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  • CCSS.Math.Content.HSG-MG.A.1
Polygon
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An interactive applet and associated web page that demonstrate polygons. The applet shows a polygon which is initially an irregular convex pentagon. The user can drag any vertex and a message shows if it becomes concave. The user can also alter the number of sides from 3 to 99, the title changing to reflect it's name up to 12 sides. You can also make it regular, dragging a vertex then changes all vertices to maintain it as regular. The web page has many definitions and links to the various forms and orders of polygon. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Subject:
Geometry
Material Type:
Reading
Simulation
Provider:
Math Open Reference
Author:
John Page
Date Added:
02/16/2011
Polygons and Popsicle Trusses
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Educational Use
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Students learn about the role engineers play in designing and building truss structures. Simulating a real-world civil engineering challenge, student teams are tasked to create strong and unique truss structures for a local bridge. They design to address project constraints, including the requirement to incorporate three different polygon shapes, and follow the steps of the engineering design process. They use hot glue and Popsicle sticks to create their small-size bridge prototypes. After compressive load tests, they evaluate their results and redesign for improvement. They collect, graph and analyze before/after measurements of interior angles to investigate shape deformation. A PowerPoint® presentation, design worksheet and data collection sheet are provided. This activity is the final step in a series on polygons and trusses.

Subject:
Mathematics
Geometry
Material Type:
Activity/Lab
Provider:
TeachEngineering
Author:
Andi Vicksman
Maia Vadeen
Malinda Zarske
Nathan Coyle
Russell Anderson
Ryan Sullivan
Sabina Schill
Date Added:
02/07/2017
Geometry Module 2: Similarity, Proof, and Trigonometry
Conditional Remix & Share Permitted
CC BY-NC-SA
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Just as rigid motions are used to define congruence in Module 1, so dilations are added to define similarity in Module 2.  To be able to discuss similarity, students must first have a clear understanding of how dilations behave.  This is done in two parts, by studying how dilations yield scale drawings and reasoning why the properties of dilations must be true. Once dilations are clearly established, similarity transformations are defined and length and angle relationships are examined, yielding triangle similarity criteria.  An in-depth look at similarity within right triangles follows, and finally the module ends with a study of right triangle trigonometry.

Subject:
Geometry
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
07/03/2014
Optimizing Pencils in a Tray
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Educational Use
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Student groups work with manipulatives—pencils and trays—to maximize various quantities of a system. They work through three linear optimization problems, each with different constraints. After arriving at a solution, they construct mathematical arguments for why their solutions are the best ones before attempting to maximize a different quantity. To conclude, students think of real-world and engineering space optimization examples—a frequently encountered situation in which the limitation is the amount of space available. It is suggested that students conduct this activity before the associated lesson, Linear Programming, although either order is acceptable.

Subject:
Mathematics
Algebra
Geometry
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Andi Vicksman
Maia Vadeen
Malinda Zarske
Nathan Coyle
Russell Anderson
Ryan Sullivan
Date Added:
12/15/2016
Toilet Roll
Unrestricted Use
CC BY
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The purpose of this task is to engage students in geometric modeling, and in particular to deduce algebraic relationships between variables stemming from geometric constraints. The modelling process is a challenging one, and will likely elicit a variety of attempts from the students.

Subject:
Mathematics
Geometry
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
G-MG Tilt of earth's axis and the four seasons
Unrestricted Use
CC BY
Rating

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: The geometry of the earth-sun interaction plays a very prominent role in many aspects of our lives that we take for granted, like the variable length o...

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/24/2013
Solving Quadratic Equations: Cutting Corners
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 quadratics in one variable. In particular, the lesson will help teachers identify and help students who have the following difficulties: making sense of a real life situation and deciding on the math to apply to the problem; solving quadratic equations by taking square roots, completing the square, using the quadratic formula, and factoring; and interpreting results in the context of a real life situation.

