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Archimedes' Principle, Pascal's Law and Bernoulli's Principle
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Educational Use
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Students are introduced to Pascal's law, Archimedes' principle and Bernoulli's principle. Fundamental definitions, equations, practice problems and engineering applications are supplied. A PowerPoint® presentation, practice problems and grading rubric are provided.

Subject:
Applied Science
Engineering
Mathematics
Physical Science
Physics
Material Type:
Lesson Plan
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Emily Sappington
Mila Taylor
Date Added:
09/18/2014
Archimedes and the King's Crown
Unrestricted Use
CC BY
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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:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
01/04/2013
Are Random Triangles Acute or Obtuse?
Conditional Remix & Share Permitted
CC BY-NC-SA
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This learning video deals with a question of geometrical probability. A key idea presented is the fact that a linear equation in three dimensions produces a plane. The video focuses on random triangles that are defined by their three respective angles. These angles are chosen randomly subject to a constraint that they must sum to 180 degrees. An example of the types of in-class activities for between segments of the video is: Ask six students for numbers and make those numbers the coordinates x,y of three points. Then have the class try to figure out how to decide if the triangle with those corners is acute or obtuse.

Subject:
Geometry
Mathematics
Statistics and Probability
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Gilbert Strange
Date Added:
06/15/2021
Are They Similar?
Unrestricted Use
CC BY
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In this problem, students are given a picture of two triangles that appear to be similar, but whose similarity cannot be proven without further information. Asking students to provide a sequence of similarity transformations that maps one triangle to the other focuses them on the work of standard G-SRT.2, using the definition of similarity in terms of similarity transformations.

Subject:
Geometry
Mathematics
Trigonometry
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Area Builder
Unrestricted Use
CC BY
Rating
0.0 stars

Create your own shapes using colorful blocks and explore the relationship between perimeter and area. Compare the area and perimeter of two shapes side-by-side. Challenge yourself in the game screen to build shapes or find the area of funky figures. Try to collect lots of stars!

Subject:
Mathematics
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Amanda McGarry
Ariel Paul
Beth Stade
Bryce Gruneich
John Blanco
Karina Hensberry (lead)
Kathy Perkins
Date Added:
06/28/2022
Area Model Algebra
Unrestricted Use
CC BY
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Build rectangles of various sizes and relate multiplication to area. Discover new strategies for multiplying algebraic expressions. Use the game screen to test your multiplication and factoring skills!

Subject:
Algebra
Mathematics
Material Type:
Diagram/Illustration
Game
Interactive
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Amanda McGarry (co-lead)
Amy Hanson (lead designer)
Ariel Paul
Diana Lopez Tavares (artwork)
Jonathan Olson (developer)
Karina Hensberry
Kathy Perkins
Mariah Hermsmeyer (artwork)
Susan Miller
Date Added:
06/28/2022
Area Model Introduction
Unrestricted Use
CC BY
Rating
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Build rectangles of various sizes and relate multiplication to area. Partition a rectangle into two areas to discover the distributive property.

Subject:
Mathematics
Material Type:
Diagram/Illustration
Game
Interactive
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Amanda McGarry (co-lead)
Amy Hanson (lead designer)
Ariel Paul
Diana Lopez Tavares (artwork)
Jonathan Olson (developer)
Karina Hensberry
Kathy Perkins
Mariah Hermsmeyer (artwork)
Susan Miller
Date Added:
06/28/2022
Area Model Multiplication
Unrestricted Use
CC BY
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Build rectangles of various sizes and relate multiplication to area. Discover new strategies for multiplying large numbers. Use the game screen to test your problem solving strategies!

Subject:
Mathematics
Material Type:
Diagram/Illustration
Game
Interactive
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Amanda McGarry (co-lead)
Amy Hanson (lead designer)
Ariel Paul
Diana Lopez Tavares (artwork)
Jonathan Olson (developer)
Karina Hensberry
Kathy Perkins
Mariah Hermsmeyer (artwork)
Susan Miller
Date Added:
06/28/2022
Area and Perimeter of Composite Shapes
Conditional Remix & Share Permitted
CC BY-NC-SA
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This short video and interactive assessment activity is designed to give fourth graders an overview of composite figures composed of squares and rectangles.

Subject:
Geometry
Mathematics
Material Type:
Assessment
Interactive
Lecture
Provider:
CK-12 Foundation
Provider Set:
CK-12 Elementary Math
Date Added:
06/15/2021
Area of Squares and Rectangles
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
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This short video and interactive assessment activity is designed to teach third graders an overview of area of squares and rectangles - word problems.

Subject:
Mathematics
Measurement and Data
Material Type:
Assessment
Interactive
Lecture
Provider:
CK-12 Foundation
Provider Set:
CK-12 Elementary Math
Date Added:
06/15/2021
Areas of geometric shapes with the same perimeter
Unrestricted Use
CC BY
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This problem is part of a very rich tradition of problems looking to maximize the area enclosed by a shape with fixed perimeter. Only three shapes are considered here because the problem is difficult for more irregular shapes.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
01/20/2013
Are the Triangles Congruent?
Unrestricted Use
CC BY
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The purpose of this task is primarily assessment-oriented, asking students to demonstrate knowledge of how to determine the congruency of triangles.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Arithmetic
Unrestricted Use
CC BY
Rating
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Remember your multiplication tables? ... me neither. Brush up on your multiplication, division, and factoring skills with this exciting game. No calculators allowed! The students will be given mutiplication and division problems which they must answer. They also have the option of being given a number then stating the factors of how that number was attained using either multiplication or division.

Subject:
Mathematics
Numbers and Operations
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Date Added:
05/01/2006
Arithmetic (AR)
Read the Fine Print
Some Rights Reserved
Rating
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Remember your multiplication tables? ... me neither. Brush up on your multiplication, division, and factoring skills with this exciting game. No calculators allowed!

Subject:
Mathematics
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Michael Dubson
Trish Loeblein
Date Added:
05/02/2010
Arithmetic: More Long Division and Remainder Examples (Part 3 of 4)
Conditional Remix & Share Permitted
CC BY-NC-SA
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This arithmetic lesson demonstrates more long division problems with remainders.[Arithmetic playlist: Lesson 26 of 38]

Subject:
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
06/15/2021
Arithmetic Operations: Adding Decimals Example 1
Conditional Remix & Share Permitted
CC BY-NC
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You get the general idea of decimal is and what the digits in different places represent (place value). Now you're ready to do something with the decimals. Adding and subtracting is a good place to start. This will allow you to add your family's expenses to figure out if your little brother is laundering money (perhaps literally). Have fun! Common Core Standard: 5.NBT.B.7

Subject:
Mathematics
Numbers and Operations
Material Type:
Activity/Lab
Homework/Assignment
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Khan
Salman
Date Added:
06/15/2021
Arithmetic Operations: Adding Decimals Example 2
Conditional Remix & Share Permitted
CC BY-NC
Rating
0.0 stars

You get the general idea of decimal is and what the digits in different places represent (place value). Now you're ready to do something with the decimals. Adding and subtracting is a good place to start. This will allow you to add your family's expenses to figure out if your little brother is laundering money (perhaps literally). Have fun! Common Core Standard: 5.NBT.B.7

Subject:
Mathematics
Numbers and Operations
Material Type:
Activity/Lab
Homework/Assignment
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Khan
Salman
Date Added:
06/15/2021