In this activity, students will practice dimensional analysis using pre-made conversion factors on notecards to demonstrate the importance of canceling units to solve problems.
Middle School or High School
This activity will help prepare your students to meet the performance expectations in the following standards:
- Scientific and Engineering Practices:
- Using Mathematics and Computational Thinking
By the end of this activity, students should be able to
- Accurately model dimensional analysis problems.
- Solve problems requiring conversion factors.
- Distinguish between units used for mass, time, volume, and length.
- Describe what a conversion factor is and be able to explain that the two values of a conversion factor are equal to each other.
This activity supports students’ understanding of
- Dimensional Analysis
Teacher Preparation: 30 minutes (initially), 5 minutes (reuse after initial use)
Lesson: 50 minutes
- 1 Notecard set containing conversion factors and initial values for each person or group
- Notecards can be 3x5 or 4x6 (activity works best if the notecards are all the same size)
- Dimensional analysis worksheet
- No specific safety precautions need to be observed for this activity.
- The following initial values and conversion factors need to be written on notecards the first time you perform this activity for each person or group. If you are short on time, students could create the notecards.
- Each row represents a different notecard.
- A picture is provided to show the proper format for creating the notecards.
|Front Side of Notecard||Back Side of Notecard|
|2.4 cm||“leave blank”|
|10 inches||“leave blank”|
|2,500 min||“leave blank”|
|210 g/mL||“leave blank”|
|14 yd||“leave blank”|
|12 m/s||“leave blank”|
|84 yr||“leave blank”|
|268,000 mL||“leave blank”|
|9,000 cL||“leave blank”|
|15 kg||“leave blank”|
|1 day/ 24 hr||24 hr / 1 day|
|365 days/ 1 year||1 year/ 365 days|
|1 hr/ 60 min||60 min/ 1 hr|
|1000 m/ 1 km||1 km / 1000 m|
|1 m/ 100 cm||100 cm/ 1 m|
|1 in/ 2.54cm||2.54cm/ 1 in|
|1000 mL/ 1 L||1 L/1000 mL|
|1000 L / 1 kL||1 kL / 1000 L|
|1 L/ 100 cL||100 cL/ 1 L|
|1 g/ 100 cg||100 cg / 1 g|
|1000 g /1 kg||1 kg/ 1000 g|
|1 foot/ 12 inches||12 inches/ 1 foot|
|1000 mg/ 1g||1g/ 1000 mg|
|1 mL/ 1 cm3||1 cm3/ 1 mL|
|60 s/ 1 min||1 min/ 60 s|
|3 feet/ 1 yd||1 yd/ 3 feet|
|1 m/ 1000 mm||1000 mm/ 1 m|
- Teacher should do introductory lesson about dimensional analysis prior to the activity so that the students are familiar with the concept. This activity works best as a reinforcement or practice of what the teacher has already taught.
- Depending on the size of the class, this activity works best for students working independently (if class size is less than 15) or in pairs if class is larger.
- Students should set up the cards and make you sign off on their accuracy before disassembling. This allows the teacher to help clarify misconceptions and mistakes so that students learn the pattern.
- Make sure students are working on small desks or lab tables, students will need some space to setup their work.
- Students can setup more than one problem at a time if you get behind on checking their setups.
- Additional problems can be assigned as needed.
- Advanced students are challenged to create their own problems once they have finished the required problems of the assignment.
- An Answer Key has been included for teacher reference.
For the Student
Dimensional Analysis is a strategy used to solve problems that focuses on the units and measurements involved. Conversion factors are mathematical relationships that allow someone to convert from one unit to another. By using the idea of cancelation, conversion factors can be used to cancel units on opposite sides of a fraction to be able to convert them to a new unit of measurement.
- Obtain a set of conversion factor notecards and the initial values for each problem.
- Place the initial value notecard down on the table.
- Choose a conversion factor that includes that unit and orient the notecard on the side that cancels your initial unit.
- Continue to use additional conversion factors until you have obtained the required unit.
- Calculate the final answer by multiplying all values on the tops of the fractions of your notecard and then divide by each value in the denominators of each fraction.Record this answer on your worksheet.
- Have the teacher sign off on the setup of your notecards on your worksheet before dismantling it. If your teacher is busy, begin setup of the next problem that does not require the notecards already setup in the previous problem.
- Complete all required problems on the worksheet. If you finish these you should them create your own problems. These problems should require at least two separate notecards to solve.
If you finished quickly, now create your own starting values and identify a final value to complete the conversion.
Example question: How old are you in seconds?