Shadows
Welcome to the Shadows PBL web page.
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Introduction
Shadows is a Project Based Learning unit that focuses on using exponential growth and decay models to solve real-life problems. Students build a mathematical model of projected changes in moose population in the Adirondack National Forest, beginning with the selection of factors that must be reflected in the model, including migration rates, sex ratios, reproductive rates, and rates of importation. As the unit continues, students learn about exponential functions, graphs of exponential equations, the rules of exponents. Students test their moose models to learn how sensitive they are to change.
Driving Question: How can we create a mathematical model for the length of a shadow?
Culminating Project: After students solve the unit problem, they will work in groups to create a web-based business plan for a small business of their choosing. Teams will publish on the internet a plan that analyzes the constraints of their business, designs a plan to optimize the profit, and justifies their optimization plan. View Project details.
Assignments
- Unit Overview:
- Lesson 1: What Is A Shadow?
- Prep Reading
- Activity 1:
- Individual Work:
- Activity:
- Lesson 2: The Shape of It
- You've done some measufements involving shadows, and now it's time to try a different approach. For a while, you're going to leave the wodd of shadows
and enter the more abstract realm of geometry.Angles, polygons, lengths of sides-these will be the focus of your attention for much of the unit, but eventually these
ideas will fit together to answer the shadowy questions that are lurking in the background.
- Individual: Draw The Same Shape
- Activity: How To Shrink It?
- Individual: The Statue of Liberty's Nose
- Homework: Make It Similar
- Activity: Is There A Counterexample?
- Individual Work 2: Triangular Counterexamples
- Individual Work: Ins and Outs of Proportions
- Homework: Proportion Worksheet
- Individual Work: Similar Problems
- HW: Inventing Rules
- HW: Polygon Equations
- Lesson 3: Triangles Galore
- The unit now moves from polygons in general to triangles in particular, but algebra starts playing an important role as well. You will be investigating the special case of triangles in
more detail, using angles, parallel lines, and ratios. While you investigate these ideas, you might keep thinking about the unit problem that's waiting for you in the shadows,
and ask yourself what triangles and equations have to do with it.
- Activity: Why Are Triangles Special?
- Activity: Are Angles Enough?
- Individual Work: From Top To Bottom
- Activity: What's Possible?
- Individual Work: Very Special Triangles
- Activity: What's The Angle? (Vertical Angles)
- POW: Trying Triangles
- Activity: More About Angles (Transversals)
- HW: Inside Similarity
- Activity: A Parallel Proof
- Lesson 4: The Lamp Shadow
- You know that shadows have something to do with light (or lack of it). You're almost ready to solve the lamp shadow problem, but first you will look at some fascinating situations that involve light in a different context. Similar triangles continue to be the main theme.
- Activity: Bouncing Light
- HW: Now You See It, Now You Don't
- Activity: Mirror Magic
- HW: Mirror Madness
- Activity: A Shadow of a Doubt
- HW: To Measure a Tree
- Activity: More Triangles for Shadows
- Lesson 5: The Sun Shadow
- Activity: The Sun Shadow Problem
- HW: Right Triangle Ratios
- Prep Reading: Sin Cos and Tan Revealed
- Activity: Homemade Trig Tables
- HW: Your Opposite Is My Adjacent
- Activity: The Tree and The Pendulum
- HW: Smokey and The Dude
- Activity: A Bright Sunny Day
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Student Projects
Block 3
- Team 1
- Team 2
- Team 3
- Team 4
- Team 5
Block 4
- Team 6
- Team 7
- Team 8
- Team 9
- Team 10
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Resources
The following are links to resources for Exponential Functions, the topic being developed in the Wildlife PBL::
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