You friend borrows $22 from you. He pays you back $15 the next day. How much does he still owe you? Asked this way, it’s obvious he owes you $7. But give a kid the problem -22 + 15, and the answer mysteriously becomes, well, mysterious.
My students can certainly tell me how much I would still owe if I borrowed $22 and paid just $15 back. Like us, they’d probably count up from 15 to get to 22. But give a student the problem “-22 + 15″, and all bets are off.
For this number sentence, we are taught in school to find “-22″ on a number line and count to the right 15 spaces to find the number we land on. But this is not what we do in real life to find out how much someone still owes. There is a huge disconnect here. In real life, we count up from 15 to 22, keeping a tally on our fingers of how many numbers we pass by. We would never count up 15 from -22 to find how much someone owes us! It’s no wonder students have difficulty with negative numbers with the way we are taught!
To plug my product, the ZeroSum ruler allows a student to count the spaces from 15 to -22 by folding the ruler in half at the pivot and counting from 15 to +22. When the positives are aligned with their negatives, they’re essentially finding the difference between the absolute values of -22 and 15. This is the way we think and therefore a more natural way to learn.