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Math, Grade 6, Unit 3
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Ratios Type of Unit: Concept Prior Knowledge Students should be able to: ...

Ratios

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Calculate with whole numbers up to 100 using all four operations.
Understand fraction notation and percents and translate among fractions, decimal numbers, and percents.
Interpret and use a number line.
Use tables to solve problems.
Use tape diagrams to solve problems.
Sketch and interpret graphs.
Write and interpret equations.

Lesson Flow

The first part of the unit begins with an exploration activity that focuses on a ratio as a way to compare the amount of egg and the amount of flour in a mixture. The context motivates a specific understanding of the use of, and need for, ratios as a way of making comparisons between quantities. Following this lesson, the usefulness of ratios in comparing quantities is developed in more detail, including a contrast to using subtraction to find differences. Students learn to interpret and express ratios as fractions, as decimal numbers, in a:b form, in words, and as data; they also learn to identify equivalent ratios.

The focus of the middle part of the unit is on the tools used to represent ratio relationships and on simplifying and comparing ratios. Students learn to use tape diagrams first, then double number lines, and finally ratio tables and graphs. As these tools are introduced, students use them in problem-solving contexts to solve ratio problems, including an investigation of glide ratios. Students are asked to make connections and distinctions among these forms of representation throughout these lessons. Students also choose a ratio project in this part of the unit (Lesson 8).

The third and last part of the unit covers understanding percents, including those greater than 100%.

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

Subject:
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Statistics and Probability
Material Type:
Unit of Study
Provider:
Pearson
Handy Measuring Ratio
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In this activity, learners use their hands as tools for indirect measurement. ...

In this activity, learners use their hands as tools for indirect measurement. Learners explore how to use ratios to calculate the approximate height of something that can't be measured directly by first measuring something that can be directly measured. This activity can also be used to explain how scientists use indirect measurement to determine distances between things in the universe that are too far away, too large or too small to measure directly (i.e. diameter of the moon or number of bacteria in a volume of liquid).

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Exploratorium
Author:
Exploratorium
Gordon and Betty Moore Foundation
National Science Foundation
The Exploratorium
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
Circle Tool
Conditions of Use:
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An applet for students to use in exploring the area and circumference ...

An applet for students to use in exploring the area and circumference of a circle in relation to its radius and diameter. When the radius is changed, the other measures automatically change and are shown on a board. Most importantly, the ratio between any pair of these measures can be shown.

Subject:
Mathematics
Geometry
Numbers and Operations
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Scaling, Go Figure!
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Students learn how different characteristics of shapes—side lengths, perimeter and area—change when ...

Students learn how different characteristics of shapes—side lengths, perimeter and area—change when the shapes are scaled, either enlarged or reduced. Student pairs conduct a “scaling investigation” to measure and calculate shape dimensions (rectangle, quarter circle, triangle; lengths, perimeters, areas) from a bedroom floorplan provided at three scales. They analyze their data to notice the mathematical relationships that hold true during the scaling process. They see how this can be useful in real-world situations like when engineers design wearable or implantable biosensors. This prepares students for the associated activity in which they use this knowledge to help them reduce or enlarge their drawings as part of the process of designing their own wearables products. Pre/post-activity quizzes, a worksheet and wrap-up concepts handout are provided.

Subject:
Career and Technical Education
Mathematics
Measurement and Data
Numbers and Operations
Material Type:
Lesson
Provider:
TeachEngineering
Author:
Denise W. Carlson
Evelynne Pyne
Lauchlin Blue
Robotics Engineering for Better Life and Sustainable Future RET, College of Engineering, Michigan State University
How Much Is a Million?
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This lesson focuses learners on the concept of 1,000,000. It allows learners ...

This lesson focuses learners on the concept of 1,000,000. It allows learners to see firsthand the sheer size of 1 million, while at the same time providing learners with an introduction to sampling and its use in mathematics. Learners use grains of rice and a balance to figure out the approximate volume and weight of 1,000,000 grains of rice. This lesson guide includes 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
Author:
NCTM Illuminations
Thinkfinity/Verizon Foundation
Tim Granger
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
How to Bag It?
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In this recycling activity students conduct a poll and display data showing ...

In this recycling activity students conduct a poll and display data showing which type of material the survey population feels is the best for shopping bags. Students share their results in a data display of their choice and then use the data to draw conclusions and create a recycling plan. The activity includes the student worksheet, extension suggestions, and related resources.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Salts & Solubility
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Add different salts to water, then watch them dissolve and achieve a ...

