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The sizes and distances of things in space are awe-inspiring, but hard to fathom. Things that are unimaginably massive can look tiny to us from Earth, and things that appear very large to us may be among the smallest in the sky. Although students can learn names and features of objects in the night sky, scale is one of the biggest stumbling blocks they need to overcome to actually understand what they’re looking at and to understand astronomy in general. But students have lots of daily life experience with bigger things looking smaller because of relative distance (and visa versa). How Big & How Far takes this experience of observing relative sizes and distances here on Earth and challenges students to apply it to night sky objects.

In this Night Sky Activity, the group measures how many fists tall a volunteer is. Then, students scatter and measure again, this time with outstretched fists and with much smaller and varied measurements. Students discuss how the distance you are from an object can make it appear larger or smaller. This activity sets them up to apply this idea afterwards as they observe night sky objects and attempt to better understand the actual sizes of the objects they see.

Subject:
Applied Science
Astronomy
Engineering
Physical Science
Material Type:
Activity/Lab
Provider:
Beetles: Science and Teaching for Field Instructors
05/06/2020
Educational Use
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0.0 stars

Students determine the coefficient of restitution (or the elasticity) for super balls. Working in pairs, they drop balls from a meter height and determine how high they bounce. They measure, record and repeat the process to gather data to calculate average bounce heights and coefficients of elasticity. Then they extrapolate to determine the height the ball would bounce if dropped from much higher heights.

Subject:
Applied Science
Engineering
Physical Science
Physics
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Mark Moldwin
09/18/2014
Educational Use
Rating
0.0 stars

In this video segment from Cyberchase, Inez estimates whether she has enough jelly beans in her large container to decorate all of the cookies in her batch.

Subject:
Mathematics
Material Type:
Lecture
Provider:
PBS LearningMedia
Provider Set:
PBS Learning Media: Multimedia Resources for the Classroom and Professional Development
Author:
U.S. Department of Education
WNET
07/09/2008
Conditional Remix & Share Permitted
CC BY-NC-SA
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0.0 stars

This lesson is about the estimation of the value of Pi. Based on previous knowledge, the students try to estimate Pi value using different methods, such as: direct physical measurements; a geometric probability model; and computer technology. This lesson is designed to stimulate the learning interests of students, to enrich their experience of solving practical problems, and to develop their critical thinking ability. To understand this lesson, students should have some mathematic knowledge about circles, coordinate systems, and geometric probability. They may also need to know something about Excel. To estimate Pi value by direct physical measurements, the students can use any round or cylindrical shaped objects around them, such as round cups or water bottles. When estimating Pi value by a geometric probability model, a dartboard and darts should be prepared before the class. You can also use other games to substitute the dart throwing game. For example, you can throw marbles to the target drawn on the floor. This lesson is about 45-50 minutes. If the students know little about Excel, the teacher may need one more lesson to explain and demonstrate how to use the computer to estimate Pi value. Downloadable from the website is a video demonstration about how to use Excel for estimating Pi.

Subject:
Mathematics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Renyong Feng
02/12/2015
Conditional Remix & Share Permitted
CC BY-NC-SA
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This course provides a broad theoretical basis for system identification, estimation, and learning. Students will study least squares estimation and its convergence properties, Kalman filters, noise dynamics and system representation, function approximation theory, neural nets, radial basis functions, wavelets, Volterra expansions, informative data sets, persistent excitation, asymptotic variance, central limit theorems, model structure selection, system order estimate, maximum likelihood, unbiased estimates, Cramer-Rao lower bound, Kullback-Leibler information distance, Akaike's information criterion, experiment design, and model validation.

Subject:
Applied Science
Career and Technical Education
Computer Science
Electronic Technology
Engineering
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
02/01/2006
Unrestricted Use
Public Domain
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0.0 stars

Introduction to Statistics is a resource for learning and teaching introductory statistics. This work is in the public domain. Therefore, it can be copied and reproduced without limitation. However, we would appreciate a citation where possible. Please cite as: Online Statistics Education: A Multimedia Course of Study (http://onlinestatbook.com/). Project Leader: David M. Lane, Rice University. Instructor's manual, PowerPoint Slides, and additional questions are available.

