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# Coded Hundred Square

## Coded Hundred Square

**Why do this problem?**

Possible approach

### Key questions

### Possible support

### Possible extension

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Age 7 to 11

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

*Coded Hundred Square printable sheet*

This hundred square is written in code.

It starts with one and ends with a hundred.

Can you build it up? How did you do it?

Can you build it up in a different way?

Talk to a friend who has also tried building up the hundred square. How did they do it? What do you like about their method?

You can use the interactivity below or print and cut out the pieces from these sheets.

This problem is an easily understood task so everyone can get started. It encourages children to think about the construction of the familiar hundred square and about the first one hundred numbers in our counting system. However, children may need to work on their resilience and perseverance skills as they
may discover it is not quite as straightforward as it first appears!

As they test out their ideas and become even more curious about the construction of this coded hundred square, encourage learners to offer conjectures, and to explain and justify their ideas.

Possible approach

*This problem featured in an NRICH Primary webinar in September 2021.*

You could introduce this problem first by asking the group to picture a 'standard' hundred square in their mind's eye. Challenge them to answer questions orally such as:

- Which number is in the top right-hand corner? [10]
- What is immediately below 10? [20]
- What is two squares to the left of 99? [97]
- I start on 34 and move three rows down and three places to the right. What do I land on? [67]

Each time, invite children to explain how they came to a solution. You may like to ask some learners to pose their own challenge for the rest of the group. It may be that some children will want to refer to a paper copy of a hundred square to check their responses.

You can then present the problem itself, ideally on the interactive whiteboard, and ask pupils to work in pairs so that they are able to talk through their ideas with a partner. They could either use the interactivity on a tablet/computer or cut out the pieces from these two printed sheets.

In a plenary, the group could discuss how they discovered the clues needed to put the whole square together and what they learnt about the construction of a hundred square. It is interesting to see the number of different ways adopted - each one just as valid as the others. The important point is being able to justify why one piece goes in a particular place. You may decide to highlight the
value of talking with someone else while working on this task. How did it help them?

Where could we start?

What might the first row of numbers look like? Why?

How might the highest number look different from the others?

What do you know about the multiples of 11?

What will be the same in each column?

What will be the same for the first nine numbers in each row?

What could you do if you are stuck?

Some children may benefit from having a standard hundred square to refer to as they work on this problem. It might help to try this Hundred Square Jigsaw first.

Learners could have a go at Hundred Square, which will further deepen their understanding of the structure of the number square and our number system generally. They might also like to try Alien Counting, which introduces different bases, or Which Scripts?, which looks at numbers in different languages.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?