# From Another Dimension

## Intro to Dimensional Analysis

K20 Center, Allison Shannon | Published: May 26th, 2022 by K20 Center

• Subject Mathematics
• Course Middle School Mathematics
• Time Frame 2-3 class period(s)
• Duration 135 minutes

### Summary

Students will be introduced to dimensional analysis by analyzing a veterinary lab result, focusing mainly on the metric dimensions of a tumor. Students use prior understanding of units to match a set of metric data to the English equivalents. Students will then determine the conversion factor that is needed to convert centimeters to inches. Lastly, students will read and analyze articles to determine the importance of the knowledge and use of dimensional analysis in the real world.

### Essential Question(s)

How does dimensional analysis aid scientists in translating data, uniting their data into one unit, and resolving issues of measurement beyond the classroom?

### Snapshot

Engage

Student teams are given a lab report detailing a tumor in Aunt Bessie's dog, Fluffy Mae. The students must describe the size of the tumor for Aunt Bessie using the given dimensions.

Explore

Students sort and match metric measurements to their English counterparts. Student teams use the correctly sorted and matched cards to determine the relationship between centimeters and inches.

Explain

Student teams discuss the relationship between centimeters and inches with the entire class and are then led through teacher-guided questioning related to dimensional analysis. Student teams discuss and share their answers with the group.

Extend

Student teams pair with other teams and read selected articles that detail the importance of making conversions in the real world. Students construct a presentation about what they have read.

Evaluate

As an exit ticket, students answer four questions related to the lesson. As further evaluation, students take home a writing activity that is an extension of the beginning engagement activity.

### Materials

• Lesson Slides (attached)

• Fluffy Mae's Lab Report (attached; one per student)

• Sort Cards (attached; one set per student pair)

• "From the Desk of" notecards (attached; optional; one per student)

• Student calculators

• Sticky notes

• Butcher paper

• Tape

### Engage

Introduce the essential question and lesson objectives using slides 3-4 of the attached Lesson Slides.

Place the students in pairs for the Think-Pair-Share strategy.

On the board, project slide 5 of the attached Lesson Slides–the photo of the lady and her dog–to pique the students' curiosity as they enter the classroom. Hand each student a copy of the attached "Fluffy Mae's Lab Report."

Set up the following scenario:

Your Aunt Bessie has just received a report from the vet that her beloved dog of 20 years, Fluffy Mae, has a tumor on her liver. Your poor Aunt Bessie has many questions. In particular, she wants to know about the size of tumor, but she isn't familiar with centimeters. With your partner, discuss how you should describe the size of Fluffy's tumor to your aunt and make notes.

Give the student pairs about five minutes to discuss and write down how to describe the size of Fluffy Mae's tumor. The pairs should then share out what they wrote. Mention that most lab report measurements are given in metric units, such as centimeters or millimeters. Students may want to share information from reports of their own, or from reports they've seen.

### Explore

Prior to the lesson, the attached Card Sort should be printed, cut apart, and placed in envelopes to provide one set to each pair of students. Do not give away the direct correlation between centimeters and inches. Instead, each pair of students should be given an envelope of cards and complete a Card Sort activity. Display slide 6 and have students match the metric measurement cards with their English counterparts. Give student pairs only about two minutes to complete the activity. Walk around the room to assess progress.

Student pairs should then study the measurement values on the cards in centimeters and compare them to the values in inches. Using the Create the Problem strategy, student pairs must devise a method to convert centimeters to inches. After a few minutes, the student pairs should team with other pairs to form quads. Give the newly-formed quads another few minutes to work together and share their methods of converting from centimeters to inches.

### Explain

Next, give each quad a large piece of paper and tape. The students in each quad should decide how to create visual that shows the method devised to convert centimeters to inches. Display slide 7. When the teams are finished, have them tape their visuals on the wall. Using a teacher-led version of the Gallery Walk, move from one visual to another and call on teams to share the reasoning behind the methods of conversion they devised.

Keep the quads together and display slide 8. Explain to students that converting from inches to centimeters is a common problem and that metric measurements are used in medicine. Student teams should jot down notes as they discuss other examples of units that can be converted. The teams should discuss what information is needed in order to convert units from one system into units from another system, and record the answers on paper.

At this point in the lesson, introduce and explain the term dimensional analysis and connect it to the previous activities. Then, each team should compose a list of the conversions that will be used for the course. As a class, narrow down the list.

Give teams a few minutes to share out the information they identified as necessary to know in order to convert units from one system to another. Then, lead a class discussion about the topic.

### Extend

Give each team a copy of one of the hyperlinked articles found below and display slide 9. For larger classes, some teams may need to work with the same article.

Have the teams read and discuss the articles, making note of key points. The teams should then prepare Two Minute Documentaries for the class, highlighting the key ideas of the text. Allow students the freedom to decide how to do this. As the documentaries are presented, students should take notes on the highlights and they will be used for the final portion of this lesson.

### Evaluate

Display slide 10 to introduce the essential and final question: "How does dimensional analysis aid scientists in translating data, give them the ability to unite their data into one unit, and resolve issues of measurement beyond the classroom?" Students should use the Two-Minute Paper strategy to reflect on the documentaries from earlier in the lesson in order to answer the essential question.