Subject:
Mathematics
Statistics and Probability
Material Type:
Textbook
Author:
David Lane
12/02/2019
Educational Use
Rating
0.0 stars

This activity helps students to understand numbers. The teacher should accept without comment any number a student gives and record it on the whiteboard.

Subject:
Mathematics
Measurement and Data
Material Type:
Lesson Plan
Provider:
Utah Education Network
10/21/2013
Conditional Remix & Share Permitted
CC BY-NC
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Distributions and Variability

Type of Unit: Project

Prior Knowledge

Students should be able to:

Represent and interpret data using a line plot.
Understand other visual representations of data.

Lesson Flow

Students begin the unit by discussing what constitutes a statistical question. In order to answer statistical questions, data must be gathered in a consistent and accurate manner and then analyzed using appropriate tools.

Students learn different tools for analyzing data, including:

Measures of center: mean (average), median, mode
Measures of spread: mean absolute deviation, lower and upper extremes, lower and upper quartile, interquartile range
Visual representations: line plot, box plot, histogram

These tools are compared and contrasted to better understand the benefits and limitations of each. Analyzing different data sets using these tools will develop an understanding for which ones are the most appropriate to interpret the given data.

To demonstrate their understanding of the concepts, students will work on a project for the duration of the unit. The project will involve identifying an appropriate statistical question, collecting data, analyzing data, and presenting the results. It will serve as the final assessment.

Subject:
Mathematics
Statistics and Probability
Material Type:
Unit of Study
Provider:
Pearson
Conditional Remix & Share Permitted
CC BY-NC
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Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset.

Subject:
Mathematics
Material Type:
Full Course
Provider:
Pearson
10/06/2016
Conditional Remix & Share Permitted
CC BY-NC
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Algebraic Reasoning

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Add, subtract, multiply, and divide rational numbers.
Evaluate expressions for a value of a variable.
Use the distributive property to generate equivalent expressions including combining like terms.
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true?
Write and solve equations of the form x+p=q and px=q for cases in which p, q, and x are non-negative rational numbers.
Understand and graph solutions to inequalities x<c or x>c.
Use equations, tables, and graphs to represent the relationship between two variables.
Relate fractions, decimals, and percents.
Solve percent problems included those involving percent of increase or percent of decrease.

Lesson Flow

This unit covers all of the Common Core State Standards for Expressions and Equations in Grade 7. Students extend what they learned in Grade 6 about evaluating expressions and using properties to write equivalent expressions. They write, evaluate, and simplify expressions that now contain both positive and negative rational numbers. They write algebraic expressions for problem situations and discuss how different equivalent expressions can be used to represent different ways of solving the same problem. They make connections between various forms of rational numbers. Students apply what they learned in Grade 6 about solving equations such as x+2=6 or 3x=12 to solving equations such as 3x+6=12 and 3(x−2)=12. Students solve these equations using formal algebraic methods. The numbers in these equations can now be rational numbers. They use estimation and mental math to estimate solutions. They learn how solving linear inequalities differs from solving linear equations and then they solve and graph linear inequalities such as −3x+4<12. Students use inequalities to solve real-world problems, solving the problem first by arithmetic and then by writing and solving an inequality. They see that the solution of the algebraic inequality may differ from the solution to the problem.

Subject:
Algebra
Mathematics
Material Type:
Unit of Study
Provider:
Pearson
Conditional Remix & Share Permitted
CC BY-NC
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0.0 stars

Subject:
Mathematics
Material Type:
Lesson Plan
09/21/2015
Conditional Remix & Share Permitted
CC BY-NC
Rating
0.0 stars

Proportional Relationships

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Understand what a rate and ratio are.
Make a ratio table.
Make a graph using values from a ratio table.

