# Dimensional Analysis

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## Objective

Students will be able to perform basic dimensional analysis problems, including the use of metric prefixes, by taking notes, solving practice problems, and engaging in a lab activity.

#### Big Idea

Dimensional analysis is a great tool for solving problems and converting units in chemistry.

## Introduction

This lesson gives students the opportunity to learn how to perform unit conversions using dimensional analysis as a structured technique.  Dimensional analysis problems can become very complicated so for this unit I stick to simple problems.  I use only 1, 2, or 3 step problems, where they are only changing the unit on the numerator of a ratio.  When I teach Dimensional Analysis in later units I bring in more complicated problems.

Most of my students have already learned how to convert between units in math class using multiplication, but they are not familiar with using dimensional analysis.  Therefore it is important to have students realize that this is a new technique.  This is especially important to stress with higher-level students who can mentally solve the simpler problems, but who will use this technique for more complicated problems, especially with Stoichiometry later in the year.

This lesson aligns with NGSS Science Practice 5: "Using Mathematics and Computational Thinking" because students are learning how to apply the mathematical process of unit conversions to scientific questions.

This lesson also involves NGSS Crosscutting Concept 3: "Scale, Proportion, and Quantity" because students are understanding how multiple units can be used to express the same quantity, and how proportional relationships can be used to understand how quantities are related.

For the lab activity for each group needs 1 meter stick, 4 tootsie rolls, and a stopwatch.

## Engage

10 minutes

The first section of this lesson encourages students to realize how substances can be measured with multiple units.  Students begin with a quick 5 minute activity at their tables where they find the length of a pencil in both centimeters and millimeters and then read the volume of a water or soda bottle in both milliliters and ounces.

After all students have recorded their measurements in their notes I point out to the class that although the pencil length and water bottle volume did not change, that they were able to record the values in more than one unit.

I then ask my students, "Do you need to always remeasure an object if you want to record a new unit value?" I give them a few seconds to think and then ask for volunteers to answer the question.  Some students respond yes, others say that you can use math.  I tell them that there are ways to do this using math that we will discuss today.

I find that doing this activity helps students get into the mindset of why dimensional analysis is an important technique.

## Explain

30 minutes

In this section I lead students in notes concerning dimensional analysis while they fill in their notes and I present the PowerPoint.

While teaching students the steps of dimensional analysis I encourage students to use the method of underlining what they know, circling what they want, determining the equivalence statements, and then plugging in with dimensional analysis. I refer back to the previous lesson (Unit 1 lesson 5: Temperature) where I taught them the plug and chug technique.

Also, I tell students that they, "Need to try this my way for now, even if they feel that they can do these problems in their heads, because the problems will get more complicated later".

While students are doing the notes and practice questions I make sure that they are using their calculators and setting up the DA problems by walking around the classroom.

I also have students watch a Dimensional Analysis video at the end of the notes to see a real-world example of dimensional analysis and to give them a quick break before moving on to example questions.

## Elaborate part I

20 minutes

In this next section of the lesson I have students perform four practice dimensional analysis problems with partners through partner appointments (see reflection on partner appointments for more details).

The questions are on the PowerPoint, and a place for students to write their appointments, the problems, and answers is on the back of their notes

All of these questions are ones that are not very complicated, but give students an opportunity to practice what they have learned.  I encourage students to show all of their work and work with their partners.  This picture shows student work with the partner practice examples.

## Elaborate part II

30 minutes

As another way to reinforce dimensional analysis I have students perform a Dimensional Analysis lab.  In this lab students perform three different activities (jump, walk 10m, and eat a tootsie) and then perform some calculations using the data they gathered.

I have students continue to work with their table groups for this activity so that they can get comfortable with the same group of students.  Materials necessary for the lab include meter sticks, tootsie rolls, a stopwatch, and a marked 10m area for students to walk.  Being in San Diego with outdoor space right outside my classroom I mark 10m in front of my classroom using two chalk lines.

The lab is a little bit tricky with the calculations, but it is a nice opportunity for students to get up and move by jumping, walking, and eating tootsie rolls.  I encourage students to help their partners, and to all participate in the lab.  Because there are three major activities, I tell them that within their group they should rotate who is doing each activity so that one person isn't always the one moving.  Also before the lab I remind them that all members should be plugging into the equations on their own, and then checking their answers with each other.

Because the equations can get quite complicated, I scaffold the problems for my students by setting up the calculations as you can see on the lab paper.  However, if I have a more advanced class I will take out the calculation outline portion and have students try to set them up on their own, and then will walk around and help out when and where needed.

## Evaluate

20 minutes

The evaluation component of this lesson is two different worksheets.

• The first Medical Chemistry Worksheet has a medical focus with dosage and pharmaceutical calculations.  I adapted the medical worksheet from HASPI's medical chemistry resource website which has some great resources for showing how chemistry relates to medicine.  I have students do these in class as individual/guided practice where I have them start the problems, and then help them as they go. This is the answer key.

For both of these worksheets the most common errors by students is not correctly setting up the DA problems.  This includes student who can do the problems in their heads so don't see the point of DA as well as those who mix up the conversion factors so end up dividing instead of multiplying or visa versa.