Challenge #06

Pieces of Eight

For this challenge, you may only use the symbols 8 and + (the addition symbol), though you can use as many of each symbol as you like.

Create an expression that equals 1000. Can you find more than one way to do this? How many ways can you find?

Follow-up Challenges

Can we create an expression that equals 1000 using only 7’s and +’s? Explain why or why not.

Create an expression that equals 1000 using as many +’s as you like, but which contains exactly twenty 5’s.

The commutative and associative properties of addition might help us out when it comes to counting solutions here. We can consider two sums as "the same" if they contain the same addends. For instance 88+8 and 8+88 can be considered "the same". But, what if we were to consider those two sums as unique? How might we tackle this if the order of the addends does matter?

Response Videos

Dani's response video

Blog post from Carrie with some pictures of student work.