Lesson 13The Shadow Knows
Learning Goal
Let’s use shadows to find the heights of an object.
Learning Targets
I can model a real-world context with similar triangles to find the height of an unknown object.
Warm Up: Notice and Wonder: Long Shadows and Short Shadows
Problem 1
What do you notice? What do you wonder?
![Three pens standing up with a lamp shining on them causing a long shadow on the pen farthest away from the lamp and a smaller shadow from the middle pen and non from the third.](../../../../../../embeds/a66e5d9e--8.2.D1.Image.01.png)
![Only the three pens with shadow of approximately the same length.](../../../../../../embeds/b603039e--8.2.D1.Image.02.png)
Activity 1: Objects and Shadows
Problem 1
![A picture of an adult and two children standing next to a lamp post on a sunny day. The lamp post has the longest shadow.](../../../../../../embeds/296b63dd--8.2.D1.Image.04.png)
Here are some measurements that were taken when the photo was taken. It was impossible to directly measure the height of the lamppost, so that cell is blank.
height (inches) | shadow length (inches) | |
---|---|---|
younger boy | ||
man | ||
older boy | ||
lamppost |
What relationships do you notice between an object’s height and the length of its shadow?
Make a conjecture about the height of the lamppost and explain your thinking.
Activity 2: Justifying the Relationship
Problem 1
Explain why the relationship between the height of these objects and the length of their shadows is approximately proportional.
![The same picture of the people and the lamp post, now with lines drawn from the top of the lamp post to the ground to make a triangle and the lines from the top of the people.](../../../../../../embeds/78e3bc3a--8.2.D1.Image.05.1.png)
Activity 3: The Height of a Tall Object
Problem 1
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Head outside. Make sure that it is a sunny day and you take a measuring device (like a tape measure or meter stick) as well as a pencil and some paper.
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Choose an object whose height is too large to measure directly. Your teacher may assign you an object.
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Use what you have learned to figure out the height of the object! Explain or show your reasoning.