Shapes Around Us

Chapter 1

A Note to Teachers about this Teacher Resource Document

This Teacher Resource Document has been designed to support teachers in effectively teaching “SHAPES AROUND US” to students in an inclusive classroom environment. The document emphasises meaningful understanding and application of 2D and 3D shapes through inclusive teaching strategies, differentiated adaptations, and engaging learner-centered activities that address diverse learning needs.

In addition to detailed classroom guidance, the resource provides a comprehensive range of supporting materials, including videos, ISL-enabled videos, audio resources, learning-teaching materials, learning cards, and visual organisers. Textbook activities have been further enriched and adapted using the principles of Universal Design for Learning (UDL) to ensure accessibility and participation for all learners. Teachers may effectively integrate the provided content, strategies, and aids to create an inclusive learning experience and achieve the intended learning outcomes for every student.

Learning Objective

1. Trace 2D shapes from the faces of 3D objects.
2. Match real-life objects with their corresponding geometric shapes.
3. Sort a given set of objects based on their shapes.
4. Construct simple models using 3D objects or classroom materials.
5. Use correct geometric vocabulary while describing shapes and objects.
6. Explain orally the difference between a flat shape and a solid shape.

Concepts and Sub-concepts Covered

• Recognising, Understanding the difference between 2D and 3D shapes.
• Identifying, recognising and understanding that 3D shapes are made of 2D faces.
• Identifying, recognising 3D shapes in the real world
• Identifying, recognising faces, vertices and edges of 3D shapes

Prerequisites

1. Identify basic 2D shapes such as square, rectangle, triangle, and circle in everyday objects.
2. Name and recognise common 3D objects such as cube, cuboid, cylinder, cone, and sphere.
3. Classify objects as flat (2D) or solid (3D).
4. Identify flat and curved surfaces on common 3D objects.
5. Construct 2D shapes with toothpicks.
6. Match, sort 2D/3D objects based on size and shape.
7. Identify, recognise the different angles formed by various 2D shapes

Prerequisites Reinforcement

Pre-teach Vocabulary

flat, curved, face, edges, corners, vertices, base, slide, roll, angles, right, acute, obtuse, diameter, radius, length, shortest, longest, cube cuboid, sphere, cylinder, cone, prism, pyramid

Learning Cards: Vocabulary with Picture Card

Pre-teach Critical Concepts

• 2D shapes have length and width, 3D shapes have length, width and height.
• Parts of a solid shape – face, edge, vertex/corner, flat surface, curved surface
• Show them a 3D model and ask them how many 2D shapes are being used.
• Show them a light house or any and ask what shapes will they use to build this?
• Parts of a solid shape – face, edge, vertex/corner, flat surface, curved surface
• What an angle is? Measuring a right angle using a set squareor using a corner of a book.
• Visually recognizing acute angle( less than right angle) and obtuse angle (more than right angle).
• Nets of solids – a flat pattern that folds to solids. Students can be made to physically fold a cube template, unfold a syrup box and fold it back before learning about it in a book.

Goals

Visual Cards: Building 3D Shapes

Activity 1: Exploring Nets of 3D Shapes

Content:

• Construct 3-D shapes by folding printed nets.
• Record the number of faces, vertices and edges for each shape in a structured table.
• Verify Euler’s Formula (F + V − E = 2) for all six shapes.

Materials required:

Students will work in a small group of 3

Nets activity 

• Printed net templates (A4/A3 size) on thick card paper for all 6 shapes – triangular prism, rectangular prism, hexagonal prism, triangular pyramid, square pyramid and pentagonal pyramid
• Scissors
• Tape/glue sticks
• Coloured pencils
• Rulers

Visual supports 

• Step by step visual chart for folding the nets
• Pre-folded 3-D models at each table for reference

Safety Measures:

For Scissors and Tools

• Cut away: Always cut away from your body. Keep your hands behind the blades.
• Helper hand: Keep the hand turning the paper at least 3 inches away from the blades.
• Passing: Pass the scissors handle-first with the blades closed in your hand.
• Right tools: Give left-handed scissors to left-handed students, and easy-squeeze (loop) scissors to those who need help.

For Desk and Movement

• Clear desks: Clear away water bottles and bags before starting.
• Stay seated: Always stay seated while cutting. Never walk with scissors.
• Easy glue: Use scent-free glue sticks. If using liquid glue, use a small dish and a cotton swab to avoid messes.

