Measurement

Therese Donatello              Archbishop Weber High School
                               5252 W. Palmer St.
                               Chicago IL 60639
                               (312) 637-7500

Objectives:

1. The students will learn the necessity for the use of standards.
2. The students will be able to distinguish units of measure.
3. The students will be able to derive units of measure.
4. The students will be able to measure length, volume, mass, and angles.
5. The students will be able to measure indirectly.

Materials needed: 
 
rulers      blocks      cardboard      graduated cylinders      straws
cups        string      paper clips    coat hangers             protractors
nails       sticks      bottle tops    mini blind slats         graph paper

Strategy:

1. Standards
   a. Using your hand (from the wrist to the tip of your middle finger) 
      measure the length of your desk.
   b. Measure the length of the room using your foot.
   c. Pick the best measurement from your group and record it on the board.
   d. Discuss the reasons for the differences in readings and the difficulty
      of choosing  "the best measurement".
   e. The idea of different sized hands and feet should lead to the idea of
      using the same measurement for agreement or a standard.
   f. Using the stick provided (sticks of the same size) measure the desk
      and room again and record the answers on the board.
   g. Point out how much closer the answers are using the stick as a standard.

2. Units of measure
   a. Measure the block of wood (length, width, and height) using the stick.
   b. Record any problems in using the stick as a standard.
   c. The idea of the edge of the block not matching the end of the stick 
      should be brought out.
   d. Using the instruments provided (mini blind slats are marked off in
      larger units and on another slat this larger unit is marked off
      in tenths) measure the block of wood again.
   e. The idea of the smaller unit being more accurate should be brought out 
      along with the idea that the measurement is the same even if there are
      more smaller parts than larger parts.

3. Derived units 
   a. Using the marked slat with the smaller units draw a line four units long
      in the center of your cardboard marking off each unit.
   b. Measure one unit to the right of this unit and draw another line four 
      units long next to the first.
   c. At the second measurement on the right hand line draw one unit to the
      right, one unit down from the end of this line, and one unit to the left
      from the end of this line.                                             
   d. Repeat step c on the left left hand line forming the same figure.    
   e. Cut out the figure, bend the cardboard along the lines and connect.  
   f. What is the shape of the figure?  (The shape should be a cube one unit
      long on each side or one cubic unit).
   g. The idea of cubic measure being the unit for volume should be brought
      out in the discussion.     
    
4. Volume
   a. Measure five cubic cm of water in a one hundred milliliter graduated
      cylinder. (Remind the students that one milliliter is equal to one
      cubic centimeter.)
   b. Pour the five cc of water from the 100 mL graduate into the 10 mL
      graduate.
   c. Record the reading from the 10 mL graduate.
   d. Repeat steps a-c using the 25 mL graduate.
   e. Were all the results the same?  (The results should be somewhat
      different due to the smaller units on the 10 mL graduate.)

5. Mass
   a. Set up your balance. (A balance was made by attaching a 45 cm long
      1"x 2" piece of wood to a 20 cm 2"x 4" piece of wood.  A hole was
      drilled to accommodate a dowel stick 30 cm long.  A piece of coat-
      hanger 30 cm long was attached by string to a metal washer.  Two 
      plastic cups were attached to the ends of the hanger with string to
      complete the balance.  This entire assembly is placed on the dowel rod.)
   b. Find the mass of the two articles in your kit using the large paperclips 
      as units of mass. 
   c. Would the mass change if you used smaller paperclips?  (Remind students 
      that mass does not change if the units change.) 

6. Indirect measurement
   a. Review measuring angles using a protractor and scale drawings.
   b. Measure twenty meters on the floor.
   c. Using the astrolobes have two people stand at the opposite ends of
      the 20 meter line and point their astrolobes at the point marked on
      the ceiling.  (The astrolobe was made by attaching a washer to a
      string and then attaching the string to a protractor.)
   d. Record the angles measured on the astrolobes.
   e. Using graph paper make a scale drawing. 
   f. Drop the perpendicular from the intersecting lines of the triangle.
   g. Measure the perpendicular line and using the scale for the drawing
      record the height of the ceiling.
   h. Use the same procedure to find the height of other objects.