Most students, and many of my (now former) colleagues, find stoichiometry to be one of the most challenging topics in a first year (and yes, even a second year) chemistry class. But my students and I have always looked forward to the challenge, and the fun. Certainly, stoichiometry means diligent work, and for some it means frustration. But there is no reason it has to be dire, difficult, or drudgery.

Yes, the new Next Generation Science Standards (NGSS) do not specify stoichiometry. This was a concern of many reviewers. The review committee that considered and responded to the initial comments about the NGSS received numerous comments concerning topics such as stoichiometry, in particular from teachers concerned about students who were planning STEM majors in college. They felt that the existing standards, while not requiring stoichiometry, were sufficient to allow inclusion of stoichiometry in classes where that would be appropriate, stating “In some cases, like stoichiometry, the conceptual understanding for why chemists do stoichiometry was already in the standards. The teams wanted to make the mathematical practice more explicit through the clarification statements, but not have a separate performance expectation requiring that all students do gram to gram calculations.” (NGSS Public Release II, Appendix B – Responses to the May Public Draft, January 2013). Also see the ChemEdX blog post by Dan Meyers from 11 Nov 2014 titled “Next Generation Science Standards (NGSS)” at http://www.jce.divched.org/article/next-generation-science-standards-ngss (accessed 15 Nov 2014).

I had vacillated over the years between using an algorithmic method, and an inquiry-based approach to teaching stoichiometry. After six years trying both methods in alternating years, I decided my students got more out of the algorithmic approach, and that in the process they learned several lessons that made the rest of their chemistry work easier. The five steps my students learned are in no way unique, but the setting that we use is fun, memorable, confidence-building, and very much appreciated.

Benefits of the Algorithmic Approach to Stoichiometry

I did not use algorithms in any other topic. As much as possible, I preferred to introduce topics using inquiry-based methods – or at least I tried to get as close as possible whenever I could. That is not always straightforward when teaching a topic inherently bound to mathematical calculations. But in the case of stoichiometry, I felt the benefits of teaching an algorithm were well worth the practice (pun intended). Before I reveal the essence of what I did, let me describe the beneficial side effects:

1. Students learned to follow directions. This lesson is especially important as it enhances laboratory safety practices.

2. Students learned to organize their work and present it in a readable, sensible fashion. Not only does it make it easier for the teacher to follow student work and simplify grading free-response tests and quizzes, but it is a great boon to students in AP and IB classes that have high-stakes exams with extensive free-response sections.

3. Students learned to clearly identify measures that are made in the laboratory or given in a word problem and assess what those measures mean.

4. Students agreed with the importance of understanding what quantity they were to find before beginning mathematical work. “Experts” in problem solving will recognize the importance of items 3 and 4.

5. As the practice of stoichiometry problems was extended to make use of percent composition data and limiting reactant problems, students learned the importance of understanding a problem and dividing it into manageable sub-problems. They felt comfortable that they would know what to do with the stoichiometry part of a question. Once they grasped the available information, they felt more comfortable in setting the stoichiometry aside while they worked on some other aspect of the information that would allow them to either find moles of the “given” substance or the required measure of the “unknown” substance.

Because of these five important benefits, I always placed stoichiometry (and therefore study of the mole, and making unit conversions involving this quantity) relatively early in the class. In general, I normally began stoichiometry immediately after the (US) Thanksgiving break (that is, just before December 1). I know many teachers who place it much later, some who are willing to wait until either just before, or even just after the California state mandated testing. My students were convinced that working on stoichiometry early not only helped them with the rest of their chemistry, but they felt more confident on state tests. As I have been retired for more than two years, I no longer have access to the exact state testing data from my high school or district, so I cannot present verified data for my assertion, but here is my assertion – students in my classes consistently outperformed the rest of the high school, and the other six schools in our district on all the mathematically-based portions of the California Standards Test in Chemistry (CST-Chemistry).

