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The Art of Insight in Science and Engineering: Mastering Complexity
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CC BY-NC-SA
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In this book, Sanjoy Mahajan shows us that the way to master complexity is through insight rather than precision. Precision can overwhelm us with information, whereas insight connects seemingly disparate pieces of information into a simple picture. Unlike computers, humans depend on insight. Based on the author’s fifteen years of teaching at MIT, Cambridge University, and Olin College, The Art of Insight in Science and Engineering shows us how to build insight and find understanding, giving readers tools to help them solve any problem in science and engineering. (Description courtesy of MIT Press.)

Subject:
Applied Science
Engineering
Mathematics
Physical Science
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Mahajan, Sanjoy
Date Added:
09/01/2014
Baby Proportions
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CC BY-NC
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Baby Proportions is an activity designed to challenge students to compare body measurement proportions of adults, students and infants. They then use these proportions to create a scale drawing of themselves and an infant enlarged to be their same height. The idea is to use real world measurements in practicing proportional relationship skills while creating an interesting image when finished.  

Subject:
Measurement and Data
Ratios and Proportions
Material Type:
Lesson Plan
Author:
Katie Barngrover
Date Added:
11/21/2019
Build an Approximate Scale Model of an Object
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Educational Use
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Students create models of objects of their choice, giving them skills and practice in techniques used by professionals. They make sketches as they build their objects. This activity facilitates a discussion on models and their usefulness.

Subject:
Career and Technical Education
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Date Added:
02/17/2017
Designing a Color-Changing Paint Using pH
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Educational Use
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How can an understanding of pH—a logarithmic scale used to identify the acidity or basicity of a water-based solution—be used to design and create a color-changing paint? This activity provides students the opportunity to extract dyes from natural products and test dyes for acids or bases as teams develop a prototype “paint” that is eventually applied to help with a wall redesign at a local children’s hospital. Students learn about how dyes are extracted from organic material and use the engineering design process to test dyes using a variety of indicators to achieve the right color for their prototype. Students iterate on their dyes and use ratios and proportions to calculate the amount of dye needed to successfully complete their painting project.

Subject:
Applied Science
Chemistry
Engineering
Mathematics
Numbers and Operations
Physical Science
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
Activities
Author:
Benjamin McCombs
Carly Monfort
Joseph Duncan
Linda Gillum
Miyong Hughes
Date Added:
01/30/2019
Estimating Planar Areas Using Analogue Methods
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Some Rights Reserved
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This math problem determines the areas of simple and complex planar figures using measurement of mass and proportional constructs. Materials are inexpensive or easily found (poster board, scissors, ruler, sharp pencil, right angle), but also requires use of an analytical balance (suggestions are provided for working with less precise weighing tools). This resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.

Subject:
Geoscience
Mathematics
Physical Science
Physics
Material Type:
Lecture Notes
Provider:
NASA
Provider Set:
NASA Wavelength
Date Added:
11/05/2014
Exploring Planetary Moons
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This is a collection of mathematics problems relating to the moons of the solar system. Learners will use simple proportional relationships and work with fractions to study the relative sizes of the larger moons in our solar system, and explore how temperatures change from place to place using the Celsius and Kelvin scales.

Subject:
Mathematics
Physical Science
Physics
Space Science
Material Type:
Assessment
Diagram/Illustration
Lecture Notes
Provider:
NASA
Provider Set:
NASA Wavelength
Date Added:
11/05/2014
The Invisible Radar Triangle
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Educational Use
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Students learn about radar imaging and its various military and civilian applications that include recognition and detection of human-made targets, and the monitoring of space, deforestation and oil spills. They learn how the concepts of similarity and scaling are used in radar imaging to create three-dimensional models of various targets. Students apply the critical attributes of similar figures to create scale models of a radar imaging scenario using infrared range sensors (to emulate radar functions) and toy airplanes (to emulate targets). They use technology tools to measure angles and distances, and relate the concept of similar figures to real-world applications.

