Mini Minds Hub · Free printable
Binary to Denary Match-Up: Free Printable Game for Year 8
- ForYear 8
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Binary to Denary Match Up is a free printable game for Year 8 (ages 12 to 13), in Key Stage 3 computing. Pupils decode eight binary numbers and match each one to its denary partner. It needs only a pencil, and page 2 gives the grown up notes, help for children who find it hard and a stretch idea.
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 pupil and keep page 2 for yourself. Black and white printing works well.
What is on the sheet
Pupils decode eight binary numbers made of 0s and 1s. For each one, they work out its value in denary, which is the ordinary counting system, then join it to the matching number with a pencil. The task rewards careful reading of place values and a clear method, so it suits quiet, focused practice on paper.
A worked example
Convert the binary number 1010101 to denary.
This example uses a longer number than the place value row on the help idea, so it adds a 64 place. It shows two ways to work. Pupils can use either one.
Method 1: place value row- Write the place values from the right: 1, 2, 4, 8, 16, 32, 64. Each place is double the one before.
- Write the digits underneath, so 64 has 1, 32 has 0, 16 has 1, 8 has 0, 4 has 1, 2 has 0 and 1 has 1.
- Add only the places that have a 1: 64 + 16 + 4 + 1 = 85.
- Start with the first digit on the left, which is 1.
- For each next digit, double your running total, then add that digit.
- The totals go 1, 2, 5, 10, 21, 42, 85. The last total is the answer.
Build the skill before you start
Know the places
Binary place values start at 1 on the right and double each time to the left. Ask the pupil to say the row out loud until it feels familiar: 1, 2, 4, 8, 16, 32.
Read from the right
The place on the right is the smallest. Pointing a pencil at each digit as you move left helps pupils keep their place and not skip a digit.
Add only the ones
A 1 means that place counts. A 0 means it does not. Pupils then only add the values under the 1s.
Check by working backwards
Once a pupil has an answer, they can ask whether it makes sense. A number with a 1 in a big place cannot be tiny.
Why learn binary at Key Stage 3?
Computers store and process information using two states, which we write as 0 and 1. A single 0 or 1 is called a bit, short for binary digit. Numbers, text, pictures and sound can all be stored as patterns of bits. Learning to read binary helps pupils see that a computer does not understand words or pictures directly, it works with numbers.
Denary is the counting system we use every day. It has ten digits, and each place is worth ten times the one to its right. Binary works in the same way, but with only two digits, and each place is worth two times the one to its right. Seeing the two systems side by side helps pupils understand place value more deeply.
Binary facts
- Binary uses only two digits, 0 and 1.
- Denary is the ordinary counting system. It uses ten digits, 0 to 9, and is also called decimal.
- A bit is one binary digit. Eight bits together make a byte.
- Each place in a binary number is worth double the place to its right.
- Computers use binary because their parts can be in one of two states, such as on or off.
Skills and curriculum link
- Binary place values
- Converting numbers
- Logical thinking
- Careful reading
- Checking answers
Ideas for helpers
- Start from the rightRemind pupils that the smallest place is at the right hand end. Ask them to write 1 under it, then double as they move left.
- Say the method aloudAsk the pupil to talk through each number: which places have a 1, what are they worth and what is the total? Speaking the steps helps spot slips.
- Use the matching to checkBecause each number is joined to a partner, a pupil who has a choice left over can look again at the numbers they were unsure about.
- Praise the methodA correct answer found with a clear method is worth more than a lucky guess. Ask, "How did you know?" after every join.
Key words
- BinaryA number system that uses only the digits 0 and 1.
- DenaryThe ordinary number system with ten digits, 0 to 9. It is also called decimal.
- BitOne binary digit, either a 0 or a 1.
- DigitA single symbol in a number. The number 305 has three digits.
- Place valueThe value a digit has because of where it sits in a number.
- ConvertTo change a number from one system into another without changing its value.
How to use it
- Print both pages. Page 1 is for the pupil. Keep page 2, which has notes for you.
- Write the place values above the first binary number to model the method. Say what each place is worth as you write it.
- Let the pupil join the rest with a pencil. Work through the first go together and talk about each choice.
- Check against the notes on page 2. Ask the pupil to explain how they worked out any number they got wrong.