The CST-Chemistry is the state mandated exam based on the California State Chemistry Framework adopted in 2004 (which will soon be superceded by a revised framework based on the Next Generation Science Standards). This exam was used in calculating a school’s “annual yearly progress” (AYP) which is a measure of whether a school is improving its academic standing. Schools are expected to meet an AYP goal. Failure to advance over several years means state sanctions. Therefore, the exam becomes a very high-stakes indicator for both schools and districts.

For details on research into teaching stoichiometry and access to a host of other references on the topic, see these two articles from a recent issue of the *Journal of Chemical Education:*

Gulacar, Ozcan; Eilks, Ingo; Bowman, Charles R. Differences in General Cognitive Abilities and Domain-Specific Skills of Higher- and Lower-Achieving Students in Stoichiometry. *J. Chem. Educ.* July, 2014 (Vol. 91, No. 7) pp 961–968.

Tang, Hui; Kirk, John; Pienta, Norbert. Investigating the Effect of Complexity Factors in Stoichiometry Problems Using Logistic Regression and Eye Tracking. *J. Chem. Educ.* July, 2014 (Vol. 91, No. 7) pp 969– 975.

Students responded very positively to the stoichiometry lessons. They became confident that they could manage anything in chemistry – particularly since students in other teachers’ classes dreaded having to do these calculations. Years later students returned to say how much they enjoyed class, and how pleased they were to find that they really could do all of the work in chemistry. The “secret” of the method is *“Stoichiometry is Easy,”* a song that recites a five-step algorithm for stoichiometry, and is sung to the tune of Felix Mendelssohn’s *“Hark! The Herald Angels Sing.”* My classes frequently went “chemistry caroling” to the other chemistry classes. They had a “carol” to sing to the German classes and administration when those groups came caroling to my room. Last year, several of my former students showed up at the house while we were hosting a Christmas party for 30 friends and neighbors to sing Christmas carols – they started with *“Stoichiometry is Easy.”* Our guests still talk about how much fun it was for them to hear and see the dedication shown by the students, and see the impact my class had made.

Students have fun singing a chemistry song to what they have learned as a Christmas tune. The silliness of it makes the song so memorable. For this reason, college students frequently return, or email, and ask for the lyrics to share with their college friends – some just for fun, but others because they are tutoring students who have fallen behind. When I have taken long-term substitute jobs for friends, and had stoichiometry in the lesson plans, I used the song at these other high schools with great success in the classes, and with positive reviews from students. When I return to those schools to substitute for other teachers I am almost always asked to lead the chemistry students in singing *“Stoichiometry is Easy,”* again. Students have often asked for the lyrics to share with their friends at other high schools who are having trouble with stoichiometry. It is fun to see students excited about learning something that their friends think of as drudgery.

Using Guided Instructional Activities

I learned to use Guided Instructional Activities (GIAs) as part of the “Mastering Chemistry on the Web” (MCWeb) program, a part of the National Science Foundation Molecular Science Project (http://www.molsci.ucla.edu). Dr. Patrick Wegner (California State University, Fullerton) developed these POGIL-like (Process-Oriented Guided-Inquiry Learning) activities for use in preparatory and general chemistry classes. While some of the activities are true guided inquiry, many are simply cooperative learning activities that give students an opportunity to work toward a common goal while discussing and practicing skills of particular interest.

I divided students randomly into groups of two (which change for each activity). They work at tables of two groups each. Students who have difficulty with an item are to consult their partner, then the other group at their table, and then may ask me. I did not allow students to move from group to group. I circulated around the class making sure each group was on task, and revealing the answers a little at a time so students could confirm they were correctly doing what they were asked to do. This put students in charge of their own learning, gave some the opportunity to “teach” others, and allowed me more time to work with students who needed extra attention during class time in a nonthreatening environment. At the same time, students policed each other to make certain everyone (OK, nearly everyone) was on task.

GIA files referred to in this article are linked in association with the “Main Topics Before Stoichiometry” and “Stoichiometry Lesson Plan” as they are discussed.

