Exploring and noticing

A cube is made from smaller cubes, 5 by 5 by 5, then some of those cubes are removed. Can you make the specified shapes, and what is the most and least number of cubes required ?

Explore the relationship between resistance and temperature

Repeat a pattern of numbers to form a larger number. Can you find the sum of all the digits?

Jasmine buys three different types of plant. How many triffids did she buy?

A bicycle passes along a path and leaves some tracks. Is it possible to say which track was made by the front wheel and which by the back wheel?

From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?

A sequence is generated using these rules. For which values of n is the nth term equal to n?

How many times a day does a 24 hour digital clock look the same when reflected in a horizontal line?

Edith had 9 children at 15 month intervals. If the oldest is now six times as old as the youngest, how old is her youngest child?

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?