Tock's Book of Clever Thinking
Solve big problems the way computer scientists do.
What is computational thinking?
Computational thinking is a way of solving problems, step by careful step.
You don't need a computer to do it. You need four thinking tools. Mathematicians, scientists, engineers and game makers use them every day, and so can you.
- Break it downSplit one big problem into small ones.
- Spot the patternFind what repeats, so you can predict what comes next.
- Keep what mattersLeave out the details you don't need.
- Make a planWrite clear steps that anyone could follow.
This book teaches you all four, plus four helpers that make your plans even better: loops, decisions, bug hunting and smart searching.
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 · Thinking tool one
Break it down
Imagine someone says, "Plan a birthday party." Where do you even start? It feels huge.
Here is the trick. Don't try to solve the whole thing at once. Chop it into smaller jobs. Then chop those jobs again, until every piece is small enough to do.
When every piece is easy, you solve the big problem one small piece at a time. You can even share the pieces out, so friends can help.
In maths: break up a hard sum
6 × 14 looks tricky. So break 14 into 10 and 4. Now you have two easy sums.
60 + 24 = 84
Tock wants to lay new grass on this L-shaped garden, so it needs the area. An L-shape is awkward, but two rectangles are easy. Choose where to cut, then find the area of each piece. Every little square is 1 square metre.
Tip: area of a rectangle = squares across × squares down. You can also count the squares.
Away from the screen: job tree
You need: paper and a pencil
Pick a big job, like "tidy my bedroom" or "plan a picnic". Write it at the top of the page. Draw three or four branches for the smaller jobs inside it. Can you break each of those down again? Stop when every job is something you could do in five minutes.
Quick checkEarn your star
Chapter 2 · Thinking tool two
Spot the pattern
Patterns are everywhere. Stripes on a zebra crossing. The days of the week. The beat of a song. The numbers in your times tables.
When you spot a pattern, you get a superpower: you can predict. You know what comes next without working it all out again.
Some patterns repeat, like red, blue, red, blue. Others grow by a rule, like 2, 4, 6, 8. To find the rule in a number pattern, look at the jump from each number to the next.
What goes in the yellow box?
In maths: times tables are patterns
Count by 5s and every answer ends in 5 or 0. Count by 2s and every answer is even. Once you know the pattern, you can check your answers in a blink.
Pick a number to count by. Tock paints every number you land on. What shape does each times table make?
Away from the screen: pattern hunt
You need: your eyes, plus a calendar
Find five patterns around your home or school. Look at floor tiles, fences, clothes and music. Then look at a calendar. Pick any date and read straight down the column. What is the jump each time? Why do you think that is?
Quick checkEarn your star
Chapter 3 · Thinking tool three
Keep what matters
Think about a map of train lines. It doesn't show trees, houses or what the driver had for lunch. It shows stations and the lines between them.
That's all you need to catch the right train. Leaving things out might sound lazy, but it's smart. Too many details hide the answer.
Before you start a problem, ask: "What am I trying to find out?" Then keep only the details that help you answer that question.
In maths: stories become number sentences
"Mia has 12 stickers in a red tin and gives 5 to her friend Sam." A mathematician keeps just three things:
12 − 5 = 7
The tin, the colour and the friend's name have all gone. The answer hasn't changed.
Tap the facts you need to answer the question. Leave the rest alone.
Away from the screen: the simplest map
You need: paper, a pencil and a helper
Draw a map from your bedroom to the kitchen. The rule: you may only use straight lines, arrows and three labels. Give the map to someone else. Can they follow it? If they get lost, which detail did you leave out that really mattered?
Quick checkEarn your star
Chapter 4 · Thinking tool four
Make a plan
A recipe is an algorithm. So are the instructions for building a brick model, and the steps you use to add big numbers.
Computers are fast, but they can't guess what you mean. Tell me "put jam on the bread" and I might balance the whole jar on top of the loaf! A good algorithm has steps that are clear, small and in the right order.
Order matters. Socks, then shoes: that works. Shoes, then socks: not so much.
In maths: you already know some algorithms
Adding in columns is an algorithm. The same steps work for any numbers. Try 47 + 38:
- Add the ones: 7 + 8 = 15. Write 5, carry the 1.
- Add the tens: 4 + 3 + 1 = 8.