Main Topics Before Stoichiometry

Matter

Elements, Compounds, Atoms, and Ions – Strong emphasis on the particulate nature of matter with many sessions illustrating various species on the white board or using 3-D computer animation. Students draw and criticize their conceptions, evaluate and criticize conceptualizations I present (and the quality of my drawings), and make and manipulate models to emphasize the concepts.

Naming Chemical Compounds – includes memorizing common ions and writing compound formulas.

Uncertainty and Measurement in Chemistry – Quantities and Units. We devote an entire day to learning that chemists write measures with numeral, unit, and substance identity [GIA: Writing Conversion Factors].

The Mole and Calculations with Measurements – strong emphasis on the concept of conversion factors; writing them correctly with numeral, units, and substance identity; and both factor-label (dimensional analysis) methods of doing unit conversions and proportional reasoning. Student practice GIA: Finding and Writing Molar Mass, then they do a GIA on Mole Conversions using a blank Mole Conversion Format that requires them to include units and identity. There are additional practice items, both One- and Two-step Conversions using the Framework, and Additional Problems for which I allow students to use blank Mole Conversion Format (link above) if they choose, or to write the problems on their own paper (as formats are not included on quizzes or exams).

Balancing Equations – we spend time describing the meaning of a chemical equation, modeling the particulate nature of what is going on, relate that to lab experiences, and learn several Types of Reactions. I spend particular time discussing the fact that a chemical reaction is like a recipe: it can be scaled up or down, but must remain in proportion, that the reactants are like the list of ingredients, and the products are like the statement of how many people will be served by the recipe. Students recognize that there are directions for doing the mixing of a recipe that they will learn later (kinetics).

Stoichiometry Lesson Plan

Day 1 – Socratic lecture: relation of chemical equation coefficients to number of moles, how a change in one coefficient must affect the values of others. Do an example of a question based on a chemical reaction. Start simply by asking how many moles of reactant there are if given a particular mass of that reactant. Then determine moles of a product formed from that much reactant based on the balanced equation (I usually use a mass that gives a simple, but fractional number of moles such as 0.2, 0.4, etc.). Finally, convert moles of product to mass. Summarize the steps that students used.

The “Recipe” (steps) for Stoichiometry

1. Balance the chemical equation.

2. Identify the given chemical and measure and the unknown (to be found) chemical and measure.

3. Change the measure of the given chemical into moles. (NOTE – later students will get questions where they realize the measure is given in moles, and they learn to “thank” the question author for doing some of the work for them and move on to the next step).

4. Use the balanced chemical equation coefficients to form a ratio with the coefficient of the unknown chemical in the numerator, and the coefficient of the given chemical in the denominator. Multiply the given moles by this ratio to find the moles of unknown chemical.

5. Change the unknown number of moles to the measure that was requested.

(NOTE – again, students will notice that the requested measure is sometimes the number of moles, and they can, in fact must, stop their calculations at that point).

Day 2 – Repeat the steps that students used the previous day, and show how they can be applied to a stoichiometry problem selected from the textbook. Introduce *“**Stoichiometry is Easy**”* *[NOTE: this file format may not cooperate well with the Firebox browser]* and sing with the class (several times, until everyone is comfortable) I usually solo first (something I know not all teachers will feel comfortable doing). Then students are invited (instructed) to join me as I project the words onto the screen (and play a MIDI file with the music). I circulate around the class singing softly to make sure everyone participates; reluctant students are told they may sing a solo instead – most will eventually decide to make an effort, even if they feel they cannot sing. We sing again before each succeeding day’s activity.

Day 3 – Do a “guided instructional activity” (GIA) to practice the steps of stoichiometry using a framework to help organize work – GIA: Stoichiometry 1. GIAs are done in groups of two, each day with a new, randomly assigned partner (see above). All three of the Stoichiometry GIAs are in a single file, and there is a separate file with Answers. The first GIA is done using another framework. This is more complex than the framework for the mole conversions. I use the Stoichiometry Framework, with the Steps already written in for the students with the first GIA. Then students must write the steps for themselves on the remaining GIAs (or use their own blank paper for the third of these activities).

