Lesson Notes By Weeks and Term v3 - Primary 2
Three Dimensional shapes.
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Three Dimensional shapes.
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Subject: General Mathematics
Class: Primary 2
Term: 1st Term
Week: 11
Theme: Mensuration And Geometry
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Watch on YouTubeidentify and count the flat faces of a cube and a cuboid; identify and count the corners of a cube and a cuboid; identify and count the edges of a cube and cuboid; identify objects at home that are cuboids and cubes; identify the curved surfaces of a cylinder; mention three dimensional objects in the ir homes that are cylinders and spheres.
Three Dimensional (3D)
Shapes: These are solid shapes that have length, width, and height (or depth). Unlike flat (2D) shapes like squares and circles, 3D shapes occupy space and can be held. Common 3D shapes include cubes, cuboids, cylinders, and spheres.
Key Features of 3D Shapes: Faces: These are the flat or curved surfaces that make up the outside of a 3D shape.
Flat Faces: Smooth, flat surfaces like the sides of a box.
Curved Surfaces: Rounded surfaces, like the side of a tin or a ball.
Edges: These are the lines where two faces meet. For Primary 2, we focus on straight edges.
Corners (Vertices): These are the points where three or more edges meet. A single corner is called a vertex.
Specific 3D Shapes and Their Properties: Cube: Definition: A 3D shape with six identical square faces. All its faces are flat.
Properties: Faces: 6 flat square faces.
Edges: 12 straight edges.
Corners: 8 corners.
Examples in Nigerian context: Dice, sugar cubes, some small wooden blocks used for craft. Worked
Example: Imagine a standard dice. How many flat surfaces can you touch? (Answer: 6) How many straight lines can you trace on its body? (Answer: 12) How many sharp points does it have? (Answer: 8)
Cuboid: Definition: A 3D shape with six flat faces, where opposite faces are identical rectangles. Sometimes, two opposite faces can be squares.
Properties: Faces: 6 flat faces (usually rectangles, but can include squares).
Edges: 12 straight edges.
Corners: 8 corners.
Examples in Nigerian context: Matchbox, brick for building, shoebox, textbook, carton of milk, packet of biscuits. Worked
Example: Consider a typical building brick used in Nigeria. How many flat surfaces does it have? (Answer: 6) How many straight lines where surfaces meet? (Answer: 12) How many sharp points does it have? (Answer: 8) Observe that the faces are not all squares, some are longer rectangles. This differentiates it from a cube.
Cylinder: Definition: A 3D shape with two identical flat circular faces at opposite ends, connected by a single curved surface.
Properties: Flat Faces: 2 flat circular faces.
Curved Surfaces: 1 curved surface.
Edges: 0 straight edges (has two curved edges where the flat faces meet the curved surface, but for Primary 2, we focus on straight edges).
Corners: 0 corners.
Examples in Nigerian context: Tin of Milo/Peak Milk, soft drink can, drum, battery, "Gala" sausage roll. Worked
Example: Take a tin of Peak Milk. How many flat surfaces can you place it on? (Answer: 2, top and bottom) Can you find any straight lines where surfaces meet? (Answer: No straight lines, only curved ones where the top/bottom meets the side). Can you find any sharp points? (Answer: No) What kind of surface is the main body of the tin? (Answer: Curved surface)
Sphere: Definition: A perfectly round 3D shape where every point on its surface is the same distance from its centre.
Properties: Flat Faces: 0 flat faces.
Curved Surfaces: 1 single curved surface.
Edges: 0 edges.
Corners: 0 corners.
Examples in Nigerian context: Football, orange, tennis ball, marble, globe. Worked
Example: Examine a football. Can it be placed flat on a table without rolling? (Answer: No) Does it have any flat surfaces? (Answer: No) Does it have any sharp points or straight lines? (Answer: No) What kind of surface does it have? (Answer: A single curved surface)
Materials: Real-life objects representing cubes (dice, sugar cubes), cuboids (matchbox, brick, shoebox, textbook, carton), cylinders (Milo tin, drink can, battery, "Gala" roll), and spheres (football, orange, tennis ball). Pictures of these objects if real ones are scarce. A chart showing properties of shapes.
Teacher Activities: Introduction (10 minutes): Teacher displays a collection of real 3D objects (e.g., a matchbox, a dice, a tin of milk, a football). Teacher asks students to observe the objects and describe what they notice about their shapes (e.g., "some are flat on the sides, some are round"). Teacher introduces the term "Three Dimensional (3D) shapes" and explains that these are solid shapes that take up space.
Exploring Cube and Cuboid (20 minutes): Teacher distributes cubes (e.g., dice) and cuboids (e.g., matchboxes) to small groups of students. Teacher demonstrates how to identify a face by touching a flat side. Students count the faces on their objects, guided by the teacher. Teacher demonstrates how to identify an edge by tracing a straight line where two faces meet. Students count the edges on their objects. Teacher demonstrates how to identify a corner by pointing to a sharp point where edges meet. Students count the corners on their objects. Teacher asks students to compare the cube and cuboid in their hands: "What is similar? What is different?" (Similar: number of faces, edges, corners; Different: shape of faces). Teacher asks students to identify other objects in the classroom or at home that are cubes or cuboids. Exploring Cylinder and Sphere (20 minutes): Teacher distributes cylinders (e.g., milk tin) and spheres (e.g., small ball) to the groups. Teacher asks students to try placing the cylinder on different sides. "Can it stand on a flat surface? How many flat surfaces does it have?" (2). "What about the side? Is it flat or curved?" (Curved). Students identify the curved surface.
