Parallelogram's Dilemma

The Misfit

Coach did not know of any sports that used parallelograms like Parallela, nor any that even wanted to. Parallela was always left out of all the games her friends played and this feeling became unbearable when the mean coach decided to give all unwanted shapes a final warning: if Parallela did not find a sport that needed her shape by the end of the day, she would be banished from Geoville forever.
Day turned into evening as Parallela, now under the pressure of the looming deadline, began her desperate search.
Even the most disliked and annoying student in Geoville, Pompous Rhombus, had found his calling playing second base on the baseball infield - shaped like a perfect rhombus.
Hope was dwindling, and all her geometric friends worried about her. She wondered why she just couldn't be like her best friend Mangle.

Mangle the Rectangle

Mangle was not a good athlete. In fact, he would much rather be playing his piano with his rectangle friends, but he was a sweet guy and everybody liked him. He never wanted to be an athlete but because he had such a common shape in sports - with his four right angles and unequal adjacent sides - Coach Grumpylateral demanded that Mangle play almost every single sport.

First, there was tennis. The rectangle of the court was divided into two perfect rectangles for doubles. Mangle moved with ease through the lines of the service boxes and the baselines.

Next, he was called on to play soccer. He did enjoy being outside in the sun and on the grass of the rectangular field, with its goal and penalty areas, having unequal adjacent sides - just like his own.

Mangle Just Needs a Break

Trapezoid Tony

When Mangle heard about the struggles of his friend Parallela, he thought of every sport he had ever played but but could not come up with any that needed a parallelogram shaped like Parallela. He did however, find a sport for their common friend, Trapezoid Tony. During his trip to Geoeurope, Mangle noticed that the hockey ring uses an unusual quadrilateral shape with one, and only one pair of parallel lines. It was a trapezoid. When Trapezoid Tony heard about this he was jumping with joy - Tony, like Parallela, thought he would never fit in anywhere. Tony grew to become the most intimidating goalie anybody would ever see on a hockey ring.

Once, when Mangle finally thought he could take a break on a family trip to Geoeurope, he realized that he was adept at playing sports he had never even heard of: the Frenchilateral children wanted Mangle to play rugby with them; the Britishlateral students begged him to play on the pitch of the cricket field - whatever that meant?

Trapezoid Tony

Dwight

Of all the shapes remaining in Geoville without a sport to play, this left just Parallela and Dwight. Dwight was a kite with two pairs of adjacent that were equal, but his opposite sides were not equal to each other. Here again, Mangle came to the rescue. On one of his family trips, Mangle had been to a country where kite fighting was the most popular sport in the land. Upon hearing this, Dwight ran home and started making plans for his own kite-fighting league.

CAPTION Half page image nullam nunc eros, vehicula feugiat

CAPTION Half page image nullam nunc eros, vehicula feugiat

The sun was setting now and Coach Grumpylateral found Parallela and said, "Well, I'm sorry but time is up. Unless you find a sport that needs your shape by tomorrow morning, you are forever banished from Geoville." Parallela's friends pleaded for her, but she said, "No, he's right. I'm not a rectangle or a square because I don't have four right angles, and I'm not a rhombus because all of my sides are not equal length. I have two pairs of parallel sides, so I can't be a trapezoid, and according to coach, I'm not even a kite because my opposite sides are equal to each other. I guess I just wasn't meant to play sports," said Parallela.

Nowhere Left To Go

Having given up all hope, Parallela wanted to be by herself and so she walked along a path she had never walked before. Suddenly, she found herself amidst tall, abandoned building; a building that seemed just as sad and lonely as she was; a building that must not have used in decades. Inside this building, Parallela noticed one thing that stood out: an old-fashioned, perfectly preserved basketball court. The building was in disrepair but the floor was in perfect condition. When she brushed the floor clean with her hand, she was astonished at what she saw.

Parallela's Calling

It was the most beautiful, shiny, and polished parquet floor she had ever seen. The parquet floorboards came in all shapes and sizes, including: hundreds of parallelograms with angles and sides just like hers. She had found her sport.

When she ran to find Mangle and tell him the great news, Mangle said, well, "I guess your now a basketball player." "Are you kidding me said Parallela, I'm going to use that perfect parquet floor to become a sports Dance champion."

Introduction to Quadrilaterals: The story provides a creative and engaging way of introducing the concept of quadrilaterals, namely squares, rectangles, parallelograms, rhombuses, and trapezoids. The different quadrilaterals' features are highlighted through the story, including the number of equal sides, parallel sides, and right angles.

Visualizing Geometric Shapes: As students follow along with the narrative, they are encouraged to visualize the different quadrilaterals and how they fit into the real world, such as the shape of a boxing ring, tennis court, or basketball court.

Understanding Unique Features of Shapes: By setting a rule that each shape could participate in a sport only if the sport needed its shape, the story underscores the importance of understanding the unique properties of each shape.

Comparing and Contrasting Shapes: The narrative provides ample opportunities to compare and contrast different types of quadrilaterals, understanding how they are similar and how they are different. For instance, how a square and a rectangle both have four right angles, but only a square has all sides of equal length.

Applying Mathematical Knowledge: Lastly, the story can help students see how math is applied in the real world. They can understand how different shapes are used in different sports fields, and this can help them see the practical relevance of what they are learning.

Georgia Standards of Excellence for Mathematics:

MGSE4.G.1 - Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

MGSE4.G.2 - Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

MGSE5.G.3 - Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

Van Heile Level

This story seems to fall primarily within Level 1: Analysis.

The story discusses the properties of various quadrilaterals (parallelograms, squares, rectangles, trapezoids, rhombuses) and their defining features. It helps students identify the difference between these quadrilaterals based on their properties, like the number of parallel sides, the presence of right angles, or the congruence of sides.

The story may introduce Level 2. It has some elements of informal deduction as well, in how it hints at the interrelationships of different properties within quadrilaterals. For instance, Parallela realizes that her lack of right angles and unequal adjacent sides determines how these properties differentiate her from other quadrilaterals.