Being resourceful

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.