Students learn about the concepts of accuracy and approximation as they pertain to robotics, gain insight into experimental accuracy, and learn how and when to estimate values that they measure. Students also explore sources of error stemming from the robot setup and rounding numbers.

This task is a refinement of ``Carbon 14 dating'' which focuses on accuracy. Because radioactive decay is an atomic process modeled by the laws of quantum mechanics, it is not possible to know with certainty when half of a given quantity of Carbon 14 atoms will decay. This type of question is very important in science and it also provides an opportunity to study the very subtle question of how errors behave when applying a function: in some cases the errors can be magnified while in others they are lessened.

Measuring the dimensions of nano-circuits requires an expensive, high-resolution microscope with integrated video camera and a computer with sophisticated imaging software, but in this activity, students measure nano-circuits using a typical classroom computer and (the free-to-download) GeoGebra geometry software. Inserting (provided) circuit pictures from a high-resolution microscope as backgrounds in GeoGebra's graphing window, students use the application's tools to measure lengths and widths of circuit elements. To simplify the conversion from the on-screen units to the real circuits' units and the manipulation of the pictures, a GeoGebra measuring interface is provided. Students export their data from GeoGebra to Microsoft® Excel® for graphing and analysis. They test the statistical significance of the difference in circuit dimensions, as well as obtain a correlation between average changes in original vs. printed circuits' widths. This activity and its associated lesson are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note below for details.

Beginning kindergarteners are introduced to science and engineering concepts through questions such as “What is a Scientist?” and “What is an Engineer?”, and go on to compare and contrast the two. They are introduced to five steps of the engineering design process and explore these steps using the “I do, we do, you do” set of guided instruction. At the end of the project, students produce a set of purple popsicles that they design using various materials and by following a set of criteria.

Students investigate the weather from a systems approach, learning how individual parts of a system work together to create a final product. Students learn how a barometer works to measure the Earth's air pressure by building a model using simple materials. Students analyze the changes in barometer measurements over time and compare those to actual weather conditions. They learn how to use a barometer to understand air pressure and predict actual weather changes.

This problem involves the meaning of numbers found on labels. When the level of accuracy is not given we need to make assumptions based on how the information is reported. The goal of the task is to stimulate a conversation about rounding and about how to record numbers with an appropriate level of accuracy, tying in directly to the standard N-Q.3. It is therefore better suited for instruction than for assessment purposes.

Accuracy of measurement in navigation depends very much on the situation. If a sailor's target is an island 200 km wide, sailing off center by 10 or 20 km is not a major problem. But, if the island were only 1 km wide, it would be missed if off just the smallest bit. Many of the measurements made while navigating involve angles, and a small error in the angle can translate to a much larger error in position when traveling long distances.

Accuracy of measurement in navigation depends very much on the situation. If a sailor's target is an island 200 km wide, sailing off center by 10 or 20 km is not a major problem. But, if the island were only 1 km wide, it would be missed if off just the smallest bit. Many of the measurements made while navigating involve angles, and a small error in the angle can translate to a much larger error in position when traveling long distances.

Student teams design and create LEGO® structures to house and protect temperature sensors. They leave their structures in undisturbed locations for a week, and regularly check and chart the temperatures. This activity engages students in the design and analysis aspects of engineering.

The purpose of this task is to illustrate through an absurd example the fact that in real life quantities are reported to a certain level of accuracy, and it does not make sense to treat them as having greater accuracy.

Students discover the mathematical constant phi, the golden ratio, through hands-on activities. They measure dimensions of "natural objects"—a star, a nautilus shell and human hand bones—and calculate ratios of the measured values, which are close to phi. Then students learn a basic definition of a mathematical sequence, specifically the Fibonacci sequence. By taking ratios of successive terms of the sequence, they find numbers close to phi. They solve a squares puzzle that creates an approximate Fibonacci spiral. Finally, the instructor demonstrates the rule of the Fibonacci sequence via a LEGO® MINDSTORMS® NXT robot equipped with a pen. The robot (already created as part of the companion activity, The Fibonacci Sequence & Robots) draws a Fibonacci spiral that is similar to the nautilus shape.

Students investigate the difference between qualitative and quantitative measurements and observations. By describing objects both qualitatively and quantitatively, they learn that both types of information are required for complete descriptions. Students discuss the characteristics of many objects, demonstrating how engineers use both qualitative and quantitative information in product design.

Students use a watt meter to measure energy input into a hot plate or hot pot used to heat water. The theoretical amount of energy required to raise the water by the measure temperature change is calculated and compared to the electrical energy input to calculate efficiency.

Students use LEGO® motors and generators to raise washers a measured height. They compare the work done by the motor-generator systems with the energy inputs to calculate efficiency.

This site is a series of video lectures and interactive exercises for teaching basic mathematics skills to first graders. It has separate addition and subtraction skills reviews numbers up to 10, 20, and 100; a section on telling time and reading clocks as well as course material on measurement and geometry.

This unit provides the framework for conducting an “engineering design field day” that combines 6 hands-on engineering activities into a culminating school (or multi-school) competition. The activities are a mix of design and problem-solving projects inspired by real-world engineering challenges: kite making, sail cars, tall towers, strong towers and a ball and tools obstacle course. The assortment of events engage children who have varied interests and cover a range of disciplines such as aerospace, mechanical and civil engineering. An optional math test—for each of grades 1-6—is provided as an alternative activity to incorporate into the field day event. Of course, the 6 activities in this unit also are suitable to conduct as standalone activities that are unaffiliated with a big event.

This Lesson provides two different activities that require students to measure energy outputs and inputs to determine the efficiency of conversions and simple systems. One of the activities includes Lego motors and accomplishing work. The other investigates energy for heating water. They learn about by products of energy conversions and how to improve upon efficiency. The teacher can choose to use either of these or both of these. The calculations in the water heating experiment are more complicated than in the Lego motor activity. Thus, the heating activity is suitable for older students, only the Lego motor activity suitable for younger students.

Students use simple materials to design an open spectrograph so they can calculate the angle light is bent when it passes through a holographic diffraction grating. A holographic diffraction grating acts like a prism, showing the visual components of light. After finding the desired angles, students use what they have learned to design their own spectrograph enclosure.

Subject has three goals: introduces students to the classic works on ethnic politics, familiarizes students with new research and methodological innovations in the study of ethnic politics, and helps students design and execute original research projects related to ethnic politics. Readings drawn from across disciplines, including political science, anthropology, sociology, and economics. Students read across the four subfields within political science. Graduate students specializing in any subfield are encouraged to take this subject, regardless of their previous empirical or theoretical background. Subject designed as a year-long research workshop, but may also be taken in either semester. This course is designed mainly for political science graduate students conducting or considering conducting research on identity politics. While 17.504 Ethnic Politics I is designed as a primarily theoretical course, Ethnic Politics II switches the focus to methods. It aims to familiarize the student with the current conventional approaches as well as major challenges to them. The course discusses definition and measurement issues as well as briefly addressing survey techniques and modeling.

Gain practical insight and improved understanding of engineering experimentation through design and execution of "project" experiments. Building upon work in 16.621, students construct and test equipment, make systematic experimental measurements of phenomena, analyze data, and compare theoretical predictions with results. Written final report on entire project and formal oral presentation. Includes instructions on oral presentations. Provides valuable link between theory and practice.