. Part C: answers vary, such as why children chose them, or what they do on rainy days. Part D: a column graph or a pictograph both suit categories; a column graph is easier to read for exact totals.

Day 5 · Worksheet

Read and discuss

NameClassDate

A. Read the graph.

Which activity is the most popular? __________

Which is the least popular? __________

How many more chose handball than reading? ____

How many children altogether? ____

Which activity did 5 children choose? __________

B. Write two things the graph tells you about the class.

1. __________________________________________________________

2. __________________________________________________________

C. Write a question the graph cannot answer.

______________________________________________________________

D. For the Day 2 transport survey, would you choose a pictograph or a column graph? Why?

______________________________________________________________

Cut-out cards 1 of 2Question cards

Question cards

One set per pair, for Day 1. Cut out the two headings and the twelve cards, then sort each question under the kind of data its answers give.

Categorical

the answers are named groups

Numerical

the answers are counts

What is your favourite fruit?

How many pets do you have?

How many people live in your home?

How do you get to school?

What colour is your school bag?

How many letters are in your first name?

Which sport do you like best?

How many books did you read this week?

How many brothers and sisters do you have?

Which season do you like best?

How many goals did your team score?

What pet would you most like to have?

Teacher note: categorical A, D, E, G, J, L; numerical B, C, F, H, I, K.

Cut-out sheet 2 of 2Survey sheet

Our survey sheet

One per pair. Collect the class answers on Day 2; graph them on Day 4.

Our question: ________________________________________________

Kind of data: categorical / numerical (ring one)

We asked: __________ people

Answers

Answer	Tally	Total

Check: the totals add up to ______, the number of people we asked.

What we found: ______________________________________________

Mini-check · End of the weekData

What we know: Data

NameClassDate

Ring the questions that give numerical data.
a) How many pets do you have?b) What is your favourite colour?c) Which month were you born in?d) How many letters are in your name?
Write the total for each tally.
hats= ____
caps= ____
none= ____
How many on Tue? ____
Mon
Tue
Key: = 4
Use the graph for questions 4 to 6. Which fruit is the most popular? __________
How many more children chose apples than pears? ____
6 children chose oranges. Draw the oranges bar on the graph.
Is a graph of how many pets children have categorical or numerical data? __________
Write one thing the fruit graph shows. ________________________________________

Mini-check · Answers and markingFor the teacher

Answers and marking guide

Answers

a and d.
hats 7, caps 12, none 4.
10: 2 stars and a half, with each star 4.
apples.
5.
A bar up to 6, as wide as the others.
Numerical: the answers are counts.
Answers vary, such as “apples are the most popular”.

A quick three-level guide

Idea	Working towards	At standard	Beyond
Data and collecting (Q1, Q2)	calls any answer with a number numerical, or miscounts the tally	tells categorical from numerical data and counts tallies in fives	writes a clear survey question for either kind of data
Representing (Q3, Q6, Q7)	counts symbols without the key, or draws a bar to the wrong line	reads a pictograph with half symbols and draws a bar to its height	chooses a scale and a display that suit the data
Interpreting (Q4, Q5, Q8)	reads one bar but not differences between bars	answers most, least and how many more from a graph	says what a graph shows and what it cannot

Eight questions, three ideas. A child at standard tells the two kinds of data apart, collects and counts it, shows it in a pictograph or a column graph, and reads the display.

Weekly recordClass checklist

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	Kinds of data	Tallies	Pictographs	Column graphs	Reads and discusses

The five columns are the five days: kinds of data, tallies, pictographs, column graphs, and reading and discussing.