Open Middle®
Directions: Using the digits 1 to 9 exactly one time each, place a digit in each box to make the difference as close to 200 as possible.
Hint
How can you rearrange the digits to get even closer to 200?
Which place value is most helpful to think about? Why?
Which place value is most helpful to think about? Why?
Answer
738 – 542 = 196
Source: Tara Trifiletti and Jessica Goree
357 – 168 = 199
We keep getting 189 with this equation.
697-485=213
481 – 279 – 202
It looks like a lot of the solvers aren’t using the “using 1-9 once each” rule. In a classroom, how would you encourage students to notice this rule, check themselves, or check each other? Is it helpful to give little cutout 1-9 squares to physically place so that they can have only one of each?
I’ve given students “number tiles” like you described so that they can keep track of which digits they’ve used. It also lets them rearrange and manipulate the numbers without a bunch of erasing. I just wrote numbers on some extra round counters that I had because they hold up better than paper numbers. I also partner students up so that they have another person to bounce ideas off and to help check that they’ve met all the rules of the challenge.