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  • MCCRS.Math.Content.HSG-MG.A.3
A-CED Regular Tessellations of the plane
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CC BY
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This task examines the ways in which the plane can be covered by regular polygons in a very strict arrangement called a regular tessellation. These tessellations are studied here using algebra, which enters the picture via the formula for the measure of the interior angles of a regular polygon (which should therefore be introduced or reviewed before beginning the task). The goal of the task is to use algebra in order to understand which tessellations of the plane with regular polygons are possible.

Subject:
Mathematics
Algebra
Geometry
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
01/21/2013
Acoustic Mirrors
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Students play and record the “Mary Had a Little Lamb” song using musical instruments and analyze the intensity of the sound using free audio editing and recording software. Then they use hollow Styrofoam half-spheres as acoustic mirrors (devices that reflect and focus sound), determine the radius of curvature of the mirror and calculate its focal length. Students place a microphone at the acoustic mirror focal point, re-record their songs, and compare the sound intensity on plot spectrums generated from their recordings both with and without the acoustic mirrors. A worksheet and KWL chart are provided.

Subject:
Mathematics
Geometry
Physical Science
Physics
Material Type:
Activity/Lab
Provider:
TeachEngineering
Author:
Nick Breen
Steven C. Thedford
Date Added:
02/07/2017
All about Linear Programming
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Students learn about linear programming (also called linear optimization) to solve engineering design problems. As they work through a word problem as a class, they learn about the ideas of constraints, feasibility and optimization related to graphing linear equalities. Then they apply this information to solve two practice engineering design problems related to optimizing materials and cost by graphing inequalities, determining coordinates and equations from their graphs, and solving their equations. It is suggested that students conduct the associated activity, Optimizing Pencils in a Tray, before this lesson, although either order is acceptable.

Subject:
Mathematics
Algebra
Geometry
Material Type:
Lesson
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Andi Vicksman
Maia Vadeen
Malinda Zarske
Nathan Coyle
Russell Anderson
Ryan Sullivan
Date Added:
12/16/2016
Area of Irregular Shapes
Conditional Remix & Share Permitted
CC BY-NC
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Overview: Math in Real Life (MiRL) supports the expansion of regional networks to create an environment of innovation in math teaching and learning.  The focus on applied mathematics supports the natural interconnectedness of math to other disciplines while infusing relevance for students.  MiRL supports a limited number of networked math learning communities that focus on developing and testing applied problems in mathematics.  The networks help math teachers refine innovative teaching strategies with the guidance of regional partners and the Oregon Department of Education.

Subject:
Mathematics
Geometry
Material Type:
Activity/Lab
Author:
Mark Freed
Date Added:
08/24/2020
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
Maia Vadeen
Malinda Zarske
Nathan Coyle
Russell Anderson
Ryan Sullivan
Date Added:
02/07/2017
CTE Architecture: Fences
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This task was developed by high school and postsecondary mathematics and design/pre-construction educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

Subject:
Architecture and Design
Geometry
Material Type:
Activity/Lab
Homework/Assignment
Lesson Plan
Provider:
National Association of State Directors of Career Technical Education Consortium
Provider Set:
Career Technical Education
Date Added:
03/01/2012
CTE Architecture: Framing a House
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This task was developed by high school and postsecondary mathematics and design/pre-construction educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

Subject:
Architecture and Design
Geometry
Ratios and Proportions
Material Type:
Activity/Lab
Assessment
Homework/Assignment
Lesson Plan
Provider:
National Association of State Directors of Career Technical Education Consortium
Provider Set:
Career Technical Education
Date Added:
03/05/2012
Designing a Spectroscopy Mission
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Students find and calculate the angle that light is transmitted through a holographic diffraction grating using trigonometry. After finding this angle, student teams design and build their own spectrographs, researching and designing a ground- or space-based mission using their creation. At project end, teams present their findings to the class, as if they were making an engineering conference presentation. Student must have completed the associated Building a Fancy Spectrograph activity before attempting this activity.

Subject:
Engineering
Physics
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Date Added:
10/14/2015
Determining Densities
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Students use two different methods to determine the densities of a variety of materials and objects. The first method involves direct measurement of the volumes of objects that have simple geometric shapes. The second is the water displacement method, used to determine the volumes of irregularly shaped objects. After the densities are determined, students create x-y scatter graphs of mass versus volume, which reveal that objects with densities less than water (floaters) lie above the graph's diagonal (representing the density of water), and those with densities greater than water (sinkers) lie below the diagonal.

