Lesson 19The 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.
Only the three pens with shadow of approximately the same length.

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.

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

  1. What relationships do you notice between an object’s height and the length of its shadow?

  2. 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.

Activity 3: The Height of a Tall Object

Problem 1

  1. 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.

  2. Choose an object whose height is too large to measure directly. Your teacher may assign you an object.

  3. Use what you have learned to figure out the height of the object! Explain or show your reasoning.