*Foundations of Geometry and Measurement for Teachers* is an activity-based, problem based, manipulative-based, and technology-based laboratory manual that can be used in a mathematics course in geometry and measurement for elementary and middle school preservice teachers. Most activities are organized around the key areas of area, perimeter, symmetry, similarity, properties and calcification, Pythagorean Theorem, and algebraic connections. Some of the labs have a PowerPoint presentation designed to accompany the questions in the lab so that instructors who may not have used the class activity extensively have some guidance for developing the key concepts of the lab. This laboratory manual is designed as loose leaf with hole punches so that students can easily organize their mathematical explorations into a notebook that is a detailed record of what has been done in class along with any supplemental materials. This expected organization is integral to the author’s approach of requiring significant depth of understanding on assessments. Because there is also an explicit focus on the child’s perspective, the questions in each activity and on the assessments are meant to elicit responses that would match the language of teachers as they are interacting with a child in that mathematical/social context our match the language that a child with deep understanding would use.

Big Ideas

Geometry Talks

Vocabulary Word Sort

Venn Diagrams

Painted Cube

Quadrilateral Quandary

Area of Squares, Rectangles, Parallelograms, and Triangles

Area of Trapezoids

Area of a Circle

Common Core Mathematical Practices

Calculator Triangle Area

Triangle Area Lab with GeoGebra

Spatial Visualization with Tangrams

Area with Tangrams

Perimeter with Tangrams

Tangram Efficiency (Area to Perimeter Ratio)

Patterns in Special Right Triangles

Centroid

Medians and Centroid with GeoGebra

Geoboard Familiarization

Geoboard Symmetry

Geoboard Perimeter and Semi-perimeter

Geoboard Area of Parallelograms and Triangles

Geoboard Advanced Area Strategies

Geoboard Reasoning

Ratio of Similarity

Polyhedra

Area and Perimeter Using Color Tiles

Area and Perimeter Extensions

Area and Perimeter Efficiency Extension

Pythagorean Theorem

Triangle Properties, Constructions, and Proofs

Triangle Centers

Polygon Angle Relationships

Introduction to van Hiele Levels

Journal Reflection Prompts

Children’s Literature and Mathematics