In this activity students will identify benchmark angles as they are embedded into a circle grid.
For teacher:
For each student:
Additional Resources
Books
The ancient Babylonians established a system for measuring angles in degrees. They set the measure of an angle that completely surrounds a point at 360˚. This number was likely chosen because the Babylonians used a number system based on 60, or because 360 has many factors.
When looking at angles, students may struggle to appropriately measure angles because they are based on the number 360. The benchmark strategy is a useful strategy for students to use when dealing with these abstract concepts. This strategy teaches students useful benchmarks, or reference points, to use when measuring objects. Some common angle benchmarks are 45˚, 90˚, 180˚, and 360˚.
We often talk of benchmark angles. Although students may have difficulty relating to specific angle measures, many students understand what a 180˚- turn or a 360˚-turn is in the context of snowboarding. Another common example of angles is seen in the marks on a clock.
In this activity, students identify benchmark angles as they are embedded into a circle grid like the one shown here.
Circular grids are similar to coordinate grids. As with coordinate grids, circular grids are used to identify the locations of points given by ordered pairs. Astronomers often use circular grids to identify objects in the night sky. To locate points on a circular grid, start at the vertex (center), move out the number of units given by the first coordinate, and then move counterclockwise along that circle the number of degrees indicated by the second coordinate.
Vocabulary terms used in this lesson:
angle - The opening between two straight lines that meet at a vertex, measured in degrees or radians. The sides of an angle are rays that have the vertex as a starting point.
coordinate grid - A two-dimensional system in which the coordinates of a point are its distances from two intersecting, straight lines called axes.
coordinates - An ordered pair of numbers that identify a point on a coordinate plane or grid.
3. Reason mathematically.
Invitation to Learn
Instructional Procedures
Students create a 15˚ benchmark game board. They can use this board to play again or can take them home to play Four-In-A-Row with a family member (see family connections).
Family Connections
Use the Tomb Robbers Game Boards to play Four-In-A-Row. This
game is similar to Tic-Tac-Toe. Before making a move, each
player must accurately say the coordinates of a point. They may
then place an "X" or "O." over their point. The first player to get
four marks in a row wins.
Give an Angle Summary worksheet to each student. Ask them to first record their estimates of the angles, then to check their measures using an angle ruler.
Research Basis
Joram et. al., (2005). Children's Use of the Reference Point Strategy for Measurement Estimation. Journal for Research in Mathematics Education, 36(1), 4-23.
"Mathematics educators frequently recommend that students use strategies for measurement estimation, such as the reference point or benchmark strategy… Relative to students who did not use a reference point, students who used a reference point had more accurate representations of standard units and estimates of length."