Implementation of “Geometry Hidden Behind the Old Walls” (SOI-HR-453)
In eighth grade as part of the curriculum of mathematics in Croatia, learning about solid geometric bodies serves as a foundational step towards developing a deeper understanding of geometry and spatial reasoning. This journey not only enhances students’ mathematical skills but also nurtures the development of critical thinking and problem-solving capabilities.
By studying solid geometric bodies such as cubes, prisms, pyramids, cylinders, and cones, students grasp fundamental concepts like volume, surface area, and spatial relationships. These concepts are not only applicable within the realm of mathematics but also serve as building blocks with practical application into various real-world scenarios, including architecture, engineering, and design.
Exploring solid geometric bodies cultivates visual-spatial skills, enabling students to mentally manipulate and analyze three-dimensional objects. This spatial awareness is crucial in fields such as science, technology, engineering, and mathematics (STEM), where understanding and manipulating physical structures are essential.
Through this educational pursuit, students not only deepen their mathematical understanding but also acquire a versatile skill set that prepares them for success in an increasingly complex and interconnected world.
Exploring Croatian castles and geometric solids
The original learning scenario served as an inspiration to devise a lesson plan in which eighth-grade pupils were tasked to explore different castles across Croatia, identify the geometric shapes present in their architecture, choose a castle to inspire their own design, sketch their castle incorporating various geometric solids, calculate the area and volume of each solid, and assemble their castle model.
Materials needed:
- Images and information about Croatian castles (e.g., Krka Castle, Dubovac Castle, Trakošćan Castle)
- Drawing paper
- Rulers
- Graph paper
- Calculators
1. Introduction
– The pupils were shown various images of Croatian castles, with an emphasis placed on the presence of geometric shapes like prisms, pyramids, cylinders, and cones in their architecture.
– We discussed the significance of geometric shapes in architecture and how they contribute to the structural integrity and aesthetic appeal of castles.
2. Research and selection
– The pupils were allocated time to research different Croatian castles using various resources (e.g., articles, websites and Europeana).
– Working in pairs, they were instructed to choose one castle that inspired them and gather information about its geographic location, history, size, year of construction, and interesting facts.
3. Design and sketch
– The pupils were given time to sketch their chosen castle, incorporating various geometric solids (prisms, pyramids, cylinders, cones) into the design.
– For each chosen geometric solid, they had to apply their mathematical knowledge to describe its properties and basic elements, such as the number of faces, edges, and vertices.
4. Area calculation
– The pupils were provided with graph paper and rulers and asked to draw grids representing the base of each geometric solid in their castle design. They were reminded to carefully sketch the outlines of each grid, ensuring precision and accuracy in depicting the bases of the various solid shapes essential to their architectural creations.
Equipped with the necessary formulas, they applied their knowledge to calculate the area of each grid. For prisms and pyramids, the focus lay in determining the base area, while for cylinders and cones, their attention shifted to calculating the circular area. Both tasks required attention to detail and applying basic geometric principles.
Through this hands-on experience, they not only deepened their mathematical knowledge but also applied a deeper appreciation for the connection of artistry and mathematics within the realm of architectural design.
5. Volume calculation
– The next step was to calculate the volume of each geometric solid in their castle design using appropriate formulas (e.g., volume of prisms and pyramids, volume of cylinders and cones). This task required further precision and concentration.
6. Castle assembly
– Having checked all their calculations, the pupils proceeded to assemble all parts of their castle model, using glue or tape to secure the geometric solids together.
– In the final activity of the lesson plan, the pupils were encouraged to engage in a comprehensive analysis and comparison of the total surface area and volume of their castle models. This activity serves as an important moment for students to reflect on their learning journey, consolidate their understanding of geometric concepts, and showcase their newfound skills in a meaningful context.
– As they showcased their creations, they were prompted to discuss the various geometric shapes and components utilized in the construction of their castles. They highlighted the diverse solid bodies such as cubes, prisms, pyramids, cylinders, and cones incorporated into their designs, emphasizing the application of mathematical concepts in real-world scenarios.
– Armed with their calculations, they recorded their findings on a Flipchart and engaged in discussions focused on comparing and contrasting the surface area and volume of their castle models. They identifyed patterns, similarities, and differences in the geometric properties of various castle designs, considering factors such as size, shape complexity, and arrangement of components.
