Visualising and representing

Make one big triangle so the numbers that touch on the small triangles add to 10.

Move just three of the circles so that the triangle faces in the opposite direction.

What is the least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

What is the greatest number of squares you can make by overlapping three squares?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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.