Dimensional Analysis/Factor Label Method

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SWBAT use dimensional analysis to solve conversion problems using the Factor Label method of problem solving.

Big Idea

Dimensional analysis simplifies the mathematical processes of chemistry.


Given what I have already seen from students working with ratios, the use of dimensional analysis to help students with poor math skills is crucial this year.  To introduce it, I don't deal with chemistry at all, we just start with things that are open to conversions: money and measurements. 

This decision is rooted in something I learned during my online teaching courses: introduce a new technology, or new content, but never both together.  I have expanded this to be "Teach a new strategy, or new content, but never both together" and especially not with something as alien to many of my students as dimensional analysis.  By focusing on the process in conversions they are already familiar with, students can learn the process without sweating the content.

This lesson is a skill builder, and is rooted in two parts of the NGSS.  The Scale, Proportion and Quantity Cross Cutting Concept states at the middle school level that "Scientific relationships can be represented through the use of algebraic expressions and equations."  This leads right into the fifth Science and Engineering Practice: Using mathematics and computational thinking.

Computational thinking is the correct term, because by utilizing units and thinking through the problem, dimensional analysis is an easy process.  However, for students who do not write out their units, or don't understand what the units mean, it is quite daunting.  This skill will be a major part of the rest of the unit, so it is important we get a good start today.

This lesson ended up on another late start day due to extreme wind chills.  We had most of the students present, but it had to run in a 35 minute period instead of 50 minutes.  There are some modifications due to this change.  Instead of requiring all of the practice to be completed, I assigned either the odd or even problems to different classes.

Opener -- Getting Organized

5 minutes

When the period begins, I pass back their molar mass practice from the previous day.  Students did a nice job when the chemical formula didn't defeat them.  I explain the progression to the class: started with molar mass, today we learn the math process that will use it, and then we will put both parts together.

Students are chagrined at having to do more math, but I promise them it is simply multiplying or dividing, depending on the problem.  Furthermore, I tell them the way they set it up will tell them which one to do.

At this point, I pass out the Factor Label handout to the class.

Introducing Dimensional Analysis

10 minutes

I ask students to read the opening paragraph of the Factor Label handout.  I ask students what the key is for this process based on the paragraph.  Students respond with "the units seem important."

We next go over the how to, focusing on writing the units and then being sure the unit in the conversion you want to cancel is diagonal to the starting unit.  I go over the money example as seen in the screencast below.

I remind students how the day before our mass units were g/mol, or the number of grams in one mole.  I explain that we will use that to convert between mass of a chemical and number of moles.  However, today we are staying focused just on how to set up the problems.

We then focus on the generic set up at the bottom as to how to do the problems.  We always put our starting information from the question at the top left, and then let the units guide how we set up the next step.

I have the class turn to the next page so we can look at a couple examples.

Independent Practice

20 minutes

Students turn to the length conversion page.  I explain the layout, that there are two sets of conversion factors on the top right.  The top row begins with one meter and all the smaller units that are equivalent to a meter.  The bottom row begins with one kilometer and goes to the smaller units that are equivalent.

Depending on which problems I am going to have the class do, I select one from the other column.  So if the class will do the evens, we begin on number one.

I have the students follow with me as I did in this screencast to get them started.

We do one more problem together and then I turn them loose to work and practice independently, allowing them to check answers while they work.  I want them all working through the process, but I want them to catch their errors early, and I can't be with 28 students at once, so allowing them to check with each other helps that tremendously.

When they finish the length problems, I check their answers and have them work on the capacity problems.

While students work, I circulate the room.  I am constantly reminding students who are stuck to write down the units and set the starting units diagonal to cancel out.  I remind students of the template on the front page, and the promise that when they write the units they are nearly guaranteed right answers.

Many students fly through these examples.  Those who struggle tend to be those who resist writing down the units on their work.

I tell students we will check them in at the start of the period tomorrow, during their molar mass quiz.  If students have not finished, they take the papers for homework.