Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make the largest (or smallest) absolute difference.
Hint
What are the biggest and smallest numbers you can make with these digits in scientific notation?
Try thinking of the numbers you create on a number line.
Try thinking of the numbers you create on a number line.
Answer
Largest: 8×10^9 – 2×10^1
Smallest 1×10^3 – 9×10^2
Smallest 1×10^3 – 9×10^2
Source: Marie Isaac
For smallest difference, one of my classes found the following:
1 x 10^3 – 9 x 10^2
1 x 1000 – 9 x 100
1000 – 900 = 100
Aw, shoot! One of my students came up with one better than the solution for smallest difference, and I was going to email it in, but now I see that someone else (Bob Perez) already found it. She came up with 1 x 10^3 – 9 x 10^2.
Respect to your student for finding it too Amanda!
Thanks for sharing this solution Bob – your class is awesome to have found it. I’ve updated the answer to reflect this – do let them know!