Lesson plan at a glance...

In this lesson plan…

• Lesson Overview
• Materials and Equipment
• Preparation Tasks
• The Lesson
• Learning Objectives and Standards
• Additional Information and Resources

Confirm that your computer is on and logged-in

1 to 3 minutes

Confirm that your projector is turned on and is projecting properly

1 to 4 minutes

Confirm that all students’ computers are turned on, logged-in, and connected to the Internet

3 to 5 minutes

Confirm that Python 2.x is installed (https://www.python.org/), or navigate to Trinket (https://trinket.io/)

3 to 5 minutes

Warm-up Activity: What do you know?

5 to 10 minutes

Activity 1: Speed of light

30 minutes

Activity 2: The Uncanny Valley and drawing a circle

30 minutes

Wrap-up Activity: Assessment

10 to 15 minutes

Activity:

Have students answer the following questions in a class-wide discussion.

Q1: What is the speed of light?

Q2: Is it always constant? Does the speed of light ever change?

Q3: How have people measured the speed of light in the past? How do people measure it today?

Teaching Tips:

• Be sensitive to the classroom environment; create a safe learning environment for students who may feel uncomfortable with the activity. Start the activity by letting students select partners or small groups in which they can discuss the questions. Allow five to ten minutes for small group discussion, floating between groups to hear answers and encourage critical thought, and return to the large group to discuss.

Assessment:

Do not assess formally at this time. Allow students to freely offer their thoughts and ideas. Let them know you will discover more as you continue.

Activity:

1. Share the Speed of Light Fusion Table with your students.
2. Have the students spend one minute looking over the data and writing down their observations. Afterwards, have the students look away from their computers and share what they noticed.
3. Ask students to explore the following questions:

Q1: What patterns do you see? What do the numbers have in common and how do they differ?

Q2: Would this data be continuous or discrete?

4. Have the students click on View and then Aggregate.
5. As in the pictures below, select average, maximum, and minimum for each year and Apply.

6. To make it even easier to see the Information, have students click on Visualize in the top left, and from the drop down menu, click Scatter.
7. Set the X Axis to Count. For the Y Axis hold down the Shift  key while you select each year’s Maximum, Minimum, and Average (do not select count at the bottom).
8. Ask students this question:

Q3: What do you notice about this graph? What does it tell us about the value of c (speed of light)?

Notes to the Teacher:

A Fusion Table is like a spreadsheet for large amounts of data. This table is based on experiments conducted throughout the years (http://en.wikipedia.org/wiki/Speed_of_light#History).

The students should see the calculated values for each year. They may not understand the significance of what they have done, so remind them that, in less than a second the computer has sifted through 600 points of data to make these calculations. Imagine having to do these calculations by hand! In the past, scientists and mathematicians had no choice but to calculate large amounts of data by hand, and were it not for their patience, we would be centuries behind in technology and discovery.

Assessment:

A1: Numbers are relatively large, numbers are close together, some have decimals while others do not, numbers get progressively more precise as time goes on.

A2: Continuous. If they say discrete, it may be because these are numbers written in a table. Discuss the following:

• These were experiments conducted by scientists over time to measure the speed of light. Velocity is distance divided by time, which can never be measured exactly, therefore the data is continuous.
• Have them ask themselves whether or not a valid value could exist between any two values in the data. (They could find a value between them by calculating the average of the two, and this would also be a valid value for the speed, so the data is continuous.)

A3: Answers will vary. An example could be: As the year the data was measured (and therefore the precision of those measurements) increases, it converges closer and closer to the accepted constant value for c.

Notes to the Teacher:

Computers have improved dramatically over the last 20 years and every industry has seen significant increase in what they are able to do. One sector that has found an upper bound to what they can do is the entertainment industry. Computer graphic artists and designers are able to make better-looking images and animations because the computers are able to handle more complex geometry at a high speed. However, an interesting thing occurred in 2001 when the popular game Final Fantasy (http://en.wikipedia.org/wiki/Final_Fantasy:_The_Spirits_Within) released a movie.

While it was not the first movie to be made with 100% computer graphics, it was by many accounts the most realistic, and this lead to viewers feeling “awkward.” This has been referred to as the “Uncanny Valley” (http://en.wikipedia.org/wiki/Uncanny_valley) It describes a limit of similarity people are able to tolerate in non-human analogs (e.g. video, robots, etc).

Activity:

Begin by summarizing the Uncanny Valley phenomenon, and projecting the three images below. Explain the following:

Computer graphics are all about geometry, memory, and speed. A virtual object is made up of shapes tessellated and oriented until they follow the contours of the real model. The more sides the object has, the smoother the object can look.

