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  • CCSS.Math.Content.HSG-MG.A.2
A Chance at Monte Carlo
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At its core, the LEGO MINDSTORMS(TM) NXT product provides a programmable microprocessor. Students use the NXT processor to simulate an experiment involving thousands of uniformly random points placed within a unit square. Using the underlying geometry of the experimental model, as well as the geometric definition of the constant π (pi), students form an empirical ratio of areas to estimate a numerical value of π. Although typically used for numerical integration of irregular shapes, in this activity, students use a Monte Carlo simulation to estimate a common but rather complex analytical form the numerical value of the most famous irrational number, π.

Subject:
Engineering
Electronic Technology
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Carleigh Samson
Janet Yowell
Michael Trumpis
Date Added:
09/18/2014
Archimedes and the King's Crown
Unrestricted Use
CC BY
Rating

The famous story of Archimedes running through the streets of Syracuse (in Sicily during the third century bc) shouting ''Eureka!!!'' (I have found it) reportedly occurred after he solved this problem. The problem combines the ideas of ratio and proportion within the context of density of matter.

Subject:
Mathematics
Geometry
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
01/04/2013
Toilet Roll
Unrestricted Use
CC BY
Rating

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 A Ton of Snow
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: Eric and Julianne are shoveling snow. After an hour of hard work, Eric remarks ''I bet we have shoveled more than a ton of snow.'' Explain what measure...

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
01/07/2014
Solving Quadratic Equations: Cutting Corners
Only Sharing Permitted
CC BY-NC-ND
Rating

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
Rating

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
Running Around a track II
Unrestricted Use
CC BY
Rating

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
Ampere's Law
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Educational Use
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The lesson begins with a demonstration introducing students to the force between two current carrying loops, comparing the attraction and repulsion between the loops to that between two magnets. After formal lecture on Ampere's law, students begin to use the concepts to calculate the magnetic field around a loop. This is applied to determine the magnetic field of a toroid, imagining a toroid as a looped solenoid.

Subject:
Engineering
Physics
Material Type:
Activity/Lab
Lesson Plan
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Eric Appelt
Date Added:
09/18/2014
How Thick is a Soda Can II?
Unrestricted Use
CC BY
Rating

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
How Many Leaves on a Tree? (Version 2)
Unrestricted Use
CC BY
Rating

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
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
Solar Eclipse
Unrestricted Use
CC BY
Rating

Total solar eclipses are quite rare, so much so that they make the news when they do occur. This task explores some of the reasons why. Solving the problem is a good application of similar triangles

Subject:
Mathematics
Geometry
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
01/11/2013
G-MG Indiana Jones and the Golden Statue
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 following clip shows the famous opening scene of the movie Raiders of the Lost Arc. At the beginning of the clip, Indiana Jones is replacing the go...

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
09/11/2013
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