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Archimedes' Puzzle
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In this math activity, learners explore the history of the Stomachion (an ancient tangram-type puzzle), use the pieces to create other figures, learn about symmetry and transformations, and investigate the areas of the pieces. The Stomachion, believed to have been created by Archimedes, consists of 14 pieces cut from a square, which can be rearranged to form other interesting shapes.

Subject:
Mathematics
Geometry
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
NCTM Illuminations
Samuel E. Zordak
Thinkfinity/Verizon Foundation
Date Added:
11/09/2008
Area and Perimeter
Conditional Remix & Share Permitted
CC BY-NC
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CESA #1 EL OER Project A visual guide to area and perimeter. Great for English Learners and students with special needs.

Subject:
Mathematics
Material Type:
Lesson
Author:
Jessica Sciborski
Date Added:
08/02/2019
Area of Triangles
Conditional Remix & Share Permitted
CC BY-NC-SA
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This Desmos activity allows students to explore the area of triangles with online geoboards.  This resource was helpful in understanding that a triangle is half of a square/rectangle.  Students were able to conceptualize why the formula for a triangle includes the "multiply by 1/2".  Students can work at their own pace and encourage math discourse.

Subject:
Mathematics
Material Type:
Lesson Plan
Author:
Ashley Gaulke
Date Added:
04/01/2019
Attributes of Plane Figures (engageny)
Conditional Remix & Share Permitted
CC BY-NC-SA
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Students explore area as an attribute of two-dimensional figures and relate it to their prior understandings of multiplication. Students conceptualize area as the amount of two-dimensional surface that is contained within a plane figure.

Subject:
Geometry
Material Type:
Activity/Lab
Assessment
Lesson
Lesson Plan
Author:
J. Cherf
Date Added:
03/14/2018
Building a Box
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This lesson helps students develop spatial visualization skills and geometric understanding by exploring the different nets that can be folded into a cube. The lesson is placed in the context of a young woman who is trying to build a jewelry box. The lesson provides an activity sheet, a link to a helpful applet (Cube Nets, cataloged separately), questions for students and teachers, and ideas for assessment and extensions.

Subject:
Mathematics
Geometry
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Dr. Bob Mann
Date Added:
11/05/2000
Build the Biggest Box
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Educational Use
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Student pairs are given 10 minutes to create the biggest box possible using one piece of construction paper. Teams use only scissors and tape to each construct a box and determine how much puffed rice it can hold. Then, to meet the challenge, they improve their designs to create bigger boxes. They plot the class data, comparing measured to calculated volumes for each box, seeing the mathematical relationship. They discuss how the concepts of volume and design iteration are important for engineers. Making 3-D shapes also supports the development of spatial visualization skills. This activity and its associated lesson and activity all employ volume and geometry to cultivate seeing patterns and understanding scale models, practices used in engineering design to analyze the effectiveness of proposed design solutions.

Subject:
Mathematics
Geometry
Measurement and Data
Material Type:
Activity/Lab
Provider:
TeachEngineering
Author:
Aaron Lamplugh
Andi Vicksman
CU Teach Engineering (a STEM licensure pathway), Engineering Plus Degree Program, University of Colorado Boulder
Maia Vadeen
Malinda Zarske
Nathan Coyle
Russell Anderson
Ryan Sullivan
Date Added:
10/13/2017
Circle-Square
Unrestricted Use
CC BY
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This resource could be used an a precurser for a lesson on comparing areas of circles and squares. There is guess and check involved, as well as digging deeper to find the correct answer. Students could do part of this on their own device, using GeoGebra to help with graphing the equations. If students do not have access to devices, then the teacher can use it as a class discussion.

This includes questions that can be posed to students, as well as visuals to make the entire task make sense to students. Answer is included.

Subject:
Mathematics
Material Type:
Alternate Assessment
Interactive
Learning Task
Simulation
Provider:
Dan Meyer
Date Added:
04/18/2016
Circle Tool
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An applet for students to use in exploring the area and circumference of a circle in relation to its radius and diameter. When the radius is changed, the other measures automatically change and are shown on a board. Most importantly, the ratio between any pair of these measures can be shown.

Subject:
Mathematics
Geometry
Numbers and Operations
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Date Added:
11/05/2011
Complex Digital Systems, Spring 2005
Conditional Remix & Share Permitted
CC BY-NC-SA
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This course is offered to graduates and is a project-oriented course to teach new methodologies for designing multi-million-gate CMOS VLSI chips using high-level synthesis tools in conjunction with standard commercial EDA tools. The emphasis is on modular and robust designs, reusable modules, correctness by construction, architectural exploration, and meeting the area, timing, and power constraints within standard cell and FPGA frameworks.