Add different salts to water, then watch them dissolve and achieve a dynamic equilibrium with solid precipitate. Compare the number of ions in solution for highly soluble NaCl to other slightly soluble salts. Relate the charges on ions to the number of ions in the formula of a salt. Calculate Ksp values.

Subject:
Chemistry
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Adams, Wendy
Danielle Harlow
Excellence Center of Science and Mathematics Education at King Saud University
Harlow, Danielle
Kathy Perkins
Koch, Linda
LeMaster, Ron
Linda Koch
Loeblein, Trish
National Science Foundation
O'Donnell Foundation
Perkins, Kathy
PhET
PhET Interactive Simulations
Ron LeMaster
The William and Flora Hewlett Foundation
Trish Loeblein
Wendy Adams
Salts & Solubility (AR)
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Add different salts to water, then watch them dissolve and achieve a ...

Add different salts to water, then watch them dissolve and achieve a dynamic equilibrium with solid precipitate. Compare the number of ions in solution for highly soluble NaCl to other slightly soluble salts. Relate the charges on ions to the number of ions in the formula of a salt. Calculate Ksp values. Arabic Language.

Subject:
Chemistry
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Adams, Wendy
Harlow, Danielle
Koch, Linda
LeMaster, Ron
Loeblein, Trish
Perkins, Kathy
Math, Grade 7, Unit 4
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Zooming In On Figures Unit Overview Type of Unit: Concept; Project Length ...

Zooming In On Figures

Unit Overview

Type of Unit: Concept; Project

Length of Unit: 18 days and 5 days for project

Prior Knowledge

Students should be able to:

Find the area of triangles and special quadrilaterals.
Use nets composed of triangles and rectangles in order to find the surface area of solids.
Find the volume of right rectangular prisms.
Solve proportions.

Lesson Flow

After an initial exploratory lesson that gets students thinking in general about geometry and its application in real-world contexts, the unit is divided into two concept development sections: the first focuses on two-dimensional (2-D) figures and measures, and the second looks at three-dimensional (3-D) figures and measures.
The first set of conceptual lessons looks at 2-D figures and area and length calculations. Students explore finding the area of polygons by deconstructing them into known figures. This exploration will lead to looking at regular polygons and deriving a general formula. The general formula for polygons leads to the formula for the area of a circle. Students will also investigate the ratio of circumference to diameter ( pi ). All of this will be applied toward looking at scale and the way that length and area are affected. All the lessons noted above will feature examples of real-world contexts.
The second set of conceptual development lessons focuses on 3-D figures and surface area and volume calculations. Students will revisit nets to arrive at a general formula for finding the surface area of any right prism. Students will extend their knowledge of area of polygons to surface area calculations as well as a general formula for the volume of any right prism. Students will explore the 3-D surface that results from a plane slicing through a rectangular prism or pyramid. Students will also explore 3-D figures composed of cubes, finding the surface area and volume by looking at 3-D views.
The unit ends with a unit examination and project presentations.

Subject:
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Geometry
Material Type:
Unit of Study
Provider:
Pearson
Math, Grade 7, Unit 6
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Samples and ProbabilityType of Unit: ConceptualPrior KnowledgeStudents should be able to:Understand the ...

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
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Statistics and Probability
Material Type:
Unit of Study
Provider:
Pearson
Statistical Method in Economics, Fall 2006
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The course introduces statistical theory to prepare students for the remainder of ...

The course introduces statistical theory to prepare students for the remainder of the econometrics sequence. The emphasis of the course is to understand the basic principles of statistical theory. A brief review of probability will be given; however, this material is assumed knowledge. The course also covers basic regression analysis. Topics covered include probability, random samples, asymptotic methods, point estimation, evaluation of estimators, Cramer-Rao theorem, hypothesis tests, Neyman Pearson lemma, Likelihood Ratio test, interval estimation, best linear predictor, best linear approximation, conditional expectation function, building functional forms, regression algebra, Gauss-Markov optimality, finite-sample inference, consistency, asymptotic normality, heteroscedasticity, and autocorrelation.

Subject:
Statistics and Probability
Economics
Material Type:
Assessment
Full Course
Homework/Assignment
Lecture Notes
Syllabus
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Chernozhukov, Victor
Design of Medical Devices and Implants, Spring 2006
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" This design course targets the solution of clinical problems by use ...

