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Grade 7 Module 5: Statistics and Probability
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In this module, students begin their study of probability, learning how to ...

In this module, students begin their study of probability, learning how to interpret probabilities and how to compute probabilities in simple settings.  They also learn how to estimate probabilities empirically.  Probability provides a foundation for the inferential reasoning developed in the second half of this module.  Additionally, students build on their knowledge of data distributions that they studied in Grade 6, compare data distributions of two or more populations, and are introduced to the idea of drawing informal inferences based on data from random samples.

Subject:
Statistics and Probability
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
How Big Is a Foot?
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In this math lesson, learners read the book "How Big Is a ...

In this math lesson, learners read the book "How Big Is a Foot?" by Rolf Myller to explore the need for a standard unit of measure. Students then create non-standard units (using their own footprints) and use the footprints to make "beds." This lesson guide includes a student activity sheet, questions for learners, assessment options, extensions, and reflection questions.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
How Big is Your Heart?
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This lesson emphasizes the connections between science and mathematics by using a ...

This lesson emphasizes the connections between science and mathematics by using a performance, or authentic, assessment format. Students will develop measurement skills as they relate the size of their fists to the size of their hearts. Students have the opportunity to explore applications involving their own hearts. An activity sheet (pdf) is included.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Lisa M. Passarello and Francis (Skip) Fennell
How High Can a Super Ball Bounce?
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Students determine the coefficient of restitution (or the elasticity) for super balls. ...

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:
Engineering
Physics
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering NGSS Aligned Resources
Author:
Mark Moldwin (now at University of Michigan, Atmospheric, Oceanic and Space Sciences) (This activity was classroom tested in second grade classes at El Rincon Elementary and Linwood E. Howe Elementary School within the Culver City Unified School District in California with additional support from a NSF Geosciences Education grant.)
Science and Engineering of the Environment of Los Angeles (SEE-LA) GK-12 Program,
How Long? How Wide? How Tall? How Deep?
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In this lesson, students use historical nonstandard units (digits, hand, cubit, yard, ...

In this lesson, students use historical nonstandard units (digits, hand, cubit, yard, foot, pace, fathom) to estimate the lengths of common objects and then measure using modern standard units. They will discover the usefulness of standardized measurement units and tools. An activity sheet (pdf), assessment options and other commentary are provided.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Donna Coe
How Many Steps?
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In this lesson activity students use nonstandard units (baby steps) to measure ...

In this lesson activity students use nonstandard units (baby steps) to measure lengths of different types of "steps" (giant, regular, umbrella, scissor, wooden-soldier, and backwards steps). Once each student gathers this data they will display their own data on a bar graph. Then the class will discuss the data and compare graphs among students. A students worksheet for data collection is included in PDF format.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Helene Silverman
How to Estimate the Value of Pi
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This lesson is about the estimation of the value of Pi. Based ...

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:
M.I.T.
Provider Set:
M.I.T. Blossoms
Author:
Renyong Feng
Identification, Estimation, and Learning, Spring 2006
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This course provides a broad theoretical basis for system identification, estimation, and ...

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:
Engineering
Material Type:
Full Course
Textbook
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Asada, Harry
Introduction to Estimation Theory
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This module introduces estimation theory and its terminology, including bias, consistency, and ...

This module introduces estimation theory and its terminology, including bias, consistency, and efficiency. In searching for methods of extracting information from noisy observations, this chapter describes estimation theory, which has the goal of extracting from noise-corrupted observations the values of disturbance parameters (noise variance, for example), signal parameters (amplitude or propagation direction), or signal waveforms. Estimation theory assumes that the observations contain an information-bearing quantity, thereby tacitly assuming that detection-based preprocessing has been performed (in other words, do I have something in the observations worth estimating?). Conversely, detection theory often requires estimation of unknown parameters: Signal presence is assumed, parameter estimates are incorporated into the detection statistic, and consistency of observations and assumptions tested. Consequently, detection and estimation theory form a symbiotic relationship, each requiring the other to yield high-quality signal processing algorithms.

Material Type:
Reading
Syllabus
Provider:
Rice University
Provider Set:
Connexions
Author:
Don Johnson
Investigating the Dynamic Martian Polar Caps
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In this activity, students download NASA Hubble Space Telescope (HST) images of ...

In this activity, students download NASA Hubble Space Telescope (HST) images of the Martian polar ice caps in summer and winter. Using image processing techniques, students measure and compare various images of the changing Martian and Earth polar ice caps.

Subject:
Algebra
Functions
Material Type:
Activity/Lab
Assessment
Lesson Plan
Provider:
Montana State University
NASA
Provider Set:
NASA/MSU Center for Educational Resources (CERES)
Junior Architects
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In this 4-lesson unit, students identify, compare, and analyze attributes of two- ...

In this 4-lesson unit, students identify, compare, and analyze attributes of two- and three-dimensional shapes, and develop geometric vocabulary. Students use basic linear measurement, understand and create scale representations, and explore perimeter and area measurement as they design their clubhouses. Activity sheets (pdf), lesson extensions and other commentary are provided.

Subject:
Mathematics
Geometry
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Jennifer Suh
Ladybug Lengths
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This lesson introduces students to the measurable attribute of length and provides ...

This lesson introduces students to the measurable attribute of length and provides practice in measuring length using non-standard units. The lesson is launched using the story Ladybug on the Move by Richard Fowler. Lesson objectives, teaching ideas, and handouts are included.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Magnificent Measurement
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In this 5-lesson unit, students engage in measurement activities involving length, area, ...

In this 5-lesson unit, students engage in measurement activities involving length, area, volume, time, and weight, using objects, pictures and symbols. Students practice measuring using standard and nonstandard units. Some lessons are introduced using children's literature.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Math, Grade 6, Unit 8
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Distributions and Variability Type of Unit: Project Prior Knowledge Students should be ...

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
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Statistics and Probability
Material Type:
Unit of Study
Provider:
Pearson
Math, Grade 7, Unit 2
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Proportional Relationships Type of Unit: Concept Prior Knowledge Students should be able ...

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
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Ratios and Proportions
Material Type:
Unit of Study
Provider:
Pearson
Math, Grade 7, Unit 2, Lesson 1
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Students are asked whether they can determine the number of books in ...

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 Concepts

As 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 Objectives

Explore numerical relationships

SWD:
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
Provider:
Pearson