– Through guided questioning and facilitated discussions, the pupils delved deeper into their analysis, exploring the implications of their findings. They reflected on how variations in surface area and volume impact the overall aesthetic appeal, structural integrity, and functionality of their castle models.
– At the end of the lesson the entire class participated in making connections between geometric principles and real-world applications. This collaborative reflection fosters a deeper understanding of mathematical concepts and reinforces the relevance of geometry in everyday life.
6. Assessment
The detailed instructions including the rubrics upon which the work was evaluated, was documented in a Genially. This enabled the pupils to learn a new digital tool while also being able to view the criteria upon which their work was assessed including the accuracy and creativity in incorporating the geometric solids of choice.
– The calculations of area and volume for each geometric solid were assessed and the final castle models were reviewed for completeness and adherence to the design concept.
By applying this learning scenario, the pupils were able to connect their mathematical knowledge in a new and exciting way. Learning about solid geometric bodies encourages interdisciplinary connections. Students can explore how geometry intersects with other subjects like art, physics, and history.
The educational outcomes of learning about solid geometric bodies in the eighth grade extend beyond mathematics, empowering students with essential skills and knowledge applicable across various disciplines and real-world contexts. This foundational understanding lays the groundwork for more advanced mathematical and scientific pursuits in the future.
Using the Europeana learning scenario, the pupils of my eight-grade classes enhanced various 21st century skills.
Working in pairs enabled them to deepen their communication, collaboration, and teamwork skills. Using the resources on Europeana developed their critical thinking and digital skills while their creativity skills were unleashed in all the tasks. This activity helped them develop problem solving skills while ultimately providing them with the confidence to face real-world challenges with mathematical proficiency and creativity.
Outcomes for the educator
By applying various resources from Teaching with Europeana, pupils are able to develop many 21st century skills, while at the same time applying digital cultural heritage. This unique way of learning and teaching has many outcomes:
1. Enhanced understanding of geometric concepts:
Through hands-on experience building castles from geometric solids, students deepen their understanding of geometric shapes, spatial relationships, and three-dimensional figures. They gain practical insights into how these concepts manifest in real-world contexts.
2. Improved mathematical proficiency:
Engaging in calculations of surface area and volume requires students to apply mathematical formulas and problem-solving strategies. By integrating these mathematical concepts into a creative project, students develop stronger computational skills and a deeper appreciation for the relevance of mathematics in everyday life.
3. Critical thinking and analytical skills:
Analyzing the surface area and volume of their castle models prompts students to think critically about the geometric properties of each solid body used in construction. They learn to identify patterns, make comparisons, and draw conclusions, fostering the development of analytical skills essential for academic success and beyond.
4. Creativity and design thinking:
Designing and building castles from geometric solids encourages students to unleash their creativity and exercise their imaginations. They explore different architectural styles, experiment with structural elements, and make design decisions, honing their creativity and design thinking skills in the process.
5. Collaborative learning and communication:
Working in pairs to construct castles and calculate surface area and volume fosters collaboration and communication skills. Students learn to collaborate effectively, share ideas, delegate tasks, and resolve conflicts, promoting a positive and inclusive learning environment.
6. Application of learning across disciplines:
Integrating geometry with practical applications such as castle construction bridges the gap between theoretical concepts and real-world scenarios. Students recognize the interdisciplinary nature of learning, discovering connections between mathematics, architecture, history, and engineering.
7. Increased engagement and motivation:
The hands-on nature of the lesson, combined with the opportunity to create tangible products, enhances student engagement and motivation. By actively participating in the construction of their castle models and calculations, students take ownership of their learning, leading to greater investment and enthusiasm.
8. Formative assessment opportunities:
Observing students as they construct their castle models and complete calculations provides valuable insights into their understanding and mastery of geometric concepts. Educators can use formative assessment strategies such as questioning, observation, and peer feedback to gauge student progress and address misconceptions in real time.
Overall, the outcomes for an educator in a lesson involving the application of this learning scenario extend beyond mathematical proficiency to include critical thinking, creativity, collaboration, and interdisciplinary learning. By fostering these skills and competencies, educators empower students to become lifelong learners equipped to navigate the complexities of the modern world.
Link to the learning scenario implemented: Geometry Hidden Behind the Old Walls (EN-CUR-159) – Teaching With Europeana (eun.org)
Do you want to discover more stories of implementation? Click here.
CC BY-SA 4.0: the featured image used to illustrate this article has been found on Europeana and has been provided by the Museum of Arts and Crafts, Zagreb.