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Slope and Division of Negative Numbers

What’s the fastest way to help this kid?

Incidentally:

4 replies on “Slope and Division of Negative Numbers”

Visualize is good, for sure; that probably happens in my head as a sanity check of the answer even if I don’t plot the points on paper.

More to the point, how about other ways of checking? There’s not only a diagram, but also plugging the points in at the end If you used (2,7) to find the intercept, then use the other point to check your answer. At the end, instead of thinking “Done!”, how can we get them into the habit of thinking “wait, -1/2 times -6 + 8 isn’t anywhere near 3” so that they are prompted to look back and find the mistake?

newmansays:

Oh man… I’ve seen this a million times.

I usually find that the kids making this mistake couldn’t to plug a number into an equation and check it without making another one and compounding the problem. For these kids, I have them graph it, count the slope, THEN check it with the slope equation (if they insist on using it). I’ve also gone so far as to have kids create a flow chart describing, in excruciating detail… “I took 7 away from 3. I did this because… This is important to know because… this -4 tells me I am going in the negative direction on the Y-axis…” But this really doesn’t address the neg/neg = pos issue, does it?

Would you mark it wrong if they left it as -1/-2?

I’d like them to be able to move past the sketch however and ultimately use just the formula. I see this as mostly a negative number operation mistake, and then secondarily a slope formula mistake. Yes, they could identify it if they sketched it, but it’s so important with slope to remind them that when they “fall” and “run backward” these two things together make a positive line. Also, slope formula is a GREAT time to learn that the negative in a fraction is “attached” to the numerator or the denominator. And, I would consider -1/-2 not simplified so I would penalize the student for that.

Oh, and sorry – that’s also how I would help “fix” this student fast. I’d show them their answer -1/-2 means to “fall one” and “run backward” 2 which created a positive line. My students go, “Ahhhh!” when I do that.