“Perfect” Rulers

Is it possible to measure all possible integer lengths on a ruler without marking every integer on that ruler? This is an engaging and challenging problem for all. Beautiful mathematics can be revealed while delving deeper into this seemingly easy question. 

“Perfect rulers” fits the criteria for a “rich mathematical task”:

• Easy to understand with a low barrier to entry
• Offers opportunities for initial success to promote engagement
• An “open middle” that allows for creativity and multiple strategies and tools
• Encourages collaboration and discussion
• Easily extendable with ’what if ’ and ’what if not’ questions