For Material and Sensory Safety

• Watch for paper cuts: Thick paper edges can be sharp. Do not slide fingers quickly along cut edges.
• Safe folding: Use a blunt tool (such as a plastic ruler) to make dents along the fold lines. Never use scissors or sharp needles.
• Fresh air and clean hands: Keep windows open to air out glue fumes, and keep wet wipes on hand for sticky fingers.

For Teacher Checklist (Before Class)

• Dark lines: Use a thick black marker on templates for students with visual impairments.
• Pre-cut paper: Have some shapes pre-cut for students who tire easily.
• Pre-dent lines: Pre-score fold lines so students with disabilities can feel where to fold.

Session 1 – Exploring Nets – Prism

Step 1: Shape in a bag – Pass a 3D shape in a bag and ask the students to feel and describe the shape without looking. Teacher can ask “how many flat sides can you feel? Do you find anything pointy? Introduce key vocabulary words – face, vertex, edge and label the shape.

Step 2:  Show an unfolded gift box or syrup box (square prism net). Ask: ‘What shape is this when flat? What do you think happens when I fold it?’ Prompt the children to count the faces of the square prism net and then the teacher folds and glues it to demonstrate how a square prism net can be folded back into its 3D shape. 

Ask: What is the name of this shape? Can you count the vertices and edges on this shape? 

Introduce all three prism nets using the visual charts. Ask the students to name each shape and count the number of faces together as a class.

VISUAL CHART – NETS of PRISMS

Step 3: On each table keep prefolded 3D shapes and a vocabulary card with names of all the 6 shapes for reference. 

Distribute net templates printed on thick card paper.

Ask how many triangles do you see, how many rectangles do you see on the net?

Students cut out, score fold lines, fold and tape their triangular prism, rectangular prism and hexagonal prism. 

As they fold, the teacher can prompt “Count the faces and the edges. Mark each vertex with a red colour dot. 

Students label each completed shape.

Step 4: Distribute Euler’s table worksheet to each student. Filling up the chart can be an individual activity.

Students fill in the values of F, V and E for the three prisms 

Guide the students to check the Euler’s Formula: F + V − E = ? 

Teacher says “Let’s try the triangular prism together first. A triangular prism has how many faces, vertices and edges?” The students will give the answers as 5 faces, 6 vertices and 9 edges. “Apply the Euler’s formula 5 + 6 – 9 = 2”. Now complete this formula, for the rest of the prisms, what answer do you get?”

Step 5: Each student shows one completed net and states: ‘My ___ prism has ___ faces, ___ vertices and ___ edges.

Make the whole class chant the Euler’s Formula  ‘F + V − E = 2!’ 

Here is a short, simple summary of the variations and scaffolds using bullet points:

Suggested Variation in Rules and Pace:

• One shape at a time: Pass out only one paper template at a time instead of all three. This keeps desks clean and stops students from feeling overwhelmed. Fast workers can make extra shapes or help peers.
• Partner up: Let students work in pairs with clear jobs. An ‘Engineer’ holds the ruler and counts the parts, while a ‘Crafter’ does the folding and taping. This lets students with motor difficulties focus on the math without getting frustrated.
• Fun ways to share: Let students show what they learned using movement. They can use flat palms for faces, point a finger for corners, or chant a rhythmic beat together: “F (clap) + V (clap) minus E (stomp) equals TWO!”

Suggested Scaffolds for Assistance:

• Easy-to-see and feel templates: Put puff paint, yarn, or hot glue on the cutting lines so they are easy to feel. Colour-code the paper so that the flat ends (bases) are one colour and the sides are another.
• Skip the hard parts: Keep some pre-cut, pre-creased paper ready. This helps students who tire easily or find it hard to hold a ruler straight, go straight to folding and math.
• 3D stickers for counting: Use small foam stickers, clay dots, or tape on the corners and edges. Students can touch or peel them off to count without losing track.
• Picture schedules: Show real objects on the board in a row: [Flat Paper] ➔ [Bent Paper] ➔ [Finished Shape]. This helps students see what step comes next.
• Simple math worksheets: Break the formula down into two smaller steps on the worksheet (First add F + V, then subtract E) to make the math easier to follow.

Session 2 – Exploring Nets – Pyramids

Step 1: Recall:  Display a prism net and a pyramid net side by side. Ask: ‘What is the same? What is different?’ Allow students to discuss among themselves for about 60 seconds. What does a prism net have?  Two polygons and a strip of rectangles. How about a pyramid net?

