Transformations in Action

Overview

Lesson 5 of 10 in Shape Shifters: Transformations. Students investigate translations, reflections and rotations using transparent grids and dynamic geometry software, then explain transformation rules to a partner. The lesson is designed for 25 Year 5–6 students working in pairs.

Learning intentions

• WALT describe and perform translations, reflections and rotations of 2D shapes.
• WALT record a transformation rule and the resulting image accurately.
• WALT use mathematical language to explain how a shape has changed.
• WALT check whether a transformation rule produces the intended image.

Success criteria

• I can identify whether a shape has been translated, reflected or rotated.
• I can describe what happened to a shape using direction, distance, line or centre of rotation, and angle where appropriate.
• I can draw or create the image accurately on a grid.
• I can explain and check my rule with a partner.

Curriculum links

• Geometry: describe, visualise and transform two-dimensional shapes using position, direction, reflection, rotation and translation.
• Mathematical communication: use diagrams, grids, labels and precise mathematical language to explain thinking.
• Mathematical processes: notice patterns, make conjectures, test rules and justify conclusions.
• Key competencies: thinking; using language, symbols and texts; relating to others; managing self.

Lesson structure (60 minutes)

1. 0–7 minutes – Hook and recall Open with the transformation hook and learning intentions. Display a shape before and after it has moved, but do not name the transformation. Ask: “What changed? What stayed the same?” Students give a silent think, pair discussion and class responses. Revisit the meanings of translation, reflection and rotation.

2. 7–17 minutes – Teacher modelling Use a transparent grid or projected grid alongside the transformation modelling slides. Model one example of each transformation, thinking aloud about the vertices and recording a rule and image. For example: “Translate 3 squares right and 2 squares up”; “reflect in the vertical mirror line”; or “rotate a quarter-turn clockwise around this point.” Emphasise that size and shape stay the same, while position or orientation may change.

3. 17–30 minutes – Guided investigation In pairs, students use transparent grids over printed or projected shapes and complete the first section of the transformation investigation worksheet. They perform one translation, one reflection and one rotation, recording the original image, the rule and the new image. Pause halfway for a quick accuracy check: vertices should move consistently and remain connected in the same order.

4. 30–42 minutes – Dynamic geometry exploration Students use a suitable classroom dynamic geometry tool, following the software instructions and investigation prompts. They create or select a simple polygon, apply each transformation and compare the original and image. Students test one rule, change one part of it, and record what happens on the worksheet. Remind students to use only one transformation at a time before combining transformations.

5. 42–53 minutes – Transformation coach activity Pair students as coach and mathematician. The mathematician completes a transformation on a grid or software screen without naming it. The coach asks precise questions such as: “Which direction?” “How many squares?” “Where is the mirror line?” or “What is the centre and angle of rotation?” The mathematician states the rule and the coach checks the image against it. Swap roles after one challenge.

6. 53–60 minutes – Share and exit assessment Return to the discussion and plenary slides. Invite pairs to share a rule that was easy or difficult to communicate. Students complete the final reflection on the transformation investigation worksheet: draw one image, write its rule, and explain how they checked it. Collect worksheets and address any common misconception in the next lesson.

Resources

• the transformation teaching deck displayed throughout the lesson
• the transformation investigation worksheet for recording rules and images
• Transparent grids or acetate sheets with grid lines
• Printed polygon shapes or teacher-prepared grid diagrams
• Device access for pairs to use dynamic geometry software
• Projector or interactive whiteboard
• Pencils, rulers and coloured pens
• Spare smaller grids for students needing reduced visual complexity

Assessment

• Observe whether students distinguish translation, reflection and rotation and use accurate vocabulary.
• Check worksheet images and rules for consistent movement of every vertex, correct orientation and clear labelling.
• Listen during coaching for explanations that include direction, distance, mirror line, centre or angle as appropriate. Use the final rule-and-image task as an individual check.

Differentiation

• Support: provide smaller grids, simpler polygons, marked vertices and one transformation at a time. Model movement of one vertex before students move the whole shape.
• Support for EAL and learning needs: display picture-supported vocabulary and sentence frames such as “The shape was ___ because ___.” Pair students carefully and allow oral explanations before written recording.
• Core challenge: ask students to predict the image before using the software, then explain how they verified it.
• Extension: ask students to compare multiple transformation rules that produce the same image, and discuss whether the shape’s orientation or position provides useful evidence.