Teacher asks students about the sphere: "Does it have any flat sides?" (No). "Can it stand still without rolling?" (No). "What kind of surface does it have?" (One curved surface). Teacher explicitly states that cylinders and spheres do not have straight edges or sharp corners like cubes and cuboids. Teacher asks students to identify other objects in the classroom or at home that are cylinders or spheres. Consolidation and Chart Completion (10 minutes): Teacher draws a simple table on the board with columns for "Shape," "Flat Faces," "Curved Surfaces," "Edges," "Corners." Teacher guides students to complete the table for cube, cuboid, cylinder, and sphere based on their exploration. Teacher uses real objects to confirm answers.
Student Activities: Actively observe and handle various 3D shapes. Touch, count, and identify faces (flat and curved), edges, and corners of cubes and cuboids. Identify the curved surfaces and flat faces of cylinders. Identify the single curved surface of spheres. Participate in group discussions and share their observations. Name objects from their homes or surroundings that are cubes, cuboids, cylinders, and spheres. Complete a chart identifying the properties of the shapes.
Instructions for Teacher: Present these questions orally or write them on the board. Guide students to answer using the real objects they have explored. Discuss each answer fully.
Question 1: Look at this shoebox. (Teacher holds up a shoebox). a) Is it a cube or a cuboid? b) How many flat faces does it have? c) How many straight edges does it have? d) How many corners does it have?
Solution 1: a) Cuboid. (Comment: Students should observe that not all faces are squares; it's elongated.) b) It has 6 flat faces. (Comment: Guide students to count top, bottom, front, back, two sides.) c) It has 12 straight edges. (Comment: Guide counting: 4 on top, 4 on bottom, 4 vertical connecting them.) d) It has 8 corners. (Comment: Guide counting: 4 on top, 4 on bottom.)
Question 2: I have a tin of Milo. (Teacher holds up a Milo tin). a) Is it a cube, cuboid, cylinder, or sphere? b) Does it have any flat faces? If yes, how many? c) Does it have a curved surface? If yes, how many? d) Does it have any sharp corners?
Solution 2: a) It is a cylinder. (Comment: Students should recognize its round body and flat circular ends.) b) Yes, it has 2 flat faces (the top and the bottom circles). c) Yes, it has 1 curved surface (the round body of the tin). d) No, it has 0 sharp corners.
Question 3: Name two objects in your home that look like a cube.
Solution 3: A dice. A sugar cube. (Other possible answers: Small wooden block, some puzzle cubes). (Comment: Encourage students to think of actual objects they use daily.)
Question 4: A football is a three-dimensional shape. a) Does it have any flat faces? b) Does it have any curved surfaces? c) Which 3D shape does a football represent?
Solution 4: a) No, it has 0 flat faces. b) Yes, it has 1 curved surface. c) A football represents a sphere. (Comment: Emphasize its perfectly round nature and lack of flat parts.)
Differentiation Strategies: Visual Aids: Use large, clear pictures or posters of 3D shapes alongside real objects.
Manipulatives: Ensure all students, especially visual and kinesthetic learners, have ample opportunity to handle and manipulate the 3D objects. Provide a variety of objects.
Group Work: Allow mixed-ability groups where stronger students can support those who are struggling.
Remediation (for struggling learners): Targeted Re-teaching: Focus on one shape at a time (e.g., first cube, then cuboid) before introducing new ones.
Simplified Counting: For students struggling with counting, start with only two or three faces/edges/corners to count, then gradually increase. Use only very simple, clear objects.
One-on-One Support: Provide individual attention, physically guiding their hands to trace faces and edges or point to corners.
Drawing and Tracing: Ask students to trace the outlines of the flat faces of cubes and cuboids on paper to reinforce the concept of a "face." Matching Game: Create cards with pictures of 3D shapes and cards with their names or properties (e.g., "6 flat faces") for a matching activity.
Extension (for high-achieving learners): Exploring Complex Objects: Challenge students to identify the different 3D shapes that make up more complex objects (e.g., a house might have a cuboid body and a triangular prism roof, or a toy car might have cuboid body and cylindrical wheels).
Drawing 3D Shapes: Encourage students to try drawing simple 3D shapes (e.g., a cuboid) on paper, focusing on representing depth, even if basic.
Shape Building: Provide materials like toothpicks and gumdrops/playdough for students to construct simple skeletons of cubes and cuboids, thus visually understanding edges and corners.
Categorization Challenge: Ask them to sort a larger collection of objects into various categories, including "objects that can roll" (spheres, cylinders) versus "objects that can stack" (cubes, cuboids).
Construction and Housing: Students can observe how many buildings, especially in urban and rural Nigeria, are constructed primarily from cuboid-shaped bricks or blocks. The rooms themselves are often cuboids. Identifying these shapes helps them understand the structure of their homes and schools. They can also look at water tanks on roofs, some of which are cylindrical.
Packaging and Products: Almost every item bought in the market or local shop comes in 3D packaging.
Cuboids: Cereal boxes, biscuit packets, cartons of milk, shoeboxes. Understanding cuboids helps them appreciate how products are contained and stacked efficiently in kiosks or supermarkets.
Cylinders: Cans of soft drinks, tins of Peak milk or Milo, local drums for water storage, "Gala" sausage rolls. This helps them identify common food and drink items by their shape.
Sports and Play: Spheres: Footballs, tennis balls, marbles, and oranges (a common fruit in Nigeria) are perfect examples of spheres, used in games and as food.
Cubes: Dice used in board games. This directly relates mathematics to recreational activities.