Once the similarities and differences are identified, the rest of the conclusion discussion should focus on the meaning of the slope and the significance of the y-intercept from the linearized graph and equation.

When students look at the values of the y-intercepts, they will have small positive or negative values. The question becomes whether these values are significant or insignificant. To help students judge the significance of a y-intercept, it is not enough to just look at the value. The value of the y-intercept must be compared with the range of values collected on the y-axis, in this case, the kinetic energy values. The threshold is somewhat arbitrary, but I tell my students that the y-intercept is insignificant if it is less than 5% of the maximum y-value.

The y-intercept of the linearized graph can also be considered insignificant if it can be reasoned away. Have the students think about what they would expect the kinetic energy to approach if the value of the velocity squared approached zero. Through a guided conversation, students will be able to identify that the velocity squared value will approach zero as the velocity approaches zero. And as discussed before, all students will say that they expect the car’s kinetic energy should be zero when its velocity is zero. Since the y-intercept can be reasoned away, it can be left out of the algebraic equation.

When students look at the slope of the linearized graphs and equations, they should find two groupings of values. Also, if students simplified the slope units, they should find that the slope units are just kilograms. Ask students why there are two groupings of slope values. If students can determine the cause of different slope values, this will help them determine the meaning of the slope. The slope of any linear relationship represents the change in the y-variable for each unit of change in the x-variable. For this lab that would be the increase in the car’s kinetic energy for one unit of increase in velocity squared. This may be a true statement, but it’s not the meaning of the slope you want students to have. It turns out that the slope represents half of the car’s mass, but how do you guide students to that conclusion?

Start by reminding students that the slopes of their linearized graphs are constant. This is true for any linear relationship. So this means that the slope must represent something that stayed constant during each trial in their experiment. This constant thing must also explain why groups got different slope values. Discuss each shared idea to help students decide if this is the meaning of the slope. If students simplified the slope units, they should find that the slope only has units of kilograms. This suggests that the values represent a constant mass.