Transforming Shapes on Grids

Overview

Lesson 8 of 15 in Shapes, Space and Reasoning. Students investigate translations, reflections and rotations by moving shape tiles on grids, then describe what changed and what stayed the same. The lesson uses visible modelling, gesture-supported explanations and clear visual language for a class of five Year 4–6 learners.

Learning intentions

• WALT describe translations, reflections and rotations of shapes.
• WALT use a grid to show how a shape has moved.
• WALT identify properties that remain unchanged during a transformation.
• WALT explain our mathematical thinking using words, gestures and diagrams.

Success criteria

• I can name or show a translation, reflection or rotation.
• I can move a shape accurately on a grid.
• I can describe what changed and what stayed the same.
• I can preserve the shape’s size, side lengths, angles and overall form.

Curriculum links

• Geometry: describe, classify and transform two-dimensional shapes and objects.
• Position and orientation: use grids, directions and spatial language to locate and move shapes.
• Mathematical reasoning: identify patterns, explain strategies and justify conclusions.
• Key competencies: thinking; using language, symbols and texts; managing self; relating to others.

Lesson structure (60 minutes)

1. 0–5 minutes – Hook and prior knowledge

Open with the transformation hook slide. Display three identical shapes in different positions and ask: “What has changed? What has stayed the same?” Students silently indicate movement with gestures, then share ideas. Establish that a transformation changes a shape’s position or orientation, not its essential properties.

2. 5–15 minutes – Explicit teaching and modelling

Use the transformation vocabulary slides to introduce:

• Translation: a slide in a direction; the shape does not turn or flip.
• Reflection: a flip over a mirror line.
• Rotation: a turn around a fixed centre.

Model each movement on a large visible grid using a coloured shape tile. Use arrows, hand gestures and colour coding. Show the movement one step at a time, and use the agreed local NZSL signs or signs supported by the Deaf/hearing team for “move/slide”, “flip”, “turn” and “same”. Do not rely on spoken instructions alone.

3. 15–25 minutes – Guided investigation

Give each student a grid, a shape tile and a pencil. Display the guided examples in the worked grid examples. Call out one transformation at a time, such as “translate three squares right” or “reflect across the vertical line”. Students move the tile, draw the result and show the movement using an arrow or gesture.

Pause after each example and ask: “Did the size change? Did the number of sides change? Did the shape turn or flip?” Correct misconceptions immediately, especially stretching, resizing or rotating when a translation was required.

4. 25–42 minutes – Partner challenge rotations

Organise students into pairs, with one student moving the tile and the other recording. The fifth student works with the teacher, then joins a pair. Distribute the transformation grid practice sheet. Students complete tasks involving one transformation at a time, recording the transformation name, direction or turn, and one property that stayed the same.

After each task, partners swap roles. Encourage precise language such as “four squares left”, “over the horizontal mirror line” or “a quarter-turn clockwise”. Use gesture, pointing and written examples to support communication.

5. 42–52 minutes – Reasoning and extension

Display the predict-and-check challenge slides. Students first predict where a shape will finish after two transformations, then use tiles and grids to check. Suggested combinations include “translate two squares up, then reflect” or “rotate a quarter-turn, then translate”. Students explain whether the order of transformations affects the final position.

Support learners may complete a single transformation with a larger grid and teacher prompting. Advanced learners can design a two-step transformation for a partner to solve and describe precisely.

6. 52–58 minutes – Share and consolidate

Select two examples to discuss. Ask students to show the transformation with a gesture and complete the sentence: “The shape moved by…, but its … stayed the same.” Revisit the three transformation names and compare their features using the summary and comparison slide.

7. 58–60 minutes – Exit assessment

Students complete the final task on the transformation exit question: identify the transformation shown, draw the result on a small grid and state one property that stayed the same. Collect responses for planning the next lesson.

Resources

• the complete transformation slide deck
• the transformation grid practice sheet
• Large demonstration grid, displayed visibly
• Small square grids, one per student
• Shape tiles or transparent shape cut-outs
• Coloured pencils or markers
• Rulers
• Arrows or movement cards
• Local NZSL vocabulary/sign support, confirmed with the Deaf/hearing team

Assessment

• Observe whether students move tiles accurately and distinguish slide, flip and turn.
• Listen for precise descriptions of direction, mirror line or turn, while accepting signed, gestural, drawn and written explanations.
• Use the worksheet and exit question to assess naming transformations and preserving shape properties.

Differentiation

• Support: use physical tiles, enlarged grids, arrows, colour coding and one transformation at a time. Keep the original shape outlined in one colour and the image in another.
• Provide sentence frames: “This is a ___ because the shape ___.” “The ___ stayed the same.” Allow students to point, gesture, draw or sign before writing.
• EAL and Deaf learners: pre-teach vocabulary visually, keep all instructions on display, face students when communicating, and use agreed NZSL terms and consistent gestures.
• Extension: combine two transformations, predict the final position before moving the tile, investigate whether changing the order changes the result, and create a challenge for a partner.