Lesson Flow

Students start the unit by predicting what will happen in certain situations. They intuitively discover they can predict the situations that are proportional and might have a hard time predicting the ones that are not. In Lessons 2–4, students use the same three situations to explore proportional relationships. Two of the relationships are proportional and one is not. They look at these situations in tables, equations, and graphs. After Lesson 4, students realize a proportional relationship is represented on a graph as a straight line that passes through the origin. In Lesson 5, they look at straight lines that do not represent a proportional relationship. Lesson 6 focuses on the idea of how a proportion that they solved in sixth grade relates to a proportional relationship. They follow that by looking at rates expressed as fractions, finding the unit rate (the constant of proportionality), and then using the constant of proportionality to solve a problem. In Lesson 8, students fine-tune their definition of proportional relationship by looking at situations and determining if they represent proportional relationships and justifying their reasoning. They then apply what they have learned to a situation about flags and stars and extend that thinking to comparing two prices—examining the equations and the graphs. The Putting It Together lesson has them solve two problems and then critique other student work.

Gallery 1 provides students with additional proportional relationship problems.

The second part of the unit works with percents. First, percents are tied to proportional relationships, and then students examine percent situations as formulas, graphs, and tables. They then move to a new context—salary increase—and see the similarities with sales taxes. Next, students explore percent decrease, and then they analyze inaccurate statements involving percents, explaining why the statements are incorrect. Students end this sequence of lessons with a formative assessment that focuses on percent increase and percent decrease and ties it to decimals.

Students have ample opportunities to check, deepen, and apply their understanding of proportional relationships, including percents, with the selection of problems in Gallery 2.

Subject:
Mathematics
Ratios and Proportions
Material Type:
Unit of Study
Provider:
Pearson
Conditional Remix & Share Permitted
CC BY-NC
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0.0 stars

Students are asked whether they can determine the number of books in a stack by measuring the height of the stack, or the number of marbles in a collection of marbles by weighing the collection.Students are asked to identify for which situations they can determine the number of books in a stack of books by measuring the height of the stack or the number of marbles in a collection of marbles by weighing the collection.Key ConceptsAs students examine different numerical relationships, they come to understand that they can find the number of books or the number of marbles in situations in which the books are all the same thickness and the marbles are all the same weight. This “constant” is equal to the value BA for a ratio A : B; students begin to develop an intuitive understanding of proportional relationships.Goals and Learning ObjectivesExplore numerical relationshipsSWD: Some students with disabilities will benefit from a preview of the goals in each lesson. Have students highlight the critical features or concepts to help them pay close attention to salient information.

Subject:
Numbers and Operations
Material Type:
Lesson Plan
09/21/2015
Conditional Remix & Share Permitted
CC BY-NC
Rating
0.0 stars

Samples and ProbabilityType of Unit: ConceptualPrior KnowledgeStudents should be able to:Understand the concept of a ratio.Write ratios as percents.Describe data using measures of center.Display and interpret data in dot plots, histograms, and box plots.Lesson FlowStudents begin to think about probability by considering the relative likelihood of familiar events on the continuum between impossible and certain. Students begin to formalize this understanding of probability. They are introduced to the concept of probability as a measure of likelihood, and how to calculate probability of equally likely events using a ratio. The terms (impossible, certain, etc.) are given numerical values. Next, students compare expected results to actual results by calculating the probability of an event and conducting an experiment. Students explore the probability of outcomes that are not equally likely. They collect data to estimate the experimental probabilities. They use ratio and proportion to predict results for a large number of trials. Students learn about compound events. They use tree diagrams, tables, and systematic lists as tools to find the sample space. They determine the theoretical probability of first independent, and then dependent events. In Lesson 10 students identify a question to investigate for a unit project and submit a proposal. They then complete a Self Check. In Lesson 11, students review the results of the Self Check, solve a related problem, and take a Quiz.Students are introduced to the concept of sampling as a method of determining characteristics of a population. They consider how a sample can be random or biased, and think about methods for randomly sampling a population to ensure that it is representative. In Lesson 13, students collect and analyze data for their unit project. Students begin to apply their knowledge of statistics learned in sixth grade. They determine the typical class score from a sample of the population, and reason about the representativeness of the sample. Then, students begin to develop intuition about appropriate sample size by conducting an experiment. They compare different sample sizes, and decide whether increasing the sample size improves the results. In Lesson 16 and Lesson 17, students compare two data sets using any tools they wish. Students will be reminded of Mean Average Deviation (MAD), which will be a useful tool in this situation. Students complete another Self Check, review the results of their Self Check, and solve additional problems. The unit ends with three days for students to work on Gallery problems, possibly using one of the days to complete their project or get help on their project if needed, two days for students to present their unit projects to the class, and one day for the End of Unit Assessment.

