Lesson 13
The Shadow Knows
Let’s use shadows to find the heights of an object.
13.1: Notice and Wonder: Long Shadows and Short Shadows
What do you notice? What do you wonder?
![Photograph of 3 pens standing upright. Lamp on right. Longest shadow formed by pen on far left, shorter shadow on middle pen, no shadow on pen on right.](https://cms-im.s3.amazonaws.com/dpKeHCHxeR5ThpW6zkoAJeDm?response-content-disposition=inline%3B%20filename%3D%228-8.2.D1.Image.01.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.D1.Image.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T162212Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=02c85ba42a0c9367f332fbe769ecc5c3bd99b5dd735095d3066341b6324013a6)
![Photograph of 3 pens standing upright forming shadows on the desk](https://cms-im.s3.amazonaws.com/hucHV4yxHVBpo9Pjjxtk66tY?response-content-disposition=inline%3B%20filename%3D%228-8.2.D1.Image.02.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.D1.Image.02.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T162212Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ea5b1d9cda45e4fb17c75f77297f2fdb927b2bddad0c885734c68166a5eefea0)
13.2: Objects and Shadows
![Photograph of 2 boys, a man, and a lamp post, each have a shadow to their left.](https://cms-im.s3.amazonaws.com/jMFCcfQXzV7HHnohx2rdPfsE?response-content-disposition=inline%3B%20filename%3D%228-8.2.D1.Image.04.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.D1.Image.04.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T162212Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=2e0cd9da693c6d1a31e96246e413d1b581e1dafcf605b4491c36fa238ea24f78)
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 | 43 | 29 |
man | 72 | 48 |
older boy | 51 | 34 |
lamppost | 114 |
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What relationships do you notice between an object’s height and the length of its shadow?
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Make a conjecture about the height of the lamppost and explain your thinking.
13.3: Justifying the Relationship
Explain why the relationship between the height of these objects and the length of their shadows is approximately proportional.
![Photograph of 2 boys, a man, and a lamp post. Triangles drawn using person or post as height and its shadows as the base.](https://cms-im.s3.amazonaws.com/mybn92VJ5qdLWyPvF1ZP6EwU?response-content-disposition=inline%3B%20filename%3D%228-8.2.D1.Image.05.1.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.D1.Image.05.1.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T162212Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=92733bdd8104f1bd2460988345bc7e755e35129408e88ca6537df7725e193f99)
13.4: The Height of a Tall Object
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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.