Day 4 – Do a second GIA (GIA: stoichiometry 2) using the Stoichiometry Framework (link on Day 3), but without steps written in the framework.

Day 5 – Introduce varying types of problems and work through examples using whiteboards: mole-mole, mass-mole, mole-mass, and the same with particles and volume, as well as conversions between different units. Students practice additional problems on their own and for homework using frameworks (writing steps into the framework each time). Students may do a third Stoichiometry GIA.

Day 6 – Quiz on Steps of Stoichiometry (memorization of steps, and completion of a stoichiometry problem). This quiz uses the Stoichiometry Framework format (see above) to help encourage students to organize their work, and emphasize that all students are expected to cooperate with each other and use common methods. I assign one point for correctly memorizing step and one for correctly performing the step. Almost all students get at least seven points (five for the steps and two more for identifying the unknown and given and balancing the equation), so even students who have difficulty can show some measure of success. More in-class practice (finish for homework). Reading about percent yield.

Day 7 – Discuss percent yield. Do some cooperative problems on percent yield. Prepare for “Mass of a Reaction Product” lab.

Day 8 – Laboratory exercise: “Mass of a Reaction Product” (a “prescriptive” lab to illustrate the application of stoichiometry in percent yield calculations). Begin calculations for lab report (on scratch paper).

Day 9 – Write lab report – guided by teacher, with careful explanation and modeling of how to present data and calculations in a report based on calculations (crucial for future lab reports involving numeric data). Calculate percent yield. I have students report their percent yield, and then we discuss the reasonable uncertainty of the measurements made and discuss whether the Law of Conservation of Mass seems valid based on class data. This also helps them to understand why significant figures are important.

Day 10 – Stoichiometry relay using whiteboards (teams of five). Each student does a step of the method on their white board. Entire team stands when the last student completes the calculation. They hold their boards next to each other to show the completed problem. Study for lab test on the following day.

Day 11 – Stoichiometry Fireworks Lab Quiz. Students may choose to have randomly assigned groups of two or work with their regular lab partner (the whole class must do the same thing). They mix potassium chlorate and sugar in correct stoichiometric amounts, then the teacher lights the mixture in a fume hood producing purple flames and sparks. There are six different masses of reactant to discourage students using data from another group. Students are given bonus points for finishing first through fifth. Points are deducted from students who have a “big a-a-a-sh-sh-sh-sh-sh-huh.” (This announcement is repeated several times, starting three or four days in advance, to create anticipation, and, of course, for the humorous effect of the similarity in sound between the English work “ash” – which I always pronounce carefully, clearly, and with particular emphasis – and the classroom-inappropriate English term for a person’s posterior side). Reading assignment on limiting reactant.

Day 12 – Discussion and examples of limiting reactant. Point out that the Stoichiometry Lab Test on the previous day is an example of the presence of a limiting reactant. Do some limiting reactant practice problems.

Day 13 – Chapter test review. In class cooperative work on limiting reactant problems.

Day 14 – Stoichiometry Exam. I did not reproduce my exam, which is a combination of free-response and multiple choice items as the questions are copyrighted by the textbook publisher.

As the hyperlinks in the lesson plan above indicate, most of the material that I use is linked to this article. Instructors are welcome to access the items. If you find them useful, I would appreciate comments to let me know what you used and if it was helpful. While I know that most teachers, including myself, like to customize worksheets, labs, etc. for their own classrooms, I have prepared the items in PDF format as the exact formatting on the page is often important (at least to me). Honestly, I cannot produce anything the way I want to see it print using Microsoft Word. I use WordPerfect to get things the way I want them to appear. PDF files seemed the logical alternative so that everyone would be able to access the files.

Lyrics for “Stoichiometry is Easy”

*Tune: “Hark! The Herald Angels Sing,” Felix Mendelssohn*

*Lyrics: David P. Licata, 1996*

Stoichiometry is easy

with the five-step recipe.

(1) Balance chemical equation.

(2) I-D unknown and given.

