I'm a grade one teacher who gave out some math homework last night to my students. It consisted of 9 questions to practice simple addition and subtraction. I always discourage them from using a calculator and say "Only if you need to double-check your answers!"

Anyways, one student's homework stood out in particular. It started out okay

$ 5 + 4 = 9\\ 8 + 0 = 8\\ 2 + 6 = 8\\ 7 - 6 = 1$

but suddenly the answers were all wrong

$ 3 + 1 = 3\\ 6 + 0 = 8\\ 6 + 5 = 6\\ 3 + 4 = 9\\ 1 + 1 = 1$

I thought "surely they couldn't have got all these questions wrong on purpose", and called the student to the front. I asked them all the questions they got wrong, and sure enough, they answered them correctly. So I showed them the homework asking "what happened with these five questions?"

They answered "I double-checked all my answers with a calculator like you said we could, and that's what the calculator said, so I changed my answers."

"Even the ones that are correct?" I asked. The student nodded.

Needless to say, I was stumped. I had no clue what this calculator was doing. I asked the student to bring in the calculator tomorrow.

In the meantime, does anyone know what is happening with this calculator?

  • $\begingroup$ Were the first four answers using the calculator as well, or just the last five? $\endgroup$ – MMAdams Oct 14 '16 at 20:25
  • 1
    $\begingroup$ @MMAdams I'll add clarification to the story $\endgroup$ – jstnthms Oct 14 '16 at 20:30
  • $\begingroup$ Was it a Reverse Polish Notation calculator? :) $\endgroup$ – PartyHatPanda Oct 14 '16 at 20:38
  • $\begingroup$ Just a regular North American calculator. $\endgroup$ – jstnthms Oct 14 '16 at 20:42
  • $\begingroup$ @PartyHatPanda: Would an RPN calculator even have an = button? $\endgroup$ – Peregrine Rook Oct 14 '16 at 20:43

The calculator is

performing the mathematical operations the lines of a 7 segment LED display

i.e. each number displayed on a 7 segment display, use all lit segments of both numbers for addition, and remove from the first number the lit segments of the second number for subtraction, results in the answer shown on the calculator.

As mentioned in the comments, 7-6=1 would result in the upper right vertical segment still lit, which the student interpreted as a 1

Sorry, I would add pictures, but I don't have time to make some right now.

  • $\begingroup$ This works for all the + but not the -. I'd expand that the - is doing an X to make the 1 $\endgroup$ – Ryan Smith Oct 14 '16 at 20:45
  • $\begingroup$ It leaves enough that a first grader could interpret it as the correct asnwer $\endgroup$ – CDspace Oct 14 '16 at 20:46
  • $\begingroup$ @RyanSmith actually, I thought a bit more, and it's not the operation I previously posted, and an X still wouldn't give the correct answer on the minus, see edits for clarification $\endgroup$ – CDspace Oct 14 '16 at 20:54

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