Challenge students to think about what makes stairs so hard to climb and slides are so fun to go down. The answer will be steepness. Reveal to students the carpenter’s rule for deeming a safe staircase and the slide safety guidelines for the slope at a playground. Challenge students to go around the school and measure the stairs around the school to see if they are in fact “safe.” Show them a video on people falling down the stairs to grab their attentions.
- When measuring steepness, what are the variables being looked at? (rise to run ratio)
- When examining slope are there different forms/representations of slope?
- Does a slope determine speed?
- Does force come into effect when considering speed?
- Will different materials on the slide cause friction and decrease speed?
The real world connection is how the safety regulations determine the structure’s parameters and measurements.
Unit Academic Standards
- 8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
- 8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the y = mx + b for a line intercepting the vertical axis at b.
- 8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
- 8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
- In simple cases, describe the motion of objects and conceptually describe the effects of forces on an object.
- 3.B.3: Explain that an unbalanced force acting on an object changes that object's speed and/or direction.
- 3.D: Describe that energy takes many forms, some forms represent kinetic energy and some forms represent potential energy; and during energy transformations the total amount of energy remains constant.
A misconception that I always see from students is that speed/velocity is only Science and not connected to Math too. I’m hoping to close the gap between this misconceptions.
How to Make This a Hierarchical Unit
To increase this to a high school level lesson, teachers could go into how the equations of the positional change related to the speed is actually a non-linear function.Parabolas can be discussed in more depth.
This lesson was very engaging for the students. They had big ideas. I felt the students really bought in to the project after they contributed five essential questions during the engineering design process. I instructed them to write down five things they could investigate in a project with the big idea of slides, slopes, and safety. I told them that I would base the challenge off of a combination of what everyone’s ideas were. The next day when I presented the challenge, they really bought in to the project, knowing that they created it.
One of the shortcomings of the lesson were the lack of materials that I had available. I used cardboard and duct tape and kept running out of both of them. Due to the large size of the slides, I underestimated how much cardboard to purchase. I also anticipated that the students would bring in and add to the amount of supplies, but they did not reciprocate. Stability was also an issue as well. In the future I would like to use a material that is more sturdy than just cardboard such as foam board or balsa/breakable wood. Or perhaps I would make the scale factor different so that the slides would be smaller. However, the students really liked how large they were because they were able to test a doll to go down in. I had 4 students in each group which I realize was too large for this particular project. I felt that I was dealing with making sure everyone was participating equally. I would do groups of 2-3.
Lastly, I really liked the reflection that students had to complete at the end. It really helped me determine if they understood the math involved with slope and velocity. However, I had to require that the students revise their reflections because they were not complete enough. Perhaps I did not give them enough time to focus on the importance of the reflection. So I will give them more class time to complete this.