Geometric Problem Solving

Overview

Lesson 13 of 15 in the unit Shapes, Space and Reasoning. In a small group of five, students use shape properties, transformations and spatial language to solve visual challenges, explain their strategies and justify their answers.

Learning intentions

• WALT use properties of shapes to solve problems.
• WALT use transformations and spatial language accurately.
• WALT select an efficient strategy and show our thinking.
• WALT explain and justify a geometric answer.

Success criteria

• I can identify and use relevant shape properties.
• I can describe movement using words such as rotate, reflect, translate, turn, clockwise, anticlockwise and quarter-turn.
• I can show my strategy with a diagram, labels, materials or words.
• I can justify my answer and check that it fits all the clues.

Curriculum links

• Geometry: identify, describe, compare and classify two-dimensional shapes using features such as sides, angles, symmetry and parallel lines.
• Position and orientation: describe and interpret locations, routes and movements using grid references and spatial language.
• Transformations: recognise and apply slides, flips and turns to shapes and patterns.
• Mathematical communication and reasoning: choose strategies, explain thinking, use representations and justify conclusions.
• Key competencies: thinking; using language, symbols and texts; managing self; relating to others.

Lesson structure (60 minutes)

1. 0–7 minutes – Visual hook and success focus Open with the mystery shape hook. Display a shape hidden behind three clues, such as “I have four sides, two pairs of parallel sides and no right angles.” Students silently sketch or point to a possible answer, then share what evidence they used. Introduce the WALT and success criteria visually, allowing wait time before responses.

2. 7–15 minutes – Model a problem-solving routine Show a worked example in the strategy model: “A robot starts at A2, moves two squares north, turns clockwise and moves three squares. Where does it finish?” Think aloud using the routine: understand the clues, choose a representation, solve, check and explain. Model drawing the grid and using precise language rather than guessing.

3. 15–20 minutes – Explore properties and language In a teacher-led discussion, students handle or point to examples from the 2D shape property cards. Ask: “Which clues would identify this shape?” and “Which properties are shared?” Briefly revisit vertices, sides, right angles, symmetry and parallel lines. Clarify that a shape may fit more than one description unless the clues are sufficiently specific.

4. 20–40 minutes – Tiered problem-solving stations Form flexible pairs, with one student working independently if appropriate. Distribute the geometric problem-solving worksheet and provide task cards at an accessible, appropriate level:

• Support: identify a mystery shape from two or three clues; complete a simple repeating pattern; follow a route on a labelled grid.
• Core: solve mixed challenges requiring at least two clues or transformations, then record the strategy and justification.
• Extend: solve a multi-step grid route or determine which transformation changes one pattern into another.

Students may use tiles, mirrors, grid paper, tracing paper and shape cards. Circulate with prompts: “What do you know?”, “Which clue matters most?”, “Can you prove it?”, and “How will you check?” The teacher or TA supports reading, vocabulary and recording without reducing the mathematical challenge.

5. 40–51 minutes – Compare and justify strategies Select two contrasting solutions for a brief group discussion. Students display their work, point to evidence and explain why their answer works. Ask peers to respond with “I agree because…” or “I wonder whether…”. Revisit inaccurate or imprecise use of terms, and invite students to show reasoning in another way, such as a diagram, gesture, model or oral explanation.

6. 51–57 minutes – Create a challenge Each student or pair writes a short challenge for another group: a mystery shape, pattern or grid route. It must include clear clues, a question and an answer key. Advanced learners write a multi-step challenge with at least two transformations or conditions. Swap challenges and allow classmates to solve and check them.

7. 57–60 minutes – Exit reflection Return to the plenary prompts. Each student completes one oral, drawn or written response: “My strategy was…”, “My evidence was…”, and “Next time I will…”. Ask one final student to explain how they know an answer is justified.

Resources

• the geometric problem-solving slide deck
• the geometric problem-solving worksheet
• the 2D shape property cards
• Shape tiles, pattern blocks or other 2D shape manipulatives
• Small mirrors or tracing paper for reflection tasks
• Grid paper and pencils
• Whiteboards and pens
• Prepared tiered task cards
• Visual word bank for spatial and transformation language
• Timer and display surface for student solutions

Assessment

• Observe whether students select a suitable representation or strategy and use accurate geometric vocabulary.
• Confer during group work: ask students to identify evidence, explain their process and check their answer.
• Collect the worksheet and student-created challenge. Look for correct properties, transformations, diagrams and a clear justification.
• Use the exit reflection to identify students needing further support with shape properties, spatial language or reasoning in Lesson 14.

Differentiation

• Provide tiered tasks, worked examples, manipulatives, enlarged grids and a visual vocabulary bank. Read instructions aloud or offer them in short, clearly separated steps.
• Use flexible grouping and allow students to communicate reasoning through speech, drawing, pointing, gesture, models or signed language. Do not require spoken explanations as the only evidence.
• For Deaf learners, keep instructions and clues visible, face students when communicating, avoid talking while writing, provide wait time and use high-expectation visual problems.
• Support EAL and students with additional learning needs through paired rehearsal, labelled diagrams, sentence frames such as “I know this because…”, and teacher/TA scribing where needed.
• Extend confident learners with ambiguous clues to improve, multiple possible answers to classify, or a multi-step challenge involving rotations, reflections and route constraints.