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.