Lesson plan of Quadrilaterals: Introduction

Learning Objectives (5 - 7 minutes)

1. Understanding Quadrilaterals: Students should be able to identify and describe the different types of quadrilaterals, with specific attention to their unique characteristics and properties.

2. Identifying Quadrilaterals in the Real World: Students will learn to apply this knowledge of quadrilaterals to identifying these shapes in real-life situations or in diagrams.

3. Developing Logical-Mathematical Reasoning Skills: The aim is for students to demonstrate logical and mathematical reasoning in their ability to identify and describe quadrilaterals.

   Additional Learning Objectives:

   • Encourage Self-Directed Learning: Facilitate students' independence in learning by actively encouraging discovery of knowledge and engagement with lesson materials.

   • Promotes Meaningful Learning: Aim for connections between lesson activities and real-world context and scenarios.

   • Builds Critical Thinking Skills: Provide opportunities for reflection and analysis of mathematical concepts to encourage student development of critical thinking skills.

Introduction (10 - 15 minutes)

1. Review of Prior Knowledge: Begin class time by reviewing concepts of plane figures and polygons. It will be important emphasize that a quadrilateral has exactly four sides before progressing to its more specific classification. (3 - 5 minutes)

2. Challenge Problem #1 - Quadrilateral Challenge: Pose a scenario such as, "an architect needs to find the area of a quadrilateral shaped room but she needs all the sides of quadrilateral shaped room of the quadrilateral shaped area to be different lengths, is it possible?, what about if it were all equal sides? " to encourage them to think about possibilities with the creation and limitations on creating the different shaped quadrilaterals. (3 - 5 minutes)

3. Real-World Examples of Quadrilaterals : Transition and share how we see quadrilateral shapes in our own environment with examples such as: stop signs and street signs or a computer or television screen and note that this is the shape of a cell phone and the whiteboard in our class or even a dollar or playing cards or even a tissue box, all quadrilaterals. This can help students see that this topic is applicable in other scenarios. (2 - 3 minutes)

4. Challenge Problem #2 - The Mysterious Symbols: Students move beyond the standard symbols and engage in thinking of how and why we use various symbols to represent certain terms and ideas with examples such as "Have you considered why the plus or minus or equals sign is a kind of quadrilateral shape, look and see if you discover a reason behind why this is the case and share with the entire group". This helps to spark curiosity, drive engagement with outside sources and promote further research. (2 - 3 minutes)

5. Introduce Today's Topic - Fascinating Quadrilateral Classification: Transition with the introduction of topic: classifying quadrilaterals. State that just like with people, quadrilaterals have various "personalities " and throughout instruction, students will become familiar with identifying these and understanding their unique characteristics as we see and utilize them throughout our world. (1 - 2 minutes)

Development (20 - 25 minutes)

1. Activity #1 - Construction Time (10 - 12 minutes): Assign students to groups (4-5 students per group). They will be provided various supplies: chart paper (large and small), rulers , protractors and a pair of compasses (per students or per pair) for a hands on activity where they will be expected to create the various shaped quadrilaterals (rectangular, square, isosceles trapezoid parallelogram, rhombus) which can be teacher assigned randomly with a list for each and have precut chart construction or provide the whole group one large chart paper that they all contribute and collaborate to complete or provide each a large and a smaller sheet so they create a few examples to share out. Each person in the group should complete at three examples, so encourage collaboration within the groups for efficiency as well as ensuring understanding amongst members for each example they produce. While circulating and checking in with their progress during creation time provide positive feedback, answer questions to enhance the learning and growth in the areas they demonstrate a good approach to the process or where they may be misunderstanding the concepts, to promote deeper understanding of what is expected within the project for success in their creations.

   • Step 1: Each group should draw out (with rulers), the different types to categorize the different sides.

   • **Step 2 **: Then determine and write a description of the characteristics (number of sides) and the specific sides that are parallel and the sides that are perpendicular and the number or line segment lengths which are equal in each of their shapes.

   • Step 3: Teams will rotate around viewing, discussing and comparing their examples to see the various examples that demonstrate the learning from this first activity.

2. Activity #2 - Scavenger Shapes (10 - 12 minutes): Now that all groups have created a few sample models of shapes that meet the criteria of the quadrilaterals, facilitate a gallery walk where students will circulate around the classroom looking at each other creations as well to look at various real world examples that you, yourself have placed around for their exploration (these can range from a photograph that is a quadrilateral shape posted for their view or actual objects within the classroom that have those quadrilateral shaped forms). As they rotate, allow and opportunity to engage them in discussion to identify the specific qualities such as "How are the angles different and alike. Which quadrilateral shape has the most right or perpendicular line segments? " which allow opportunities for deeper communication as well as analysis and discussion of the characteristics amongst the groups.

   • Step 1: Have the different quadrilaterals posted around in various location for observation and discussion

   • Step 2: Allow the teams an opportunity to walkabout (quietly) and discuss and analyze their findings

   • Step 3: Provide guidance and assistance in answering clarifying questions to deepen their discussion.

