SBS:Sample Completed Math Template

From Westminster Public Schools Wiki
Jump to: navigation, search

Go back to main Math Level 09 page

Contents

Geometry: Transformation, Congruency, Similarity

Transforms geometric figures using translation, rotation, reflection, and dilation (Colorado Math Standard 9.4.1a)

Learning Target Connections

Interdisciplinary Connections

Intradisciplinary Connections

Instructional Strategies

1. Lesson: Symmetry

Prerequisite Knowledge: Students should be familiar with plotting points on the coordinate plane. They should also recognize basic polygons

Learning Objectives: Students will be introduced to symmetry. Students will be able to identify line and point symmetry. Students will be able to discover symmetries of regular polygons, letters and pictures.

Key Ideas:

Motivational Problem:

Using a large face from a magazine picture, copy only half of the face (this must be done vertically) On the students' sheet ask them to finish the other half of the face. Discuss how they knew to do this. Introduce the idea of symmetry.

Place students in groups of 3 or 4. Give each student 2 note cards. On one note card ask them to draw a regular polygon, on the other ask them to draw a capital letter (each person must draw a different letter and shape) Ask the students to trade cards. Then, have the students identify what type(s) of symmetry each letter and shape has by drawing a dashed line of symmetry. Place on a poster at the front so that all students can see the results.

Important Questions: How do we know what type of symmetry a figure has? Do all triangles have the same number of lines of symmetry?

  • Differentiated Instruction
    • Content -
    • Process -
    • Product -

2. Lesson: Composition of Transformations

Prerequisite Knowledge: Students should be familiar with reflections, dilations, rotations and translations. They should also be familiar with isometry.

Learning Objectives: Students will be able to perform more than one transformation with regular polygons on a coordinate plane. Students will understand the concept of a glide reflection.

Key Ideas: A special two step transformation called a glide transformation consists of a translation and then a reflection. The line of reflection must be parallel to the direction of the translation.

Motivational Problem: Have students plot the points A(-1,0) B(4,0) and C(2,6). First have them perform the transformation T(4, -3). Tell the students to label the new points A’B’C’. They should also record the new coordinates. Next have the students transform triangle A’B’C’ under T(3, 2). Tell the students to record the new coordinates and label the new figure A’’B’’C’’. Then have them answer these questions.

1. How would I transform A’’B’’C’’ back to the original figure?

2. If I wanted to give directions to combine both translations into one transformation, what would the directions be? Show your calculations or write down an explanation.

Important Questions: What can you say about the congruence of the preimage (original figure) and the image after multiple transformations?

  • Differentiated Instruction
    • Content -
    • Process -
    • Product -

Assessments

Marzano Scoring Guide
MA.09.07.05.01 Scoring Guide
Sample Sources of Evidence
Score 2
Score 3
Score 4
Exemplars

Capacity Matrix

Resources

Primary

Glencoe/McGraw-Hill Geometry 2008 (pg 496-532)

Transformations

  • Reflections (9-1)
  • Translations (9-2)
  • Rotation (9-3)
  • Tessellation (9-4)
  • Dilation (9-5)

Open Source

  • Interactive: Translations, Reflections, and Rotations
  • Interdisciplinary Art and Math Tessalations