Shadows challenges
Questioning is the foundation of all learning.
The first step in rejecting not knowing is to ask, why?
Sweetland
Shadow challenge
What can shadows tell us?
Coach is finishing talking to the team when someone says you have two shadows!
Are you a twin?
Everyone looks around and notices the following.
- Coach is six feet tall.
- It looks like her shadow is being cast from two towers of lights.
- They lights are 50 yards apart.
- They are 12 yards tall.
- The shadows are in opposite directions.
Focus questions
- Can you take this to math class to share and determine how tall the lights are?
- You decide to make a diagram of the situtation.
Draw your diagram with labels below.
Hint:
Draw a diagram on graph paper!
- Create a drawing (mathematical model) of the situation and identify key ideas that can be used to reason about the situation.
- Similar triangles have congruent corresponding angles and the lengths of their corresponding sides have a common scale factor.
- To justify two triangles as similar, means finding corresponding angles are congruent and corresponding sides are scaled proportional.
Extension - Using shadows to measure height - trees, flag poles, buildings, water towers, ...
Shadow length challenge
Challenge
- How long should you make the shadows?
Diagram
Bonus
If coach walked half way toward one of the lights, what would be the length of both of her shadows?
Graph paper