Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make the smallest (or largest) difference.
Hint
What number does each box represent?
Answer
No answers yet. If you have one, post it in the comments.
Source: Robert Kaplinsky
My fourth grade students came up with 0.14 is the smallest difference. This could be achieved by a few different ways. However, the tenths and hundredths had to be ___.12 – ___.98
That’s what we got too!
But you can’t use 0s, you can only use whole number digits 1-9.
In the boxes you can only use the digits 1-9, but the result has no restrictions: It can have any digits, any number of digits and can have digits that were already used in the 6 boxes pictured.
If the result also had to abide by the same rules, the image would be something like ▢.▢▢ – ▢.▢▢ = ▢.▢▢. In that case, the answer for the smallest difference would be 7.83 – 6.59 = 1.24 and the largest difference would be 9.36 – 1.52 = 7.84
the awnser is 1.23-2.45
We thought about negative numbers. My class came up with -9.36 if you consider negative numbers.
I’m rethinking our logic now. The smallest difference would mean show two numbers that are as close as possible on a number line.
My fifth graders also got .14 as the smallest difference, but we did it using the digits 1-9. Both 4.12-3.98 and 5.12-4.98 can give you this result.
They also figured 9.87-1.23 = 8.64 as the largest difference.
My 4/5th grade students also got 0.14 several ways using _.12-_.98= 0.14. We did not use negative numbers.
1.3 -0.42 =.98
wroung on 2.9-1.8=1.1
9.87+1.23
2.76-1.89
Greatest result: 9.87 – 1.23 = 8.64
Smallest positive result: 7.12 – 6.98 = 0.14
Greatest negative result: 6.98 – 7.12 = –0.14
Smallest result: 1.23 – 9.87 = –8.64
.55