The State of Slope

We have been working on slope for a week now and I decided to give my students a warm up that will (unknown to them) be an assessment on Friday. When I looked at this warm up, I did not foresee any great obstacles for my students to get hung up on. I am just using this as an assessment on how my students will process finding slope when presented a line or equation.

Here are a few student examples:

From this paper I can see that this student does know how to set up the fraction for slope, but does not bother to indicate whether the slope is positive or negative, or even reduce the fraction. Given the slope-intercept equation they readily identify the slope and intercept correctly, but from the previous evidence I wonder if they have a good picture of what is happening; where does the line cross the axis? Which axis does it cross? Is it going up or down? The last two examples allow me to focus in on what the student sees when they are looking at slope, and although they may know how to find a slope from the equation or a line, they do not transfer that into creating a line with a given slope. On the first example they correctly identify the intercept, but the second they mistakenly identify positive two as the intercept. Both examples do not have an accurate slope representation, meaning this student needs to review the process they did in the first four problems and make that connection to re-creating the line in the last two.

In this example we see the student using a visual to determine slope. This is one way my students have found to find slope, and I like this method since it allows a good connection to finding the Pythagorean Theorem later in the year. They can correctly identify the slope given a line or equation, although they still do not reduce fractions. They were successful in writing equations given the slope and intercept, and while they accurately drew the line with a positive slope, they incorrectly displayed the negative slope. This student has a good grasp on the concept and I would anticipate them getting all of the questions correct when tested.

In this last example, the student shows proficiency in finding the slope of a graphed line using the same triangle method. They are unable to identify the slope in the equation, instead choosing the intercept which also leads to confusion on the last two problems. This student needs to revisit the Slope-Intercept equation and how to graph the line given a slope and point.

Overall the class did fairly well on this warm up, and it was given as an informal assessment to what we have covered this past week. I do still have students who can’t get a grasp on slope with the examples, stories and diagrams I have used in the classroom, please share your ideas on how you present slope to your students.