Collecting and Recording Data: 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 question cards, tally cards, a mini-check and every 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 question cards and the tally 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. Data answers a question. Categorical data names a group (favourite fruit, eye colour); discrete numerical data is a count in whole numbers (number of pets, books read). A tally records answers as they come, in groups of five, and a frequency table turns the tallies into numbers that add up to the total counted. A spreadsheet is the same table on a screen, which can add the total for you.
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 | Categorical or numerical? | Tell data that names a group from data that is a count, and write a question of each kind | Categorical or numerical? |
| 2 | Tally as you go | Run a class survey and record each answer with a tally mark, grouped in fives | The tally counter |
| 3 | Read the tally | Read tallies as numbers by counting the fives, then the leftovers, and draw tallies for numbers | Read the tally |
| 4 | Frequency tables and spreadsheets | Turn tallies into a frequency table that adds up, find a missing count, and set out a spreadsheet | The frequency table; The missing count |
| 5 | Collect to fit the question | Choose to observe, ask or use data someone has collected, then plan and run a small survey | Good question, right method |
How the week builds
Day 1 names the two kinds of data. Days 2 and 3 record answers with tallies and read them back. Day 4 turns tallies into a frequency table and a spreadsheet that add up, and Day 5 chooses how to collect data for a question and runs a small survey. It leans on Surveys, Lists and Tables (AC9M2ST01) and Numbers Beyond 10 000 (AC9M3N01).
Materials for the week (one trip)
- From the classroom: scissors, pencils, mini whiteboards, this pack printed.
- A computer or tablet with a spreadsheet, for one demonstration on Day 4 (not essential).
- Clipboards, if children will survey other classes on Day 5.
- Cut out once, use all week: the question cards and the tally cards.
Words for the word wall
data, question, survey, categorical, numerical, count, category, tally, tally mark, frequency, frequency table, total, spreadsheet, column, row, observe, collect
Dear families
This week in maths, Year 3 is collecting data to answer a question, and recording it with tally marks and frequency tables.
Try this at home
- Ask a question at dinner (favourite food, number of pets) and tally the answers.
- Count the cars of each colour passing your window for five minutes, with tally marks.
- Read a tally together: count the groups of five, then the leftover marks.
- Ask: does this question give a name or a number? Is it categorical or numerical?
Our data this week
Fill one row a day: a question you asked or counted at home, and what you found.
| Day | Our question | What we found |
|---|---|---|
| Monday | ||
| Tuesday | ||
| Wednesday | ||
| Thursday | ||
| Friday |
Printed from the free seegongsik Collecting and Recording Data teaching pack · seegongsik.com/au/y3/statistics/AC9M3ST01/pack
Categorical or numerical?
Data answers a question, and the question decides the kind of data. Categorical data names a group: favourite sport, eye colour, type of pet. Discrete numerical data is a count in whole numbers: number of siblings, books read. The quick test is whether the answer is a word that names a group or a number you get by counting.
We are learning to
- tell categorical data from numerical data,
- explain the test: a name or a count,
- write a question of each kind.
Success criteria
- I can say if data is categorical or numerical, and why.
- I can write a survey question of each kind.
You need
Mini whiteboards. The question cards (cut-out sheet 1). The worksheet.
Lesson flow (about 50 minutes)
| 10 min | Answer and sort Ask two questions: “What is your favourite colour?” and “How many pets do you have?” Children write their answers on whiteboards; sort the answers into words and numbers. Ask: “Which question gave us words? Which gave us numbers?” |
| 25 min | Name the kind Decide on the board (see the box). Pairs sort the question cards into categorical and numerical, then children sort the worksheet variables. Ask: “‘Month of your birthday’ has numbers on a calendar. Is it a count?” |
| 15 min | Write your own Children write one categorical and one numerical question they would like to ask the class; pairs check each other’s. Ask: “How do you know your question will give a count?” |
Two half-sessions instead? Split after the card sort; start Session B with the worksheet.
