Purpose:

This lesson plan may be inserted at any point in the curriculum where measurement is relevant. The anticipatory set could be assigned as homework or covered in a mentor session; the body could be conducted in a mentor session or in a whole-class session.

Goal:

To acquire the skill of using unit conversion tables

Instructor preparation:

Photocopy the two attachments "Introduction to unit conversions," "Some Unit Conversions," and "Unit Conversion Grid" for distribution to each student in the class. Make two copies of the Conversion Cards and cut them out along the lines; if you copy these back-to-back in order, reciprocals will be back-to-back (e.g. 5280 ft/mi is on the back of .000189 mi/ft).

Anticipatory set:

Hand out "Introduction to unit conversions" and "Some Unit Conversions." Either as homework or in a mentor session, ask students to complete the exercises.

Body:

Lay the conversion cards on a table and give students the following instructions:

1. Draw a card from the table.
2. Locate another student who has a card that will make a conversion equation (e.g. I have 5m and you have 3.28 ft/m, so there will be a cancellation). If you cannot find a "fit," draw again.
3. With the person you have met, go to the board and write down the resulting equation (e.g. 5m x 3.28 ft/m = 16.4 ft).
4. Introduce yourself to the person with a "matching" card.
5. When finished, return your card and draw another for another try with a different student.

Follow up with a whole-class discussion, including:

Why does .31 m/ft x 5280 ft/mi x .621 mi/km = 1016 m/km,

when we know there are 1000 m/km?

(Something like this will appear on the board eventually).

Many of these conversion factors are approximations, and multiplication can compound the error. Similarly, error in measurement is compounded when used in computations.

Student assessment:

Hand out the "Unit Conversion Grid" and ask students to fill it in, either as homework or in class.

Project assessment:

Success of this lesson will be demonstrated by correct responses in the grid; a key to the grid is attached.

Whenever someone says "100-meter dash--how many yards is that?" how do you feel? Ugh! I can never remember the conversion factor (which is some ugly decimal) and even if I knew the conversion factor, do I multiply or divide?

Since the United States has not yet adopted the metric system, we are often faced with ugly conversions. (In fact, it was the failure to make a conversion that caused a Mars probe to crash!)

The easy approach: Remember the cancellation process when you multiply fractions?

For example, the easy way to multiply 2/3 x 3/5 is: The easy way to multiply 5 x 3/5 is:

2 x 3 = 2 5 x 3 = 3

3 5 5 1 5 1

Just arrange units so that they cancel out: Since 1 meter is 1.094 yards (No, I didn’t have it memorized!), we’ll think "1.094 yards per meter" or 1.094 yds/m and write:

100 m x 1.094 yards = 109.4 yards

m

More conversion examples:

So taking the reciprocal of the number and the units of .621 mi/km, we have:

A building is 82 ft high, what is its height in meters?

3 ft 1.094 yards

Now you try it! (Use the table on the next page)

1. A beetle that is .25 cm long is __ inches long

1/12 ft/in x 39.4 in/m x 1000 m/km = ft/km

THE METRIC SYSTEM

The metric system is a system of measurement in which all fundamental unit conversions are powers of ten, making conversions within the metric system very easy!

Common Metric Units of Length

Metric Unit Abbreviation Number U.S.

of Meters Equivalent

meter m primary unit 39.4 inches

kilometer km 1000m 0.621 mile

centimeter cm 0.01m 0.394 inch

millimeter mm 0.001m 0.039 inch
 
 

SOME COMMON CONVERSION FACTORS

FOR UNITS OF LENGTH, VOLUME, MASS, AND WEIGHT

Length

1 foot = 12 in 1 in = 2.54 cm 1cm = .39 in 1 meter = 1000 mm

(12 in/ft) (2.54 cm/in) (.39 in/cm) (1000 mm/m)

1 yard = 3 feet 1 m = .025 m 1 m = 1.094 yards 1 meter = 100 cm

1 yard = 36 in 1 ft = .305 m 1 m = 3.28 ft

1 mi = 5280 ft 1 mi = 1.61 km 1 km = .62 mi

Volume

1 pint = 16 oz 1 gal = 3.785 L 1 L = 1.057 quarts 1 L = 1000 cm³

= .2642 gal

1 gal = 4 quarts 1 ft³ = 28.32 L 1 m³ = 1,000,000 cm³ 1 quart = 32 oz 1 oz = 29.6 mL

(fluid ounces)

Mass and Weight

1 ton = 2000 pounds 1 lb = .454 kg 1 kg = 2.205 lb 1 kg = 1000 g

1 lb = 16 oz 1 oz = 28.35 g 1 g = .035 oz 1 g = 1000 mg

= 454 g (ounce as a weight unit)

Fill in the grid, converting the quantity at the top of the column into the units designated in each row. Write "nonsense" where the type of unit does not match; for instance a length cannot be converted into an area or a volume.
 
 
 

	5 inches	2 meters	3 gallons	4 liters
Centimeters	12.7 cm	200 cm	Nonsense	Nonsense
Feet	.417 feet	6.57 feet	Nonsense	Nonsense
Quarts	Nonsense	Nonsense	12 quarts	4.228 quarts
cm3	Nonsense	Nonsense	11,355 cm3	4000 cm3

 
 
 
 
 
 
 

Fill in the grid, converting the quantity at the top of the column into the units designated in each row. Write "nonsense" where the type of unit does not match; for instance a length cannot be converted into an area or a volume.
 
 
 

	5 inches	2 meters	3 gallons	4 liters
Centimeters
Feet
Quarts	Nonsense
cm3

 
 
 
 
 
 
 
 
 
 
 
 
 

ï 32 ft/sec² ï 6 mi²

ï

ï

2 lb ï 3 m³

ï

ï

50 mi/hr ï 12 kg

ï

ï

20 m³/sec ï 10 m/sec

ï

ï10 in ï 5 mi

ï

ï

4 m ï 7 g

ï

ï

10 ft³ ï 10 cm/sec

ï

ï

8 km² ï 15 in/sec

ï

ï1000 mg/g ï .000189

ï mi/ft

ï

35.3 ft³/m^{3 ï}1,000,000

ï cm³/m³

ï

.035 oz/g ï.0027

ï hr/sec

ï .2642

1000cm³/L ïgal/L

ï

ï5280 ft/mi ï .001 g/mg

ï

ï

.000001 ï .028 m³/ft³

cm³/m³ ï

ï

3600 sec/hr ï 28.35 g/oz

ï

ï

3.785 L/gal ï .001 L/cm³

ï

ï.45 kg/lb ï .002 lb/g

ï

ï

2.54 cm/in ï2.6 m²/mi²

ï

ï

3.28 ft/m ï .025 m/in

ï

1,000,000 ï 1.61

m²/km² ï km/mi

ï

ï454 g/lb ï 2.21 lb/kg

ï

ï

38 mi²/km² ï.39 in/cm

ï

ï

39.4 in/m ï .305 m/ft

ï

ï .000001

.62 mi/km ï km²/m²

ï