A pyramid net has one polygon base and many triangular faces.

Step 2: Unfold a pre-made square pyramid. Show the net flat. Count the faces together along with students. Fold the net slowly. Repeat the same steps for triangular pyramid and pentagonal pyramid using a visual chart.

VISUAL CHART – NETS of PYRAMIDS

Step 3: Folding Pyramid nets:  Students in a group of 3 fold 3 pyramid nets.

Students cut, score, fold, tape and label: ‘Triangular Pyramid’, ‘Square Pyramid’ and ‘Pentagonal Pyramid’. 

Teacher asks: ‘What do you notice about the flat shape before you fold it? How many triangles can you count on the net? Can you count the edges on the base?’ 

Step 4: EULER’S TABLE (Pyramids): 
Distribute Euler’s table worksheet to each student. Filling up the chart can be an individual activity.

Students complete the pyramid rows in the Euler’s Table.  

Students swap the tables with their peers, and check each other’s F + V − E calculation. 

Colour Coding: To differentiate between prism and pyramid shapes, prism rows can be in blue, pyramid rows in orange.

The teacher can prompt the students if they see any pattern in the Euler’s Formula??

Step 5: Prisms vs Pyramids – Class creates a Venn diagram chart on prisms and pyramids.  What do they have in common? What is unique? How is a triangular prism net different from a triangular pyramid net? Students share their ideas and display the chart on the wall.

Note to the Teacher: 

Euler’s Formula

Comparison – Prism and Pyramid

Video: Exploring Nets of 3D Shapes

ISL Video: Exploring Nets of 3D Shapes

Suggested Variation in Rules and Pace:

• The ‘un-tape’ rule: Use painter’s tape or dots instead of glue so students can unfold 3D shapes back into 2D nets to easily recount the sides.
• Pre-counted bases: Use patterned or shaded bases so students count the bottom shape first and don’t mix it up with the walls.
• Calculator clearance: Allow calculators for Euler’s Formula (F + V – E) to remove arithmetic stress and keep the focus on geometry.
• One shape at a time: Pace the class together. Cut, fold, and log the Triangular Pyramid before moving to the next shape.
• The ‘stuck edge’ gauge: If cutting takes too long, switch to pre-cut templates for complex shapes to save time for math.

Suggested Scaffolds for Assistance:

• Feel the shapes: Trace the cutting lines with puff paint, and use textured paper (like sandpaper) for the bases to assist visual learners.
• Pre-scored lines: Provide pre-creased or perforated templates to make folding easier for students with motor difficulties.
• Velcro and magnets: Use Velcro or magnets on edges during demos so shapes can be folded and unfolded repeatedly.
• Assigned group roles: Divide tasks into three roles: a Cutter for precision, a Folder for assembly, and a Recorder to count and log data.
• Colour-coded counting: Mark faces with colour, corners with clay dots, and edges with thick lines to match worksheet colours.
• Pattern clues: Help students spot the shortcut: for any pyramid, the number of Faces (F) always equals the number of Vertices (V).
• Touch before writing: Require students to physically touch and count corners and edges on their models instead of guessing the math.

Activity 2: Constructing 3D Shapes

Objective: Build 3-D shapes using straws (edges) and plasticine/clay (vertices).

Materials required:

• Drinking straws 
• Plasticine or air-dry clay
• Scissors

Setting for the activity: Students seated in small groups of 4 on a table. Each group will be provided with 50 straws and clay.

Type of Activity: Whole class activity

Role of the Teacher: Demonstrator and Observer

Preparation of Activity: The teacher distributes straws and clay to each group. Teacher demonstrates how to construct 3D shapes without faces and with only straws and clay balls. She also guides students while they construct the 3D shapes.

Procedure:

Step 1: Teacher asks “Can we build a 3-D shape without any flat faces and with only edges and corners?” The teacher shows a straw-and-clay model. The teacher asks students to predict “What does each straw represent? What does each clay ball represent?”

Step 2: Teacher explains that straws are edges and clay balls are vertices. The teacher demonstrates how to build a triangular pyramid. First roll 4 balls of clay, cut 6 straws of equal length. Make a triangle shape using 3 straws and  then push straws into clay balls at each vertex. Take three more straws, push one end of each straw into the three clay balls that form the vertices of the triangle. Gather the other end of the straws, join them together with a clay ball which forms the apex. The triangular pyramid is ready. Students count edges and vertices aloud as teacher builds the triangular pyramid.

