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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?

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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?

Path to the Stars

Stage: 2 Challenge Level:

Why do this problem?

This problem requires children to apply knowledge of factors and multiples, and is a great opportunity for making generalisations.

If you go to the Printable Resources page, you can open and print PDF files of the circles (Circle templates > Without central point).

Key questions

What have you tried so far?

What could you try next?

Can you explain why that did/did not work?

Possible extension

Some learners may like to investigate this more fully using the Stars problem.

Divisibility. Trial and improvement. Factors and multiples. Odd and even numbers. Working systematically. Making and proving conjectures. Properties of numbers. Multiplication & division. Addition & subtraction. Interactivities.