Categories

## Linear Modeling and Graphing

What’s the mistake? How would you help?

Thanks to John Weisenfeld for the submission.

Categories

## Slippery Slope

The submitter of this mistake reports that the student is a “high flyer.”

1. What is this student’s confusion?
2. Why made this mistake so tempting? After all, if a student just doesn’t understand “slope” there are a million things that they could do wrong. Why this one?

Thanks to Jeff de Varona for the submission. Go check out his blog and follow him on twitter.

Categories

Categories

## “Graph x = 3”

The mistake is pretty easy. But what’s the underlying misconception?

Categories

## Explanations of Slope from 9th Graders

Today’s submitter asked the following question:

Here are a selection of student responses:

• Slope is how far apart the two points are. You can use the idea of rise over run. You rise a certain amount and then run right or left depending ona negative or positive.
• Slope is how you measure two or more points or equations on a graph.
• It’s the y-intercept divided by the x intercept and intercept is the coordinates.
• Slope is the change in the dependent (which can be anything) over the independent (which can be anything).
• Slope is one point of a line on a graph minus another point on the same line in that graph.
• The slope is the difference of the dependent variable (y) over the independent variable (x).
• Slope is the rate of change between the dependent and the independent. If the dependent went up by 2 every time x, the independent, went up by 1, then the slope would be y over x which in this case is 2.
• Slope is when you take one point on a graph and a second one and see the difference between them and the numbers whatever y go over the numbers of the difference of x and that’s your answer.
• Slope is the rate of change in an equation, graph or story. For example, 2x -4 = y, take two possible solutions the rate of change is 2.
• Slope is the unit that you “go up by”. Let’s say you buy 4 apples for \$4. The slope is 1 because it always goes up by one, 6 apples would be \$5.
• Slope is the rate of change in an equation.
• The rate of change, between an independent and depending things.
• You have two points so all you do is see how far apart they are. We see that it goes from (4, 2) to (2,1) so it’s 2/1.
• Slope shows how a number increases or decreases and by how much.
• A slope is the change of rate in a problem for example, a man gets paid \$5 an hour How much does he get after working for 3 hours? He gets \$15, so 5 is the slope.
• Slope is when you have 2 numbers and find out what the answer will be.

There’s a lot to work on here. In the comments, pick a student and dig into their understanding of slope. And also, can you infer what the approach of the unit was from the students’ responses? How could the unit be improved?