Geometry Lesson Plan: Plane Figures and Tangrams
Overview
This lesson plan introduces students to plane figures through the engaging medium of tangrams. Students will explore basic geometric shapes, understand their properties, and discover how these shapes can be combined and manipulated to create complex figures and designs.
Target Grade: Grades 3-5
Duration: 60-90 minutes
Subject: Mathematics / Geometry
Learning Objectives
By the end of this lesson, students will be able to:
- Identify and name basic plane figures (triangles, squares, parallelograms)
- Describe properties of different shapes (number of sides, vertices, angles)
- Understand the relationships between shapes and their composite forms
- Develop spatial reasoning and problem-solving skills using tangrams
- Communicate mathematical ideas about geometry effectively
Key Concepts
Plane Figures: Two-dimensional shapes that lie on a flat surface. They include triangles, quadrilaterals, circles, and more.
Tangrams: A traditional Chinese puzzle consisting of seven flat shapes (called tans) which are put together to form shapes. The seven pieces are:
Large Triangle
Medium Triangle
Small Triangle
Square
Parallelogram
Materials Needed
- Cardstock tangram sets (one per student or pair)
- Large teacher demonstration tangram set
- Worksheets with tangram puzzles
- Graph paper
- Markers or colored pencils
- Projector or whiteboard for demonstrations
- Optional: Tangram puzzle books or cards
Vocabulary
- Polygon: A closed plane figure with straight sides
- Triangle: A three-sided polygon
- Quadrilateral: A four-sided polygon
- Square: A quadrilateral with four equal sides and four right angles
- Parallelogram: A quadrilateral with opposite sides parallel
- Vertex: A corner point of a polygon
- Congruent: Having the same size and shape
- Similar: Having the same shape but possibly different sizes
Lesson Procedure
1. Introduction (10-15 minutes)
- Begin a discussion about shapes by asking students to identify shapes in the classroom.
- Introduce the concept of plane figures as two-dimensional shapes that lie on a flat surface.
- Show students examples of basic plane figures using the whiteboard or projector.
- Introduce tangrams as a traditional Chinese puzzle that has been used for centuries to explore geometry and develop spatial reasoning.
- Demonstrate how tangram pieces can be combined to form various shapes.
2. Direct Instruction (15-20 minutes)
- Distribute tangram sets to students (or pairs).
- Guide students to identify and name each of the seven tangram pieces by shape and size.
- Discuss properties of each shape (number of sides, vertices, angles).
- Demonstrate how to create larger shapes using combinations of the basic tangram pieces.
- Show students how to transform shapes by rotating, sliding, and flipping pieces.
3. Guided Practice (20-25 minutes)
Lead students through these structured activities:
- Activity 1: Have students sort the tangram pieces by shape, then by size, counting and recording how many pieces of each type they have.
- Activity 2: Challenge students to create a square using only two pieces, then three pieces, continuing until they use all seven pieces.
- Activity 3: Provide simple tangram puzzle outlines and guide students in solving them, discussing strategies as a class.
- Activity 4: Ask students to create specific shapes (like different types of triangles or quadrilaterals) using their tangram pieces.
4. Independent Practice (20-25 minutes)
Provide opportunities for students to work independently or in pairs:
- Activity 1: Challenge students to solve increasingly complex tangram puzzles from worksheets or cards.
- Activity 2: Ask students to create their own tangram designs and draw outlines for partners to solve.
- Activity 3: Have students measure and calculate the area of different tangram pieces (for advanced students).
- Activity 4: Guide students to create animals, people, objects, or abstract designs using their tangram pieces.
5. Discussion and Reflection (10-15 minutes)
- Invite students to share their tangram creations with the class.
- Ask questions such as:
- "What strategies did you use to solve the tangram puzzles?"
- "Which pieces were the most challenging to work with and why?"
- "How did you decide which pieces to use for different parts of your designs?"
- "What did you learn about plane figures through working with tangrams?"
- Discuss real-world applications of geometry and shape combinations.
Assessment
Evaluate student understanding through:
- Observation of student participation and engagement during activities
- Review of completed tangram puzzles and designs
- Student responses to discussion questions
- Short exit ticket asking students to identify and describe properties of specific plane figures
- Portfolio of student-created tangram shapes with written descriptions
Differentiation
| For Students Who Need Additional Support | For Advanced Learners |
|---|---|
| Provide outlines showing how many pieces of each shape are needed in tangram puzzles | Challenge students to solve puzzles without outlines |
| Work in small groups or pairs rather than independently on challenging puzzles | Have students calculate the area of composite shapes |
| Provide physical manipulatives and visual references for shape properties | Challenge students to create puzzles with specific area or perimeter requirements |
| Offer step-by-step verbal guidance for solving puzzles | Intourage students to create and name their own geometric proofs about tangram relationships |
Resources and Extensions
- Virtual tangram puzzles and apps for interactive whiteboards
- Books on tangram puzzles and the history of tangrams
- Geometric art activities using tangram pieces
- Connection to fractions by having students determine what fraction of the total square each tangram piece represents
- Cross-curricular connections to art (creating tangram art), history (Chinese culture), and language arts (writing stories about tangram characters)
Tangram Storytelling
Students create a sequence of tangram figures that tell a story, then write or present the narrative to accompany their geometric illustrations.
Fraction Tangrams
Students explore the fractional relationships between tangram pieces, determining what fraction each piece is of the whole square and comparing these relationships.
Tangram Symmetry
Students create designs that demonstrate line and rotational symmetry using their tangram pieces, identifying lines of symmetry in their creations.
Outdoor Tangram Art
Students use natural materials or sidewalk chalk to create large-scale tangram designs outdoors, applying geometry concepts in a different context.
Tangram Challenge Day
Set up stations with different tangram challenges and have students rotate through, collecting points for completing increasingly difficult puzzles.
Digital Tangram Design
Students use digital tools or apps to create tangram designs, exploring additional functionality like rotation, color changes, and scaling.
Standards Alignment
Common Core Mathematics Standards
- 3.G.A.1: Understand that shapes in different categories may share attributes, and that the shared attributes can define a larger category.
- 3.G.A.2: Partition shapes into parts with equal areas.
- 4.G.A.1: Draw points, lines, line segments, rays, angles, and perpendicular and parallel lines.
- 4.G.A.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.
- 4.G.A.3: Recognize a line of symmetry for a two-dimensional figure.
- 5.G.B.3: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.
Mathematical Practices
- Make sense of problems and persevere in solving them
- Reason abstractly and quantitatively
- Construct viable arguments and critique the reasoning of others
- Model with mathematics
- Use appropriate tools strategically
- Look for and make use of structure
- Look for and express regularity in repeated reasoning
Geometry Lesson Plan: Plane Figures And Tangrams and Reference File Download Link
