Unit 4. Data Acquisition
Revision Date: Oct 13, 2015 (Version 1.2)Pre-lesson Preparation
Your students will need computers for this lesson. If you would like to show students a working dartboard simulation (with a circular dartboard), check that your browser can run a Java plug-in. Be sure to update, activate, and disable the plug-in as needed for security purposes.
Summary
In this lesson, students will explore basic data analysis concepts in Python, learn about code extensibility, create a simple simulation from scratch, and reuse their code to make a more elaborate simulation.
Outcomes
Overview
Session 1:
Session 2:
Part of this lesson was adapted from http://www.nzmaths.co.nz/resource/dartboards and http://www.nzmaths.co.nz/resource/more-dartboards.
The development of a program from scratch to solve a specific problem is presented to students by creating a simulation that lets them see how software can model a real-world process. Additionally, the concepts of extensibility and code reuse are shown through hands-on programming experience.
Student computer usage for this lesson is: required
The Lesson Resources folder contains an example program showing how to use Python's random function to simulate tossing a coin.
An alternative lesson outline using Runestone and PyCharm to code a simulation and use it to develop, refine and test hypotheses in is the lesson folder. The lesson is in a file named "Monte Carlo Simulation to Calculate Pi.docx".
Think-Pair-Share: Writing programs "from scratch"
Get students' attention by asking them to play with the Dartboard Simulator (requires the Java browser plug-in) as they think about the following scenario and answer the related questions:
Suppose you want to write a program that simulates tossing virtual darts. Each dart will land at a point on a square virtual dartboard that is one unit long on each side. Each point on this dartboard has both an x and a y coordinate, both of which are between 0 and 1. The bull's-eye is a square in the center of the dartboard with sides of length 0.5 units.
Have the program ask the user how many darts they want thrown. The program should then simulate throwing these darts by generating a random landing location (a random x and a random y coordinate) on the dartboard for each dart. Recall how to use Python's random functions (by reviewing the previous lessons' dice simulation). As darts are thrown, the program counts how many darts land within the center square, the bull's-eye. The bounds of bull's-eye are [0.25, 0.75] on both the x and y axes. Finally, the program should print out the number of darts thrown and the number that landed within that rectangle.
Have your students answer the following questions:
Take the rest of the class time to have your students begin programming their simulation. If they are not able to finish before the session ends, you may want to assign the program as homework, or devote the beginning of the second session to finishing the program. They will need their programs for the work in the next session.
You may want to remind students how to use Python's random function. The following code may be a useful example:
Example random coin flipping code (the python file is available in the Lesson Resources folder):
import random # Needed for random number generation
number_of_heads = 0
for i in range(0, 100):
x = random.random() # Generates a random floating point (decimal) number between 0 and 1
if x > 0.5:
number_of_heads = number_of_heads + 1
print "The number of heads in 100 coin flips is ", number_of_heads
Have your students finish their dartboard programs, as they are needed in the next session. Alternatively, if they have finished their programs, you could assign the "Collecting and Analyzing Data" think-pair-share of the next session as a homework, to be discussed in the next session.
Journal: Making your programs extensible
Think-pair-share: Collecting and analyzing data
Discuss with your students how we often want to reuse our code for a new project, and how it is not uncommon when developing a program for the requirements to change. Both of these changes benefit from extensibility in code. Your students will get to test the extensibility of their dartboard program by reusing what they have to fit with a new objective: make a three-ringed circular dartboard.
As before, this program should first ask a user how many darts they would like to throw. Then, it should use that input to simulate throwing darts at a circular dartboard. Finally, it should print the number of darts thrown, the number of darts that hit the bull's-eye, the number that hit the middle ring, the number that hit the outer ring, and the number that missed completely. This circular dartboard is similar to the one from the previous session's robot exercise: it has a central circular bull's-eye surrounded by a middle ring, which is in turn surrounded by an outer ring. The coordinates for this dartboard are: the center is at coordinate (0,0); the outermost ring is a circle with radius of 3; the middle has a radius of 2; and the bull's-eye has a radius of 1. Simulate throwing a dart by picking random x and y coordinates, each between -3 and 3. Since this range is a square, some darts may miss the dartboard completely. For this program, students may reuse as much of their square dartboard code as they need, but make sure to preserve their original program separately.
Have your students finish their circular dartboard programs and answer the following questions:
Note: graphics.py may be used with this lesson to create a visualization - http://mcsp.wartburg.edu/zelle/python/ppics2/code/graphics.py
The students will produce two simulation programs on their own: the square dartboard simulation and the circular dartboard simulation.
The students will record their understanding of extensibility in their journal.
The students will gain experience collecting data in both sessions.
The students will think analytically about their programs by answering the questions in Session 1 and in the homework for Session 2.