Watch for these ideas
- Thinking any answer with a number in it is numerical. A birthday month names a group; it is not a count.
- Sorting by topic (pets, sport) instead of kind. Ask: is the answer a name or a count?
- Writing a numerical question that gives words, such as “Do you have pets?”. Ask “How many?”
Answers
- Categorical: favourite season; month of your birthday; type of drink in your lunch box; favourite playground game. Numerical: the 4 “number of” ones.
- Own questions: a categorical one asks for a name or a group; a numerical one asks how many.
- Sam: no. A month names a group, even though months can be numbered; it is not a count.
Categorical or numerical?
Name the kind of data
Is the answer a name (categorical) or a count (numerical)? Tick one.
| The data | Categorical | Numerical |
|---|---|---|
| favourite season | ||
| number of teeth you have lost | ||
| month of your birthday | ||
| type of drink in your lunch box | ||
| number of pockets on your clothes today | ||
| number of letters in your first name | ||
| favourite playground game | ||
| number of windows in your home |
Write your own
A question that gives categorical data (a name or a group):
A question that gives numerical data (a count):
Explain
Sam says “month of your birthday” is numerical, because months have numbers. Do you agree? Why?
Tally as you go
A tally records answers as they come in: one mark for each answer, beside its category, with every fifth mark drawn across the four before it. The groups of five keep a long count easy to read. Crossing out or ticking each answer as it is tallied keeps every answer counted once.
We are learning to
- record answers with tally marks as they come in,
- group tally marks in fives,
- check that every answer is counted once.
Success criteria
- I can tally answers in groups of five as I hear them.
- I can check my tally against the number of answers.
You need
The question cards (cut-out sheet 1). The worksheet. A class list, to tick off who has answered.
Lesson flow (about 50 minutes)
| 10 min | Tally on the board Tally the class on the board (see the box), one answer at a time. Ask: “Why is every fifth mark drawn across the others?” |
| 25 min | Tally the list Children tally the 22 pet answers on the worksheet, crossing out each answer as they tally it, then check that the marks add up to 22. Ask: “Your tally has 21 marks but there were 22 answers. How can you find the one you missed?” |
| 15 min | Our own survey The class chooses a categorical question card. Children ask it around a group or the room and tally the answers on the worksheet. Ask: “How many children did you ask? Does your tally have that many marks?” |
Two half-sessions instead? Split after the list; start Session B with our own survey.
Watch for these ideas
- Drawing a fifth upright mark. The fifth mark goes across the four.
- Losing count when answers come fast. Cross out each answer once it is tallied.
- Thinking a group of five is one answer. Each mark is one answer; a group is five answers.
Answers
- Pets: dog 8, cat 7, fish 4, bird 3; 22 marks in all.
- Our survey: the marks add up to the number of children asked.
Tally as you go
Tally the list
“What is your favourite pet?” 22 children answered. Cross out each answer as you tally it.
| Pet | Tally |
|---|---|
| dog | |
| cat | |
| fish | |
| bird |
How many marks altogether? ______ Is that the number of answers? ______
Our own survey
Our question: ____________________________________________
| Answer | Tally |
|---|---|
Read the tally
Reading a tally is counting in fives, then adding the leftover marks: two groups and three more is 5, 10, then 11, 12, 13. The marks become a number, the frequency, ready for a table. Drawing a tally for a number goes the other way: as many groups of five as fit, then the rest.
We are learning to
- read a tally by counting the groups in fives, then the leftovers,
- draw the tally for a number,
- explain why tallies are grouped in fives.
Success criteria
- I can read a tally quickly.
- I can draw the tally for a number.
You need
Mini whiteboards. The tally cards (cut-out sheet 2). The worksheet.
