Mini Minds Hub · Free printable
Binary Search Game: Free Printable Game for Year 7
- ForYear 7
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Binary Search Game is a free printable game for Year 7 (ages 11 to 12), in Key Stage 3. One player picks a secret number and the other tries to find it in the fewest guesses. It takes about 10 minutes, needs only paper and a pencil, and is played with two players who swap roles each round.
It comes from the Mini Minds Hub, the free library of printables from Jaques of London, the British games and toy company that has been making games for families since 1795. Print both pages, give page 1 to the players and keep page 2 for the grown-up. Black and white printing works well.
What is on the sheet
Children play a number guessing game and record each round in a table. The table has three columns: the guess, whether the secret number is higher or lower, and how many numbers are left. Filling it in shows how each clue changes what is still possible. Players then think about their method, count their guesses and explain the choices they made.
- Guess
- Higher or lower
- Numbers left
Setting up a round
Choose a range
Agree the range before you start, for example 1 to 20 for a first go. Both players write it at the top of the table so everyone plays the same game.
Pick and hide
The setter chooses a secret number in the range and writes it on a scrap of paper, folded over. This stops any arguments about changing the number later.
Guess and record
The guesser says a number. The setter answers higher, lower or correct. The guesser fills in one row of the table each time before guessing again.
Swap and compare
Swap roles for the next round. Afterwards, compare your tables and talk about which guesses helped most and why.
What is a binary search?
A binary search is a method for finding something in a range or list that is in order. Each time you check one place, the answer tells you which part to ignore. Computers use methods like this to find items in sorted data. The idea is a good example of an algorithm: a clear set of steps that anyone can follow to reach a result.
The game on this sheet lets children feel the idea before they name it. Playing the guesser, they notice that some guesses leave a lot of numbers in play and others leave far fewer. Playing the setter, they see how the clues are given. Talking about the pattern is the real learning, so leave time to chat after each round.
Computing facts to share
- A binary search only works if the items are in order, such as numbers from smallest to largest.
- An algorithm is a set of clear steps for solving a problem. A recipe is a good everyday example.
- Computers can check very large lists quickly because they follow careful methods rather than looking at every item.
- Contact lists and other sorted lists on devices are kept in order so that things can be found faster.
- Computer scientists compare methods by asking which one needs fewer steps.
Skills and curriculum link
- Algorithms
- Logic
- Reasoning
- Computational thinking
- Recording in a table
This sheet supports the area below. It is matched to the published England framework. Please check it against your own school plan.
| Framework | Subject or area | Strand | Year |
|---|---|---|---|
| National Curriculum (England) | Computing | Computational thinking | Year 7 |
What children will be able to do
- I can play a number guessing game by halving the range.
- I can explain why halving finds the number quickly.
- I can count how many guesses I need.
Ideas to help you talk about it
- Use the cluesEvery answer of higher or lower tells you something. Ask your child what the clue has told them and which numbers they can now forget about.
- Plan before guessingEncourage a pause before each guess. Ask, "Why that number?" A reason is more useful than a lucky hunch.
- Compare methodsPlay one round with a plan and one round with random guesses. Look at the tables side by side and talk about what you notice.
- Check the tableThe last column shows what is still possible. Ask whether the numbers left make sense after each guess.
Key words
- AlgorithmA set of clear steps that solves a problem or does a job.
- Binary searchA method for finding something in an ordered range by using each clue to rule out part of it.
- RangeAll the numbers from the lowest to the highest that the secret number could be.
- SortedPut in order, for example from smallest to largest.
- StrategyA plan for how you will make your choices.
- EfficientReaching the answer using fewer steps or less time.
How to use it
- Print both pages. Page 1 is for the players. Keep page 2, which has the notes, help and stretch ideas.
- Read the rules out loud together so everyone plays the same game. Agree the range and who will be the setter first.
- Play the first round together and fill in the table row by row. Talk about each guess as you go.
- Swap roles and play again. Compare your tables and check against the notes on page 2.
- Come back another day and play with a different range. Repeating a familiar game builds confidence.
Help, stretch and game ideas
If it feels too hard
Start with the range 1 to 20. Fill in the table one row at a time and say aloud which numbers are still possible. Cross out the numbers that are ruled out on a spare strip of paper so they are easy to see.
To stretch confident children
Play with the range 1 to 1000 and count how many guesses you need. Then try to explain your method in a few sentences to your partner, so that someone else could copy it and get the same result.
Make it a game
Play best of five rounds. The guesser who needs fewer guesses wins the round. Swap roles each time. Before each round, both players say their plan out loud, then see whose plan worked better.
Talk about it
- What did the clue higher or lower tell you about the numbers left?
- Why did you choose that number for your first guess?
- What would you do differently if you played again?
- Did the numbers left column help you plan the next guess? How?
- How would a computer follow your method without any hints from you?
- Where else might a method like this be useful?
Take it off the page
Guess the page
Open a book with numbered pages. Choose a secret page and let a partner find it using only higher or lower clues. Talk about where they opened first.
Step by step instructions
Write clear steps for a simple job, such as making a sandwich. Ask someone to follow them exactly and notice any steps that were missing or unclear.
Card line up
Put some number cards in order face down. Take turns turning over one card at a time to find a target number, and explain why you chose each card.
Who it is for
Parents
Sit beside your child for the first round, then let them lead. About 10 minutes is plenty. If they get stuck, ask what the last clue told them. You do not need any computing knowledge to play.
Teachers
Use it as a starter, plenary, early finisher task or table activity. It needs no preparation beyond printing. Listen for reasoning as pairs play, and use the help and stretch ideas on page 2 for mixed ability groups.
Home educators
Print it as part of a wider computing plan. It pairs well with talk about algorithms and everyday problem solving. The sheet is free to print again for brothers and sisters, or for revision a few weeks later.
Where this fits
Before this game, children benefit from describing a task as clear steps and from being comfortable with ordering numbers. Those ideas make it easier to see why a plan beats a random guess.
After it, children can go on to think about other ways computers find and arrange information, and to compare methods by how many steps they need. The habit of explaining a method in words is useful across the whole of computing.
Check it worked
Ask these when the sheet is finished. Listen for the reasoning, not just the answer.
- Why is guessing the middle number a good first move?
- How many guesses might you need for a number between 1 and 100?
- What would happen if you guessed at random instead?
Questions parents and teachers ask
- What age is Binary Search Game for?
It is written for Year 7 (ages 11 to 12), in Key Stage 3. Younger children can try the smaller range of 1 to 20 with an adult. Older children can use the larger ranges to stretch themselves.
- How long does it take?
It takes about 10 minutes. Rounds are short, so you can play one or two games in that time. The notes on page 2 suggest ways to make the game easier or more challenging.
- How many players do I need?
You need two players. One picks a secret number and the other guesses it. Swap roles each round so both players practise setting and guessing. An adult can play as one of the two.
- What if it feels too hard?
Start with the range 1 to 20 first. Fill in the table one row at a time and talk about which numbers are still possible after each clue. Then move on to bigger ranges.
- Is it free?
Yes. It is free to print for home and classroom use. You can print it again for brothers, sisters or a whole group, and use it as often as you like.
- Do I need a computer or tablet?
No. It is a screen free printable that needs only paper and a pencil. It works well for quiet time, rainy days, school holidays or a calm moment away from devices.
- Can teachers use it in class?
Yes. Teachers can use it as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing. Please check it against your own school plan.
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Made by Jaques of London, making games for families since 1795. A printable supports classroom learning and does not replace a teacher.