(3) Change the given into mo-o-o-oles.

(4) Use the-e-quation ratio-o-o-o:

(*Forte*) Put the unknown on the top;

(*Piano*) Bottom the given,

(*Staccato*) But don’t stop.

(5) Change unknown moles in-to the-e-e

Measure the question asked of thee.

A page of lyrics (in several forms) is linked to this article. Also linked is a version of the song with lyrics sung by Mr. Licata and the Cinque Chamber Ensemble (Irvine, CA). All of the missed notes are my responsibility and should not reflect negatively on Cinque. In class I used an instrumental MIDI version of the song from the U-Fonts website, at the following URL: http://www.ufonts.com/midi/h/page5.html. My preferred file was harkherald.mid. Individual teachers may download this file for personal use, or check other files on that page for one in the preferred key. A note on using this tune for something other than Christmas music: Mendelssohn himself once wrote of this music, "It will never do to sacred words." I therefore feel no disgrace has been done to the church or any religious theme by using this setting for teaching chemistry.

Acknowledgments

I would like to thank my son-in-law, Ben Hunter, for arranging time with Cinque Chamber to record this song for ChemEd Xchange. Allison Hunter (my daughter and a former student) and Gale Licata provided refreshments for the rehearsal and recording session.

The GIA assignments were originated by Dr. Patrick Wegner; I have modified some of these, and created the frameworks used with others. And I acknowledge the support of Dr. Barbara Gonzales, both from California State University, Fullerton for her work in leading the MCWeb development and dissemination in cooperation with Dr. Wegner.

Thanks also go to Deanna Cullen, Associate Editor for the precollege section of the *Journal of Chemical Education,* (JCE) and ChemEd X for her helpful review, comments and suggestions in the preparation of this article. And thanks to Jon Holmes, webmaster of ChemEd X and Managing Editor of JCE for his encouragement and his efforts to troubleshooting some of the idiosyncracies of the website and managing file formats.

## Comments 2

## Conceptual Chemistry to Introduce Stoichiometry

Larry Dukerich writes a very nice blog on ChemEd X. In a recent post he made some important comments about the need for conceptual understanding of chemistry in addition to merely success with the mathematics. He included some details about how he introduces stoichiometry with examples. I did not give these details, as I felt my article was more than long enough, as it was. I wanted to get the labs and worksheets into ChemEd X along with the essentials of my lesson plans and activities. So I did leave out the specific details of the lessons that preceede stoichiometry, particularly the balancing equations sessions. I also omitted details on the first couple days of stoichiometry during which my students spend quite a bit of time modeling and drawing chemical reactions to show what is happening to the atoms and molecules, so that they develop a conceptual understanding of the point of stoichiometry before we tackle the mathematics.

I encourage you to read Larry's blog post at http://www.jce.divched.org/blog/conceptual-chemistry. His ideas are important and very useful.

Thank you Larry!

## Great lesson, but add some conceptual work too!

I found this article about a year ago and it's part of the reason I subscribed to the JCE. I have struggled teaching stoichiometry for years, and needed a new way. I used most of the lesson as written, and it works pretty well. I'm sure with a little practice I would even see results like Larry reports (students excited about stoichiometry, and asking for the lyrics years later) but I did see some fairly good assessment results in the Pre-AP class where I attempted it. It has a great mix of the algorithmic approach, with Guided Instruction and a few labs to support. Kids really loved the fireworks lab assessment (limiting reactant)

I also see the point of later posts about a conceptual approach to stoichiometry. One main push I have noticed in the past few years in chemical instruction is the 3 levels of representation. I agree that students have alot of trouble moving between the three domains (symbolic, macro, and nano) and the better they get, the better able they are to follow not only me , but the text, the labs, and their scores improve too.

Long story short, Algorithms are great for teaching a topic like stoichiometry, and I'll continue to use a version of this lesson, but I will be adding a conceptual approach (ICE charts, particulate views) to deepen the understanding, once the basics are mastered. I'm excited to see if I get further improvement.

Thanks for he amazing lesson!