40 open-ended investigations encouraging students to apply and extend their mathematical knowledge.
I particulary like investigation:
9 consecutive sums in which students have to add consecutive numbers to make as many different results as possible. It is interesting to see whether students ask whether zero and negative numbers can be used. What happens if the answer is yes? Extend the investigation to ask what happens if consecutive even numbers are used? What happens if consecutive odd numbers are used?
8 Polyominoes There are lots of investigations that can be done using tetrominoes. Find some here http://stem.org.uk/rx7vc , http://stem.org.uk/rx98h , http://stem.org.uk/rx9r2
12 number chains in which students explore the number chain produced when students produce the next number in the chain by taking halve the number if it is even or by adding 1 if it is odd. The investigation can be extended by asking students to think of their own rules.
I have described just three, there are many more to choose from.