Sliding Through Slopes

Author:
Kelly DeNu

Unit Title:
Sliding Through Slopes

Grade:
8

Subject:
Math

Estimated Duration:
7 Block Classes

Unit Activities:
Activity 1: Using Stairs to Model Slope
Activity 2: Forces & Motion Using Roller Coast Model
Activity 3: Slide Challenge
Activity 4: Testing & Conclusion

Background Knowledge:
Students need to know how to solve equations and have some understanding on how to graph equations with tables.  We will move from tables to slope-intercept form in this lesson. 

Additional Resources:
Playground Safety Guidelines

Date:
July 2013

The Big Idea

When construction workers and designers create public facilities including stairs and slides for playgrounds they must consider certain guidelines to maintain safety.  The guidelines for stairs must fit a 0.45-0.65 ratio or slope and slides must have no more than a 0.577 slope.

Essential Question
  1. Can we design a slide model that meets the safety guidelines of slope and measure its velocity based on forces and motions?
The Challenge

Students will design and build a model slide based proportionally on a playground slide with a slope ratio not to exceed the safety guidelines of 0.577.  They will use the following criteria:

  • Take measurements of the actual slide and scale/dilate it down to make a model slide.
  • Design a model slide within the safety guidelines not to exceed a slope of 0.577
  • Use materials that will allow the slide mobility considering forces and motions (Science Lesson)
  • Check for a relationship between the slope and the velocity of the object going down the slide
  • Write an equation for your slide that compares ground to height to visually represent your slide including starting height and an equation to represent the velocity of the object traveling
  • Group with the fastest time without breaking the object, wins.
The Hook

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.

Guiding Questions
  1. When measuring steepness, what are the variables being looked at? (rise to run ratio)
  2. When examining slope are there different forms/representations of slope?
  3. Does a slope determine speed?
  4. Does force come into effect when considering speed?
  5. Will different materials on the slide cause friction and decrease speed?
ACS

The real world connection is how the safety regulations determine the structure’s parameters and measurements.

Unit Academic Standards

Math

  • 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.

Science

  • 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.
Assessments

Pre-test
Post-test

Misconceptions

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.

Reflection

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.