MidSchoolMath 1

Similar figures are used in many real life situations, particularly when actual dimensions are too large to be measured comfortably, as in architecture and astronomy. In Dakota Jones and the Hall of Records, archaeologist Dakota Jones must provide reasonable evidence that she has located the ancient Hall of Records to obtain permission to excavate the site. The data provided are her two resources, the Amarna drawing and a map created by Terrain Infiltrating Radar, which appear to show similar images.

LESSON: DAKOTA JONES AND THE HALL OF RECORDSHow can Dakota prove this could be the site of the Hall of Records?

Dakota Jones and the Hall of Records

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

The Math SimulatorTM

ImmersionPlay Dakota Jones and the Hall of Records Immersion video, whole-class. Restate the question: How can Dakota prove this could be the site of the Hall of Records?Facilitate classroom discussion; ask students: "What are your ideas?"

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2 Data & ComputationPrint the Data Artifact, cut into halves, 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 Dakota Jones and the Hall of Records 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.4Geometry

MidSchoolMath 2

Clicker QuizLaunch the Clicker Quiz, whole-class.

8.G.A.4Geometry

Dakota Jones and the Hall of Records

Gladys: As students explore similarity with transformations, take time to analyze the images afterward. Measure the side lengths and the angles. What do students notice? Angles are the same measure; side lengths have been changed by the factor of dilation; side lengths in new image have the same ratio as side lengths in the pre-image.

Kevin: After having experience with similar figures on a coordinate grid, help students transition to analyzing figures without a grid to determine if they are similar or not.

Megan: Help students understand that a dilation works by moving the points of a figure along a ray, beginning at a fixed center, and multiplies the distance from the center by a common scale factor. A scale factor greater than 1 will enlarge the figure, while a scale factor less than one will reduce the figure (similar to concepts in 5.NF.B.5).

KevinSimpson

GladysGraham

MeganLeBleu

Ex. Clicker Quiz #2Standard Math Procedures

Instruction at a Glance

1 Analyze transformations given in answer options.

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C:

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D:

Reflection & translation are rigid transformations. New figure would be congruent.

Rotation & translation are rigid transformations. New figure would be congruent.

Rotation & reflection are rigid transformations. New figure would be congruent.

Translation is rigid, but dilation scales a figure proportionally. New figure would be similar.

translation 2 units down, dilation by a scale factor of 2

2 Choose option that would create a similar shape.

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DAKOTA JONES AND THE HALL OF RECORDSHow can Dakota prove this is the sanctuary of the Small Aten Temple?

Dakota Jones is an archaeologist working on a dig in Egypt. She has just used her knowledge of transformations to locate the site of the ancient Hall of Records. As she continues to study the drawing of Amarna, she spots a shape that looks like the sanctuary of the Small Aten Temple (both shown in blue). Use the Amarna drawing, the aerial photo of the site, the coordinate grid, and your knowledge of transformations to tell whether she is correct.

8.G.A.4

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

About this standard

Date PeriodName

MidSchoolMath Dakota Jones and The Hall of Records 1 of 2

APPLYING THE STANDARD

You are given triangle XYZ. You want to use a sequence of transformations to create another triangle that is smaller but not congruent to XYZ. Which transformation must be included in that sequence? Explain why.

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. Then tell whether ABC and GHJ are congruent, similar, or neither. Explain why.

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

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MidSchoolMath 2 of 2

Date PeriodName

How might this standard appear on a test?

Dakota Jones and The Hall of Records

Check out my worked example #2

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