Lesson 1, 2, 3 Geometry PDF

Sphere Icosahedron WHAT IS GEOMETRY? - Geometry is the branch of mathematics that explores the properties of space and the 3. 2D Shapes (Two-Dimensional Shapes) arrangement of objects within it....

Sphere Icosahedron WHAT IS GEOMETRY? - Geometry is the branch of mathematics that explores the properties of space and the 3. 2D Shapes (Two-Dimensional Shapes) arrangement of objects within it. - are flat figures that have only length and - Geometry deals with the measurement and width, existing in a plane. These shapes relationships of points, lines, angles, and are typically depicted on paper or surfaces. screens. - Geometry is the study of shapes and their properties in space. BASIC GEOMETRIC TERMS 1. Point - A location in space, represented by a dot. It has no size or dimension. a. Segment – part of a line that has two endpoints. b. Ray – part of a line that has one endpoint and extends infinitely in one direction. c. Line – straight path that extends infinitely 4. 3D Shapes (Three-Dimensional Shapes) in both directions. It is defined by two - are solid objects that have length, width, points. and height (or depth). These shapes 2. Angles resemble physical objects and can be - The space between two intersecting lines or held and manipulated in space. line segments, measured in degrees. STANDARD VS NON STANDARD Standard units of measurement - They are used consistently and uniformly across the world for precise and accurate  measurements. Common examples of Present students with challenging geometric standard units include: problems that require critical thinking and a. Meter (m) for length. problem-solving skills. b. Kilogram (kg) for mass. Encourage them to analyze given information, c. Second (s) for time. deduce conclusions, and apply geometric d. Kelvin (K) for temperature. principles to find solutions. Non-standard units of measurement 5. Group Activities and Discussions - They are often used for approximate Organize group discussions, collaborative measurements in everyday life but lack projects, and peer-to-peer teaching. the precision and consistency of standard units. Non-standard units can This promotes active learning, as students vary from one context or culture to explain concepts to each other, share insights, another. Examples include: and collectively solve problems. a. Footsteps to estimate distance. b. Handful to estimate quantity or volume. c. Thumb’s length for rough estimations of length. WAYS TO TEACH GEOMETRY TO INTERMEDIATE LEARNERS 1. Hands-On Activities Use physical models, manipulatives, and interactive tools to help students visualize and manipulate geometric shapes. Activities like building 3D models with paper or using geometric puzzles can make learning more engaging and concrete. 2. Real-World Applications Connect geometry to real-life situations and practical examples. Show how geometry is used in architecture, art, engineering, and everyday scenarios. This helps students understand the relevance of geometric concepts. 3. Visual Aids and Technology Utilize visual aids such as diagrams, charts, and animations to illustrate geometric concepts. Incorporate technology like interactive software or apps that allow students to explore and experiment with shapes in a dynamic way. 4. Problem-Solving Tasks  LESSON 2: PERIMETER, CIRCUMFERENCE & AREA Perimeter - is the distance around the outside of any shape. It's like adding up all the sides. Circumference - is the distance around the edge of a circle. It's like measuring the circle’s "outer border." Ways to Teach Measurement to1 𝜋 = 3.14 Intermediate Learners C= 2 π r 1. Area Tile Models C= 𝜋d - Provide square tiles or grid paper to help students visualize area. - Have them count the number of tiles within a shape to calculate its area. 2. Drawing Shapes and Calculating Area Perimeter - the amount of space taken up by a 2D - Have students draw various shapes and shape or surface. calculate their perimeters using appropriate formulas (e.g., P = 2l + 2w for rectangles). - This reinforces the connection between shapes and their perimeters. 3. Geometric Shape Puzzles - Give students puzzles that involve rearranging geometric shapes to find the total area. - This encourages spatial reasoning and problem-solving skills. 4. Real-Life Area Applications - Explore real-life scenarios where area calculations are necessary, such as calculating the area of a room for carpeting or the surface area of a box for packaging. - This demonstrates the practical relevance of area measurement. ½ = 0.5 LESSON 3: PYTHAGOREAN THEOREM History of Pythagorean Theorem Pythagoras - for whom the theorem is named, lived in ancient Greece, 2500 years ago. - It is believed that he learned the theorem during his studies in Egypt. c2 = a2 + b2 Surface Area - The measure of the total area that covers the outer part of a three-dimensional object. - It is typically expressed in square units, such as square inches or square meters. - Surface area is like the wrapping paper that covers the outside of an object. - It tells you how much space the object's surface covers. Volume - the measure of the amount of space that a three-dimensional object occupies. - It is typically expressed in cubic units, such as cubic inches or cubic centimeters. - Volume is like the amount of stuff that can fit inside an object. - It tells you how much space is inside the object. Ways to Teach Measurement to Intermediate Learners 5. Math Games - Pythagorean theorem can be integrated 1. Hands-On Activities into treasure hunt-style games where a. Pythagorean Theorem: Have students students use the theorem to find hidden create right triangles with cardboard or clues. sticks and measure the sides to see if the theorem holds true. 6. Peer Teaching b. Volume: Provide containers of different - Encourage students to explain these shapes and sizes, and ask students to concepts to their peers. measure the volume of water they can - This reinforces their understanding and hold. helps both the explainer and the listener. c. Surface Area: Use cardboard boxes and have students calculate the amount of 7. Project-Based Learning wrapping paper needed to cover them. - Assign projects that require students to design and build something, like a model house using the Pythagorean theorem to 2. Drills ensure right angles. a. Pythagorean Theorem: Provide a set of - Have them design a product package right triangles with various side lengths and calculate its volume and surface and ask students to calculate the missing area. side length using the Pythagorean theorem. b. Volume: Offer a series of 3D shapes (cuboids, cylinders, spheres, etc.) and ask students to calculate their volumes and surface areas. Provide objects with irregular shapes and have students estimate and then calculate their volumes and surface areas. 3. Storytelling - Create stories or scenarios that involve these concepts. - For instance, tell a story about a character who needs to calculate the distance to find a treasure using the Pythagorean theorem. 4. Teacher-Made Worksheets - These teacher-made worksheets serve as a tool for students to apply their knowledge, reinforce understanding, and develop problem-solving skills. - They can be used for in-class practice, homework assignments, or assessment to gauge students' proficiency in these mathematical concepts.