3. Extension Activity - The Quadrilateral Connection (5 - 8 minutes): Transition the learning by connecting with technology, encourage research to find real examples to connect this mathematical idea. Have students take out personal technology to connect and find real - life application examples. Students should be encouraged, throughout instruction, to make these connection and provide examples, so during this segment, they are encouraged to explore various media platforms to support the research and understanding, for example, if a student enjoys video clips, encourage this form for research or perhaps a student may want more of a hands - on interaction such as visiting websites with interactive applets related to the learning. This can occur during classroom environment or be provided to student as individual exploration to be brought back in a collaborative share to the entire class during the following class session as well as a formative grade on the research they have conducted.

- **Step 1**: Individually or within their preassigned team(s), students research examples of quadrilaterals in the real or natural environments

- **Step 2**: Each research team is to come up to three specific unique representations of quadrilaterals found (with supporting evidence of image(s), and short description). 

- **Step 3**: Students present findings, showcasing real world connection and solidifies their understanding through their presentation of learning.

Debrief (8 - 10 minutes)

1. Whole Class Discussion (3 - 5 minutes): Open floor for whole group participation. Each team should share out a few key points of learning for the two activity portions as well as providing 1- 2 interesting real-world examples they came across during their quadrilateral investigation as well as 1 additional question they came up throughout the activity (which can be added into an exit ticket for individual self-reflection and assessment of growth during their learning). Provide ample time for student sharing and discussion of their findings and questions as well as opportunities to ask any clarifying questions to strengthen their knowledge and understanding. This can be a time where they discuss misconceptions amongst group members as well for clearing misunderstandings or misconceptions.

   • Step 1. Each group presents their findings.

   • Step 2. Students discuss and analyze the findings in order to consolidate their learning.

2. Connecting the Activity/Real World to Theory and Concepts (2 - 3 minutes): Transition the conversation from the activity portion into how this connects with their prior understanding of shapes within mathematics. This can look like: "Can you explain how constructing the models aided and supported your identification of characteristics? Where you able to visualize or understand the concepts any better by creating and comparing various examples with your peers?"

This can also be a reflective portion where they discuss challenges that they faced during construction and what they would differently, and how this has supported growth in their understanding or has provided a deeper level or understanding in geometry, specifically with quadrilateral classification.

-  **Step 1**.  Discuss the relevance or connection to the real world examples.

3. Individual Reflection Questions (2 - 3 minutes). To close the lesson allow students time to provide a 1-2 sentence summary as an opportunity for individual self-assessment on their learning of how they did today with understanding the learning objective and what improvements they may consider doing differently to enhance their learning experience. This also provides the teacher feedback on areas for future lessons.

-  **Step 1:** Provide an individual moment (allow them to write their response, and encourage no names written).

-  **Step 2:** Collect the responses for further analysis and review to provide future tailored supports for individual learners within your class.

Conclusion (5 - 7 minutes)

1. Summarize Key Learning (2 - 3 minutes): Begin to provide a recap or review with students, reminding them of the learning from the lesson. Provide the definition of a quadrilateral with its attributes (4 sides) reinforcing how to categorize them by common attributes. Ask questions and provide various examples and non-examples to help solidify and deepen their understanding as we review together, ensuring all are prepared to successfully move forward into the forthcoming related topics.

   • Step 1: Review the definition of a quadrilateral.

   • Step 2. Provide various examples (non –examples and non- examples), to further solidify the concept.

2. **Connect with Mathematical Practices 1 - 2 minutes): Quickly emphasize how these activities support and build mathematical thinking through identifying shapes in a real - world context and through their model creations to demonstrate their conceptual understanding. Encourage students to connect and identify which Mathematical Practices (as defined by the CCSS) this lesson specifically supported them developing.

• Step 1. State which Mathematical Practice this learning experience addressed or supported.

• Step 2. Discuss and emphasize how it relates to what was learned today in regards to mathematical practices.

3. Provide Next Steps or Resources to Support 1 - 2minutes) Provide opportunities for further student exploration or engagement, this will vary according to the time, resources and specific objectives being addressed by the teacher. It can range in formats such as a follow-up activity (worksheet) or additional online/offline games to reinforce skills as well as provide extension and enrichment opportunities for differentiation for the classroom. This also provides opportunities for self-directed learning where students pursue deeper understanding by extending concepts learned during direct instructions with teacher provided additional tools to support their continued mathematical growth. These additional resources may focus and provide deeper learning of the specific topic that was taught within their lesson.

   • Step 1. Introduce additional resources that students can independently access.

   • Step 2. Highlight how these extra tools can enhance student exploration and learning of the subject material.

4. **Exit Ticket - What's Next (1 minute)*: Provide time and opportunity (5-7 minute) for a closing and summary of their understanding with a short exit ticket. Students can answer a series of questions, or provide a brief 1-2 word response to a reflection question. This allows for formative assessment for the teacher and also provides students to demonstrate their understanding in various forms as well as promote their self–awareness regarding their level as it was instructed within the lesson.

   • **Step 1. ** Pose 2- 3 reflection or summary question (on notecard slips/index cards) or use a QR/Online digital response tool (Google, Microsoft or Nearpod type response for immediate online feedback to student and teacher).

   • Step 2: Collect slips as the students exit, review and grade, provide any necessary follow up needed in the next classroom meeting (re -teach/ reteaching, small or whole guided group time with teacher or peer to provide reinforcement and/or enrichment).