Tock's Data Detective Book
Find the answers hiding in the numbers.
What is data?
Data is information you collect to answer a question.
How many kids ride to school? Which lunch is most popular? Is the park busier on Saturdays? You can't know by guessing. You find out by collecting data, then sorting it, drawing it and reading what it says.
People who can do that are hard to fool. This book gives you eight data detective skills, from asking a good question to spotting a graph that is playing tricks.
How this book works
Every chapter has the same four parts.
- Read it. One big idea, with pictures.
- Try it. An activity you play right here on the screen.
- Away from the screen. A game for paper, pencils and friends.
- Quick check. Three questions. Get them all right to earn a star.
There are 9 stars to collect. Got a question wrong? No problem. Read the hint and have another go. That's how thinkers learn.
Choose a chapter
Chapter 1 · Data skill one
Ask a good question
Detectives don't guess. They collect clues. In maths, the clues are called data.
Data can be numbers, like heights or scores. It can also be words, like favourite colours or types of pet.
Every investigation starts with a question. A good data question has lots of possible answers, so you have to ask many people or measure many things to find out.
In maths: two kinds of data
Number data comes from counting or measuring: 3 pets, 142 cm tall. Category data is words: dog, cat, fish. You'll sort and draw them in different ways.
Read each question. Would you need to collect data to answer it, or is there one quick answer?
Away from the screen: question factory
You need: paper and a pencil
Write three questions about your class or your family that would need data to answer. Pick the one you're most curious about. Before you collect anything, write down what you predict the answer will be. Detectives love checking a prediction.
Quick checkEarn your star
Chapter 2 · Data skill two
Collect the clues
To find the class's favourite pet you could guess. Or you could ask everyone and write the answers down. That's a survey.
Counting in your head is risky when answers come quickly. Tally marks keep track for you. Draw one line for each answer. The fifth line goes across the other four, like a gate. Then you can count the gates in 5s.
Two rules make a survey fair. Ask everyone the same question in the same way. And ask enough people, from different groups. The people you ask are called your sample.
In maths: tallies are skip counting
Three gates and 2 extra lines is 5, 10, 15, then 16, 17.
5 + 5 + 5 + 2 = 17
Sixteen kids are telling Tock their favourite pet, one at a time. Tap the right pet to add a tally mark for each answer.
Away from the screen: traffic tally
You need: paper, a pencil and a safe spot near a path or road
Watch for five minutes with a grown-up. Make a tally chart with rows for cars, bikes, trucks and walkers. Which was most common? Would the answer change at a different time of day?
Quick checkEarn your star
Chapter 3 · Data skill three
Sort it out
A pile of answers is a mess. Sorting turns the mess into something you can read.
Put the answers that are alike into groups. Each group is a category. Then count how many are in each one. A table keeps the counts neat, with one row for each category.
| Pet | Tally | Total |
|---|---|---|
| Dog | 6 | |
| Cat | 5 | |
| Fish | 3 | |
| Bird | 2 | |
| All answers | 16 |
You can sort by two things at once. Is the number even or odd? Is it under 20, or 20 and over? A two-way table has a box for every combination.
In maths: make the totals match
The totals in a table must add up to the number of answers you collected. If they don't, an answer got lost or counted twice.
6 + 5 + 3 + 2 = 16
Each number belongs in exactly one box of this two-way table. Which box?
| Under 20 | 20 or more | |
|---|---|---|
| Even | Box A | Box B |
| Odd | Box C | Box D |
Away from the screen: sort it twice
You need: a handful of buttons, blocks or pencils
Sort your objects by colour and count each group. Now mix them up and sort the same objects by size. Draw a two-way table with colours down the side and sizes across the top, and write the count in every box.
Quick checkEarn your star
Chapter 4 · Data skill four
Picture the data
A table tells you the numbers. A graph shows you the story in one look.
In a picture graph, little pictures stand for the things you counted. Always read the key! One picture might mean 1 vote, or 2, or 10.
