Applying Transformations

Overview

Lesson 2 of 3 in Transformations and Tessellations, for a class of 25 Year 5–6 learners. Students apply and compare reflections, rotations and translations, then use repeated transformations to create and explain a tessellating pattern.

Learning intentions

• WALT apply reflections, rotations and translations to shapes.
• WALT describe movement using accurate mathematical and positional language.
• WALT compare transformations and explain how they can create a tessellation.
• WALT explain our thinking, listen to others and justify our decisions.

Success criteria

• I can perform and identify a reflection, rotation or translation.
• I can describe a movement using arrows, position, direction and turn language.
• I can show three different transformations of a shape.
• I can explain whether a repeating pattern tessellates, referring to gaps and overlaps.

Curriculum links

• Geometry: recognise, describe and apply transformations to shapes and objects.
• Geometry: investigate repeating patterns and identify when shapes tessellate.
• Mathematical and statistical thinking: notice relationships, compare strategies and justify conclusions.
• Communicating mathematically: use diagrams, positional language and explanations to share reasoning.

Lesson structure (45 minutes)

1. 0–3 min – Settle, connect and hook Display the opening of the transformation introduction deck and show a small shape beside several repeated copies. Ask: “How could this one shape move to make a pattern with no gaps or overlaps?” Briefly connect to the previous lesson and share the learning intention and success criteria.

2. 3–8 min – I do: revisit and model Revisit the four key terms: reflection, rotation, translation and tessellation. Using the whiteboard and the transformation introduction deck, model one shape being flipped, turned and slid. Use arrows, positional language, and quarter-turn, half-turn and full-turn descriptions. Emphasise that transformations preserve the shape and size, even though its position or orientation may change.

3. 8–17 min – I do: repeated translations Model copying a simple irregular shape and translating it the same distance in the same direction several times. Think aloud: “The copies meet edge-to-edge, so there are no gaps or overlaps.” Invite students to identify the movement and describe it precisely. Show a contrasting example with a gap or overlap and ask students to justify whether it tessellates. Keep the model visible on the transformation introduction deck.

4. 17–25 min – We do: guided transformations Students draw a simple shape in their maths books. Guide them to show a reflection, then a rotation and a translation. Pause after each example for partner talk: “What changed? What stayed the same?” Use the whiteboard to collect useful language such as “across the mirror line”, “clockwise quarter-turn”, “half-turn” and “three squares to the right”. Display the guided prompts in the transformation introduction deck.

5. 25–34 min – We do: test a tessellation Work through two repeating-pattern examples together. Students copy or complete each pattern in their books, using arrows to show the repeated movement. Ask: “Where do the edges meet?” and “Can you find any gaps or overlaps?” Invite different students to explain whether each pattern tessellates and to compare how the transformations were used.

6. 34–40 min – You do: transformation challenge Distribute the transformation challenge worksheet. Students draw a shape, show three different transformations, and extend one transformation into a repeating pattern. They annotate each step using mathematical language and write one sentence explaining why their pattern does or does not tessellate. Encourage students to use their maths books if they need more space.

7. 40–45 min – Plenary and reflection Display selected solutions from the transformation introduction deck or invite students to hold up their books. Ask classmates to identify the transformations and check the explanation against the success criteria. Finish with: “Which word or diagram helped you explain your pattern most clearly?” Collect the worksheets for assessment.

Resources

• Main whiteboard and markers
• Maths books and pencils
• Rulers and coloured pencils
• the transformation introduction deck
• the transformation challenge worksheet
• Optional classroom shape or grid display for modelling

Assessment

• Observe whether students correctly identify and perform reflections, rotations and translations during guided practice.
• Check worksheet diagrams for preserved shape and size, accurate movement, and clear mathematical annotations.
• Assess the tessellation explanation: students should refer to repeated movement and the absence or presence of gaps and overlaps.

Differentiation

• Support learners with a pre-drawn simple shape, squared paper, a visible word bank and sentence frames such as “The shape was ___ because ___.”
• Model one transformation at a time and allow students to physically trace, turn or slide a paper shape before drawing.
• Pair students strategically for oral rehearsal; support EAL learners with gestures, labelled diagrams and repeated positional language.
• Extend confident learners by asking them to create a tessellation using two different transformations, or explain why a particular shape or pattern cannot tessellate.