Foundations and Pre-Calculus 10 – Ski Hill Project
Learning Outcomes Addressed:
3.1 Determine the slope of a line segment by measuring or calculating the rise and run.
3.4 Explain why the slope of a line can be determined by using any two points on that line.
3.6 Draw a line, given its slope and a point on the line.
3.7 Determine another point on the line, given the slope and point on the line
3.9 Solve a contextual problem involving slope.
Purpose:
The purpose of the project is to take what you have learned about slope and apply it to a real world scenario in which slopes are used.
Scenario:
An indoor ski hill recently opened in Dubai in the United Arab Emirates. You and your two partners have been hired by a retail developer to propose a design for an indoor ski hill to be placed inside a mall in Southern California. You will start with a short warm up to give you an idea of where to start; then you will be responsible for producing your own profile and a 3-D mock up of what the hill may look like in reality.
Warm-up:
1) Graph the following co-ordinates on grid paper. Join the points to create a simplified elevation profile of a ski hill.
Horizontal Position (ft) | Vertical Position (ft) |
0 | 100 |
50 | 70 |
65 | 65 |
100 | 60 |
125 | 35 |
145 | 30 |
165 | 10 |
170 | 3 |
180 | 2 |
190 | 0 |
200 | 0 |
2) Calculate the slope between the following pairs of points:
a) (0, 100) to (50, 70) m =
b) (65, 65) to (100, 60) m =
c) (145, 30) to (165, 10) m =
3) Which part of the run has the steepest slope?
4) Find the slope for the last 10 feet of the run. m =
5) Find the average slope from beginning to end. m =
6) Calculate the length of this ski run. l =
Your Proposal:
Your proposal is to include three aspects.
- Your ski hill elevation profile is to meet the following specifications:
· The total height of the ski hill should be 100 feet.
· The total horizontal distance should be 120 feet.
· The total length of the run should be no more than 300 feet.
· You should include at least 3 different slopes and a more gentle finish to allow the skier to slow down and stop.
· Your drawing should be on grid paper with an appropriate scale given.
- You must also include a paragraph description of the ski hill with the following information:
· The total length of the ski run.
· The slope of the steepest section.
· The average slope of the ski run.
- Your 3-D Model is to meet the following specifications:
· Must be done to scale, ideally the scale you used for your elevation profile.
· Must include your scale on your model.
· Must be able to see the 3 different slope sections and the gentle finish.
· Must look like it would in reality, i.e. make it look like you would see it in the mall (add snow, the lift, skiers, etc…, be creative)
Timeline:
· You will have one class period to complete the warm up and discuss what your proposal will look like.
· You will have an additional 2 class periods to work as a group to develop your profile, written description and model.
· If additional time is needed the classroom will be open after school for one additional week so you may complete your work at that time if necessary.
Extensions:
If you wish to go above and beyond the project specifications here are some ideas for you; you may choose one or you may choose to do them all.
- Research the Dubai project – cost to build, timeline from start to finish, slopes involved, cost to keep hill operational.
- Research the practicality (cost to build, marketing, cost to run yearly, etc…) of developing an indoor ski hill in a Western Canadian mall.
- Research how outdoor ski hills are run and how they may use slopes to classify the different runs.
- What is the connection between man-made ski hills (not necessarily indoor) and polygons?
Rubric for the ski hill project:
Knowledge and Understanding - Calculations show complete understanding of the mathematical concepts used to complete the assignment. All calculations are done correctly; co-ordinates are graphed accurately on grid paper. /10
Completeness of Assignment - Contains all the required parts: graph, slopes, steepest slope, slope for the last 10 feet, average slope and total length of the ski run. The proposal for the ski hill elevation profile meets all required specifications. Includes a brief description with all required information . /15
Neatness and organization - The work is presented in a neat, clear, organized fashion. /5
Total /30
Susan's comments on your project presentation:
ReplyDeleteDeb, Zsofia and Nadine: Polyhedra project
Beautiful and varied polyhedral models!
Very good critique of the project! Good, thoughtful analysis that offers good improvement ideas.
Note: Kepler -- 3D fractals ? (I’d be interested to hear more about this!)
Geomag: neat!
I like your good suggestions for modifications of the project. Good work! (Now I’d like to try the project again incorporating your modifications.) Excellent idea to connect this with the surface area unit.
New project: Indoor ski hill (!) (what an astounding concept, an indoor ski hill…)
I like the constraints you’ve given, which forces some mathematical thinking. Question about slope: are ski hill slopes determined like the slope of a line on a graph, or are they expressed as percentages?
Good rubric.
Excellent!
Susan's comments on your project write-up:
ReplyDeleteUnfortunately, I could not access your powerpoint from any of your blogs - -I'm not sure why. Nonetheless, I've see the powerpoint already and know that it was good.
Your write-up of the indoor ski hill project is good in many ways. You address the PLOs included, give a good rubric for assessment, and break the project down into its components to help kids make sense of it.
However, I have some caveats about presenting the project in the way you've done here:
•The "warm-up" is a good idea, but if you turn it into a fill-in-the-blanks worksheet, kids will simply treat the project as a worksheet, and refuse to engage in the topic in any meaningful way. We math teachers sometimes have a tendency to pre-digest the thinking a little too much, and to give kids work that offers very little space for them to bring their own thinking and original ideas. If this project is simply an exercise for them to drill the "find the slope" algorithm, they will do that, and not think about ski hills or polyhedra! Beware if doing too much of the work for the kids ahead of time.
•The extension ideas are good, but making them optional means that, really, no one is likely to do them. Again, it seems to me that you might be preempting students' original thinking by presenting them pre-made extensions before they've even begun thinking about the topic, and then making them optional means that there's no need to engage with these thoughts whatsoever! Better to bring up extension ideas as they arise, and as kids get well into grappling with the main problem. Don't tell kids "you don't really have to think about this", because then they won't!
•Are your stats for constraining the ski hill design really realistic? Are real ski runs no more than 100 ft. high and 300 ft. long? (I very much doubt if that's true for Whistler, for example...) And why give these constraints at all in the first place? Again, I feel the heavy hand of the teacher doing all the pre-thinking and predigesting of ideas. Why can't the kids figure out/ research the length and height of a good ski hill -- and do the same for a ski hill located inside a mall?
•And finally -- what is the relationship between ski hills and polygons/ polyhedra?
Mark for this part of the project write-up: Adequate --> Very Good
Overall mark for the assignment: Very Good!