Parallelogram's Dilemma

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.

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Van Heile Level

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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.

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Intended Use

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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.

Activities

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.

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