Geometry

GeometryGerald B., Ashley E., Daisy M., Ani P., & Ramman T.

IntroductionA key benefit to studying geometry is that it develops spatial sense, or the ability to mentally visualize objects and spatial relationships. People with good spatial sense are able to use geometric ideas to describe analyze their world. Spatial sense is best developed by consistent participation in rich experiences with shape and spatial relationships. Over time, these experiences lead to a heightened ability to articulate and appreciated geometric ideas in art, nature and architecture.

Big IdeasWhat makes shapes alike and different can be determined by geometric properties. For example, shapes have sides that are parallel, perpendicular, or neither; they have line symmetry, rotational symmetry, or neither; they are similar, congruent, or neither.Shapes can be moved in a plane or in space. These changes can be described in terms of translation (slides), reflections (flips), and rotations (turns).

Geometric Properties

Example of Teaching and Learning for Geometric Properties

Translation, Reflection, & Rotation

Example of Teaching and Learning for Translation, Reflection, and Rotation

Third Big Idea

Example of Teaching and Learning for Third Big Idea

Applet #1Tessellation CreatorA tessellation is a repeating pattern of polygons that covers a plane with no gaps or overlaps. This applet is a virtual interactive program which allows for the manipulation of various polygons. These shapes can be rotated and placed in a workspace to form tessellations. http://illuminations.nctm.org/ActivityDetail.aspx?ID=202Reviewed by Ramman Turner, Gerald Bolden and Ashley Echang

How the applet worksClick-and-drag the shapes from the top menu to the canvas below. If the sides of shapes are dragged close to each other, those shapes will snap together. Click-and-drag a rectangle around a group of shapes to glue them together. Use the scroll bars along the right side and bottom of the canvas to view different parts of the canvas. Use buttons on the left sidebar to erase, rotate, copy, separate or color the polygons. There are also buttons for zooming in and out as the pattern grows.

Analysis

Evaluation of AppletSee criteria on pages 120 and 121 of EMSM

A Problem-Based TaskTask: What shapes tessellate? If shapes can be combined to make patterns that repeat and cover the plane, then they tessellate. What patterns can you find? Connection to the standards and/or big ideas:

This task is connected to Big Ideas #2: Shapes can be moved in a plane or in space. These changes can be described in terms of translations, reflections, and rotations.

Questions to Ask to Assess and Advance Student ThinkingLaunch (Task Set-Up):

Which of the shapes tessellate by themselves? Can you cover the plane with just triangles? just squares? just pentagons? Explore (During Task Implementation):

Try to find a way to make a tessellation with just squares and octagons. Which other combinations of shapes tessellate? Which of the shapes tessellate by themselves? Find out all of the regular polygons that will tessellate with themselves. Summarize (As students share findings, strategies, reasoning, etc.):

Is there a way to tell if shapes with tessellate by looking at the properties of those shapes? How? Hint: The length of the sides of all the shapes are all the same. Only the angles are different. What are the angles in each shape?

Applet NameGive picture and brief description of the Applet Put link for applet and who reviewed the Applet

Applet #2

How does the Applet work?

Analysis of AppletStrengths and Weaknesses

Evaluation of Applet

A Problem-Based Task

Questions to ask to Assess and Advance Student Thinking

Online Reflection Questions

National Standards by GradeOur groups first standardK-2 standard3-5

National Standards by GradeOur second standardK-23-5

National Standards by GradeOur third standardK-23-5