The Shadow Knows

5 min

Teacher Prep
Setup
Groups of 2. 2 minutes of quiet think time then share with a partner.

Narrative

The purpose of this Warm-up is to show what happens when shadows are cast from a lamp, which will be useful when students see shadows cast from the sun in a later activity. While students may notice and wonder many things about these images, the length of the shadows (which are different for the pens near the lamp and appear to be the same for the pens in the sunshine) is the most important discussion point.

This Warm-up prompts students to make sense of a problem before solving it by familiarizing themselves with a context and the mathematics that might be involved (MP1).

Launch

Arrange students in groups of 2. Display the image for all to see. Give students 1 minute of quiet think time and ask them to be prepared to share at least one thing they notice and one thing they wonder. Give students another minute to discuss their observations and questions.

Student Task

What do you notice? What do you wonder?

<p>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.</p>

<p>Photograph of 3 pens standing upright forming shadows on the desk</p>

Sample Response

Students may notice:

  • The pens are the same in both photos.
  • The pens have shadows in both photos.
  • One photo was taken inside and one was taken outside.
  • One light source is a lamp and the other is the sun.
  • In the photo where the light source is a lamp, the light is coming from the right. In the other photo, the light is coming from the left.
  • In the photo where the light source is a lamp, the shadows are all different lengths. In the photo where the light source is the sun, the shadows are all the same length. 

Students may wonder:

  • Are there times when the pens outdoors don’t leave any shadow?
  • Why do the pens near the lamp have different length shadows?
Activity Synthesis (Teacher Notes)

Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the image. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.

If time allows, display these images where the path of the light that reaches the top of each shadow is drawn in and ask students if there is anything new that they notice or wonder based on these new images.

<p>photograph of pens standing up right. Right triangles drawn with pen as height and shadow from lamp as base. </p>

Standards
Building Toward
  • 8.G.4·Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
  • 8.G.A.4·Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

15 min

15 min