- Come back to it another day. Repeating a familiar activity builds confidence.
Help, stretch and game ideas
If it feels too hard
Write 32, 16, 8, 4, 2, 1 over each binary number. Start with the small ones, such as 101 and 1001. Point to each digit in turn, and only add the place values that have a 1 underneath.
To stretch confident children
Ask confident pupils to convert their own age and the day of the month into binary. Then they can swap with a partner, convert each other's numbers back to denary and check they get the starting numbers again.
Make it a game
Race a partner. One person reads out a binary number from the sheet, and the other shouts the denary answer. Swap roles each round. Keep rounds short, and agree beforehand that a wrong answer means a quick check together.
Mistakes to watch for
Watch forA pupil reads the binary number as an ordinary number, such as reading 11 as eleven.
Try thisRemind them that binary has its own place values. Write 4, 2, 1 above the digits and add only the places that have a 1.
Watch forA pupil starts the place values from the left, so the biggest value sits under the wrong digit.
Try thisAlways begin with 1 at the right hand end and double as you move left. Write the row before looking at the digits.
Watch forA pupil adds the values of the places that have a 0 as well as the 1s.
Try thisColour or circle the 1s first. A 0 means that place is not counted, so only the circled places are added.
Talk about it
- Why do you think computers use only 0 and 1?
- What is the same about binary and denary place value? What is different?
- Which binary number on the sheet looked the easiest to decode, and why?
- How could you check an answer without redoing the whole sum?
- What happens to a binary number if you add a 0 on the right?
- Where in everyday life might you see something that is either on or off?
Take it off the page
Light switch binary
Use a row of six sheets of paper, each showing a place value from 1 to 32. Turn each one face up for 1 or face down for 0. Read the number your row makes.
Place value cards
Make small cards for 1, 2, 4, 8, 16 and 32. Pick a denary number and see which cards add up to it. Then write the matching binary number.
Secret code notes
Write a short denary number as binary on a slip of paper and pass it to a friend or family member to decode. Swap and try the other way round.
Who it is for
Parents
Read the sheet through first and sit with your child for the first go. Let them lead and explain their choices. Short bursts work better than long sessions. If they get stuck, write the place values over the number together.
Teachers
Use it as a starter, plenary, early finisher task, supply resource or homework. It needs no preparation beyond printing. Model the first number on the board, then let pupils join the rest. Page 2 has support and stretch ideas for mixed ability groups.
Home educators
Print it as part of a wider computing plan, alongside books, puzzles and everyday talk. It works well for revision a few weeks later and can be printed again for brothers and sisters. Ask learners to explain each answer aloud as well as writing it.
Where this fits
Before this sheet, pupils need a secure grasp of place value in the denary system, and a sense that a digit's value depends on where it sits. Knowing the pattern of doubling also helps, because binary place values double each time.
After this, pupils can go on to convert denary numbers into binary, and to look at how text, images and sound are stored as binary. These ideas link to the Key Stage 3 aim of understanding how data is represented in binary digits.
Questions parents and teachers ask
- What age is Binary to Denary Match Up for?
It is written for Year 8 (ages 12 to 13), in Key Stage 3. Younger pupils who are confident with place value may manage it with help, and older pupils can use it as quick revision.
- What will pupils practise?
They convert binary numbers to denary. This links to the Key Stage 3 aim of understanding how data is represented in binary digits. They also practise place value, careful reading and logical thinking.
- How do I use it?
Print both pages. Write the place values above the first binary number to model it, then let the pupil join the rest with a pencil. Work through the first go together and check against the notes on page 2.
- What if it feels too hard?
Write 32, 16, 8, 4, 2, 1 over each number and do the small ones first, such as 101 and 1001. Point to each digit and add only the places that have a 1.
- Is it free?
Yes. It is free to print for home and classroom use. You can print it again for brothers, sisters or revision a few weeks later.
- Is this a screen free activity?
Yes. It needs only paper and a pencil, so it works well for quiet time, rainy days and school holidays. It is a computing activity that gives eyes a rest from screens.
- 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, and page 2 has help and stretch ideas for mixed ability groups.
Preview the full PDF
Made by Jaques of London, making games for families since 1795. A printable supports classroom learning and does not replace a teacher.