Polygon Detectives

Overview

Students investigate how polygons can be classified using side and angle properties. They apply triangle angle-sum reasoning, compare relationships between quadrilaterals and design a decision-making flow chart to sort unfamiliar shapes.

Learning intentions

Students will:

• classify polygons according to the number of sides, side properties and angle properties
• distinguish regular, irregular, convex and concave polygons
• use the triangle angle sum to reason about the interior angle sum of other polygons
• design and explain an algorithm for sorting polygons

Success criteria

• I can describe a polygon using accurate geometric vocabulary.
• I can classify triangles and quadrilaterals using more than one property.
• I can calculate the interior angle sum of a polygon by decomposing it into triangles.
• I can create a clear sequence of questions that sorts a set of polygons.

Curriculum links

• Classification of triangles, quadrilaterals and other polygons by side and angle properties.
• Interior angle sum of triangles and using it to determine the angle sum of other polygons.
• Designing and explaining algorithms that sort and classify sets of shapes.
• Identifying relationships between squares, rectangles, rhombuses, parallelograms, kites and trapeziums.

Lesson structure (70 minutes)

1. 0–7 min · Hook and retrieval. Display the opening polygon challenge showing a collection of differently oriented and sized polygons, including a concave shape. Ask, “What makes these shapes belong to the same family?” Students independently list visible properties, then share one observation with a partner; teacher records precise vocabulary such as side, vertex, angle, parallel, equal, regular, irregular, convex and concave.

2. 7–18 min · Build shared understanding. Use the classification teaching slides to model that polygons are closed, flat shapes made from straight line segments, and to distinguish classification by number of sides, side properties and angle properties. Students complete a quick “true, false or depends” response for statements such as “All quadrilaterals have four equal sides” and “A square is a rectangle”, explaining their reasoning.

3. 18–30 min · Angle investigation. Give each pair a paper triangle and ask students to tear or cut off its three corners and place them together on a straight line. Refer to the triangle angle investigation slide and discuss why the angles total 180°. Model drawing diagonals from one vertex of quadrilaterals and pentagons, then generalise: an (n)-sided polygon can be divided into (n-2) triangles, so its interior angle sum is (180(n-2)). Students calculate the sums for a quadrilateral, pentagon and hexagon and explain the pattern.

4. 30–47 min · Guided classification task. Distribute the polygon classification and angle reasoning worksheet. Students work in pairs to classify a mixed set of polygons, identify overlapping relationships among quadrilaterals and calculate missing angle sums or unknown angles using the triangle rule. Pause halfway for a whole-class check: students hold up or point to the property that justifies each classification, rather than naming a shape only by appearance.

5. 47–62 min · Algorithm design. Use the flow-chart modelling and challenge slides to model a decision tree beginning with “Does it have three sides?” and using yes/no questions about sides and angles. In groups of three, students design an algorithm that sorts a provided set of polygons into useful categories, such as triangles, quadrilaterals, regular/irregular or convex/concave. They test it on two shapes, revise any question that causes ambiguity and prepare to explain the sequence of decisions.

6. 62–70 min · Share and assess. Invite two groups to display their algorithms and test them with a shape chosen by the class, using the plenary and exit-ticket slide. Students complete the final three questions on the worksheet: define a polygon property, find the interior angle sum of an octagon, and write one decision that would separate a square from a non-square quadrilateral. Collect responses to identify next steps.

Resources

• the polygon classification and reasoning slide deck
• the polygon classification and angle reasoning worksheet
• Paper triangles for cutting or tearing
• Scissors and glue
• Rulers and protractors
• Mini-whiteboards or scrap paper
• A3 paper and markers for group flow charts
• Calculators, if required for checking
• Optional visual reference: the angle relationships foldable reference

Assessment

• Listen for accurate use of polygon, vertex, parallel, equal, regular, irregular, convex and concave during pair and group discussion.
• Check worksheet classifications and calculations, particularly whether students justify a category using properties and apply (180(n-2)) correctly.
• Use the exit responses and group algorithms to assess whether students can sequence decisions clearly and reason about relationships between quadrilaterals.

Differentiation

• Support students with a visible vocabulary bank, labelled example shapes, pre-drawn diagonals and sentence starters such as “I classified this as ___ because ___.”
• Provide a partially completed flow chart and a reduced set of clearly contrasting shapes for students who need additional structure; allow practical cutting and rearranging to reinforce the angle sum.
• For EAL learners, pair visual examples with the key terms and rehearse explanations orally before writing. Permit labelled diagrams as part of the response.
• Extend students by requiring an algorithm that places a shape in more than one valid category, such as square, rectangle, rhombus and parallelogram, and asking them to explain why classifications can overlap.