Length in the Customary System
By: Harry Marshall
1. Summary
o This lesson is intended to accompany Glencoe’s Mathematics: Applications and Concepts - Course 1 text book.
o Chapter 12 – Measurement
o Lesson 12-1 – Length in the Customary System
o Grade 6
o Intensive Mathematics
o This lesson is intended to be used in a computer lab (one student per computer is ideal) or on a home computer.
o The students will need a basic understanding of computers and internet access.
o The students should also be familiar with the math concepts of customary measurement as presented in Lesson 12-1 of Glencoe’s Mathematics: Applications and Concepts - Course 1. The students should have an understanding of the concepts of area and perimeter and the formulas for the areas and perimeters of basic shapes (Lessons 4-5, 4-6, 14-3). The teacher may wish to provide students with a copy of the 6th grade/ FCAT reference sheet which lists these formulas. The reference sheet can also be found inside the back cover of the Glencoe: Course 1 text. The students should also be familiar with scales and rations (Lessons 10-1, 10-3).
o The objective of the lesson is to provide students with practical experience in measurement without the need for manipulatives, rulers, or other costly classroom supplies.
o The lesson should take 30-45 minutes to complete.
o Students will need internet access and paper and pencil to record their results; the computer should have Java software installed prior to beginning the lesson. A standard ruler should also be provided or brought by the student for comparison to the virtual ruler.
o In this lesson, students will maneuver a virtual ruler to measure common shapes to the nearest half, quarter, or eighth of an inch. They will then answer the questions that follow.
o Sunshine State Standards - MA.B.1.3.3-1, MA.B.1.3.3-2, MA.B.1.3.3-3, MA.B.2.3.1-1, MA.B.2.3.1-2, MA.B.2.3.2-1, MA.B.3.3.1-1, MA.B.3.3.1-3, MA.B.3.3.1-4, MA.B.4.3.1-2, MA.B.4.3.2-1, MA.B.4.3.2-2, MA.B.4.3.2-3
o Key words include: Customary measure (as opposed to metric), length, diameter, radius, area, perimeter, and Pi; the students should also be reminded to use 3.14, 22/7, or simply the symbol for Pi as the value for Pi depending on teacher preference.
2. Lesson plan
The teacher should start out with a brief historical background, such as:
The system for measuring length in the United States' customary system is based on the inch, foot, yard, and mile, which are the only four customary length measurements in everyday use.
Wikipedia
The students should first open internet explorer (preferably) and type in the following web address:
http://www.geogebra.org/en/upload/files/MSP/HarryMarshall/CustomaryLength.html
o They should be directed to first click on the window in the center of the screen to activate the control, to complete the activity, and to answer the questions that follow on their own sheet of paper.
o Each student will each measure three common shapes, a square, a triangle, and a circle to the nearest half, quarter, or eighth inch by dragging the onscreen ruler to the proper positions on the screen.
o They will then plug the measurements into the formulas to figure out the areas and perimeter/circumference of the square and the circle.
o The students should then attempt to answer the beyond the basics questions by measuring the virtual ruler with an actual ruler. In most cases, the virtual ruler will not be identical to the real ruler. Students should attempt to deduce the relationship or scale of the virtual ruler. In the case where all students are using identical computers with identical screen resolutions, the teacher may wish to either set one computer’s resolution differently or project the activity onto a wall and allow students to measure the image to illustrate the different scales that are possible to arrive at from this one activity.
o The teacher should walk around the room assisting students and answering questions. One common error is that of students beginning their measure from the edge of the ruler as opposed to the first hash line, an error that occurs frequently with physical manipulatives as well.
o At the end, a brief (5-10 minute) class discussion should ensue.
· Anticipatory set - This is a fun activity. Most students do not need to be eased into a lesson that involves the use of a computer yet the key vocabulary and underlying concepts of the activity should be reviewed beforehand.
· Real world examples of scales (such as an architect designing blueprints or computer animators creating video games) should be stressed so the students find real-world value in the activity.
Explanation of the math involved – Customary measurement, area, perimeter, Pi, and scale are all key concepts that are to be explained.
Instructional methods
• Teacher-centered approaches
§ The vocabulary, key concepts, and real-life tie-ins to the lesson should be instrumented by the teacher prior to the students completing the online activity.
§ Following the activity, the teacher should summarize and discuss the results with the students.
• Student-centered approaches
§ Discovery Learning
§ Simulation
§ Problem-based learning, inquiry, and discussion
Key Questions to be asked
· Compare / Contrast customary measurement with metric measurement.
· Name professions that use the skills you are using here.
· Will items you measure in the real world always measure exactly to the nearest half, quarter, or eighth inch?
· What effect would using a ruler that is divided into sixteenths of an inch have on the measurement of real objects?
· For aeronautical engineers, are sixteenths of an inch precise enough?
Closure to the lesson
· Review answers to all the questions with the students.
Answer Key
1. What is the length of the base of the triangle? 1 ¾ inches
2. What is the length of the side(s) of the square? 1 5/8 inches; perimeter? 6 ½ inches; area? 2 41/64 inches
3. What is the diameter of the circle? 2 ¼ inches; radius? 1 1/8 inches; perimeter? 7.07 inches or 2 ¼ Pi inches; area? 3.98 inches or 1/64 Pi inches
*Beyond the Basics* - Use an actual ruler to answer the following questions:
1. Is one inch on the virtual ruler = one standard inch? Answers may vary.
2. If not, what is the scale (or relationship) between the virtual ruler and an actual ruler? Answers may vary.
3. Will everyone attempting this exercise reach the same conclusion for the scale? No
4. Why or why not? Because of differences in monitor size and resolution, the ruler may appear larger or smaller than an actual ruler.
· As this point the instructor may wish to lead into the next section and compare/contrast standard with metric measurement.
Assessment
· The answers to the questions are to be turned in and graded by the teacher and returned to the students with feedback.
· A participation grade can also be given for the class discussion.
Supplemental activities lesson
· In the case of students with learning and/or physical disabilities, the teacher may present the material on a screen with the use of an LCD projector and perform or call up a few students to measure the objects. In addition, the teacher may wish to implement the follow-up questions as either group work or as a class project/ discussion.
· Extensions to the lesson should include measurement of real objects, such as a pencil, comb, toothbrush, television remote control, etc. to give the student real world practice with customary measurement.
Connections
· This lesson integrates measurement, perimeter, area, and scale while providing the teacher with an inexpensive practicum and the student with practical measurement drills. It can also be used as a review for the multiplying decimals, fractions, and algebra sections since it draws upon all these skills.
· Measurement and the concept of scales can further be tied in to the students other classes. In science, where most insects are magnified many-fold in the literature, the student can be asked to figure out to actual length of an insect’s thorax using a ruler and a scale.
· In social studies, a student can be asked to find the distance between two locations on a map.
· Finally, this lesson could serve as an introduction to the Geogebra software used to create it.