## Resources

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Resource Type (750)

Modeling Scenario(293) Technique Narrative(20) Potential Scenario(354) Article or Presentation(51) Free Online Textbook(29) General Resource(3)

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Differential Equation Type (750)

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Qualitative Analysis (750)

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Application Area (750)

Chemistry(63) Economics(48) Engineering(100) Humanities(10) Life Sciences(316) Mathematics(409) Modeling (general)(587) Physics(225) Social Sciences(84) Other(5)

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Course (750)

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Course Level (750)

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Lesson Length (750)

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Approach (750)

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Skills (750)

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Key Scientific Process Skills (312)

Reading research papers(2) Reviewing prior research(23) Asking a question(297) Formulating hypotheses(264) Designing/conducting experiments(55) Predicting outcomes(97) Gathering data/making observations(74) Analyzing data(125) Interpreting results/data(141) Displaying/modeling results/data(139) Communicating results(115) Translating into mathematics(6)

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Assessment Type (313)

Assessment of individual student performance(1) Assessment of student groups/teams(3) Assignment(1) Homework(285) Give an oral presentation(1) Informal in-class report(1) Solve problem(s)(3) Written assignment: One minute paper(1) Written assignment: Essay(4) Written assignment: Report(278) Written assignment: Literature review(1)

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Pedagogical Approaches (275)

Case Study(11) Collaborative Work(9) Computer Model(10) Physical Model(6) Guided inquiry/investigation(252)

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Vision and Change Core Competencies - Ability (308)

Create and develop models(287) Use quantitative reasoning(273) Design simulations(52) Tap into interdisciplinary study(48) Communicate and collaborate with mathematics community(10) Communicate and collaborate with other disciplines(32) Understand the relationship between material and society(3)

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Principles of How People Learn (312)

Motivates student to learn material(301) Focuses student on the material to be learned(287) Develops supportive community of learners(8) Leverages differences among learners(8) Reveals prior knowledge(8) Requires student to do the bulk of the work(8)

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Bloom's Cognitive Level (289)

Foundational: factual knowledge & comprehension(31) Application & Analysis(271) Synthesis/Evaluation/Creation(7)

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Includes clear efforts on Issues (2)

Diversity(1) Equity(2) Inclusion(1) Enhancement of all(1)

###### Applied Filters

Modeling Scenario

##### 1-064-TorricelliBox-ModelingScenario

The time it takes a column of water to empty and the time it takes the same volume of column of water with a box (various sizes) submerged in the column of water are compared through modeling with Torricelli's Law.Modeling Scenario

##### 6-030-SaltAndTorricelli-ModelingScenario

We build on a model for the height of a falling column of water with a small hole in the container at the bottom of the column of water. We use data from one video of a falling column of water.Article or Presentation

##### 2020-TeachingModule-ModelingFallingColumnOfWater

We discuss how to model a falling column of water empirically and analytically from first principles in physics laws.Modeling Scenario

##### 1-063-ThreeHoleColumnOfWater-ModelingScenario

We consider a column of water with three holes or spigots through which water can exit and ask students to model the height of the column of water over time.Modeling Scenario

##### 1-015-Torricelli-ModelingScenario

We help students develop a model (Torricelli's Law) for the height of a falling column of water with a small hole in the container at the bottom of the column of water through which water exits the column.Potential Scenario

##### 2009-G_Recktenwald-Tank Draining Exercise

This paper describe deep mathematics, including differential equations concerned with modeling the draining of tank and the shape of the water coming out the bore hole at the bottom of the tank of water.Modeling Scenario

##### 1-036-NeutralBuoyancy-ModelingScenario

An object may hang suspended at, say, ten foot depth in a column of water if at ten feet underwater the density of the object equals the density of water. We study this phenomenonModeling Scenario

##### 1-059-ContainerShapeFallingWater-ModelingScenario

We examine many different physical situations to determine the time it takes a fixed volume of water to flow out of different shape containers through the same size exit hole at the bottom of the container.Modeling Scenario

##### 1-057-FiguringFluidFlow-ModelingScenario

We propose three differential equations models for the height of a column of falling water as the water exits a small bore hole at the bottom of the cylinder and ask students to determine which model is the best of the three.Modeling Scenario

##### 1-140-LeakyBucket-ModelingScenario

We seek to model the height of water in a cylindrical tank (bucket) in which water flows out the bottom of the tank through a small bore hole while we are pouring water into the tank at the top of the tank at a constant (or varying) rate.Potential Scenario

##### 2015-Goodnow-EtAl-Mathematical Models of Water Clocks

This is a historical tour of water clocks, known as clepsydra a Greek word meaning water thief. These devices were for telling time.Potential Scenario

##### 2012-Bech-EtAl-Resources For Engineering Applications Of Math

Illustrations of applied mathematics including statics, truss, heat equation, column analysis, coupled oscillators, feedback control, AC circuit, chemical reactions, kinetics.Modeling Scenario

##### 1-090-EmptySphericalTank-ModelingScenario

We model the emptying of water from a spherical tank. First, we pump out water at a constant rate. Second, we allow the water to exit through a small hole in the bottom of the tank. We seek to determine how fast the water level is falling in both...Modeling Scenario

##### 1-029-ConeToCubeFlow-ModelingScenario

An inverted right circular cone with a hole at the bottom is suspended above an open-topped cube which also has a hole in the center of the bottom. The cone is filled with water and we model water flow from cone to cube and out the bottom of the...Potential Scenario