Open Middle®
Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to make the smallest (or largest) difference.
Hint
What number does each box represent?
Answer
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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