Lesson flow (about 50 minutes)
| 10 min | Count in fives Count in fives to 50 and back. Draw a tally on the board and count it together, groups first. Ask: “Why do we count the groups first?” |
| 25 min | Read and draw Read tallies on the board (see the box). Children read the six tallies on the worksheet and draw tallies for the four numbers. Ask: “This tally has three groups and one more. How did you count it?” |
| 15 min | Tally memory Pairs play memory with the tally cards, turning over two at a time to match each tally with its number. Ask: “Which cards were quickest to match? Why?” |
Two half-sessions instead? Split after reading the tallies; start Session B with drawing them.
Watch for these ideas
- Counting a group as four, missing the mark across. Each crossed group is five.
- Counting every mark one by one. Count the groups in fives, then the leftovers.
- Drawing groups of six. A group is four upright marks and one across them.
Answers
- Read: A 8, B 13, C 17, D 4, E 20, F 11.
- Draw: 6 is one group of five and 1 more; 10 is 2 groups of five; 14 is 2 groups of five and 4 more; 19 is 3 groups of five and 4 more.
- Ali: 7 is one group of five and 2 more.
Read the tally
What number?
Count the groups in fives, then the leftover marks.
Draw the tally
Help Ali
Ali drew 7 as seven upright marks in a row. Draw 7 the tally way.
Frequency tables and spreadsheets
A frequency table pairs each category with its tally and its frequency, the number the tally stands for. Every answer is counted once, so the frequencies add up to the total: a built-in check that also finds a missing count. A spreadsheet is the same table on a screen, with the categories in one column and the counts in the next, and it can add the total for you.
We are learning to
- turn tallies into a frequency table,
- check that the frequencies add up to the total,
- set out data in a spreadsheet, categories in one column and counts in the next.
Success criteria
- I can make a frequency table that adds up.
- I can find a missing count from the total.
You need
The Day 2 pet tallies. The worksheet. A computer or tablet with a spreadsheet, if you have one.
Lesson flow (about 50 minutes)
| 10 min | Tally to table Turn the Day 2 pet tally into a frequency table on the board, with a total row. Ask: “The frequencies add up to 22. Why must they?” |
| 25 min | Tables that add up Check and complete tables on the board (see the box). Children finish the sports table and find the three missing counts on the worksheet. Ask: “How did you find the missing count without asking anyone again?” |
| 15 min | Spreadsheet Type the sports table into a spreadsheet: sports in column A, counts in column B, and =SUM(B2:B5) in B6 for the total. Children fill in the paper spreadsheet. No computer? Draw the grid on the board. Ask: “Where would you type a new sport? What would happen to the total?” |
Two half-sessions instead? Split after the tables; start Session B with the spreadsheet.
Watch for these ideas
- Copying the tally marks into the frequency column. The frequency is the number the tally stands for.
- A total that does not match the number of answers. Something was missed or counted twice.
- Adding the known counts to the total to find a gap. Take the known counts away from the total.
Answers
- Sports: soccer 9, netball 6, cricket 4, swimming 7; total 26.
- Missing: blue 6, fish 4, bus 7.
- Spreadsheet: A2 to A5 the sports, B2 to B5 the counts 9, 6, 4, 7; B6 shows 26.
Frequency tables and spreadsheets
Finish the table
“What is your favourite sport?” Write the frequency for each tally, then the total.
| Sport | Tally | Frequency |
|---|---|---|
| soccer | ||
| netball | ||
| cricket | ||
| swimming | ||
| total |
Find the missing count
| red | 6 |
| blue | ? |
| green | 3 |
| total | 15 |
| cats | 5 |
| dogs | 7 |
| fish | ? |
| total | 16 |
| walk | 9 |
| bus | ? |
| car | 7 |
| bike | 2 |
| total | 25 |
Missing counts: ______ ______ ______
A paper spreadsheet
Copy the sports table into the cells. What number should cell B6 show for the total?
| A | B | |
|---|---|---|
| 1 | sport | frequency |
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 | total |
B6 = ______
Collect to fit the question
Different questions need different ways of collecting. A favourite sport is found by asking and tallying; the kinds of birds in the garden by watching and tallying; how many days it rained last month by looking up weather records that someone has already collected, a data set. The method must fit the question, or it gathers the wrong thing.
