Open Middle®
Directions: Using the digits 0 to 9, at most one time each, find two numbers that round to 500, and have the greatest possible difference.
Hint
How can we figure out the greatest number that rounds to 500?
What tools or models might be helpful?
What does the “greatest possible difference” mean?
Can you make a bigger difference than what you have now?
What tools or models might be helpful?
What does the “greatest possible difference” mean?
Can you make a bigger difference than what you have now?
Answer
539 – 460 = 79
Source: Michael Wiernicki, Graham Fletcher, and Rachel Nelli.
I’m trying to understand the wording in this one. It reads as though students are supposed to round two numbers to 500 and then subtract. This makes no sense because the greatest possible difference when subtracting 500 from 500 is going to be 0.
So I knew the problem as written made no sense but I didn’t know what was being asked.
How about “Using the digits 0 through 9, find two numbers that round to 500, and have the greatest possible difference. Each digit can only be used once.”
I’ll be honest. I struggled with the wording of this myself. I wish I had seen your suggestion earlier. I’ll be using your new wording next week. Thanks for your suggestion!
Rachel,
I’d love to add your name to the contributor’s list for this problem, if that’s ok. I should have done this last year when I saw your suggestion. My apologies.
I’ve updated the task according to Rachel’s suggestion.
Actually, the answer had 9 in there twice.
The correct answer is 539 – 461 = 78
We found 539-460 = 79
XD
539 – 451 = 88