In the land of Trianglia the worms are made of isosceles right triangles - and they grow fast! As you can see above, a worm that is 1 day old is made of 4 of these triangles. You can also see worms that are 2 days old and 3 days old. If that growth rate remains constant, how many triangles will be needed for a 4-day-old worm? a 10-day-old worm? a 63-day-old worm?

Be sure to explain your strategy.

**Extra:** I found a worm that was made of 60 triangles. How old was it? Explain how you know.

**Super Extra:** Can you make a rule that uses a worm's age (in number of days) to find out how many triangles it is made of? You may express your rule with words or with numbers and symbols.

Inspired by *Navigating through Algebra in Grades 3-5*, National Council of Teachers of Mathematics.