Transformation Studio
Using tracing paper, students slide, flip, and turn figures to discover what rigid motions preserve — and then prove two shapes are congruent by finding the sequence that maps one onto the other.
Common Core standards covered
- 8.G.A.1Verify experimentally the properties of rotations, reflections, and translations:
- 8.G.A.1.aLines are taken to lines, and line segments to line segments of the same length.
- 8.G.A.1.bAngles are taken to angles of the same measure.
- 8.G.A.1.cParallel lines are taken to parallel lines.
- 8.G.A.2Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
Teacher-facing overview
Big idea: Verify experimentally that rotations, reflections, and translations preserve length, angle measure, and parallelism, and use them to establish congruence.
Student target: “I can translate, reflect and rotate a figure, show that lengths and angle measures do not change, and describe a sequence of moves that carries one figure onto another.”
Success criteria: Accurate strategy, clear representation, reasonable answer, and mathematical explanation.
Essential question
When a figure slides, flips or turns, what changes and what stays exactly the same?
Learning target: I can translate, reflect and rotate a figure, show that lengths and angle measures do not change, and describe a sequence of moves that carries one figure onto another.
The task students work on
Work with triangle ABC on a coordinate grid: A(1, 1), B(4, 1), C(1, 3). You will move it three ways — a slide, a flip and a turn — and measure carefully each time to find out what the moves preserve.
Measure each version of the triangle and record what you find.
| Measurement | Original ABC | After translation | After reflection | After rotation |
|---|---|---|---|---|
| Length AB | ||||
| Length AC | ||||
| Length BC | ||||
| Angle A | ||||
| Angle B |
Lesson script
Students trace triangle ABC and slide the tracing paper. Collect the word 'translation'. Most will say nothing changed except position — record that claim on the board so it can be tested rather than assumed.
Demonstrate all three moves with the tracing paper under a document camera: slide (translation), flip (reflection, turn the paper over), turn (rotation, pin one point with a pencil). Build an anchor chart with the everyday word, the mathematical word, and what the hands do.
- Translation — slide. Every point moves the same distance in the same direction.
- Reflection — flip over a line. Points land the same distance from the line, on the other side.
- Rotation — turn about a fixed center by a given angle and direction.
🔒 The remaining 4 steps — fully scripted with teacher-says lines, discourse questions, look-fors, and interventions — are in the full lesson. See plans →
Misconceptions and how to respond
- “The triangle got smaller when I turned it.” A rotation changes orientation, not size. Have the student measure one corresponding side before and after; the tracing paper itself is the proof that nothing was resized.
- “Reflecting changes the side lengths, because the coordinates changed.” — the teacher response is in the full lesson.
- “Congruent means it is sitting the same way up.” — the teacher response is in the full lesson.
- “I only need to check one vertex to identify the transformation.” — the teacher response is in the full lesson.
🔒 Every misconception ships with a tested classroom response. See plans →
Exit ticket
- Triangle PQR has vertices P(2, 1), Q(5, 1) and R(2, 4). It is translated 3 units left and 1 unit down. Write the coordinates of P', Q' and R'.
🔒 2 more exit-ticket questions are in the full lesson. See plans →
Worked answers, the completed answer tables, and the scoring rubric are in the downloadable kit, included with membership. See plans and pricing.
Printable handouts in the kit
All handouts are in Printable_Handouts.pdf inside the kit download.
Materials and classroom resources
Student experience
Students enter through a low-floor prompt, build or sketch a model, test a strategy, revise their thinking, collaborate, and present a final solution. The task remains accessible while allowing for sophisticated reasoning.
Detailed facilitation notes
- Step 1: Students test each rigid motion and measure side lengths, angles, and parallel pairs before and after. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 2: Record findings in a properties-preserved chart. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 3: Teams receive two congruent figures and search for a sequence of motions mapping one onto the other. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 4: Present sequences and compare different valid routes between the same two figures. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
Differentiation and inclusion
Support: Start with single translations for support; extend to sequences of three or more motions.
Language support: “I started by…”, “My model shows…”, and “I know my answer is reasonable because…”.
Extension: Require a second solution, alter a condition, or have students write a challenge for another group.
Accessibility: Manipulatives, enlarged visuals, oral response choices, partner reading, and reduced-copy student pages.
Assessment plan
Formative checks: Strategy choice, accuracy, representation, collaboration, and explanation.
End evidence: Students describe a sequence of rigid motions proving two given figures are congruent.
Mastery: The student completes the task accurately and explains the strategy with limited prompting.