Connect the Mathematical Dots
Teachers can choose visual activities that demonstrate the elegance associated with the coordinate plane.
By Donna Iadipaolo
Connect-the-dots is an easy puzzle that almost everyone fondly recalls from kindergarten. So for a non-threatening, enjoyable way to become familiar with the Cartesian coordinate grid, why not incorporate such a puzzle? Either the teacher or student may create some images made with connecting specific coordinates in all four quadrants to have students practice plotting ordered pairs. Another approach to this concept might be to have students draw a design on a coordinate plane that extends into all four quadrants, and then have them think about what points would be best to select in order to make a connect the dots puzzle for younger children. The teacher, or the students, may choose to design Cartesian connect-the-dots pictures of vehicles, buildings, plants, animals, people, and cartoon characters. The key is to require the points to be located in all four quadrants, and to use at least 30 points.
A related activity using the coordinate grid is to explore the elegance and symmetry of certain shapes and pictorial relations, and then delve deeper into associated formulas and covariance analysis. For instance, you may ask students to draw a proper square, circle, triangle, parallelogram, regular hexagon or dodecagon (the complexity of the figure would depend on grade level and ability). Then you can leave it up to students to determine how they will design and prove the symmetry, as well as prove the strict definition of each shape. For instance, students may apply the slope, distance formula, and midpoint formulas to their shapes; or they might examine the diagonals of their parallelogram.
In terms of the study of the shape of beautiful relations, you may first have students research real-world representations of parabolas, circles, ellipses, and hyperbolas. Then students could create scaled representations of situations on the coordinate grid, which would connect nicely to having students understand the standard equations of conic sections.
For a precalculus class that is being introduced to polar coordinates, a study of the beautiful classical curves including the rose, lemniscate, limacon, cardioid, and spiral of Archimedes would capture students’ attentions. An extra challenge could be for students to convert the polar coordinate equations into it rectangular equations.
Here are some further lessons that explore the elegance associated with the coordinate plane.
Coordinate Plane Lesson Plans:
Students examine and classify given quadrilaterals on the coordinate grid by applying the slope, midpoint, and distance formulas. Students create various quadrilaterals using three given points on the coordinate grid and determining the four points that will fulfill the required properties.
The Order of Things on a Coordinate Grid
Students identify quadrants on the coordinate plane, graph ordered pairs, and create a design or picture using ordered pairs. Students also view video clips and utilize worksheets embedded in this plan.
Students use Geometer’s Sketchpad to help them identify, name, and classify polygons. Students also apply translations, reflections, and rotations of polygons.
Students engage in a study of the parabola that is displayed on a graph to investigate the fall of a victim from a bridge to determine if it was a crime committed as foul play. They are given the opportunity to try example problems to master the objective.
Students explore how to plot ordered pairs using the coordinate plane and determine in which quadrant these ordered pairs lie. They show mastery of plotting ordered pairs by playing the game Battleship.