Subject:
Education
Physics
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Mary R. Hebrank
Date Added:
10/14/2015
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
Maia Vadeen
Malinda Zarske
Nathan Coyle
Russell Anderson
Ryan Sullivan
Date Added:
02/07/2017
Edible Rovers – High School
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Students act as Mars exploratory rover engineers, designing, building and displaying their edible rovers to a design review. To begin, they evaluate rover equipment and material options to determine which parts might fit in their given NASA budget. With provided parts and material lists, teams analyze their design options and use their findings to design their rovers.

Subject:
Engineering
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Ben Sprague
Chris Yakacki
Daria Kotys-Schwartz
Denise W. Carlson
Geoffrey Hill
Janet Yowell
Malinda Schaefer Zarske
Date Added:
10/14/2015
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
Fractals in Geometry: Fractal Cities *Final*
Conditional Remix & Share Permitted
CC BY-NC
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This lesson was created by School Library Media Specialist, Pam Harland, and Math teachers Rebecca Hanna and Carissa Maskwa to model text-based inquiry in STEM. Over the course of the unit, students will explore a variety of texts and grow in their knowledge of fractals, city design, and ability to use informational text to support their inquiry and research.The unit was created in year two of the School Librarians Advancing STEM Learning (SLASL) project, led by the Institute for the Study of Knowledge Management (ISKME) in partnership with Granite State University, New Hampshire, and funded by the Institute for Museum and Library Services (IMLS).

Subject:
Mathematics
Material Type:
Unit of Study
Author:
Pam Harland
Carissa Maskwa
Rebecca Hanna
Date Added:
06/22/2017
G-MG Coins in a Circular Pattern
Unrestricted Use
CC BY
Rating

This task complements ``Seven Circles'' I, II, and III. This is a hands-on activity which students could work on at many different levels and the activity leads to many interesting questions for further investigation.

Subject:
Mathematics
Geometry
Trigonometry
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
08/21/2012
Geometry Module 3:  Extending to Three Dimensions
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CC BY-NC-SA
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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
Here Comes the Hurricane! Saving Lives through Logical Reasoning and Computer Science
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Students use a hurricane tracking map to measure the distance from a specific latitude and longitude location of the eye of a hurricane to a city. Then they use the map's scale factor to convert the distance to miles. They also apply the distance formula by creating an x-y coordinate plane on the map. Students are challenged to analyze what data might be used by computer science engineers to write code that generates hurricane tracking models. Then students analyze a MATLAB® computer code that uses the distance formula repetitively to generate a table of data that tracks a hurricane at specific time intervals. Students come to realize that using a computer program to generate the calculations (instead of by hand) is very advantageous for a dynamic situation like tracking storm movements. Their inspection of some MATLAB code helps them understand how it communicates what to do using mathematical formulas, logical instructions and repeated tasks. They also conclude that the example program is too simplistic to really be a useful tool; useful computer model tools must necessarily be much more complex.

Subject:
Engineering
Atmospheric Science
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Armando Vital
Fritz Claydon
Justin Chang
K. B. Nakshatrala
Rodrigues
Stuart Long
Date Added:
09/18/2014
Ice Cream Cone
Unrestricted Use
CC BY
Rating

This rich task is an excellent example of geometric concepts in a modeling situation and is accessible to all students. In this task, students will provide a sketch of a paper ice cream cone wrapper, use the sketch to develop a formula for the surface area of the wrapper, and estimate the maximum number of wrappers that could be cut from a rectangular piece of paper.

Subject:
Mathematics
Geometry
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Let’s Build an Aqueduct!
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Students explore in detail how the Romans built aqueducts using arches—and the geometry involved in doing so. Building on what they learned in the associated lesson about how innovative Roman arches enabled the creation of magnificent structures such as aqueducts, students use trigonometry to complete worksheet problem calculations to determine semicircular arch construction details using trapezoidal-shaped and cube-shaped blocks. Then student groups use hot glue and half-inch wooden cube blocks to build model aqueducts, doing all the calculations to design and build the arches necessary to support a water-carrying channel over a three-foot span. They calculate the slope of the small-sized aqueduct based on what was typical for Roman aqueducts at the time, aiming to construct the ideal slope over a specified distance in order to achieve a water flow that is not spilling over or stagnant. They test their model aqueducts with water and then reflect on their performance.

Subject:
Mathematics
Geometry
Material Type:
Activity/Lab
Provider:
TeachEngineering
Author:
Lauchlin Blue
Malinda Zarske
Nathan Coyle
Date Added:
02/07/2017
Modeling: Rolling Cups
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help teachers assess how well students are able to: choose appropriate mathematics to solve a non-routine problem; generate useful data by systematically controlling variables; and develop experimental and analytical models of a physical situation.

Subject:
Functions
Geometry
Measurement and Data
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
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