Bond with James: Uncertainty in Measurements

Tuesday, August 25, 2015

Uncertainty in Measurements

As promised, I am going to continue with my accuracy and precision lesson. If you missed my last post, you can read about it here.  

I usually will introduce the concept of uncertainty in measurements and significant figures with another small activity / discussion. In the past I created two rulers on large chart paper (similar to the Significant Figures Task Cards illustration shown below). 
Disregard the questions in the graphic. I only use or draw pictures of the rulers. I would not ask anything about sig. figs. at this point since I have not introduced that concept yet.

One ruler at a time, I would allow time for groups to discuss the precision of the instrument and come up with a measurement to share out with the class. I would write on the board the measurement provided by each group. Then I would do the same of the second ruler.  
  I would engage the class in a friendly debate about whether they believed their measurement was right. This is where students would verbally explain to me that the first number in the measurement had to be a one (1) because the object falls in between the one and the two.  I would then ask the groups how they came up with the second number as I noticed some variability between their measurements. Inevitability I would have one to a few students tell me that they guessed the second number.  At this point I would nod my head or say that was an interesting tactic before moving on to the next ruler.

Again, I would give groups time to discuss and provide me with their measurements as before. Students would confidently explain that the first number in the measurement (above) was a one because the object fell between a 1 and a 2.  Then the second number had to be 1.4 because the measurement fell in between 1.4 in. and 1.5 in. Finally, I would hear students debating about the final number. This is where I would talk about significant figures, the known digits plus the one estimated digit, in a reported measurement. 

At this point, I would move to a lab activity that involved several stations containing different instruments.  
Each station had 4 pieces of the same equipment, however, each piece was set at a different measurement.  I originally used food coloring to make it easier to see, however, it became a method to assign each student, in a group of 4, a particular color.  
For example: Student 1 = yellow, Student 2 = red,  Student 3 = blue, and Student 4 = green. Students would only measure the apparatus that contained their food coloring dye.
If there were certain instruments that did not measure liquids, like a triple beam balance, I would use color paper or Post-It notes (I know the Post-It notes in the pictures don't match here because I had run out of the color I needed and was too lazy/cheap to run to the store to get more). ;)
Students would then rotate from station to station measuring the instrument based on their assigned food coloring / Post-It note color. Once all the students were finished, I had them find three or four other students that had the same color assignment as they had in order to gather and compare their measurements. There were times where groups were larger than 4 but I only recommend that if you know your students can work quietly in large groups (this varied from year to year and from class to class).
I represented the true value for the lab activity. At the end of the activity were some reflection questions for the students to answer.  This activity allowed for students to learn to collect data and make measurements with accuracy and precision; as well as begin to learn how to express quantities using appropriate significant figures [Texas standards].
Another reason why I do this activity is because I want all students to have the opportunity to practice using and reading the lab equipment. Therefore, I would also pull this equipment out a few days later and have the students complete a lab practical. It makes it more difficult for them to cheat, especially if I utilize more than four pieces of the same equipment type (e.g. 6-8 graduated cylinders or triple beam balances, etc.). I will admit that the first time I did this it was a lot of prep (mainly because I was just grabbing equipment and didn't have a clear vision for setting it up). It now only takes me roughly 30 minutes to set up, with the burettes and ring stands taking the most time. Clean up is relatively simple as well. 

Sometimes I would leave all the equipment out and write my measurement on the bottom of each Post-It note  (for each instrument).  If students finished early or wanted extra practice prior to the practical, they could go to the lab and practice by checking their measurements against mine (they would lift the Post-It note up to reveal the answers). Students did not receive a grade for this; however, most students would practice because they wanted to do well on the practical. 
Okay...that was a lot and I'm hoping I didn't leave anything out. I think this is a great lab activity to do at the beginning of the year because you can easily identify students that come with/without measuring skills.  Some may be proficient at using all the equipment, some may be proficient using a few, and others may need help using all the pieces.  

I also think this is something you can continually pull out as a warm-up. Yes, I would sometimes use this as a warm-up to at least have students practice until I felt that 90-100% of my students could measure with accuracy and precision - reading to the correct number of significant figures.

As always, I would love to hear if you have any strategies pertaining to these topics that work in your class. 

Thanks for stopping by! 


  1. Love the lab! Going to try it again for the practical.

  2. Wish I would have seen this a week ago. I was sorely disappointed with my 9th grader's test on significant figures and precision/accuracy that they took last Fri. I realized they needed more time to actually practice only a few days too late.