1. Investigation 1D
Dimensional Analysis

2. ? If someone said you were 3 meters tall, how would you respond?
Do you know what 3 meters (m) really is?
You probably know 3 feet (ft) is small for a grown human. So how many feet are equal to 3 meters? ?
By the end of this investigations students will be able to answer these questions. It is okay if they do not know the answers at this time.
Investigation 1D: Dimensional Analysis

3. How do we translate between units?
Much of the world measures in kilograms, kilometers, meters, and centimeters instead of pounds, miles, feet, and inches.
How do we translate between units?
You know that 1 min corresponds to 60 seconds. What are other conversion factors and how do we use them?
Investigation 1D: Dimensional Analysis

4. Grab one card and flip it over. How is each side different?
Part 1: How it works
Spread out your unit conversion cards so you can see their values.
Grab one card and flip it over. How is each side different?
Investigation 1D: Dimensional Analysis

5. Part 1: How it works
Spread out your unit conversion cards so you can see their values.
60 min = 1 hour
Investigation 1D: Dimensional Analysis

6. Part 1: How it works
You can arrange the cards to solve any conversion problem. For example, convert 2 hours to seconds:
Multiplying something by 1 gives you that same something in the end!
Investigation 1D: Dimensional Analysis

7. Part 1: How it works
You can arrange the cards to solve any conversion problem. For example, convert 2 hours to seconds:
Notice how units cancel out
What is the only unit left? Is it above or below the fraction line?
Investigation 1D: Dimensional Analysis

8. Part 1: How it works
You can arrange the cards to solve any conversion problem. For example, convert 2 hours to seconds:
Investigation 1D: Dimensional Analysis

9. Part 2: Unit conversions to solve
How many milligrams (mg) are in 24 grams (g)?
How many centimeters (cm) are in 10 inches (in)?
Convert 45 inches to centimeters.
Which gas is more expensive: $3.95/gallon or $1.25/liter (L)?
Convert 23 miles to inches.
How many milliliters (mL) are in 1 gallon?
Investigation 1D: Dimensional Analysis

10. Part 2: Unit conversions to solve
Which is longer: 100 meters (m) or 1 mile? Convert miles to meters to find out.
How many feet per second is 30 miles per hour?
Which is more: 1 liters/second (L/s) or 10 gallons/minute?
A construction project calls for 250 kg of cement. Your cement supplier sells 60 lbs bags. How many bags do you need?
A doctor tells a patient to take 30 mL of a medicine. How many tablespoons of the medicine should the patient take? One tablespoon contains 15 mL.
Investigation 1D: Dimensional Analysis

11. Part 3: Area and volume conversions
When a conversion uses the same unit more than once, such as in area and volume, the conversion factor needs to be applied more than once.
For example, a volume of 2 cubic meters really has units of m x m x m. This is denoted as m3 (meter cubed). That means any length conversion needs to be applied three times.
each length unit is applied 3 times
Investigation 1D: Dimensional Analysis

12. Part 3: Area and volume conversions
Example: How many cubic centimeters are in one cubic inch?
Investigation 1D: Dimensional Analysis

13. each length conversion is applied 3 times
Part 3: Area and volume conversions
Example: How many cubic centimeters are in one cubic inch?
each length conversion is applied 3 times
Investigation 1D: Dimensional Analysis

14. Part 3: Area and volume conversions
Example: How many cubic centimeters are in one cubic inch?
Make sure that units are cancelled out correctly.
Investigation 1D: Dimensional Analysis

15. Part 3: Area and volume conversions
How many cubic centimeters are in 1 m3? This is the same as the number of milliliters in 1 m3.
How many milliliters are in 1 ft3?
How many cubic inches are in 1 ft3?
One liter is the volume of a cube that is 10 cm on each side. How many milliliters are in 1 L?
The displacement of a car engine is measured in cubic inches or in liters. The engine displacement is the volume of space that the pistons of the engine move in one complete rotating cycle. Which is a larger engine: one with a displacement of 4.3 L or one with a displacement of 250 in3?
Investigation 1D: Dimensional Analysis

16. Part 4: Other conversions
An experiment is performed in a container that has a pressure of 25 psi. How many atmospheres (atm) is this pressure?
A submarine can withstand a maximum pressure of 20 atm. How many pascals (Pa) is that?
A car is capable of producing 150 horsepower (hp). How many watts (W) does that correspond to?
An electrical generator can produce 1.5 hp. How many 100 W light bulbs can this generator supply?
Investigation 1D: Dimensional Analysis

17. ? If someone said you were 3 meters tall, how would you respond?
Do you know what 3 meters (m) really is?
You probably know 3 feet (ft) is small for a grown human. So how many feet are equal to 3 meters? ?
Investigation 1D: Dimensional Analysis