## Converting Metric Measurements

### Dale Peterson

#### Description

Converting metric measurements is an essential skill for science students. This lesson offers a formula for helping students learn the process.

#### Objectives

The student solves problems using the conversions of measurement within the metric system.

#### Materials

-One calculator per student (helpful, not required)
-Dry erase board or chalk board

#### Preparations

Ensure overhead projector is working properly
Have several sample problems ready, along with solutions to demonstrate.
Establish a checklist or rubric for measuring the Goal 3 Standards. Critieria may include the following:
Information Managers -
a. Does the student correctly identify what he/she is to solve?
b. Is the student able to suggest other possible scenarios where metric conversions may be necessary?
Numeric Problem Solvers -
a. Does the student correctly use the metric measures table (milli, centi, deci, etc)?
b. Does the student set up the problem solution correctly (labels)?
c. Does the student set up the problem solution correctly (numerically)?
Creative and Critical Thinkers -
a. Does the student correctly solve the mathematical portion of this problem?
b. Can the student suggest possible metric conversion scenarios for mass and volume?

#### Procedures

The students must have basic numeration skills and mastery of converting fractions into decimals to succeed with this lesson.

1. Write on the overhead projector, dry erase board or chalkboard:

1/1000 1/100 1/10 1 10 100 1000

(milli) (centi) (deci) (unit) (deka) (hecto) (kilo)

Unit can be meter, liter, or gram.

Initiating Strategy: Ask the students how many school buses will fit, end to end, on a football field. Allow them to ponder, discuss and suggest a few answers.

Explain that the average metric length of a school bus is one dekameter (10 meters) and a football field plus one of the end zones measures one hectometer (100 meters).

Other examples of metric length include the following:
a) 1/1000 meter = 1 millimeter = the thickness of a dime
b) 1/100 meter = centimeter = the diameter of a new piece of chalk
c) 1/10 meter = decimeter = the length of a new piece of chalk
d) 1 meter = the distance from a door knob to the floor
e) 1000 meters = 0.61 miles

Now challenge the students to determine how many school buses will fit, end to end, in a distance of one kilometer. They should divide 1000 meters by 10 meters.

2. Explain that the metric system is based upon units of ten and the conversion steps they are about to learn with length (meters) works equally well with all metric measurements, including volume and weight (mass).

Ask the students to determine how many pieces of chalk (1/10 meter = decimeter) are necessary to equal the length of one school bus. In other words, convert one dekameter into centimeters.

Solution:
1 dam (dekameter) x 100 dm (decimeters) per dam
1 dam = 100 decimeters or 100 pieces of chalk

3. Remind the students that the prefixes and the accompanying numerical values are the same, regardless if the unit is a gram, liter or meter.

4. Practice determining units of ten between pairs of prefixes found in the table (step 1). [See Attached]

5. Require the students to write down and follow each of the following problem solving steps. [See Attached]:

a. Write down the given (or starting value), with its label
b. Work through the problem using only the labels, ensuring the proper ending label. Students often get confused trying to work numbers and labels simultaneously ... this helps them focus on one thing at a time. As labels are placed in the numerator and the demoninator , students will follow how the labels will cancel each other, leaving only the desired label in the final fraction.

c. Evaluate each fraction (which now has labels), find the numerator and denominator prefixes on the chart provided. Determine how many jumps it takes to go from one to the other.
d. Multiply 10 by itself as many times as there are jumps between the prefixes
e. Place the calculated number in the numerator or denominator, whichever is to the left (or the smaller) of the other
f. Cross multiply and cancel labels wherever they are the same. One must be in the numerator and one must be in the denominator. This should leave the one label being asked for in the problem.
g. Multiply all the numerators
h. Multiply all the denominators
i. Reduce the resulting fraction and convert the fraction into decimal form

6. The teacher should demonstrate a few problems, carefully following (and pointing out) each step. Allow the students to practice some conversion problems, and insist that they carefully follow each step. As the students begin to understand the process, some will be able to provide answers without showing any work. Explain that the problem solving process is at least as important as the answer.

7. Closing step: Enable the students to discover how well they've learned the metric conversion process by asking them to work the first problem (school bus) again. Also have volunteers explain the problem solving steps to the class.

#### Assessments

Formative assessments will take place during class. Have the students form groups of two or three and work through some practice problems. Ask for volunteers to write their solutions on the board and then explain their solutions. Provide supportive feedback for each volunteer while making appropriate corrections. Provide several practice problems on at least three consecutive days, even if they are similar. Most students will realize how much progress they are making.

An additional assessment can be given to determine mastery either during a quiz or on the chapter test. I recommend scoring homework and test problems by awarding points for each of the following:

a. The correct problem setup
b. The correct label sequence throughout the problem
c. The correct numerical values