Many of my students enter into this unit lacking the necessary math skills needed to successfully understand the mole. So to start the unit I teach students how to do basic unit conversions before introducing the mole as a counting unit. I find that starting out with basic unit conversions, such as grams to milligrams or hours to days, helps students that struggle with math focus on computations without having to understand the mole. The mole can be a difficult concept for many students, so giving them a chance to practice the necessary math conversions first makes the transition to the mole easier. I typically spend several days letting students work on factor labeling before introducing the mole.
Performance Expectation (PE)/Disciplinary Core Idea (DCI)
This lesson is not directly aligned with HS-PS1-7, the uses of mathematical representations to support the claim that atoms, and therefore mass, are conserved during a chemical reaction; and DCI-PS1.B, the fact that atoms are conserved, together with knowledge of the chemical properties of the elements involved, can be used to describe and predict chemical reactions. However, students will need to perform mathematical computations to understand HS-PS1-7 which will require student to have a basic understanding of scientific notation, unit conversions and factor labeling (or proportions).
Science and Engineering Practices (SP)
HS-PS1-7 is one of the few high school Performance Expectations with the primary focuses on the use of mathematics to explain a concept. Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses using algebraic thinking and analysis. Using computational thinking, students will convert from one unit to another, helping them develop the skills necessary to understanding the mole as counting unit for the atom.
Crosscutting Concept (CCC)
This lesson is not aligned with any Crosscutting concept.
To introduce this unit students answer a bell ringer in a think-pair share (TPS). Students will work in groups of two with the person next to them. After the bell rings I instruct them to take out a sheet of paper and solve the following problem on the board with their partner: how many seconds are in one year? After several minutes of solving, I instruct each group to put their answer on the board and show any work used to solve the problem.
After all groups have their answers on the board, I have a few groups explain their answers. Since students have different ways to solve the problem, I pick a group that got the answer wrong and didn’t show their work, one that got the answer right but didn’t show their work and one that showed their work (incorrectly) and got the answer right. I use these examples to show students that are several ways to solve problems and the importance of showing work to get the right answer. After briefly showing the different ways students solved the problem, I solve the problem on the board to introduce them to the dimensional analysis method of solving problems.
After completing the bell ringer I hand out the factor label packet and work on the first four problems as a class. I got this packet from the internet on Mrs. Crane’s website and modified it slightly to accommodate my class. These four problems show students how to work through a one, two and three step problem and help them see the process of factor labeling that the 1 unit does not always go on the bottom of the ratio, such as in problem 1 (see video).
Prior to starting the problems I introduce the first page and tell the class that the top portion of the page may be used later in the unit, but for the next couple of days the bottom portion (common conversions) will be the only part that will be used. To get them familiar with conversions I start with a simple one, such as 1 ft = 12 in, and show them that the ration (conversion) can be used in a problem as 1 ft/12 in or the other way 12 in/ 1 ft. The best way to help students understand that a ratio can be used either way is to do a couple of sample problems. At this point I will work through problems 1-4 on the second page (see video).
Working through these four problems provide most students with a good foundation to begin work through the rest of the worksheet. If other students need more explanation I will group them together and work through some more problems.
The classroom practice consist of 30 problems, 1-10 on page 4 and 1-20 on page 5. I give them 30 problems because I believe that the repetition will help reinforce the proper procedure that will be used to set up stoichiometry problems later in the unit.
After assigning the 30 problems, I ask if any students need extra help…these students I will put in a group and work with them collectively. The rest of the class will start problems 1-10. While I am working with the group of students, I will stop periodically and present 2 problems at a time on the overhead to allow for the rest of the class to check their work. While I am doing this I instruct the group of students to try the next problem without my help. After showing problems one and two, I go back to help the group and see if they are making progress on the problem I assigned them. I continue this process for the next 10-15 minutes till all students have checked and corrected any mistakes on problems 1-10 (key).
The next problems, 1-20, are to be worked on for the remainder of the period. If students do not complete them they will be homework (student work). I let students know that the remaining 20 problems will be checked in for a grade tomorrow. Twenty-five minutes is enough time for a good portion of students to complete the problems in class, but the students that are still struggling I will continue to work with till the bell rings.
Since there are a wide variety of math abilities in my class, assigning this many problems allows students to work at their own pace, in addition to giving me the opportunity to help students that need help (see reflection on differentiation)
The objective was met during this lesson with over 70% of the students showing mastery of factor labeling. I believe that students benefited from learning how to factor label before learning how to do molar conversions. Students were able to focus strickly on the math process, instead of grappling with two separate skills in one unit. As the unit progressed and students learned about the mole and how to work through molar conversions, they were able to set up problems and focus on the concept of the mole and less on the math.
There was a small percentage of students that would not show work, but overall students showed work and followed my procedures. This benefited students later in the unit during molar conversions and stoichiometry. The only problems that students had difficulty with is working through the 2-step problems, 11-20 (page 3). By the end of the second day, with practice, students were able to do two-step problems.
In the future I would have students work through a series of one-step problems before moving onto two-step problems. This would enable me to monitor student progress more readily and aid students more efficiently.