Being curious

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

These clocks have been reflected in a mirror. What times do they say?

How would you move the bands on the pegboard to alter these shapes?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

How many different triangles can you make on a circular pegboard that has nine pegs?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?