We are learning to
- choose to observe, ask, or use records already collected, to fit a question,
- plan a small survey: the question, the kind of data, the method and the record,
- collect the data and record it in a frequency table.
Success criteria
- I can choose a method that fits a question.
- I can plan and run a small survey.
You need
The question cards (cut-out sheet 1). Clipboards, if children survey other classes. The worksheet. The unit’s self-check quiz.
Lesson flow (about 50 minutes)
| 10 min | Which way? Choose methods on the board (see the box). Ask: “Why would asking one friend not tell us the busiest day at the canteen?” |
| 25 min | Plan and collect Children match the worksheet questions to methods, then plan a survey with a question card or their own question, collect the answers from their group and record them in the frequency table. Ask: “Is your question categorical or numerical? How did that change how you recorded it?” |
| 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 matching; start Session B with the survey and the quiz.
Watch for these ideas
- Asking only one or two people. Ask everyone the question is about.
- Choosing a method that finds something else, such as a ruler for a favourite colour. Ask what the question wants to know.
- Thinking data must always be collected new. Library and weather records are data too.
Answers
- Methods: 1 ask and tally, 2 observe and tally, 3 use records already collected, 4 ask and record the number, 5 use records already collected.
- Our survey: any plan where the method fits the question and the table adds up to the number of people asked.
Collect to fit the question
Choose the method
Methods: observe and tally · ask and tally · ask and record the number · use records already collected
| The question | The best method |
|---|---|
| Which sport does our class like best? | |
| Which kinds of birds visit the school garden at lunchtime? | |
| How many books did each child borrow from the library this term? | |
| How many cousins does each child have? | |
| How many days did it rain last month? |
Plan and run a survey
Our question: ____________________________________________
The kind of data: categorical □ numerical □ How we will collect it: ______________________
| Answer | Tally | Frequency |
|---|---|---|
| total |
Question cards
Cut out the twelve cards. On Day 1, pairs sort them into categorical and numerical. On Days 2 and 5, the class or a group chooses one to survey.
Teacher note: the 6 “How many” cards give numerical data; the other 6 give categorical data.
Tally cards
Cut out the twelve cards: six tallies and six numbers. On Day 3, pairs lay them face down and play memory, keeping two cards that show the same number.
Teacher note: the pairs are 3, 7, 10, 12, 15, 18.
What we know: Collecting and Recording Data
Work on your own.
- Is “favourite ice-cream flavour” categorical or numerical? ______________
- Is “number of pencils in your pencil case” categorical or numerical? ______________
- What number does this tally show? ______
- Draw the tally for 9: ______________________
- Soccer 7, netball ?, cricket 5; the total is 18. How many chose netball? ______
- The weather each day: rain 4, sun 9, cloud 6. What is the total? ______
- What is the best way to find the favourite game of Year 3: ask one friend, ask and tally, or weigh the games? ______________
- A spreadsheet has the counts 3, 5, 4 in column B. What should the total cell show? ______
Answers and marking guide
Answers
- Categorical.
- Numerical.
- 14.
- One group of five and 4 more.
- 6.
- 19.
- Ask and tally.
- 12.
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Kinds of data (Q1, Q2) | sorts data by topic, not by kind | tells categorical data from numerical data | writes a survey question of each kind |
| Recording (Q3 to Q6, Q8) | tallies without grouping in fives | tallies in fives, reads tallies and totals a frequency table | records in a frequency table and a spreadsheet, and checks the total |
| Collecting to fit (Q7) | chooses a method that does not fit | chooses to observe, ask or use records to fit the question | plans a survey: question, kind of data, method and record |
Eight questions, three ideas. A child at standard tallies in fives, reads a tally back as a number, and uses the total to check a frequency table.
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 | Reads tallies | Frequency table | Fits the question |
|---|---|---|---|---|---|
The five columns are the five days: kinds of data, tallying, reading tallies, frequency tables, and collecting to fit the question.