Conjecturing and generalising

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

Can you find out which 3D shape your partner has chosen before they work out your shape?

Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.

Can you find all the ways to get 15 at the top of this triangle of added numbers?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

Amy has a box of domino pieces. Which of her domino pieces are missing?

Can you use four digits to make four two-digit numbers that add to 100?