Subject:
Computer Science
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Arvind, V.
Date Added:
01/01/2005
Developing Spatial Structuring in a Rectangle
Conditional Remix & Share Permitted
CC BY-SA
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The purpose of this task is to develop spatial structuring by showing the student that a rectangle can be partitioned into unit squares. I used it in addition to the "Partitioning a Rectangle into Unit Squares"https://www.illustrativemathematics.org/content-standards/tasks/2063, for those students who were not able to complete the first activity of drawing a grid on the rectangle by connecting each mark. On the rectangle worksheets you may need to scaffold through the rectangles, starting with placing unit tiles or squares on the rectangle. Then proceed through the rectangles scaffolding as needed.

Subject:
Mathematics
Material Type:
Learning Task
Author:
CAROLYN STEINERT
Date Added:
08/02/2019
Discovering Relationships between Side Length and Area
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Educational Use
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Through this lesson and its two associated activities, students are introduced to the use of geometry in engineering design, and conclude by making scale models of objects of their choice. The practice of developing scale models is often used in engineering design to analyze the effectiveness of proposed design solutions. In this lesson, students complete fencing (square) and fire pit (circle) word problems on two worksheets—which involves side and radius dimensions, perimeters, circumferences and areas—guiding them to discover the relationships between the side length of a square and its area, and the radius of a circle and its area. They also think of real-world engineering applications of the geometry concepts.

Subject:
Mathematics
Geometry
Measurement and Data
Material Type:
Lesson
Provider:
TeachEngineering
Author:
Aaron Lamplugh
Andi Vicksman
CU Teach Engineering (a STEM licensure pathway), Engineering Plus Degree Program, University of Colorado Boulder
Maia Vadeen
Malinda Zarske
Nathan Coyle
Russell Anderson
Ryan Sullivan
Date Added:
10/13/2017
Eight Circles
Conditional Remix & Share Permitted
CC BY-NC-SA
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The purpose of this task is to strengthen students' understanding of area. It could be assigned in class to individuals or small groups or given as a homework exercise to generate interesting discussions the following day. The relatively high levels of complexity and technical demand enhance its instructional value.

Subject:
Mathematics
Geometry
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Evaluating Statements About Enlargements (2D and 3D)
Only Sharing Permitted
CC BY-NC-ND
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This lesson unit is intended to help teachers assess how well students are able to solve problems involving area and volume, and in particular, to help you identify and assist students who have difficulties with the following: computing perimeters, areas and volumes using formulas; and finding the relationships between perimeters, areas, and volumes of shapes after scaling.

Subject:
Geometry
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
Date Added:
11/01/2017
Evaluating Statements About Length and Area
Only Sharing Permitted
CC BY-NC-ND
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This lesson unit is intended to help teachers assess how well students can: Understand the concepts of length and area; use the concept of area in proving why two areas are or are not equal; and construct their own examples and counterexamples to help justify or refute conjectures.

Subject:
Geometry
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
Date Added:
11/01/2017
Fair and Square: Using Concrete-Pictorial-Abstract Activities to Maximize Area
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Through this four part lesson students develop an understanding of the relationship between area and perimeter. The lesson involves students making human rectangles, exploring geoboard connections, playing perimeter war, and playing Square Off from Calculation Nation. The lesson plan includes all data collection worksheets, games pieces, link to Calculation Nation, extension and assessment ideas.

Subject:
Mathematics
Algebra
Geometry
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
S. Rosen
Date Added:
11/05/2011
Feel the Stress
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Educational Use
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Working individually or in groups, students explore the concept of stress (compression) through physical experience and math. They discover why it hurts more to poke themselves with mechanical pencil lead than with an eraser. Then they prove why this is so by using the basic equation for stress and applying the concepts to real engineering problems.

Subject:
Technology and Engineering
Life Science
Mathematics
Geometry
Physics
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
GK-12 Program, School of Engineering and Applied Science,
Jeffrey Mitchell
TeachEngineering.org
Date Added:
09/18/2014
Fence That Farmland!
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Educational Use
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Students develop and solidify their understanding of the concept of "perimeter" as they engage in a portion of the civil engineering task of land surveying. Specifically, they measure and calculate the perimeter of a fenced in area of "farmland," and see that this length is equivalent to the minimum required length of a fence to enclose it. Doing this for variously shaped areas confirms that the perimeter is the minimal length of fence required to enclose those shapes. Then students use the technology of a LEGO MINDSTORMS(TM) NXT robot to automate this task. After measuring the perimeter (and thus required fence length) of the "farmland," students see the NXT robot travel around this length, just as a surveyor might travel around an area during the course of surveying land or measuring for fence materials. While practicing their problem solving and measurement skills, students learn and reinforce their scientific and geometric vocabulary.

Subject:
Technology and Engineering
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering NGSS Aligned Resources
Author:
AMPS GK-12 Program,
Ursula Koniges
Date Added:
09/18/2014
Fractal Tool
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Using this tool, students build these classic fractals: the Koch snowflake, a fractal tree, a reduced square, and the Sierpinksi triangle. As these shapes grow and change using an iterative process, students can observe patterns in the images created and in the table of values as the fractals progress through several stages.

Subject:
Mathematics
Geometry
Numbers and Operations
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Date Added:
11/05/2011