03 Significant Digits and Measurement POGIL-2
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Jefferson Community and Technical College *
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Course
175
Subject
Mathematics
Date
Feb 20, 2024
Type
Pages
5
Uploaded by BaronWildcat3983
03 Significant Digits and Measurement POGIL.docx Page 1 of 5 Significant Digits and Measurement POGIL
What digits are significant when recording a measurement? Transparency Guidelines Purpose: •
We are completing this POGIL exercise to learn parts of Concept Area VII: The Mathematics of Chemistry from Chapter 1. o
We will analyze
and record
a measurement using all significant digits and one uncertain or estimated digit. o
We will determine the number of significant digits that should be recorded in a measurement when given the measuring instrument. •
We will also be practicing many of the various POGIL skills while working in our teams; these are the skills that employers want in their future employees. Task: •
The teams will complete the handout with each team member taking on the appropriate role(s). If an in-person cla
ss at each stopping point, each team’s spokesperson will share the team’s answers for discussion with the class. On-line sections, the manager should use the suggested times to keep the team moving forward. All roles use the stop signs as a place to pause to check in with all teammates to ensure everyone is ready to proceed. •
The teams will complete the handouts observing the models and reading the information given. This will allow students to complete the learning cycle: explore, invent, and apply. •
For students that have never seen this material before, it is expected that there will be some initial frustration and confusion while completing the activity. However, through discussion with teammates, at the end students will have a solid understanding significant figures and how to apply them to measurements. Criteria: •
Teams will know they are on the correct path when they are able to reach consensus about what an answer should be within the available time. Teams may reach out to the instructor as she walks around (or for on-line classes, reach out to the instructor via your favorite method) if unable to reach a consensus so that she can help clear roadblocks. •
A team is successful if they completed the questions within the allotted time, their answers match the answers shared by other teams during the report outs (or for online classes your team reaches consensus), and the team worked well together as defined by their POGIL roles, and the teamwork reflection is completed. And now, the POGIL: Why? Scientists do a lot of measuring. When scientists use an instrument (such as a ruler, graduated cylinder, spectrophotometer or balance) to measure something, it is important to take full advantage of the instrument. However, they can’t cheat and record a better mea
surement than the instrument is capable of. There is an understanding among scientists of the proper way to record valid measurements from any instrument. When you are the scientist, you must record data in this way. When you are reading other scientists’ work, you must assume they recorded their data in this way.
03 Significant Digits and Measurement POGIL.docx Page 2 of 5 Model 1 –
Ruler A 1.
What distances can you be certain of on the ruler in Model 1? 2.
Six students used the ruler in Model 1 to measure the length of a metal strip. Their measurements are shown at the right. Were all of the students able to agree on a single value (1, 2, 3…) for any digit (ones place, tenths place, etc.) in the measurement? If yes, which value and digit did they agree on? 3.
The ruler in Model 1 is not very useful, but a measurement can be estimated. Discuss in your team and record some of your ideas on how each student might have divided up the ruler “by eye” in order to get the measurement that he or she recorded. Model 2 –
Ruler B 4.
The students obtained a better ruler, shown in Model 2. What distances can you be certain of on this ruler? 5.
Were the students able to agree on a single value (1, 2, 3…) for any digit (ones place, tenths place, etc.) in their measurements using the ruler in Model 2? If yes, what value in what digit did they agree on? 6.
What feature of the ruler in Model 2 made it possible for the students to agree on a value in that digit? 7.
There will always be uncertainty in any measurement. This causes variation in measurements even if people are using the same instrument. Compare the variation in the measurements made by the six students using the rulers in Models 1 and 2. Which ruler resulted in greater variation? Explain why that ruler caused more variation. Susan 3 cm Maya 2 cm Jonah 2.5 cm Tony 3.00 cm Emily 3¼ cm Dionne 3.33 cm Susan 3.2 cm Maya 3.1 cm Jonah 3.3 cm Tony 3 cm Emily 3.25 cm Dionne 3.20 cm ~10 minutes
03 Significant Digits and Measurement POGIL.docx Page 3 of 5 Model 3 –
Ruler C 8.