47 + 38 = 85
Tock is running low on power. Build a program of arrow steps, then press Run. Tock follows your steps exactly, so watch out for the crates!
Your program
Away from the screen: robot friend
You need: a friend and some floor space
One of you is the robot. The other is the programmer. Put a cushion somewhere in the room. The programmer gives one instruction at a time, like "walk forward 2 steps" or "turn left". The robot does exactly what it hears. Can you reach the cushion? Now write all the steps down first, and run the whole program without speaking.
Quick checkEarn your star
Chapter 5 · Helper one
Do it again
Imagine writing "brush a tooth" once for every tooth in your mouth. Boring! It's quicker to say: do this for every tooth.
That is a loop. You say what to repeat and how many times. Loops make algorithms shorter. Shorter algorithms are easier to read, and it's easier to spot mistakes in them.
The long way: 8 steps
- move forward
- turn right
- move forward
- turn right
- move forward
- turn right
- move forward
- turn right
With a loop: 3 lines
- repeat 4 times:
- move forward
- turn right
In maths: multiplying is a loop
4 × 3 means "repeat 4 times: jump forward 3".
3 + 3 + 3 + 3 = 4 × 3 = 12
Tock is holding a pen. Change the two yellow numbers in the loop and see what Tock draws. Here is a clue: a shape closes up when Tock has turned all the way around, which is 360°.
Choose the turn
Can you draw all four?
- Triangle
- Square
- Hexagon
- Star (tricky!)
Away from the screen: dance loop
You need: room to move
Invent three dance moves, like clap, spin, jump. That's your loop. Now do "repeat 4 times: clap, spin, jump". How many moves did you do altogether? Work it out with a times table, then count to check. Try it again with 5 moves repeated 3 times.
Quick checkEarn your star
Chapter 6 · Helper two
If this, then that
You make decisions all day long. IF it's raining, THEN take an umbrella. ELSE, leave it at home. ("Else" means "otherwise".)
Computers decide things the same way. They ask a question that has only two answers: yes or no. Each answer leads down a different path.
A picture of those paths is called a flowchart. Questions sit inside diamonds, and arrows show where to go next.
You can join two questions together with AND or OR.
- "Even AND bigger than 10" means both must be true. 12 passes. 8 does not, and neither does 13.
- "Even OR bigger than 10" means at least one must be true. Now 8 passes, and so does 13.
In maths: > and < are yes-or-no questions
The sign > means "is bigger than". The sign < means "is smaller than". The open end always faces the bigger number.
7 > 5 → yes 3 > 9 → no 20 > 20 → no
Ten numbers roll into the machine, one at a time. Follow the flowchart and drop each number into the right bin.
Away from the screen: Tock says IF
You need: two or more players
One player is the leader and calls out IF rules. "IF you are wearing blue, THEN hop. ELSE, clap." Everyone has to work out which path is theirs. Make it harder with AND and OR: "IF you have a pet AND you are older than 8, THEN spin around."
Quick checkEarn your star
Chapter 7 · Helper three
Bug hunt
Here is something every programmer knows: almost nothing works the first time. Not for beginners, and not for experts.
A mistake in a program is called a bug. Hunting for it is called debugging. Bugs aren't bad news. Every bug you fix teaches you something about how your plan really works.
Three habits make you a great bug hunter.
- Go one step at a time. Pretend you are the computer and do only what each step says.
- Compare. What did you want to happen? What happened instead? The bug is where those two split apart.
- Change one thing. Then test again. If you change five things, you won't know which one fixed it.
In maths: checking your work is debugging
Say you worked out 9 × 6 and got 56. Check it another way: 10 × 6 = 60, then take away one 6.
60 − 6 = 54
The two answers don't match, so there is a bug to find. Two different methods that agree are a good sign you're right.
Away from the screen: plant a bug
You need: paper, pencils and a partner
Write instructions for drawing a simple house: a square, a triangle roof, a door, two windows. Hide one mistake on purpose. Swap with a partner. They follow your steps exactly, find the bug, and write the fix. Then swap back and hunt for theirs.
Quick checkEarn your star
Chapter 8 · Helper four
Find it faster
Two algorithms can both give the right answer. But one might take 100 steps and the other only 7. Which would you choose?