Step 3: Students choose 2–4 shapes to build using straws and clay. Suggested sequence would be to start building a simpler shape like triangular pyramid then move on to building slightly more complex shapes like square pyramid and triangular prism. As the students build, they count all the vertices by counting the clay balls and count all the edges by counting the number of straws.

Step 4: Students display their straw-and-clay models. 

Video: Constructing 3D Shapes

ISL Video: Constructing 3D Shapes

Suggested Variation in Rules and Pace:

• The ‘fixed length’ rule: Pre-cut all straws to the exact same length. This automatically guides students in building regular shapes, such as perfect cubes or equilateral pyramids.
• The blueprint: Require students to first draw a 2D sketch of their shape, labelling the exact number of straws and clay balls needed. They can only take that specific amount from the supply pile.
• Structured pacing: Step through the first two shapes together as a whole class. Direct everyone to roll four balls at once, then pause, then cut six straws together, keeping everyone aligned.

Suggested Scaffolds for Assistance and Practice:

For Fine Motor and Physical Support

• Pre-rolled vertices: Provide a tray of ready-made clay balls so students with motor challenges can jump straight into building pyramids without wasting energy on rolling.
• Thick straws: Use wide-diameter straws instead of thin ones. They are easier to hold, cut, and attach to the clay.

For Cognitive and Visual Tracking Support

• Colour-coded vertices: Use different clay colours to highlight shape parts—for example, blue clay for a pyramid’s base corners and red clay for the top point (apex).
• Visual anchor mats: Give students a sheet of paper with the shape’s 2D base printed on it. They can place their clay balls directly at the corners of the paper to build accurately.

Critical Safety Instructions

• Bowl-cutting rule: Cut straws inside a small plastic bowl or box. This keeps snipped straw pieces from flying across the table into anyone’s eyes.
• The ‘no-poke’ rule: Teach students to keep their hands clear of the opposite end of the straw when pushing it into clay to avoid pinching or poking fingers and faces.
• Hygiene alert: Have students wash their hands before and after using sticky clay. Remind them: “Tools, not snacks!”

Tips for the Teacher:

• The ‘don’t fix it’ rule: If a model collapses because the clay is too small or at a bad angle, do not rebuild it for them. Ask guiding questions instead: “Why is it leaning? How can we make that corner stronger?”
• Avoid the ‘flat trap’: Watch for students building 2D pictures flat on the table. Lift one corner into the air and ask: “How do we pull this up so a tiny toy bug could crawl inside?”
• Link back to Euler: Keep the formula on the board. When groups finish, ask them what their hollow skeleton models are missing to satisfy the equation (the answer is the flat faces).

Day to Day Relevance

Content:

At Home –

Kitchen vessels:
Recognising that a round pan, a rectangular tray, and a cylindrical tin are different 3D shapes helps children understand why each stores and heats food differently.

Room layout and furniture:
Beds, tables, and cupboards are cuboids; clocks and plates are circles. Noticing shapes helps children describe positions and organise spaces logically.

Windows and doors:
Identifying rectangles and squares in windows and doors connects geometry to the idea that shapes are chosen for strength and fit 

Folding and packing:
Folding a square napkin into a triangle, or fitting items into a box, is direct use of shape knowledge and spatial reasoning.

Tiles and patterns on floors:
Floor tiles form repeating patterns of squares or hexagons — children can count shapes, find symmetry, and see how shapes tessellate with no gaps.

At School –

Books and notebooks:
Every book is a cuboid with rectangular faces. 

Classroom board:
The blackboard/whiteboard is a large rectangle. Measuring and drawing shapes on it reinforces the idea that shapes have exact properties — sides, corners, angles.

Drawing and art class:
Using rulers, stencils, and compasses to draw shapes is direct application. Recognising that a triangle can be tall and thin or short and wide deepens shape understanding.

In the Neighbourhood –

Buildings and rooftops:
Walls are rectangles, rooftops form triangles, water tanks are cylinders. 

Road signs:
Stop signs are octagons, warning signs are triangles, information boards are rectangles. 

Sports fields and courts:
A cricket pitch and a football field are rectangles. A basketball circle is exactly that — a circle. 

