# 1.3: Experiment 1 - Measurements

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Measurements and the Irrational Number Pi

Learning Objectives

By the end of this lab, students should be able to:

• Accurately measure materials using a home made ruler.
• Select appropriate measuring device for each application.
• Select appropriate number of significant figures for each measurement.
• Convert between units or measurement using dimensional analysis.
• Differentiate between accurate and precise measurements in an aggregate set of data.
• Graph a set of data and determine the slope with Google sheets.

Prior Knowledge:

## Introduction

In this lab, students will work in groups of 3-5 people using Zoom breakout groups while collaborating on a Google Doc, and will create two scales based on the width of their own pointer finger (PF) as a base unit to determine the value of Pi. Students will use their PF unit to create a scale of the Fist, where 1 Fist (F) unit is equal to the width of 5 PF units. Once this scale is completed, students will then create a more precise scale, called the deciFist scale, where each deciFist (dF) unit is equal to 1/10th the length of the Fist unit (10 dF is equal to 1 F). After creating these two scales, students will then find 5 circular objects of varying sizes around their house, measure the circumference and diameter of each object with their homemade scales, and then use Google Sheets to plot these measurements and determine the value of Pi.

• Week 1:  Students work in their group to design a protocol for building a ruler based on the width of their pointer finger. Each student individually performs the experiment and plots their data in Google Sheets.
• Week 2: Students pool all of the data from their group, plot with Google Sheets, and work up their data and turn in individual worksheets.

Supplies:

In this lab you may need to obtain supplies, so if you go to the store be sure to follow proper COVID-19 hygienic protocols, wear a mask, wash your hands thoroughly and maintain safe distance from fellow shoppers. Please review these protocols from the CDC.

• two strings or shoe laces that can be marked on
• two different colored markers that will show up on your string (such as red and blue)
• firm paper (thin cardboard from food packaging can be used)
• scissors
• tape
• 5 circular objects of varying sizes (e.g. large coin, dinner plate, Lysol can, etc.)
• one object needs to have a diameter larger than the width of two of your fists
• one object needs to have a diameter smaller than the width of three of your fingers
• the other three object need to be various sizes
• ruler with metric units (cm)
• cell phone with camera
• laptop or computer with camera, speakers and microphone hooked up to internet

## Pre-Lab Primer

This assignment is an individual assignment to be completed on your own with the help of the "Prior Knowledge" links at the top of this page. The assignment will be due 10 minutes before your lab begins. Late work will not be accepted.

The document below is a preview only. You will be able to find your assignment to work on in your Google Classroom.

Interactive Element

## In-Lab Assignments

### Week 1: February 1st - February 4th

#### Measurements Experiment Design Proposal

Using Zoom breakout groups, collaboratively work with your group on the assignment in your Google Classroom called "Measurements Experiment Design Proposal". You can see a preview of this document below. Your group needs to develop a protocol for how to build the two rulers mentioned above (one with Fist Scale and one with deciFist Scale) by using the width of your pointer finger (PF) as a base unit. Since you will be measuring circular objects, the rulers need to be made of a flexible material.  Use the information on this LibreTexts page to help you complete the assignment. NOTE: You are not making the actual rulers yet. Your group is only brainstorming how those rulers could possibly be made.

The document below is a preview only. You will be able to find your assignment to work on in your Google Classroom.

Interactive Element

#### Building and Using Your Rulers

Each group will share their experiment design proposal with the class. After each group has shared, the lab instructor will generate a Standardized Experimental Protocol, which everyone will follow to create their own rulers. This document will be posted in your Google Classroom. You will then use your two rulers to make circumference and diameter measurements of the five circular objects that you found around your house.

Note

You will be in contact with your group via Zoom. You can help each other with the ruler building process and you can discuss your Google Sheets data and graphs, but each individual person will be making their own ruler and measurements.

These two scales measure the same unit of length (the width of 5 pointer fingers, which we call the Fist unit), but they both have different precision. When making measurements, students must report the correct number of significant digits based on the scale they are using (all certain values and the first "guestimate", section 1B.2.1.2 of your LibreTexts).

#### Graphing your Data to Determine the Value of Pi

As you enter your data, the Google Sheet will make a graph of the data for you. The slope for each of your graphs should be very close to the value of Pi (3.14159...) once you have entered all of your measurements. If this is not the case, you may have made your rulers incorrectly or you may not have read the correct measurement value from the ruler. Double check your work. If there is error this week that doesn't get corrected, there will still be error next week since you will be using the same measurements again.

The sheet below is a preview only. You will be able to find your assignment to work on in your Google Classroom.

### Week 2: February 8th - February 11th

#### Individual Graphing Assignment

Last week, when you input your measurement data into Google Sheets, a graph was automatically created for you. This week you will be responsible for making your own graphs. Before you begin, take 5 minutes to watch the "Graphing with Google Sheets" video below. In your graphs, you will be required to include all of the graphical elements that are mentioned in the video.

Video $$\PageIndex{1}$$: Tutorial on using Google sheets for linear graphs created by Bob Belford (https://youtu.be/muF0eJkN9CQ)

After watching the video, you can open the assignment in your Google Classroom called Individual Graphing Assignment. For this assignment, you will be combining the Week 1 measurement data from yourself and each of your group members, and then creating four graphs.

• Graph 1: Use all group members' data from the Fist Scale and include the origin point (0,0)
• Graph 2: Use all group members' data from the Fist Scale and do not include the origin point (0,0)
• Graph 3: Use all group members' data from the deciFist Scale and include the origin point (0,0)
• Graph 4: Use all group members' data from the deciFist Scale and do not include the origin point (0,0)

The sheet below is a preview only. You will be able to find your assignment to work on in Google Classroom.

#### Individual Lab Report

After you finish your individual graphs, you will be asked to complete the Individual Lab Report. This assignment is an individual assignment to be completed on your own during lab. It will be due at the end of your lab period. You can discuss questions with your group members, but all work must be your own, including the images of your supplies and rulers.

For some problems, you will be asked to show your work. You should keep track of your work on a piece of paper and label with the question number it belongs to. There will be a box at the end of the document for you to insert an image of your work. Do not insert the image under each individual question.

The document below is a preview only. You will be able to find your assignment to work on in your Google Classroom.

## Post-Lab Problem Set

After you have had a chance to work on data analysis with your group during lab, you will be given the Measurements Post-Lab Problem Set. This is an individual assignment that must be completed on your own, and it is based on your Pre-Lab Primer and your In-Lab Assignments. This assignment will be due the day after your lab meets by 5 p.m. For example, if your lab is on Monday, the Post-Lab Problem Set will be due on Tuesday at 5 p.m. No late work is accepted.

The document below is a preview only. You will be able to find your assignment to work on in your Google Classroom.