In a bar graph (also called a column graph), the height of each bar shows the count. The taller the bar, the bigger the number.
In maths: read the key, then multiply
If one picture is worth 5 and a row has 4 pictures, that row shows 4 × 5 = 20.
The library counted the books borrowed each day. Use the buttons to raise each bar to the right height.
| Day | Books |
|---|---|
| Monday | 4 |
| Tuesday | 7 |
| Wednesday | 2 |
| Thursday | 9 |
| Friday | 6 |
Away from the screen: sticky-note graph
You need: sticky notes and a wall, window or fridge
Ask everyone at home one question, like "Which fruit should we buy this week?" Write each choice along the bottom. Everyone adds one sticky note above their choice. You've made a bar graph you can see from across the room.
Quick checkEarn your star
Chapter 5 · Data skill five
Read the graph
Reading a graph is detective work too. Your clues are the title, the labels and the scale.
The scale is the row of numbers up the side. It doesn't always count in 1s. If the lines say 0, 10, 20, 30, then a bar that stops halfway between 10 and 20 is worth 15.
A line graph shows how something changes over time. When the line climbs, the number is growing. When it drops, the number is shrinking. When it's flat, nothing changed.
In maths: comparing is subtracting
If Thursday's bar shows 9 and Monday's shows 4, then Thursday has 9 − 4 = 5 more.
Use the graph to answer each question. Check the scale carefully: it counts in 10s.
Away from the screen: graph hunt
You need: a newspaper, magazine, cereal box or website
Find a real graph. What is its title? What does the scale count in? Write down one thing the graph tells you, and one question it makes you want to ask.
Quick checkEarn your star
Chapter 6 · Data skill six
Find what's typical
Seven friends, seven scores. If someone asks "How did your team go?", you don't want to read out all seven. You want one number that sums them up.
That number is called an average. There are three popular kinds, and each one answers a slightly different question.
- Mode: the value that turns up most often.
- Median: the middle value when you line them up in order.
- Mean: the fair share. Add them all up, then divide by how many there are.
The range tells you how spread out the data is: the biggest value take away the smallest.
Mode: 5 appears twice Median: 6 is in the middle
In maths: the mean is fair sharing
Three kids have 2, 4 and 9 stickers. Altogether that's 15. Shared out equally, each kid would get the mean.
15 ÷ 3 = 5
Work out all four numbers for each set of data. Scrap paper helps.
Away from the screen: how long is a minute?
You need: a timer and three or more people
Everyone closes their eyes. One person starts the timer and says "go". Each player puts a hand up when they think one minute has passed, and the timer-holder writes down their time in seconds. Put the times in order. What is the median? What is the range?
Quick checkEarn your star
Chapter 7 · Data skill seven
Don't be fooled
A graph can use true numbers and still trick your eyes. Ads and headlines do it all the time.
Here are three tricks every data detective should know.
- The chopped scale. The scale doesn't start at 0, so a tiny difference looks huge.
- The unfair sample. They asked too few people, or only one kind of people.
- The loaded question. The question pushes you towards an answer. "Don't you agree broccoli is yucky?"
Two batteries were tested. Zip lasted 48 hours and Zap lasted 50 hours. Press the button to see how the scale changes the story.
In maths: three questions for any graph
Where does the scale start? How many were asked? Who was asked?
Read each case. Which trick is being played, or is it fair?
Away from the screen: ad detective
You need: a catalogue, magazine or a walk past some shop windows
Find an ad that uses a number, like "50% more" or "4 out of 5". What would you want to know before you believed it? Write your detective questions next to the ad.
Quick checkEarn your star
Chapter 8 · Data skill eight
What's the chance?
Will it rain tomorrow? Will you roll a 6? Nobody knows for sure. But data helps you make a smart prediction.
Chance is about how likely something is. Some things are impossible, like rolling a 7 on an ordinary dice. Some are certain, like rolling a number less than 7. Most things sit somewhere in between.