Vehicles:
Wheels are circles, headlights are circles or rectangles, the body of a bus is a cuboid. 

Playground equipment:
A slide has a triangular side frame, a merry-go-round is a disc (cylinder), and a swing frame is a rectangle. 

In Nature –

Honeycombs:
Bees build hexagonal cells.

Fruits and vegetables:
Oranges and tomatoes are spheres; a cucumber is a cylinder; a watermelon is a sphere; a carrot tapers like a cone. 

Leaves:
Leaf outlines are irregular closed shapes that children can trace, compare, and classify as having curved or straight edges 

Rocks and pebbles:
Smooth pebbles approximate spheres; flat slate is like a disc. 

Sun, moon, and shadows:
The sun and full moon appear circular; shadows stretch into ovals and triangles depending on the light’s angle. 

Assessment

Worksheet: Practice Worksheet 1

Worksheet: Practice Worksheet 1 (Enlarged)

Audio Worksheet: Practice Worksheet 1

Worksheet: Practice Worksheet 2

Worksheet: Practice Worksheet 2 (Enlarged)

Audio Worksheet: Practice Worksheet 2

Worksheet: Practice Worksheet 3

Worksheet: Practice Worksheet 3 (Enlarged)

Audio Worksheet: Practice Worksheet 3

Worksheet: Assessment Worksheet 1

Worksheet: Assessment Worksheet 1 (Enlarged)

Audio Worksheet: Assessment Worksheet 1

Worksheet: Assessment Worksheet 2

Worksheet: Assessment Worksheet 2 (Enlarged)

Audio Worksheet: Assessment Worksheet 2

Worksheet: Assessment Worksheet 3

Worksheet: Assessment Worksheet 3 (Enlarged)

Audio Worksheet: Assessment Worksheet 3

Cross-Curricular Connection

Science: 

The strongest structures in nature and engineering use prisms and pyramids because of their geometric properties. 

A triangular cross-section is remarkably strong — which is why triangular trusses are used in bridges and roof frames.

Minerals:
Quartz crystals grow naturally as hexagonal prisms. Salt crystals are square prisms.

Nature:
Bees construct honeycomb cells as hexagonal prisms. The hexagonal prism is the most efficient shape for storing honey — it uses the least wax to create the most space.

Packaging design:

Every product that sits on a supermarket shelf is housed in a 3-D shape. A packaging designer had to design that net, calculate the surface area, and choose the most efficient shape for storage and transport.

Architecture:

• The Louvre Pyramid in Paris is a square pyramid made of glass
• The Flatiron Building in New York is a triangular prism
• Geodesic domes  are made from triangular faces
• Traditional houses like A-frame houses in snowy regions are triangular prisms because snow slides off the steep sides

English:

The technical vocabulary of this lesson — face, edge, vertex, vertices, prism, pyramid, apex, net, polyhedron — is an opportunity to teach morphology and etymology:

• Vertex comes from Latin meaning “highest point” or “whirlpool” — the same root as “vortex”
• Prism comes from Greek prisma meaning “something sawed” — referring to the cross-sectional cut
• Pyramid comes from Greek pyramis — possibly connected to the Egyptian word for obelisk

History:

Leonhard Euler (1707–1783)
Euler was one of the most prolific mathematicians in history — he worked even after going completely blind, dictating his discoveries to a scribe. He discovered his polyhedron formula in 1752.

Egyptian pyramids
The Great Pyramid of Giza was built around 2560 BCE as a square pyramid. How did the ancient Egyptians build such a precise 3-D shape without modern tools? What did they know about geometry?

Geography:

Landforms as 3-D shapes

• Volcanic mountains: cone or square pyramid shape
• Basalt columns (Giant’s Causeway, Ireland; Fingal’s Cave, Scotland): hexagonal prisms
• Salt flats and crystal formations: cubic structures
• River deltas: triangular prism shapes when viewed in cross-section

For inclusive classroom support, the teacher can refer to the below Adaptations and Strategies:

Adaptations and Strategies: Attention and Focus

Adaptations and Strategies: Executive Functions

Adaptations and Strategies: Fine Motor Skills

Adaptations and Strategies: Number Sense

Adaptations and Strategies: Reading Skills

Adaptations and Strategies: Organisational Skills

Adaptations and Strategies: Receptive and Expressive Language Skills

Adaptations and Strategies: Visuospatial Skills

Adaptations and Strategies: Procedural Skills

Teacher Resource Document