Slippery Slopes

Author:
Gina Ogden

Unit Title:
Slippery Slopes

Grade Level:
7th/8th

Subject Area:
Math

Total Estimated Duration:
12 – 100 minute class periods

Poster:
Slippery Slopes Poster

Video:
Slippery Slopes Unit Video

Unit Lessons:
Lesson 1: Investigating Slope & Y­-Intercept
Lesson 2: It's All in the Slope

Background Knowledge:

  • Understand connections between proportional relationships
  • Represent proportional relationships by equations
  • Determine whether two quantities are proportional from a graph or table

Date:
March 2013

The Big Idea

Students will investigate different events in the upcoming 2014 Winter Olympics. Each group will design and create a model of a practice course for the event of speed skiing. The students will demonstrate their knowledge of slope when constructing the course.

Essential Questions
  1. How does the slope of a hill affect the performance of a skier in the Olympic event speed skiing?
The Challenge

Design and create a model of a practice course for the Olympic event speed skiing. The objective is to design a slope that will minimize the time required to get from the top of the hill to the bottom.

The Hook

Franz Weber Career Highlights (YouTube video).

Guiding Questions
  • What are the different events involved in the Winter Olympics?
  • What is speed skiing?
  • How could a skier minimize the time it takes them to travel from the top of a hill to the bottom?
  • How does the height of the hill affect the the speed of the skier?
ACS (Real world applications; career connections; societal impact)

A­ – Students will gain knowledge about a world­wide competition. They will also learn how the slope of objects is applies in the real world. i.e skiing
C – ­Civil Engineer, Olympic Athlete, Carpenters
S – ­The Winter Olympics will be occurring next year.

Engineering Design

Students will be presented with a problem that will require the use of the engineering design process. It will require research about speed skiing. This information will be used to guide their solution, designing and creating a slope that minimizes the time it takes a skier to reach the bottom. Students will also build, test and evaluate their prototype. This process will bring about discussion and redesign of the solution until it best solves the problem.

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. For example, compare a distance­time graph to a distance­time equation to determine which of two moving objects has greater speed.

8.EE.6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non­vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx+ b for a line intercepting the vertical axis at b.

Assessments

Summative Assessment
Testing of the Ski Slope Project.

How to Make This a Hierarchical Unit

This is a Middle School Lesson. Students can analyze and solve pairs of simultaneous linear equations.