A fair coin has two sides, so heads should come up about half the time. The word "about" matters. Flip 10 times and you might get 7 heads. Flip 1000 times and you'll be very close to half. More data makes a better prediction.
In maths: chance is a fraction
Count the ways you can win. Then count everything that could happen. A dice has 6 faces and only one of them is a 6, so the chance of rolling a 6 is 1 out of 6.
Tock can flip a coin very fast. Start with 10 flips. Is it exactly half heads? Then keep adding flips and watch what happens to the bars.
Away from the screen: dice race
You need: two dice, paper and a pencil
Write the numbers 2 to 12 down the side of a page. Roll both dice, add them up, and put a tally next to the total. Do it 36 times. Which total wins? Can you work out why 7 has more ways to happen than 2 or 12?
Quick checkEarn your star
The last chapter · Put it all together
The big case
You now have all eight data detective skills. Here they are, with the question each one asks.
| Skill | Ask yourself |
|---|---|
| Ask a good question | What do I want to find out? |
| Collect the clues | Did I ask enough people, in the same way? |
| Sort it out | Which groups do these belong in? |
| Picture the data | What picture shows this best? |
| Read the graph | What do the title, labels and scale tell me? |
| Find what's typical | Which one number sums this up? |
| Don't be fooled | Is this graph playing a trick? |
| What's the chance? | How likely is it? |
Final testTen questions, every skill
Certificate of Data Detecting
This certificate is proudly given to
for learning to collect, picture and question data.
Look it up
Word bank
Every big word in this book, in plain language.
- Average
- One number that sums up a whole set of data.
- Bar graph
- A graph where the height of each bar shows a count. Also called a column graph.
- Category
- A group of things that are alike in some way.
- Chance
- How likely something is to happen. Also called probability.
- Data
- Information collected to answer a question.
- Key
- The part of a picture graph that says what each picture is worth.
- Line graph
- A graph that shows how something changes over time.
- Mean
- The fair share: add everything up, then divide by how many there are.
- Median
- The middle value when the data is in order.
- Mode
- The value that turns up most often.
- Range
- The biggest value take away the smallest.
- Sample
- The people or things you collect data from.
- Scale
- The numbers along the side of a graph.
- Survey
- Asking lots of people the same question and recording the answers.
- Tally
- A way of counting with lines, bundled in 5s.
Parents, carers and teachers
Notes for grown-ups
Data literacy is the habit of asking "How do we know?" and being able to check. This book follows the same investigation cycle used in school statistics: ask, collect, sort, show, explain.
The examples use small, friendly numbers so the ideas stay in front. Chapter 6 (mean, median and mode) and chapter 8 (chance as a fraction) are the most demanding and suit ages 9 and up.
How to use the book
- One chapter per sitting. Each takes about 15 to 25 minutes, plus the off-screen activity.
- Ages 7 to 8 will get more from it with someone reading alongside. Ages 9 to 12 can usually work alone.
- Chapters build on each other, so going in order works best.
- Wrong answers are part of it. Every quiz question explains itself and can be tried again.
- Stars are saved in this browser on this device. Clearing browser data may reset them.
What each chapter covers
| Chapter | Idea | Maths it connects to |
|---|---|---|
| 1. Ask a good question | Posing questions, kinds of data | Counting and measuring |
| 2. Collect the clues | Surveys, tallies, fair samples | Skip counting in 5s |
| 3. Sort it out | Categories, frequency tables, two-way tables | Classifying, adding totals |
| 4. Picture the data | Picture graphs and bar graphs | Many-to-one keys, multiplication |
| 5. Read the graph | Scales, line graphs, comparing | Reading scales, subtraction |
| 6. Find what's typical | Mode, median, mean, range | Ordering, division |
| 7. Don't be fooled | Misleading graphs and claims | Proportion, critical reasoning |
| 8. What's the chance? | Likelihood and simple probability | Fractions |