" This design course targets the solution of clinical problems by use of implants and other medical devices. Topics include the systematic use of cell-matrix control volumes; the role of stress analysis in the design process; anatomic fit, shape and size of implants; selection of biomaterials; instrumentation for surgical implantation procedures; preclinical testing for safety and efficacy, including risk/benefit ratio assessment evaluation of clinical performance and design of clinical trials. Student project materials are drawn from orthopedic devices, soft tissue implants, artificial organs, and dental implants."

Subject:
Health, Medicine and Nursing
Genetics
Material Type:
Full Course
Textbook
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Spector, Myron
Yannas, Ioannis
Gears: Determining Angular Velocity
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Students work as engineers and learn to conduct controlled experiments by changing ...

Students work as engineers and learn to conduct controlled experiments by changing one experimental variable at a time to study its effect on the experiment outcome. Specifically, they conduct experiments to determine the angular velocity for a gear train with varying gear ratios and lengths. Student groups assemble LEGO MINDSTORMS(TM) NXT robots with variously sized gears in a gear train and then design programs using the NXT software to cause the motor to rotate all the gears in the gear train. They use the LEGO data logging program and light sensors to set up experiments. They run the program with the motor and the light sensor at the same time and analyze the resulting plot in order to determine the angular velocity using the provided physics-based equations. Finally, students manipulate the gear train with different gears and different lengths in order to analyze all these factors and figure out which manipulation has a higher angular velocity. They use the equations for circumference of a circle and angular velocity; and convert units between radians and degrees.

Subject:
Engineering
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering NGSS Aligned Resources
Author:
AMPS GK-12 Program,
Jennifer S. Haghpanah, Leonarda Huertas, Jasmin Mejias, Mihai Pruna, James Cox
Should I Drink That?
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Students perform one of the first steps that environmental engineers do to ...

Students perform one of the first steps that environmental engineers do to determine water quality sampling and analysis. Student teams measure the electrical conductivity of four water samples (deionized water, purified water, school tap water and a salt-water solution) using teacher-made LED-conductivity testers and commercially available electrical conductivity meters. They use multimeters to also measure the resistance of the samples. They graph their collected data to see the relationship between the conductivity and resistance. Then, all students measure the conductivity of tap water samples brought to school from their homes; they organize and average their data by sub areas within their local school district to see if house location has any relationship to the water conductivity in their community.

Subject:
Engineering
Electronic Technology
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering NGSS Aligned Resources
Author:
Marjorie Hernandez
National Science Foundation GK-12 and Research Experience for Teachers (RET) Programs,
Introduction to Sociology 2e
Conditions of Use:
No Strings Attached
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Introduction to Sociology 2e adheres to the scope and sequence of a ...

Introduction to Sociology 2e adheres to the scope and sequence of a typical, one-semester introductory sociology course. It offers comprehensive coverage of core concepts, foundational scholars, and emerging theories, which are supported by a wealth of engaging learning materials. The textbook presents detailed section reviews with rich questions, discussions that help students apply their knowledge, and features that draw learners into the discipline in meaningful ways. The second edition retains the book’s conceptual organization, aligning to most courses, and has been significantly updated to reflect the latest research and provide examples most relevant to today’s students. In order to help instructors transition to the revised version, the 2e changes are described within the preface.

Subject:
Social Science
Material Type:
Full Course
Provider:
Rice University
Provider Set:
OpenStax College
Wear’s the Technology?
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Students apply their knowledge of scale and geometry to design wearables that ...

Students apply their knowledge of scale and geometry to design wearables that would help people in their daily lives, perhaps for medical reasons or convenience. Like engineers, student teams follow the steps of the design process, to research the wearable technology field (watching online videos and conducting online research), brainstorm a need that supports some aspect of human life, imagine their own unique designs, and then sketch prototypes (using Paint®). They compare the drawn prototype size to its intended real-life, manufactured size, determining estimated length and width dimensions, determining the scale factor, and the resulting difference in areas. After considering real-world safety concerns relevant to wearables (news article) and getting preliminary user feedback (peer critique), they adjust their drawn designs for improvement. To conclude, they recap their work in short class presentations.

Subject:
Career and Technical Education
Mathematics
Measurement and Data
Numbers and Operations
Material Type:
Activity/Lab
Provider:
TeachEngineering
Author:
Denise W. Carlson
Evelynne Pyne
Lauchlin Blue
Robotics Engineering for Better Life and Sustainable Future RET, College of Engineering, Michigan State University