Unit Circle Manipulative
Math Manipulative Design Submission
A unit circle, similar to the one above, is printed on a piece of clear plexiglass. A spindle is affixed at the
center of the unit circle. A radius like the one shown below, perhaps printed in red to distinguish it from
black lines on a piece of paper, is created on a piece of clear plastic, and is made in such a way that it fits
on the spindle, forming a radius that can be turned 360 degrees on the plexiglass unit circle. Individuals
can place the plexiglass over any geometry work which involves finding the degrees in an angle, and use
it like a protractor to measure any angle in either degrees or radians. Another piece of sheet plastic
could be printed with a fully notated protractor in order to make the tool’s measurements more
exacting. A Protractor and a unit circle can be combined in this way to make plain the relationship
between degrees and radians which is often a source of confusion for students in advanced High School
math. Additional radii can also be created and placed over the spindle as well, for use as a learning aid
in Trigonometry, when discussing adding and subtracting of radians, or for the special case
trigonometric ratios. Overall, the point would be to smooth the transition from the tools and methods
of polar to radial geometry.
Peg board Cartesian Plane Manipulative
This manipulative requires a 2 foot square piece of pegboard with 1” spaced holes, painted to
resemble a piece of graph paper, and also sufficient dowels of appropriate size to fit in the pegboard
holes. A graph comprising all 4 quadrants to a value of 12 can be modelled, or the scale of the graph or
orientation of the origin can be changed if so desired. Many students have difficulties with graphing,
and a manipulative of this type could be used at the middle and high school level to help with
comprehension of the basic rules of graphing linear and other kinds of equations and inequalities.
Multicolored lengths of yarn can be wrapped around the pegs, to visually represent equations which
have been plotted and marked with dowel pegs.