Subject:
Mathematics
Statistics and Probability
Material Type:
Unit of Study
Provider:
Pearson
Conditional Remix & Share Permitted
CC BY-NC
Rating
0.0 stars

Students estimate the length of 20 seconds by starting an unseen timer and stopping it when they think 20 seconds has elapsed. They are shown the results and repeat the process two more times. The first and third times are recorded and compiled, producing two data sets to be compared. Students analyze the data to conclude whether or not their ability to estimate 20 seconds improves with practice.Key ConceptsMeasures of center and spreadLine plots, box plots, and histogramsMean absolute deviation (MAD)Goals and Learning ObjectivesApply knowledge of statistics to compare sets of data.Use measures of center and spread to analyze data.Decide which graph is appropriate for a given situation.

Subject:
Statistics and Probability
Material Type:
Lesson Plan
09/21/2015
Rating
0.0 stars

In this activity, students explore the importance of adequate sampling strategies when conducting a scientific investigation. They are tasked with determining the average temperature of the Earth, using data sets easily found on the Internet, and determine the kind and size of sample necessary to calculate a representative average. The resource includes a student data sheet and an authentic assessment for the module, where students discuss the establishment of a habitation site on Mars. This is Activity C in module 2, titled "Modeling Hot and Cold Planets," of the resource, Earth Climate Course: What Determines a Planet's Climate? The course aims to help students to develop an understanding of our environment as a system of human and natural processes that result in changes that occur over various space and time scales.

Subject:
Atmospheric Science
Geoscience
History
History, Law, Politics
Life Science
Mathematics
Physical Science
Material Type:
Activity/Lab
Data Set
Provider:
NASA
Provider Set:
NASA Wavelength
11/05/2014
Unrestricted Use
CC BY
Rating
0.0 stars

This resource consists of a Java applet and expository text. The applet simulates a random sample from a normal distribution, and computes standard point estimates of the distribution mean and standard deviation. The bias and mean square error are also computed.

Subject:
Mathematics
Statistics and Probability
Material Type:
Activity/Lab
Interactive
Simulation
Provider:
University of Alabama in Huntsville
Provider Set:
Virtual Laboratories in Probability and Statistics
Author:
Kyle Siegrist
02/16/2011
Unrestricted Use
CC BY
Rating
0.0 stars

This interactive Flash animation allows students to explore size estimation in one, two and three dimensions. Multiple levels of difficulty allow for progressive skill improvement. In the simplest level, users estimate the number of small line segments that can fit into a larger line segment. Intermediate and advanced levels offer feature games that explore area of rectangles and circles, and volume of spheres and cubes. Related lesson plans and student guides are available for middle school and high school classroom instruction. Editor's Note: When the linear dimensions of an object change by some factor, its area and volume change disproportionately: area in proportion to the square of the factor and volume in proportion to its cube. This concept is the subject of entrenched misconception among many adults. This game-like simulation allows kids to use spatial reasoning, rather than formulas, to construct geometric sense of area and volume. This is part of a larger collection developed by the Physics Education Technology project (PhET).

Subject:
Applied Science
Education
Mathematics
Physical Science
Physics
Technology
Material Type:
Activity/Lab
Interactive
Provider:
Provider Set:
PhET Interactive Simulations
Author:
Michael Dubson
Mindy Gratny
01/22/2006
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

Physics I is a first-year physics course which introduces students to classical mechanics. This course has a hands-on focus, and approaches mechanics through take-home experiments. Topics include: kinematics, Newton's laws of motion, universal gravitation, statics, conservation laws, energy, work, momentum, and special relativity.

Subject:
Physical Science
Physics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Dourmashkin, Peter
Scholberg, Kate
09/01/2002
Conditional Remix & Share Permitted
CC BY-SA
Rating
0.0 stars

This is a first course in project management, one in which students will learn the knowledge, skills, and abilities necessary to be an effective project manager. They will learn how to plan, execute, and monitor a project. The course will cover the latest theories and concepts on scoping, stakeholder management, team leadership, budgeting and contracting, scheduling, quality control and assurance, and risk management. Students will have the option to apply their learning to a real-world project.

Subject: