Mathematics Grade 4
Strand: MEASUREMENT AND DATA (4.MD) Standard 4.MD.5
Mathematics Grade 4
Strand: MEASUREMENT AND DATA (4.MD) Standard 4.MD.6
Large Groups
Activities require students to make their own protractor and use it to identify and measure various angles.
Invitation to Learn
Using a Protractor
Classroom Protractors
Additional Resources
Books
Sir Cumference and the Great Kingdom of Angleland: A Math Adventure, by Cindy Neuschander; ISBN-10: 157091169X
Angles (Let's Investigate), by Ted Evans; ISBN-10: 1854354663
Angles are Easy as Pie, by Robert Froman & Byron Barton; ISBN-10: 069000916X
The protractor is an instrument of measurement. A protractor is used to construct and measure angles. The simple protractor is an ancient device used for plotting the position of boats on navigational charts. There are different kinds of protractors, but the one used in elementary school is called a simple protractor. We have units for measuring angles and they are called degrees. These are not the same as temperature degrees, even though the same word is used. The simple protractor looks like a semicircular disk marked with degrees, from 0o to 180o.
Angles are formed when two rays intersect. Angles are measured in degrees. A complete circle measures 360 degrees. If you take a circle and cut it into 360 slices, each of those slices is one degree. Why 360 degrees? Historians believe this is because old calendars, such as the Persian Calendar, used 360 days for a year. When they watched the stars they saw them revolve around the North Star one degree per day. This ancient measurement is still recognized today as the measurement of a circle.
To adequately use and understand using a protractor, students need to have background knowledge of the following vocabulary: angle, acute, obtuse, right, straight, reflex, vertex, and arms.
Students in 4th grade need to recognize benchmark angles:
90 degree angle= 1⁄4 of a circle
180 degree angle = 1⁄2 of a circle
270 degree angle = 3⁄4 of a circle
360 degrees = full circle
2. Become mathematical problem solvers.
4. Communicate mathematically.
Invitation to Learn
Place the strip of pre-printed letters on each student's desk. The students will cut the letters apart and manipulate the letters until they figure out what the mystery word is. Instruct students when they discover the mystery word to write it down on a piece of paper and wait for teacher to verify the word.
R C R P T R T O A O (Protractor)
After all students have discovered the mystery word, protractor, introduce the protractor lesson.
Instructional Procedures
Using a Protractor
Cut out the protractor and place in Math Journals. Divide the page into 4 equal sections. Label the sections with the following headings. Review and discuss how to label. Record directions in journal.
Zero-Edge The zero-edge is always at the same level as the 0 mark. |
Center Mark The center mark is always at the middle of the zero-edge. |
Inner Scale The numbers on the inner edge of the protractor. |
Outer Scale The numbers on the outer edge of the protractor. |
Classroom Protractors
Fourth grade students generally find it difficult to read and calculate the degree marks accurately. A "homemade" protractor (with a dark thread) helps eliminate this problem. Manipulating the thread to lay on the exact degree, helps the students identify the exact degree on the protractor.
Constructing a Student Protractor
To Measure an Angle
Constructing an Angle
Independent Practice
What's My Name Worth?
acute angles = 10 cents each
obtuse angles = 8 cents each
right angles = 5 cents each
vertical lines = 3 cents each
horizontal lines = 2 cents each
diagonal lines = 1 cent each
Example:
J A N E | |
5 acute angles @ 10 cents each = |
$.50 |
2 obtuse angles @ 8 cents each = |
.16 |
4 right angles @ 5 cents each = |
.20 |
4 vertical lines @ 3 cents each = |
.12 |
4 horizontal lines @ 2 cents each = |
.08 |
1 diagonal lines @ 1 cent each = | .01 |
____ $1.07 |
Curriculum Extensions/Adaptations/ Integration
Family Connections
Research Basis
Van Hiele, P. M. (1999, February). Developing geometric thinking through activities that begin with play. Teaching Children Mathematics, 5 (6), 310-316.
"For children, geometry begins with play," writes Pierre van Hiele (1999). He goes on to say that for students to reach the higher levels of geometric thinking, their instruction should still begin with an exploratory phase, gradually building concepts and related language, and culminating in summary activities that help students integrate what they have learned into what they already know."
Ernest, P.S. (1994). Evaluation of the effectiveness and implementation of a math manipulatives project. (Report No. SE-057 682). Nashville, TN: Annual Meeting of the Mid-South Educational Research Association. (ERIC Document Reproduction Service No. ED 391 675).
The purpose of manipulatives would be to allow students to learn a geometric principle in more than one way. In other words, instead of just hearing about a math principle, they also get to see and feel it. The study confirms that students are more willing to participate, and experiment in math projects. Their attitudes towards math improved, thus raising their self-confidence in their math ability.