My Relationship with Mole Calculations
When I was first introduced to the mole concept as a student, I remember thinking :
“ Wow… why am I putting myself through this?”
Like most students in my year, I was struggling a bit in Math, and I was feeling a bit overwhelmed with the numbers and the units and everything else that comes with it.
To make matters worse, my chemistry teacher had started things off by stating rather emphatically that “this is a difficult concept, many students struggle through this topic.” (A plus for motivation… really).
To my surprise, I managed to pass chemistry that year, but many of my classmates did not.
Fast forward a few years later, and there I was standing in front of a classroom of hesitant chemistry students and it brought back many, not so fond, memories for me. Because of my own struggles as a student, it was the topic I dreaded teaching the most (as dramatic as that sounds).
Over the years, I have noticed that students who do not fully understand the mole experience difficulties in understanding the subsequent topics, especially, stoichiometry problems since the calculations heavily involve this concept. Some of my students were struggling, especially those (like myself) who were also struggling through math. I needed a different approach.
That's when I decided to use the mole triangles
Why use Mole triangles instead of...
There are many techniques for teaching mole calculations. What works best depends on your students and their needs. The three most popular techniques (that I am aware of) are:
Dimensional analysis
The unitary method
The equations
These techniques are well and good, but what I noticed was that:
Most of my students detested dimensional analysis. They claimed that it is too confusing. To be honest, my 15-year-old brain would have been confused too!
The unitary method is popular with students who are a little more comfortable with numbers, but some students do not like all the steps involved and some have even attested that it requires too much thinking.
For the most part, the majority of students prefer using equations, however, rearranging and manipulating the expression can be problematic for some.
How do the Mole formula triangles work?
The mole triangles are essentially mole equations in a triangle form, but students are not required to rearrange or manipulate the subject of the formula like they would with the equation.
All students do is block off the quantity they wish to find, and the triangle "tells" you what needs to be done in order to solve the problem.
No transposition is necessary.
Here's an example:
How many water molecules are present in 0.5 mol of water?
Students should first recognize that they are trying to find No. of particles. They will then need to block this section off on the triangle.
The great thing about the formula triangles is that they can be layered to calculate more complex questions .
Students should first recognize (maybe with some guidance) that there is no direct conversion between mass and number of particles. So they will require two triangles.
The number of moles expression is common to both of these triangles, and therefore should act as the bridge to get from mass → particles.
Students really love that most calculations using the tringle can be completed in one or two steps.
How to Use these Formula Triangles in your classroom
It is useful to have physical copies of these formula triangles in your classroom available for students to manipulate. Laminate them, or allow students to have their own copies printed out.
I have seen kinesthetic & visual learners actually place these triangles one on top of the other to form the "bridge” between expressions when working on more complex problems.
Color-coding these are also useful, as this helps with memory.
Students have reported "remembering the colors" in exam settings.
Eventually, with enough practice, students tend not to rely on these as much.
There are mole triangles for almost every conversion students will counter in this topic.
Disadvantages of Using this Technique
Some students do not respond well to symbols and they need a written explanation on how to carry out the problem, for these students, formula triangles do not help and oftentimes lead to frustration. I would suggest the unitary method in these cases, although it may require a bit more math.
Just stating equations do not always show that students understand the theory behind the concept. I have found that when students are asked to define the mole they will simply rewrite the equation or even draw the triangle as the definition. The use of formulae becomes ritualistic without much comprehension.
Students forget! This is one of the reasons I personally do not like using equations and why I favored the unitary method as a student and even as a teacher. Put students in a high-stakes environment and the triangles become a jumbled mess in their heads.
Of course, in order to improve students’ problem-solving skills, teachers much first focus on developing students' knowledge base. Without this, students cannot succeed in true problem-solving.
Heavy emphasis should be placed first on conceptual understanding of the mole concept; then maybe the secondary emphasis should be placed on carrying out and completing drills and exercises.
Which method do you use to teach the mole? Have you used the mole triangles? How do your students like them?
