MidSchoolMath 1

The ability to create congruent figures in different orientations is an essential skill in many career fields, including architecture, engineering, and medicine. In Knee Replacement, Dr. Perkins and his assistant are directing the Transforma software through a series of geometric transformations to prepare precise knee implants. The doctor must use Transforma to map a prospective patient’s MRI to an image of the implant to make sure the piece is identical (congruent). The data provided are images on a coordinate grid of both the patient’s MRI and an image of the replacement.

LESSON: KNEE REPLACEMENTWhat series of transformations will map the MRI image onto the

Replacement Image?

Knee Replacement

Understand 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 two-dimensional figures, describe a sequence that exhibits the congruence between them.

The Math SimulatorTM

ImmersionPlay Knee Replacement Immersion video, whole-class. Restate the question: What series of transformations will map the MRI image onto the Replacement Image?Facilitate classroom discussion; ask students: "What are your ideas?"

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2 Data & ComputationPrint the Data Artifact and distribute to students. Allow students work time. Ask students: "Does your answer make sense?"Consider using a sharing protocol leading to mathematical insights and/or highlighting misconceptions. Allow students to revise their work.

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3 ResolutionPlay Knee Replacement Resolution video, whole-class. Prepare and give brief lecture (Teacher Instruction).

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Download the Detailed Lesson PlanAvailable on the Teacher Dashboard

+ Simulation TrainerAssign the Simulation Trainer.Use protocols that encourage students to help each other.Use Progress Monitoring to access real-time data for the classroom.Provide individual help for students who are not making progress.

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(Use student headphones.)

8.G.A.2Geometry

MidSchoolMath Knee Replacement

Clicker QuizLaunch the Clicker Quiz, whole-class.

8.G.A.2Geometry

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Gladys: Students are introduced to congruency (≌), which is proved at this stage by two figures being mapped onto one another by a series of rigid transformations.

Kevin: Provide students with tools to help them visualize and perform transformations (graph paper, tracing paper, rulers, compasses & proctractors).

Megan: For Grade 8, rotations are likely going to focus on multiples of 90°. Convention states that positive angles indicate a counterclockwise rotation, but for clarity, ask students to specify the direction of a rotation. Student must also indicate the point of rotation, usually a vertex on the figure or the origin of the xy-plane.

KevinSimpson

GladysGraham

MeganLeBleu

Ex. Clicker Quiz #6Standard Math Procedures

Instruction at a Glance

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Observe size of figures on graph.

Select appropriate option.

Determine if translation and reflection would move E onto the congruent figures.

E A Same size

A: Figure A

E A Translation and reflection would work.

E C Same size

E C Must be rotated.

E D Different size. Cannot be formed by E.

E D Not the same size.

E B Same size

E B Must be rotated.

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KNEE REPLACEMENTWhat series of transformations will map the MRI image onto the Replacement Image?

Dr. Perkins and his assistant are preparing a knee implant for a patient. They will use the voice-activated Transforma software to map the MRI image onto the Replacement Image.

Study the images on the screen and determine the commands (mathematical transformations) that Dr. Perkins needs to tell Transforma to map the MRI image onto the replacement image.

8.G.A.2

Understand that a two-dimensional fi gure is congruent to another if the second can be obtained from the fi rst by a sequence of rotations, refl ections, and translations; given two congruent two-dimensional fi gures, describe a sequence that exhibits the congruence between them.

About this standard

Date PeriodName

MidSchoolMath Knee Replacement 1 of 2

APPLYING THE STANDARD

MidSchoolMath 2 of 2

Date PeriodName

How might this standard appear on a test?

Knee Replacement

A student claims that any two shapes are congruent if one can be formed from the other by a series of rotations or refl ections. Is the student correct? Explain your answer.

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A transformation is made to triangle ABC to form triangle DEF (not shown). Then another transformation is made to triangle DEF to form triangle GHJ. Describe these transformations. What is the relationship between triangles ABC and GHJ? Explain your answer.

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Prove that ABCD is congruent to JKLM. Describe the transformations that would be made to ABCD to form JKLM.

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Quadrilateral A has four congruent sides that are each six units long. Quadrilateral B also has four congruent sides that are each six units long. Are the shapes congruent? How could you use transformations to prove your answer?

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2 4 6 82468

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X2 4 6 8246

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Check out my worked example #2

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