Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

It Figures

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

What Do You Need?

What Do You Need?

What do you need to find a chosen number from this hundred square?

Four of the clues below are true but do nothing to help in finding the number.
Four of the clues are necessary for finding it.

Here are eight clues to use:
1. The number is greater than $9$.
2. The number is not a multiple of $10$.
3. The number is a multiple of $7$.
4. The number is odd.
5. The number is not a multiple of $11$.
6. The number is less than $200$.
7. Its ones digit is larger than its tens digit.
8. Its tens digit is odd.
What is the number?

Can you sort out the four clues that help and the four clues that do not help in finding it?

Why do this problem?

This problem is an accessible context in which pupils can apply their knowledge of number properties. It is a great opportunity to get children explaining their reasoning to others.

Possible approach

Before trying this problem, it would be useful for the class to work on One of Thirty Six , perhaps in pairs. One of Thirty Six introduces the idea of using information in a particular order, which also applies to this problem.

Having discussed the solution of One of Thirty Six, present this problem to the group. (It might be useful to print out copies of it from this sheet.) Before setting the children off on this new challenge, ask whether they can already suggest some clues that are not needed. For example, the most obvious thing might be that the "less than $200$" clue is redundant, given the grid only goes up to $99$. Suggest that pairs work on the problem, recording whatever and however they find useful. Let them know that you will be asking them to explain and justify their reasoning, as opposed to simply focusing on the answer, in the plenary.

Key questions

Which clues do you have to have to find the number?