Lesson 19
The Shadow Knows
Let’s use shadows to find the heights of an object.
19.1: 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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T003147Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=fee99a130e84a1f7884b2a8aa7c8b5e69f97521ba504272d5266e66bc40d5611)
![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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T003147Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=06d858326aef53e6caa5322cbd0672acfc62ab9354e3ba1771578812cdf03ee7)
19.2: 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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T003147Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c3ca65457d554f10b928c317ac9d615e755a4140b65a09516e4871c8c342d4a4)
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 |
-
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.
19.3: 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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T003147Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=74b3c6014c6d23d7e3c60e93f351620ae1de422f15da4fcd75304d25795e8d95)
19.4: The Height of a Tall Object
-
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.
-
Choose an object whose height is too large to measure directly. Your teacher may assign you an object.
-
Use what you have learned to figure out the height of the object! Explain or show your reasoning.