Illustrative Mathematics Grade 8, Unit 2, Lesson 13: The Shadow Knows

Learning Targets:

  • I can model a real-world context with similar triangles to find the height of an unknown object.

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Illustrative Math
Grade 8

Lesson 13: The Shadow Knows

Let’s use shadows to find the heights of an object.

Illustrative Math Unit 8.2, Lesson 13 (printable worksheets)

Lesson 13.1 Notice and Wonder: Long Shadows and Short Shadows

What do you notice? What do you wonder?

Lesson 13.2 Objects and Shadows

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.

  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.

Lesson 13.3 Justifying the Relationship

Explain why the relationship between the height of these objects and the length of their shadows is approximately proportional.

Lesson 13.4 The Height of a Tall Object

  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.

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

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