The students obtained an even better ruler, shown above in Model 3. a.
Were the students able to agree on a single value for any of the digits in their measurements using the new ruler? If yes, what value(s) did they agree on in which digits? b.
What feature of the ruler in Model 3 made it possible for the students to agree on the values in those digits? Read This! When humans use measuring instruments, variation is expected. Everyone will estimate differently between marks on the instrument. On the other hand, digits that are certain (based on marks on the instrument) should not vary from person to person. Model 4 –
Valid Measurements 9.
The measurements taken in Models 1
–
3 have been combined in Model 4. The measurements that follow the rules of measurement agreed upon by scientists are in the “Valid Measurements” column. Those that do not follow the rules are in the “Invalid Measurements” col
umn. For each valid measurement shown in Model 4, draw a box around the certain digits (if any) and circle the digits that were estimated (if any). Susan 3.21cm Maya 3.20 cm Jonah 3.22 cm Tony 3.2 cm Emily 3.215 cm Dionne 3.205 cm Valid Invalid Measurements Measurements 3 cm 2.5 cm 2 cm 3.00 cm 3¼ cm 3.33 cm 3.2 cm 3 cm 3.1 cm 3.25 cm 3.3 cm 3.20 cm 3.21 cm 3.2 cm 3.22 cm 3.215 cm 3.20 cm 3.205 cm ~10 minutes
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03 Significant Digits and Measurement POGIL.docx Page 4 of 5 10.
Based on the examples in Model 4, circle the best phrase to complete each sentence below. a.
In a valid measurement, you record (zero, one, two) estimated digit(s). b.
In a valid measurement, the estimated digit is the (first digit, second to last digit, last digit) in the measurement. c.
In a valid measurement, the estimated digit corresponds to (the largest marks, the smallest marks, one tenth of the smallest marks) on the instrument. 11.
Using Ruler B from Model 4, Tony recorded a measurement of 3 cm. Explain why this was an invalid measurement. 12.
Using Ruler B from Model 4, Dionne recorded a measurement of 3.20 cm, which was invalid. But when Maya made the same measurement using Ruler C, it was considered valid. Explain why the zero was acceptable when using Ruler C, but not when using Ruler B. 13.
A student recorded the length of a test tube as 5.0 cm. Which ruler in Model 4 was the student using? Explain. 14.
In Model 4, Ricky recorded his measurement 3.19 cm using Ruler C. His classmates thought he was wrong because his second digit was not “2.” However, Ricky’s recorded measurement is perfectly valid. Explain. Read This! When a measurement is recorded properly, all of the digits that are read directly (certain) and one estimated (uncertain) digit are called significant digits or
significant figures
. The number of allowable significant digits is determined by the marks or gradations of the instrument. Sometimes a “0” is the estimated digit and must be recorded. 15.
Record the length of the wooden splint to the proper number of significant digits. ~10 minutes
03 Significant Digits and Measurement POGIL.docx Page 5 of 5 16.
Record the length of the wooden splint to the proper number of significant digits. Stretch Questions (remember if your brain hurts, you’re getting smarter!)
: 17.
When using an electronic device, such as an electronic balance, the measurement displayed on the screen is assumed to have one estimated digit included. In fact, you’ll often see the estimated digit changing rapidly, because there is fluctuation in the estimate. Explain why it is important to record the zero in the measurement shown to the right.
18.
Consider a 1000-mL graduated cylinder with marks every 100 mL. a.
A student records the volume of liquid in the cylinder as 750 mL. Is this a correct measurement? Explain. b.
Are all of the digits in the described measurement of 750 mL significant? Explain. 19.
A student properly records the length of a block as 120 cm. Draw the markings on the ruler that was used to measure the block. ~8 minutes