What does the student have right, and what does the student have wrong? How would you help?

# Category Archives: Algebra 1

# Classic: Zero exponents

# Fractions and Equations

# Equation of Parabola

# I have nightmares about this one

# Adding Radicals

# “Graph x = 3”

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

# 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?

# Quadratics Quiz

As we start a new week of Math Mistakes, if you have any pictures of student work that you find interesting in any way, please send it in.

Today’s student has a couple of ideas worth drawing out. Do so in the comments.

# What does he think “factoring” means?

What does this kid think “factoring” means? And, at least to me, the more interesting question is: where did that conception of “factoring” come from? Tease it out in the comments.