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Dot Product Review: Instructor's Guide

Main Ideas

This small whiteboard question (SWBQ) serves as a quick review of the dot product. It is also an opportunity to help students see the advantages of knowing many different representations of and facts about a physical concept.

This is a Small Whiteboard Question. Look here for general information about how to use swbq's in the classroom.

Students' Task

Estimated Time: 10 min.

Prerequisite Knowledge

This swbq will not work unless most students in the class have seen and used the dot product before. Use it at the beginning of term if the students need a review. If some students in your class have not seen the dot product before, you can refer them to the section GVC § Dot Products in our online text. Note, clicking on this link will take you to another website. You will need to use the “Back” button to return here.

Props/Equipment

Activity: Introduction

Prompt: On your small whiteboard, write something about the dot product.

(The generic word “something” in the prompt is important. Do not use a more specific word that cues students to give an algebraic definition or a drawing, etc.)

Activity: Student Conversations

example video

Answers you're likely to see:

Activity: Wrap-up

Walk around the room as students are answering this question and quickly pick up an example of each different representation or statement. Quickly order them in the order you would like to talk about them and prop them on the chalkboard tray. Pick up each one (or more than one if you are comparing them) and give whatever review “lecture” you would normally give. The students are far more invested if they see that you are talking about their answers and some students will even vie with each other to get you to choose their answer. You can add in any extra representations that the students haven't mentioned as you go along.

The most important thing to emphasize is that the professional physicist knows and uses all of these representations/facts.

Extensions

You may also want to assign the following homework problem which requires students to use both the algebraic and geometric definitions of the dot product to solve the problem successfully.

  1. (Tetrahedron)

    Using a dot product, find the angle between any two line segments that join the center of a regular tetrahedron to its vertices. Hint: Think of the vertices of the tetrahedron as sitting at the vertices of a cube (at coordinates (0,0,0), (1,1,0), (1,0,1) and (0,1,1)—you may need to build a model and play with it to see how this works!)


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