Subject:
Education
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Mounir Ben Ghalia
Rocio Denise Nava
Date Added:
10/14/2015
Proportional Scaling
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Educational Use
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Learn about the dynamic relationships between a jet engine's heat loss, surface area, and volume in this video adapted from Annenberg Learner's Learning Math: Patterns, Functions, and Algebra.

Subject:
Mathematics
Material Type:
Lesson
Provider:
PBS LearningMedia
Provider Set:
PBS Learning Media Common Core Collection
Author:
U.S. Department of Education
WGBH Educational Foundation
Date Added:
06/18/2012
Ratio, Proportion and Percentages
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CC BY-NC-SA
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From politics to cookery, ratios, proportions and percentages are part of everyday life. This unit is designed to help you become more familiar with how figures can be manipulated, then you can check whether that discount really is as big as they claim!

Subject:
Mathematics
Ratios and Proportions
Material Type:
Activity/Lab
Reading
Syllabus
Provider:
The Open University
Provider Set:
Open University OpenLearn
Date Added:
02/16/2011
Ratio and Proportional Reasoning: Food Labels
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Educational Use
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In this lesson designed to enhance literacy skills, students learn how to use fractions to interpret the nutritional information contained on food labels.

Subject:
Life Science
Mathematics
Nutrition
Material Type:
Activity/Lab
Provider:
PBS LearningMedia
Provider Set:
PBS Learning Media Common Core Collection
Author:
WGBH Educational Foundation
Walmart Foundation
Date Added:
07/31/2012
Recipes
Unrestricted Use
CC BY
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Proportional relationships are everywhere. They are used to compare professional athletes and to help shoppers get the “best bang for their buck” at the grocery store. They help us build models and designs and are used in many business applications. This lesson plan introduces proportional relationships, ratios and unit rates at the grade 6/7 (C) level and requires adult learners to identify and compare ratios using the Padlet application.

Subject:
Mathematics
Material Type:
Assessment
Lesson
Date Added:
09/15/2017
Recipes
Unrestricted Use
CC BY
Rating
0.0 stars

Proportional relationships are everywhere. They are used to compare professional athletes and to help shoppers get the “best bang for their buck” at the grocery store. They help us build models and designs and are used in many business applications. This lesson plan introduces proportional relationships, ratios and unit rates at the grade 6/7 (C) level and requires adult learners to identify and compare ratios using the Padlet application.

Subject:
Mathematics
Material Type:
Assessment
Lesson
Date Added:
03/26/2020
Scale Model Project
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Educational Use
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Students build scale models of objects of their choice. In class they measure the original object and pick a scale, deciding either to scale it up or scale it down. Then they create the models at home. Students give two presentations along the way, one after their calculations are done, and another after the models are completed. They learn how engineers use scale models in their designs of structures, products and systems. Two student worksheets as well as rubrics for project and presentation expectations and grading are provided.

Subject:
Geometry
Mathematics
Measurement and Data
Material Type:
Activity/Lab
Provider:
TeachEngineering
Author:
Aaron Lamplugh
Maia Vadeen
Malinda Zarske
Nathan Coyle
Russell Anderson
Ryan Sullivan
Date Added:
02/07/2017
Scaling, Go Figure!
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Educational Use
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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
Date Added:
02/07/2017
Sugar Content in Drinks
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CC BY-NC
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Students will use proportional relationships to investigate the sugar content in popular drinks.

This activity was originally created by Dan Meyer:
http://threeacts.mrmeyer.com/sugarpackets

Subject:
Applied Science
Material Type:
Activity/Lab
Date Added:
10/17/2017
Topographic Maps and Ratios: A Study of Denali
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Educational Use
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Students overlay USGS topographic maps into Google Earth’s satellite imagery. By analyzing Denali, a mountain in Alaska, they discover how to use map scales as ratios to navigate maps, and use rates to make sense of contour lines and elevation changes in an integrated GIS software program. Students also problem solve to find potential pathways up a mountain by calculating gradients.

Subject:
Applied Science
Engineering
Geometry
Mathematics
Measurement and Data
Numbers and Operations
Physical Science
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
Activities
Author:
Andrea Burrows
Jake Schell
Date Added:
10/06/2018