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This lesson is on the need for Standards of Measure, Indirect Measurement, and More




9, 10, 11  


Title – Measurement
By – Rob Duncan
Primary Subject – Math
Secondary Subjects –
Grade Level – 9th to 11th

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


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 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
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.

E-Mail Rob Duncan !

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