Parallelogram's Dilemma

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. 

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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. 

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. 

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 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&nbsp;unequal&nbsp;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.

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?

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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.

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."

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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.

Given the story's focus on properties of quadrilaterals and their real-world applications, it seems most appropriate for students in upper elementary or early middle school. This would typically include students in grades 4-6, who are usually between the ages of 9-12. In most counties, students begin learning about the properties of different quadrilaterals in these grades. In particular, the fourth and fifth grades are often when students first start learning about the distinct properties of squares, rectangles, trapezoids, and other quadrilaterals. This story could be a fun and engaging way to introduce or reinforce these concepts.

Once upon a time, in an alternate town called Geoville, where quadrilaterals once competed for sports glory, there was a notoriously rigid and grumpy quadrilateral coach. This coach, known for his stern nature, had a simple and exclusive rule for all his players: each shape could participate in a sport only if the sport needed its shape. For example, a tennis court had no need for a trapezoid (as trapezoids had only one set of parallel lines), so the poor but well-meaning Trapezoid Tony could not play tennis because a tennis court does not have any trapezoid shapes.

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No trapezoids needed here.

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Quadrilateral Sports Drawing: Students could be asked to draw different sports fields or courts and label the quadrilaterals they find in their drawings. This will help them connect the geometric shapes to real-world objects. Quadrilateral Classification: After reading the story, have students sort different quadrilateral shapes (either physically with shape cutouts or digitally with images) based on their properties, such as number of equal sides, parallel lines, or right angles. Quadrilateral Comparison: Students could create a Venn diagram comparing the properties of the different quadrilaterals introduced in the story. Geometric Shape Hunt: As an extension activity, students could be encouraged to find and take pictures of different quadrilaterals in their home or community. They could then explain why each object is a specific type of quadrilateral based on its properties. Create Your Own Sport: Challenge students to design a new sport field or court that includes a specific quadrilateral and explain the rules of this new sport. Math Storytelling: Older students could be challenged to write their own math-based stories, incorporating concepts they've learned in class. Geoville Drama: Students could perform a short play based on the story, assigning roles for each character (Blair the Square, Trapezoid Tony, etc.), and describing their respective shapes' properties.

Coach Grumpylateral's favorite and star athlete, known to all his friends as Blair the Square, found his calling in the boxing ring. He had a muscular frame with his equal sides and equal angles and the symmetry of his structure made him an unbeatable champion, a force to be feared - every bit as square as the ring he dominated. 

Meanwhile, Parallela was coach Grumpylateral's least favorite and most ignored athlete. She didn't seem to fit in anywhere. Sure, she had two sets of parallel sides, her two opposite sides were congruent, and her opposite angles had equal measures, just like Blair the Square. Then why did coach hate Parallela so much? The problem for coach was that Parallela did not have any right angles and her adjacent sides were unequal in length. .

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