A Post-Inquiry Activity: A Tiered Significant Figures Lesson

sig figs

Historically, my students report significant figures as one of the most confusing concepts in honors chemistry. My recent blog post described the process of transforming my introduction into an inquiry activity. I’ve also re-worked my practice activities to be more directed to specific student needs, more focused on spending time with small groups, and more dedicated to active learning. Here’s what works for me:

Step One: Students demonstrate current functioning.  

Create a quick, formative assessment to use after students have initially learned the rules of significant figures. Think of only three or four concepts that you’d like to check, and don’t forget that you’ll likely need to get the results together in one night. I chose 1) using estimated digits when making measurements, 2) rounding answers when adding and subtracting, 3) rounding answers when multiplying and dividing. Consider using a Google Form or other online quiz format to reduce class time needed for students and grading time required of you. My students take the quiz on Coursesites, my digital platform of choice. The platform scores the quizzes for me, and I review each student’s answers quickly to form flexible groups. 

  • Sample Question One: Take a close-up picture of a thermometer. Insert the picture in your assessment asking students to record the temperature in ˚C to the appropriate number of significant figures.
  • Sample Question Two: Describe a situation requiring water displacement. Provide a data table showing a student’s recorded values. Ask students to calculate the volume of the object.

Initial volume of water

15.8 mL

Final volume of water and object

19.6 mL

  • Sample Question Three: Describe a density determination in the lab, and provide a data table of recorded values. Ask students to calculate the density of the object.

 

 

Initial volume of water

15.8 mL

Final volume of water and object

19.6 mL

Mass

3.25 g

 

 

 

Step Two: Teacher analyzes formative data to form homogeneous groups.

Build small groups of students (3-4) based upon their answers to the formative assessment. I use a blank class roster, where I record the question number of any mistakes for each student. Then, I create small groups of students who missed the same question(s).

  • Sample Group One: Missed question one, illustrating a misconception in using instruments or estimated digits
  • Sample Group Two: Missed question two, demonstrating an error in addition or subtraction
  • Sample Group Three: Missed question three, demonstrating an error in multiplication or division
  • Sample Group Four: Missed all of the diagnostic questions, demonstrating a need for teacher intervention
  • Sample Group Five: Missed none of the diagnostic questions, illustrating a need for enrichment

Step Three: Teacher addresses individual student misconceptions.

Prepare one open-ended question for each small group that directly addresses possible mistakes on the diagnostic assessment. Create a well-organized answer key to each question, too. The highest functioning group can be asked to perform a calculation that involves multiple functions or converting metric units.

  • Set a timer, and ask students to work for five minutes with their groups to solve the problem on a sheet of butcher paper. Move around observing, but not interrupting, every group.
  • When the timer sounds, distribute the answer key to each group. 
  • Approach the highest functioning group first, correct the mistakes and send the group to the lab activity (see below). Move from group to group, tutor each small group, assign the tiered practice set portions, and send them to the lab area.  (see below.)

Step Four: Students practice skills corrected during tutoring time with the teacher.

Develop a three or four station lab activity that challenges students to make measurements and use the data in several ways. Also, construct a tiered practice problem set providing additional opportunities for students to encounter difficulties.

  • The Lab Activity: Students can only master estimated digits by making measurements. This lab activity should be designed to give students the opportunity to measure and apply calculation and rounding skills.
    • Sample Station One: Measure and record the length of a piece of wood to the appropriate number of significant figures.
    • Sample Station Two: Measure, calculate, and record the volume of a block of wood to the appropriate number of significant figures.
    • Sample Station Three: Measure, calculate, and record the volume of an irregular object to the appropriate number of significant figures.
    • Sample Station Four: Measure, calculate, and record the density of an object to the appropriate number of significant figures.
    • Enrichment for Highest Functioning Group:

                 Station One Enrichment: Convert the length to a) Hm and b) miles.

                 Station Two Enrichment: Convert the volume to dm3.

                 Station Three Enrichment: Convert the volume to ML.

                 Station Four Enrichment: Convert the density to mg/cL.

  • The Tiered Practice Problem Set: Assign specific parts of the activity to each group. Encourage students to notice that you are providing many additional practice problems while only requiring some. Suggest that students should use all of the provided examples to review for the upcoming summative assessment.
    • Part One: Addition and Subtraction of Significant Figures – Assign this section only to students who missed the addition/subtraction diagnostic question.
    • Part Two: Multiplication and Division of Significant Figures – Assign this section only to students who missed the multiplication/division diagnostic question.
    • Part Three: Combination Section – Assign this section to everyone.  Some students will be required to solve more problems than others.  If you are planning to take the tiered practice set as a grade, consider how you will score it. 

By the end of this lesson, I have spoken individually with each student about specific mistakes or misconceptions. My past lessons covered the content, and many students did well. This lesson is different though; I end the day confident that I have met each student’s needs. How do you teach significant figures? I’m always looking for new ideas!