## Geometric Park

By Jeffrey Brown, February 27, 2017

• Middle School

### Category

• City of Neighborhoods

• Mathematics

### Lesson Time

300 minutes for classroom activities.

### Introduction

The students will be tasked with designing a youth-oriented park that incorporates geometric concepts. Their design must focus on at least 4 components for the park using geometric concepts such as: types of lines and polygons, symmetry, and transformation in the design.

### National Standards

Common Core State Standards   8.G.1  Verify experimentally the properties of rotations, reflections, and translations:
1. Lines are taken to lines, and line segments to line segments of the same length.
2. Angles are taken to angles of the same measure.
3. Parallel lines are taken to parallel lines.
8.G.2  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 figures, describe a sequence that exhibits the congruence between them. 8.G.3  Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. 8.G.4  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. 8.G.5  Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so

### Objectives

Students will be able to:
1. Know and understand the different steps of the design process.
2. Identify lines, angles, polygons, and triangles as they occur in the real world.
3. Measure interior angles of a polygon.
4. Use the formula to find the sum of the interior angles of a polygon.
5. Identify parallel, perpendicular, intersecting, and skew lines.
6. Complete designs using line and rotational symmetry.
7. Identify and perform transformations using geometric figures.
8. Predict the results of transformations.
9. Work in small groups to complete a park design.

### Materials

1. Poster Paper
2. Measuring tools (protractors, rulers, etc.)
3. Drawing tools (colored pencils, crayons, markers, etc.)
4. Chart Paper and Drawing paper
5. Scissors
6. Construction paper
7. Computer Lab

### Vocabulary

1. Symmetry- the quality of something that has two sides or halves that are the same or very close in size, shape, and position.
2. Transformations- a complete or major change in someone's or something's appearance, form, etc.
3. Parallel- extending in the same direction, everywhere equidistant, and not meeting.
4. Perpendicular- going straight up or to the side at a 90 degree angle from another line or surface.
5. Intersecting- to meet and cross at one or more points.

### Procedures

1. The characteristics of lines, angles, polygons, and triangles.
2. The definition of interior angles. 3. The characteristics of parallel, perpendicular, intersecting, and skew lines. 4. The difference between line and rotational 5. The definitions of geometric transformations: translations, reflections, and rotations. 6. That geometric figures can be found in real world 7. The importance of using a survey to gather information for a real world situation.

### Assessment

See Attached Rubric.

### Enrichment Extension Activities

The activity could focus on National Parks and how they would improve upon them.