Archimedes Bathtub A Full Unit 3D Geometry Project on Surface Area and Volume

Description:

Journey into history and the fascinating world of Archimedes’. Follow his footsteps as he determines the ratio “pi”, discovers the relationship between a sphere and a cylinder, and helps King Hiero determine the density of his crown!

This project integrates history, physics, and mathematics. It is perfectly suited for your scientific students who ask “why” and “how” does that work!?! Full of hands-on learning, concrete learning and abstract practice through lessons, cards, and games.

Objectives:

This unit covers the CCSS Math 7 Standards: 7.GA.3; 7.GA.4; and 7.GA.6

By the end of this unit, students will…

Know…

· How famous philosophers such as Plato and Archimedes’ contributed to our mathematical understanding

· The names of various three-dimensional solids and their nets and slices

· How pi was “discovered”

· The relationship between diameter of a sphere and a cylinder

· How to collaborate with classmates in mathematical discovery and learning

· Vocabulary related to Three-Dimensional Geometry

Be Able To…

· Wrap solids in a net

· Predict and verify two-dimensional slices of three-dimensional solids

· Calculate pi

· Review their knowledge of area, perimeter, and circumference

· Calculate surface area

· Derive surface area formulas from “nets” of solids (enrichment)

· Find the largest diameter of a sphere using a cylinder

· Calculate volume

· Derive volume formulas from bases of solids

Included in this resource is:

· Teacher guide outlining the entire unit

· Teacher lessons on each activity and project step

· Separate Student Guide to maximize independence and self-pacing

· A History Reading on Plato and Archimedes

· 3 Project Steps that include hands-on learning for discovering pi, finding diameter of spheres and calculating volume

· 3 Key Lessons that include hands on activities using:

o Clay and solids

o Graph paper and solid nets

o Blue plastic solids for discovering surface area and volume

· Practice sheets and Quizzes for Key Lessons

· Practice Cards for Surface Area and Volume for extra practice

And…

· **BONUS** Shapes and Solids, a Stand-Alone Lesson on Surface Area and volume Formulas including a Playing Card deck to play standard card games with SA and V.

Grade Level: 6th, 7th, 8th and homeschool

Duration: 3 Weeks (15 hours)