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The Ultimate Step-by-Step Guide to Scaffolding Moles Worksheets Using Dimensional Analysis

Updated: Mar 6

how to scaffold mole calculations using dimensional analysis

Common Challenges in teaching Mole Conversions using Dimensional Analysis

Dimensional analysis the factor label method or the unit factor method is a common method used in science and mathematics to solve problems related to units of measurement and physical quantities.

This method is also quite popular and quite useful in solving mole concept calculations in chemistry. However, students often find the method difficult to apply for a few reasons:

  1. Students have difficulty understanding the question

  2. Students have difficulty choosing the correct conversion factors for the mole calculations

  3. Students often jumble up the numbers and have difficulty setting up the dimensional analysis working

  4. Apprehension with Math

To address these issues, I have adopted a step-by-step method for simplifying mole calculations, which I use when teaching the mole concept and designing my mole worksheets and class activities.

In this post, I discuss how you can easily implement these steps to get your chemistry students comfortable with using dimensional analysis to solve mole problems.

How to Simplify Mole Calculations for High School Students Using Dimensional Analysis

Step1: Ensure that Students Read the Problem and highlight Key Information

Our students do not read the problems they are given, and when they do they sometimes have difficulty pulling out the key information from the problem. This is an issue seen not only in chemistry but in almost every subject.

Whenever I am working through mole problems with my chemistry students I ask them to grab a highlighter or colored pencil and highlight/ underline all the key information in the problem. When students first begin to do this they often do not know what the key information is, especially with more complex and wordy mole problems. It is therefore important to start with very simple problems, even those we deem to be obvious.

Mole Calculations worksheets and solutions

I then review students' responses to ensure that they have identified the key information. No matter how simple the problem is, I always have my students perform this step. In so doing, when we get to the more complex problems, they have already developed the habit.

Step 2: Establish a Conversion Route for the problem

The conversion route is simply the path students will take to solve the mole problems. Oftentimes, students begin working on problems without even thinking about what they are doing, why they are doing what they are doing, and where they are trying to go. By encouraging students to map out a conversion route, students can plan the problem and therefore they will be able to see the bigger picture.

Calculate the amount of substance in 300g of calcium hydroxide
PROBLEM 1: A simple mole problem with one conversion

When working with dimensional analysis I have my students identify the units they are looking to convert.

For example in Problem 1: students are being asked to convert the amount of substance (mole) to mass in grams. I have students write this out as their conversion route, clearly identifying the units.

Mass(g)→ Moles (mol)

As I mentioned, it is important to get students into the habit of planning the problem with straightforward examples first, so that when dealing with more complex problems with multiple conversion factors, they are more comfortable mapping out their conversion route and it becomes almost second nature to them. This can be seen in problem 2 below.

Calculate the mass of 1.2 x 10^23 atoms of calcium
Problem 2: A more complex mole problem

The question deals with calculating the mass of a given number of particles. When a problem like this is first introduced, students may realize (perhaps with a little guidance) that there is no direct route from the number of particles to mass.

I point out that, typically to solve problems the conversion route always ends with the the unit you want to end up with and begins with the unit you are given in the problem.

What you are given → _____________ → what you want in the end

However, since there is no direct conversion from the number of particles to mass, what goes in the middle?

If they have been paying attention, students will realize that the number of moles would be common to both conversions and therefore this would serve as the "bridge" between conversion factors.

Number of particles (atoms) → moles(mol) → mass (g)

Calculate the mass of 1.2 x 10 ^23 atoms of calcium
Using moles to connect the number of particles to the mass of a substance

Step 3: Use the Conversion Route to determine the conversion factor(s) needed for mole conversions

As mentioned, students often have difficulty applying the appropriate conversion factor to the problem. However, once the conversion route has been established ( from step 2) I ask students to use the route to determine the conversion factor (s) needed for the calculations.

For Example:

If the route is mass to moles then the conversion factor used would be 1 mole = molar mass of the substance.

Such is the case with Problem 1.

Converting mass to moles using dimensional analysis
Problem 1: Determining the Conversion Factor

For a more complex problem 2, if the conversion route is No. of particles ( atoms) to moles to mass, then two conversion factors would be needed.

For No. of particles to moles, the conversion factor would be :

1 mol = 6.02 x10²³

For moles to mass, the conversion factor would be:

1 mole = molar mass

mass to particles calculations for moles
Problem 2: Determining the Conversion Factor

Step 4: Set up the Calculations in a Dimensional Analysis Grid

Often students have difficulty setting up the calculations for dimensional analysis correctly. They are confused as to which number is the numerator, and which is the denominator which goes back to math apprehension.

In my experience, using the dimensional analysis grid for mole conversions is a much easier layout for students than using the brackets. By using this method, students can see which number is the numerator, which is the denominator, and what needs to be placed where for units to cancel.

I try to provide a little guidance with the first few problems to support student learning, but before long students catch on.

calculating amount of substance to mass using dimensional analysis
Problem 1: Dimensional Analysis Problem Grid

converting number of particles of calcium to mass  using molar mass and avogadro's number as conversion factors
Problem 2: Dimensional Analysis Problem Grid

Step 4.5 Use Manipulatives to Help Students Practice Arranging the Grid

A great way to get students to practice arranging their dimensional analysis grid correctly is by using manipulatives.

Students can be asked to write down all the key terms from the problem e.g. the number given, and the conversion factor on pieces of paper, and have them arrange these numbers in a dimensional analysis grid such as those seen in the examples above.

I created a digital version of this activity ( Google Slides) for my chemistry students (to save time...and energy) to get them to practice arranging the expressions.

To encourage discussion and thought, I ask students to justify their arrangments to each other. With this added step students are better able to make sense of what they are doing instead of just throwing numbers around and hoping for the best.

Often, students go " Ahhh ... I see" when they can physically move the numbers around and justify their decisions.

The focus here is not on getting the correct answer but on thinking about the problem, what they are given, and how to use the information given to solve it.

A drag and drop Google Slides activity for practicing Mole Calculations
A drag and drop Google Slides activity for practicing Mole Calculations

Step 5: Do the Math

The last step is to plug the information into their calculators to arrive at the correct answer... as chemistry teachers, we know that even after doing everything correctly... students still end up with the incorrect answer.


Our students struggle with simple arithmetic, order of operations, and using their calculators correctly to input numbers written in scientific notation. They do not understand the power of brackets!

Some students will need some extra support. A method that works well is to have the entire problem set up and then simply have struggling students work out the answer.

Mole Calculations Worksheets and Solutions

Based on these steps I have prepared a series of scaffolded moles worksheets that have enabled my chemistry students to reach mastery. If you want your students to stop struggling with these dimensional analysis conversions these step-by-step worksheets are a must.

Each worksheet focuses on different mole conversions such as :

  • Moles to mass and mass to moles conversions using molar mass as the conversion factor

  • Moles to the number of particles and particles to moles using Avogadro's number as a conversion factor.

  • Mixed mole problems provide an additional challenge, such as mass to the number of particles where students will require more than one conversion factor.

You can purchase the set from my teacher's pay teachers store by clicking the link below to learn more.

scaffolded mole calculations worksheets for practicing mole conversions using dimensional analysis

What do you think about this step-by-step mole calculation tutorial? Do you implement a similar strategy in your classroom or is there another method that works well for you? Let me know in the comments.


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