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Six Is the Sum
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
(w)holy Numbers
A church hymn book contains 700 hymns. The numbers of the hymns are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?
Stage: 2 Challenge Level: 
Why do this problem?
This problem challenges learners to think about the construction of the familiar hundred square and about the first hundred numbers in our counting system. It consolidates understanding of place value and promotes useful discussion between pairs of learners working together as they will have to conjecture, explain and justify their ideas.
Possible approach
You could introduce this problem first by asking the group to picture a hundred square in their mind's eye. Challenge them to answer questions orally such as:
- 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 post 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, but don't actively encourage this!
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 computer or cut out the pieces from these two printed sheets.
At the end the group could discuss how they discovered the clues needed to put the whole 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?
Key questions
Where could we start?
What might the first numbers look like?
What might the last number look like?
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?
Possible extension
Learners could either try Alien Counting which introduces different bases or Which Scripts? which looks at numbers in different languages.
Possible support
Some children may benefit from having an ordinary hundred square to refer to as they work on this problem. It might help to try this Hundred Square Jigsaw first, but be aware that this one goes from zero to ninety-nine, not one to a hundred.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.