Say I'm thinking of a number from 1 to 100. You could guess 1, then 2, then 3. If my number is 100, that takes one hundred guesses!
Here is a smarter plan: guess the middle. I'll say "higher" or "lower", and half the numbers vanish in one go. Then guess the middle of what's left. And again. And again.
That's 7 guesses at most, against 100. Both plans work, but the halving plan is far more efficient.
In maths: halving shrinks fast, doubling grows fast
Start at 1 and keep doubling. Ten doubles later you are past one thousand.
1 → 2 → 4 → 8 → 16 → 32 → 64 → 128 → 256 → 512 → 1024
Run that backwards and it's halving. Ten halvings shrink 1024 things down to just 1.
Tock is thinking of a whole number from 1 to 100. Can you find it in 7 guesses or fewer? The green part of the bar shows the numbers that are still possible.
Away from the screen: dictionary dash
You need: a dictionary or any thick book with page numbers
Ask someone to pick a page number. Open the book in the middle. Is their page higher or lower? Split that part in half and open again. Count how many times you open the book. Then play the number game with a friend using 1 to 1000. With the halving plan you never need more than 10 guesses.
Quick checkEarn your star
The last chapter · Put it all together
The big challenge
You now own a full toolkit. Real problems need more than one tool, so before the challenge, here is every tool and the question it asks.
| Tool | Big word | Ask yourself |
|---|---|---|
| Break it down | Decomposition | What smaller jobs is this made of? |
| Spot the pattern | Pattern recognition | What repeats? What is the rule? |
| Keep what matters | Abstraction | Which details do I really need? |
| Make a plan | Algorithm | What are the steps, in order? |
| Do it again | Loop | Which steps can I repeat? |
| If this, then that | Conditional | What yes-or-no question decides? |
| Bug hunt | Debugging | Where does it first go wrong? |
| Find it faster | Efficient | Is there a way with fewer steps? |
Final testTen questions, every tool
Certificate of Clever Thinking
This certificate is proudly given to
for learning to think like a computer scientist.
Look it up
Word bank
Every big word in this book, in plain language.
- Abstraction
- Keeping the details that matter and leaving out the rest.
- Algorithm
- A list of clear steps, in order, for getting a job done.
- Bug
- A mistake in a program or a set of steps.
- Computational thinking
- Solving problems using tools like breaking down, spotting patterns and planning steps.
- Conditional
- A step that asks a yes-or-no question and then chooses a path. It often uses IF, THEN and ELSE.
- Debugging
- Finding and fixing bugs.
- Decomposition
- Breaking a big problem into smaller parts.
- Efficient
- Getting the job done in fewer steps.
- Flowchart
- A picture of an algorithm, with boxes for steps, diamonds for questions and arrows for the path.
- Loop
- An instruction that repeats steps a number of times.
- Pattern
- Something that repeats, or changes by the same rule each time.
- Program
- An algorithm written so that a computer can follow it.
Parents, carers and teachers
Notes for grown-ups
Computational thinking is problem solving, not screen time. The ideas in this book are the same ones children use in maths every day, given names and practised on purpose.
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. Chapters 5 to 8 lean on the algorithm idea from chapter 4.
- Wrong answers are part of it. Every quiz question explains itself and can be tried again. A star means every question was eventually answered correctly.
- Stars are saved in this browser on this device. They won't follow a child to another device, and clearing browser data may reset them.
What each chapter covers
| Chapter | Idea | Maths it connects to |
|---|---|---|
| 1. Break it down | Decomposition | Partitioning numbers, area of compound shapes |
| 2. Spot the pattern | Pattern recognition | Number sequences, multiples, square and triangular numbers |
| 3. Keep what matters | Abstraction | Turning word problems into number sentences |
| 4. Make a plan | Algorithms | Written addition, position and direction on a grid |
| 5. Do it again | Loops | Multiplication as repeated addition, angles and turns |
| 6. If this, then that | Conditionals and logic | Comparing numbers, odd and even, sorting by rules |
| 7. Bug hunt | Debugging | Checking work with a second method |
| 8. Find it faster | Efficiency | Halving, doubling, ordering numbers |
Good questions to ask afterwards
- "Which tool did you use there?"
- "How did you know that was the bug?"
- "Could you explain your steps so that Tock could follow them?"
- "Is there a way to do it in fewer steps?"