Conjecturing and generalising

Are these statements about number and shape always, sometimes 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?

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?

Which special types of numbers will you make with these tens and ones spinners?

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?

What score can you get on the add and take-away path?

This box does something to the numbers that go into it. What might be happening inside the box?

Create a pattern on the small grid. How could you extend your pattern on the larger grid?