Counting Sides and Corners

Overview

Lesson 2 of 9 in Shapes and Their Properties. In this 45-minute lesson, Year 2 and Year 3 students investigate how to count sides and corners (vertices) systematically, then identify and sort triangles, squares, rectangles and circles by their properties.

Learning intentions

Students will:

• identify sides and corners (vertices) on familiar 2D shapes
• count sides and corners systematically, starting at one point and moving around the shape
• describe triangles, squares, rectangles and circles using their properties
• match shape names to pictures and property statements

Success criteria

• I can point to and count every side of a shape once.
• I can count and identify the corners, or vertices, of a shape.
• I can name a triangle, square, rectangle and circle.
• I can explain one property that helps identify each shape.

Curriculum links

• Recognising, describing and classifying familiar two-dimensional shapes.
• Identifying and comparing features of shapes, including sides, corners and curved edges.
• Using mathematical language to communicate observations and justify classifications.
• Developing reasoning through sorting, matching and explaining mathematical ideas.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook and prior knowledge

Open with the hook and learning intention slides. Display a mixed group of shape cut-outs and ask: “How can we prove how many sides and corners each shape has?” Invite students to name shapes they recognise and briefly share what they already know about sides and corners.

2. 5–13 minutes – Explicit teaching

Use the shape investigation slides and model with a large triangle, square, rectangle and circle. Explain that a side is a straight boundary and a corner, or vertex, is where two straight sides meet. Demonstrate choosing one starting point, touching or tracing each side once, and recording the total.

Create a class table:

• Triangle: 3 sides, 3 corners
• Square: 4 sides, 4 corners
• Rectangle: 4 sides, 4 corners
• Circle: 0 straight sides, 0 corners; 1 curved edge

Clarify that a square and rectangle both have four sides and four corners, but their overall properties can differ. For this lesson, focus on counting and naming.

3. 13–23 minutes – Hands-on partner sort

Give each pair a set of teacher-prepared shape cut-outs and use the 2D shape property cards as an optional reference. Students sort the shapes into groups by name, then check each shape by tracing around it and counting sides and corners aloud.

Prompt with: “Where will you start counting?”, “How do you know you have counted each side once?” and “What is the same about a square and a rectangle?” With six students, listen closely to each pair and correct double-counting or counting the curved edge of a circle as a straight side.

4. 23–30 minutes – Explain and compare

Return to the discussion and comparison slides. Select one shape from each group and ask students to justify its classification using a sentence frame: “This is a ___ because it has ___ sides and ___ corners.”

Compare a square and rectangle. Ask students to identify what is alike and what is different. Include a deliberately rotated square to show that turning a shape does not change its name or properties.

5. 30–40 minutes – Independent practice

Distribute the sides, corners and shape names worksheet. Students complete tasks independently: count and record sides and corners, match shapes to their names, and connect each shape to a correct property statement. Encourage students to trace each boundary with a pencil or finger before writing.

Support students to complete the first example with the teacher, then circulate and ask them to explain their counting rather than simply supplying answers.

6. 40–45 minutes – Plenary and check for understanding

Use the plenary slides to show four final shapes, including a rotated shape and a circle. Each student gives one answer or explanation. Ask: “How can you count without missing a side?” and “Why does a circle have no corners?” Record key language and address any remaining misconception.

Resources

• the complete shape investigation slide deck
• the sides, corners and shape names worksheet
• Teacher-prepared paper or plastic cut-outs of triangles, squares, rectangles and circles
• Whiteboard and markers
• Pencils and coloured pencils
• Small trays or envelopes for each pair’s shapes
• Optional large demonstration shapes
• the 2D shape property cards

Assessment

• Observe partner sorting and listen for accurate use of “side”, “corner”, “vertex”, “straight” and “curved”.
• Check whether students start at one point and count each side and corner once during the hands-on task.
• Review the worksheet and plenary responses, noting students who confuse edges and corners or count a circle’s curved edge as a side.

Differentiation

• Support: provide larger, clearly outlined shapes; use finger tracing, a starting dot and a counting rhythm. Rehearse the sentence frame orally before writing.
• Support: work with a teacher-led group using only triangles, squares and circles before adding rectangles; pair students strategically.
• EAL/SEN: display a visual word bank with labelled examples for side, corner, vertex, straight and curved; accept pointing, drawing or oral explanations alongside written answers.
• Extension: ask students to find different shapes with four sides, compare a square and rectangle, and explain why a rotated shape remains the same shape.