Looks to me like the student doesn’t understand that X=3 is a line, since ther is no y mentioned.As for number six, the student counted the xs in the problem, separated them by +signs, and called it good. No good understanding that factors are things to be multiplied perhaps? I’d say a basic misunderstanding of factoring.

I think it’s interesting that the student had also colored in the points (0,3) and (3,3), and then erased those two choices. So first this might be some confusion as to the whole idea of an axes, and what the x-axis is.

Underneath it all there’s a bit problem with this kid’s understanding of equations and coordinates. It should be impossible to put that point down without knowing a corresponding y coordinate. Maybe what could help would be an activity where the student shades in points that fulfill a condition. For example, “Find all the points that are two units away from the origin,” “Find all the points where x = 3”, and “Find all the points where x =3 and y = 2.”

Student: Last week, when you asked us to graph the solution of 2x – 1 = 5, the answer was just a point. Teacher: Yes, but this question is asking you to plot all the points on the plane with an x-value of 3.Student: *sigh* THEN WHY DON’T YOU SAY SO?! You math teachers speak another language.

Conversation from a parallel universe:Student: Last week, when you asked us to graph the solution of 2x – 1 = 5, the answer was just a point.Teacher: But you might recall that the picture was much simpler last week. We simply drew a line and plotted a point on it. It is hard to miss the huge grid in this problem. How did you decide where to place the point?Student: Well, you told us the x-axis was that horizontal one running through the middle, and since it said “x=3”, I decided to put the point on the x-axis.

Are there bonus points for connecting the (wrong) answer in 6 to the (wrong) answer in 5?I wouldn’t be surprised if this student attempted to graph (3, 7) as a point at 3 on the x-axis and a point at 7 on the y-axis.I like the 5x^2 + 10x = x + x + x + 5 + 10… the student’s probably been asked “how many x’s in 5x^2”? And been praised for the answer “2” because there are 2 x factors. But 5x x’s might have been the better answer…Overall, I’m noticing that the student doesn’t have the concept that x is a quantity (a thing whose value we could count, measure, be told, or otherwise figure out), and operations are being applied to it, and creating another quantity.I’m also noticing that the “why didn’t you say so?” plea above seems appropriate. When we write x = 3, how do we indicate to students that we also care about this other related quantity, y, whose value is undefined, and we’d like them to represent visually the relationship between x, whose value is arbitrarily assigned 3, and y, whose relationship to x is unknown. That’s tricky!Contrast that to 5x^2 + 10x. Now, we aren’t assigning a value for x, and it’s plausible that we would want to know about the other quantity in the relationship, the result when x is squared, multiplied by 5, and added to x time 10. But in this problem, we aren’t asked about the other quantity, or the value of x, we’re just asked to write an equivalent expression.Knowing what to care about in these two contexts with only the clue of the wording of the question and the graph is tricky, I think.

PS — I wasn’t asking for bonus points for me, I just want to see what other people think when they look at both answers together!

## 8 replies on ““Graph x = 3””

There’s also a juicy little bonus mistake in #6.

Looks to me like the student doesn’t understand that X=3 is a line, since ther is no y mentioned.As for number six, the student counted the xs in the problem, separated them by +signs, and called it good. No good understanding that factors are things to be multiplied perhaps? I’d say a basic misunderstanding of factoring.

I think it’s interesting that the student had also colored in the points (0,3) and (3,3), and then erased those two choices. So first this might be some confusion as to the whole idea of an axes, and what the x-axis is.

Underneath it all there’s a bit problem with this kid’s understanding of equations and coordinates. It should be impossible to put that point down without knowing a corresponding y coordinate. Maybe what could help would be an activity where the student shades in points that fulfill a condition. For example, “Find all the points that are two units away from the origin,” “Find all the points where x = 3”, and “Find all the points where x =3 and y = 2.”

Student: Last week, when you asked us to graph the solution of 2x – 1 = 5, the answer was just a point. Teacher: Yes, but this question is asking you to plot all the points on the plane with an x-value of 3.Student: *sigh* THEN WHY DON’T YOU SAY SO?! You math teachers speak another language.

Conversation from a parallel universe:Student: Last week, when you asked us to graph the solution of 2x – 1 = 5, the answer was just a point.Teacher: But you might recall that the picture was much simpler last week. We simply drew a line and plotted a point on it. It is hard to miss the huge grid in this problem. How did you decide where to place the point?Student: Well, you told us the x-axis was that horizontal one running through the middle, and since it said “x=3”, I decided to put the point on the x-axis.

Are there bonus points for connecting the (wrong) answer in 6 to the (wrong) answer in 5?I wouldn’t be surprised if this student attempted to graph (3, 7) as a point at 3 on the x-axis and a point at 7 on the y-axis.I like the 5x^2 + 10x = x + x + x + 5 + 10… the student’s probably been asked “how many x’s in 5x^2”? And been praised for the answer “2” because there are 2 x factors. But 5x x’s might have been the better answer…Overall, I’m noticing that the student doesn’t have the concept that x is a quantity (a thing whose value we could count, measure, be told, or otherwise figure out), and operations are being applied to it, and creating another quantity.I’m also noticing that the “why didn’t you say so?” plea above seems appropriate. When we write x = 3, how do we indicate to students that we also care about this other related quantity, y, whose value is undefined, and we’d like them to represent visually the relationship between x, whose value is arbitrarily assigned 3, and y, whose relationship to x is unknown. That’s tricky!Contrast that to 5x^2 + 10x. Now, we aren’t assigning a value for x, and it’s plausible that we would want to know about the other quantity in the relationship, the result when x is squared, multiplied by 5, and added to x time 10. But in this problem, we aren’t asked about the other quantity, or the value of x, we’re just asked to write an equivalent expression.Knowing what to care about in these two contexts with only the clue of the wording of the question and the graph is tricky, I think.

PS — I wasn’t asking for bonus points for me, I just want to see what other people think when they look at both answers together!