Pictures from Wikipedia

A computer makes a 2D curve or a circle by creating a series of points along a path and drawing a line between each pair of adjacent points. If the distances between the points are small enough, then the path looks curved to the viewer. When creating objects on a computer, we need to decide how realistic we need it to be. With movies, realism is key, but in a game where speed is most important, an overly-detailed model can use up all of the memory.

Ask students:

How many points do you predict you will need to be able to draw a line which connects them, resulting in a figure that looks like a circle? What distance and angle between points will you use?

For this activity, students can use Python, Trinket, or a piece of paper.

Python/Trinket Instructions:

1. Have students predict what the maximum turning angle can be.
2. Open the Python Interpreter and type:

from turtle import *         #For simple drawings in Python.

3. You have 2 functions available that you can use to create your circle.

forward(x)        #Moves the turtle forward x number of pixels

right(ϴ)         #Turns ϴ degrees right. There is also left(ϴ)

4. See how small you need to make x and ϴ to create a seemingly smooth circle.
5. It might be helpful to use the functions:

undo()        #Removes the last instruction

reset()        #Erases everything and goes back to home

Here are two examples:

Paper and Pencil Instructions:

1. Using the ruler, create points that are a fixed distance from each other and connect them with straight lines. Experiment with the distance between the points and angle of rotation until it looks like a curve.
2. After completing this activity compare your results with your predictions.
3. Compare your drawing with 3 other students. How do yours compare (not in terms of quality, but how much they look like curves)?

Q1: Compare your drawing with 3 other students. Why do computer graphic artists use polygons like triangles and hexagons to draw curved surfaces?

Q2: How would you tell the computer to draw a perfect circle? Could it be done? If you were to tell the computer to draw a square, then a pentagon (5 sides), hexagon (6 sides), heptagon (7 sides), and so on, would there be a pattern to your instructions? What would it be?

Notes to the Teacher:

There isn’t a correct answer in this case as far as the distance between the points and angle of rotation. To one person it may look like a curve, while to another the illusion fails. This is why people who work with this type of graphics are considered by their peers to be artists.

Teaching Tips:

• Make the connections between home life and school by using culturally relevant pedagogy.
• The Uncanny Valley example is perfect for laying the conceptual groundwork for calculus and limits. As the number of polygons in a figure approaches infinity, the smoother and more realistic an object looks. Students appreciate hearing that math is used in the movies and games they love. See the Extension Activities for more on the Uncanny Valley.

Assessment:

A1: It creates the appearance of 3D Curves while using less memory.

A2: Drawing a perfect circle is technically impossible. However, as the number of sides of a polygon increases, the distance and angle would need to get smaller. So, theoretically, a polygon with an infinite number of sides (with infinitely small distances and angles) would result in a perfect circle.

Activity:

Have students submit at least two drawings/outputs with different distances and a short explanation of how they determined the optimum distance from Activity 2. This student-focused assessment provides students with feedback that can be used in self-examination of their learning.

Learning Objectives

Standards

LO1: Students will be able to use tools in a model to manipulate data, make observations, and identify patterns.

Common Core

CCSS MATH.PRACTICE.MP4: Model with mathematics.

CCSS MATH.PRACTICE.MP7: Look for and make use of structure.

CCSS MATH.PRACTICE.MP5: Use appropriate tools strategically.

Computer Science

CSTA L2.CT.9: Interact with content-specific models and simulations (e.g., ecosystems, epidemics, molecular dynamics) to support learning and research.

CSTA L2.CT.11: Analyze the degree to which a computer model accurately represents the real world.

Term

Definition

For Additional Information

Aggregate

Group information together in a way that makes it easy to interpret.

http://en.wikipedia.org/wiki/Aggregate_data

Discrete data

Consisting of distinct values that can be counted (e.g. # of pens in a box)

http://www.mathsisfun.com/data/data-discrete-continuous.html

Continuous data

Consisting of a range of values from measurements that cannot be known exactly (e.g. temperature of the room)

http://www.mathsisfun.com/data/data-discrete-continuous.html

Precision

How close successive data measurements (under the same conditions) are to each other.

http://en.wikipedia.org/wiki/Accuracy_and_precision

Concept

Definition

Decomposition

Breaking down data, processes or problems into smaller, manageable parts

Pattern Generalization

Creating models of observed patterns to test predicted outcomes

Pattern Recognition

Observing patterns and regularities in data

Contact info

For more info about Exploring Computational Thinking (ECT), visit the ECT website (g.co/exploringCT)

Credits

Developed by the Exploring Computational Thinking team at Google and reviewed by K-12 educators from around the world.

Last updated on

07/02/2015

Copyright info

Except as otherwise noted, the content of this document is licensed under the Creative Commons Attribution 4.0 International License, and code samples are licensed under the Apache 2.0 License.