Conjecturing and generalising

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

What do you notice about these squares of numbers? What is the same? What is different?

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

This box does something to the numbers that go into it. If you know the numbers that come out, what might be going on inside the box?