Subject:
Mathematics
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Surface Area, Volume, and Density Module
Unrestricted Use
CC BY
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Students will be reviewing and learning surface area, volume, and density over three days. The remaining two days will be used for the students to explore the topics with hands-on material using everyday shapes.*This work was made possible by the generous support of the National Science Foundation, grant #1755631, and the University of St. Francis Noyce STEM Educators Program

Subject:
Mathematics
Material Type:
Activity/Lab
Homework/Assignment
Author:
Lizbeth Perez
Date Added:
01/11/2021
Geometry Module 3:  Extending to Three Dimensions
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

Module 3, Extending to Three Dimensions, builds on students’ understanding of congruence in Module 1 and similarity in Module 2 to prove volume formulas for solids. The student materials consist of the student pages for each lesson in Module 3. The copy ready materials are a collection of the module assessments, lesson exit tickets and fluency exercises from the teacher materials.

Subject:
Geometry
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
07/03/2014
G-MG Tennis Balls in a Can
Unrestricted Use
CC BY
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This task is inspired by the derivation of the volume formula for the sphere. If a sphere of radius 1 is enclosed in a cylinder of radius 1 and height 2, then the volume not occupied by the sphere is equal to the volume of a Ňdouble-naped coneÓ with vertex at the center of the sphere and bases equal to the bases of the cylinder.

Subject:
Mathematics
Geometry
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Running Around a track II
Unrestricted Use
CC BY
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The goal of this task is to model a familiar object, an Olympic track, using geometric shapes. Calculations of perimeters of these shapes explain the staggered start of runners in a 400 meter race.

Subject:
Mathematics
Geometry
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
01/21/2013
How Thick is a Soda Can II?
Unrestricted Use
CC BY
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his is a version of ''How thick is a soda can I'' which allows students to work independently and think about how they can determine how thick a soda can is. The teacher should explain clearly that the goal of this task is to come up with an ''indirect'' means of assessing how thick the can is, that is directly measuring its thickness is not allowed.

Subject:
Mathematics
Geometry
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
03/04/2013
Eratosthenes and the Circumference of the Earth
Unrestricted Use
CC BY
Rating

The accuracy and simplicity of this experiment are amazing. A wonderful project for students, which would necessarily involve team work with a different school and most likely a school in a different state or region of the country, would be to try to repeat Eratosthenes' experiment.

Subject:
Mathematics
Geometry
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
12/15/2012
G-SRT, G-MG How far is the horizon?
Unrestricted Use
CC BY
Rating

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Milong and her friends are at the beach looking out onto the ocean on a clear day and they wonder how far away the horizon is. About how far can Milong...

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
10/30/2013
How Many Leaves on a Tree? (Version 2)
Unrestricted Use
CC BY
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In this problem, the variables a,b,c, and d are introduced to represent important quantities for this esimate: students should all understand where the formula in the solution for the number of leaves comes from. Estimating the values of these variables is much trickier and the teacher should expect and allow a wide range of variation here.

Subject:
Mathematics
Geometry
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
01/20/2013
Polygons, Angles and Trusses, Oh My!
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Educational Use
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Students take a close look at truss structures, the geometric shapes that compose them, and the many variations seen in bridge designs in use every day. Through a guided worksheet, students draw assorted 2D and 3D polygon shapes and think through their forms and interior angles (mental “testing”) before and after load conditions are applied. They see how engineers add structural members to polygon shapes to support them under compression and tension, and how triangles provide the strongest elemental shape. A PowerPoint® presentation is provided. This lesson prepares students for two associated activities that continue the series on polygons and trusses.

Subject:
Mathematics
Geometry
Material Type:
Lesson
Provider:
TeachEngineering
Author:
Andi Vicksman
Maia Vadeen
Malinda Zarske
Nathan Coyle
Russell Anderson
Ryan Sullivan
Sabina Schill
Date Added:
02/07/2017