In this data analysis activity students investigate data in connection with recyclable materials and develop plans to help the environment. Students collect data about aluminum can usage and graph that data in a line plot. The lesson includes student worksheet and extension suggestions.

The purpose of this learning video is to show students how to think more freely about math and science problems. Sometimes getting an approximate answer in a much shorter period of time is well worth the time saved. This video explores techniques for making quick, back-of-the-envelope approximations that are not only surprisingly accurate, but are also illuminating for building intuition in understanding science. This video touches upon 10th-grade level Algebra I and first-year high school physics, but the concepts covered (velocity, distance, mass, etc) are basic enough that science-oriented younger students would understand. If desired, teachers may bring in pendula of various lengths, weights to hang, and a stopwatch to measure period. Examples of in- class exercises for between the video segments include: asking students to estimate 29 x 31 without a calculator or paper and pencil; and asking students how close they can get to a black hole without getting sucked in.

Student teams design their own booms (bridges) and engage in a friendly competition with other teams to test their designs. Each team strives to design a boom that is light, can hold a certain amount of weight, and is affordable to build. Teams are also assessed on how close their design estimations are to the final weight and cost of their boom "construction." This activity teaches students how to simplify the math behind the risk and estimation process that takes place at every engineering firm prior to the bidding phase when an engineering firm calculates how much money it will take to build the project and then "bids" against other competitors.

Build fractions from shapes and numbers to earn stars in this fractions game or explore in the Fractions Lab. Challenge yourself on any level you like. Try to collect lots of stars!

16.225 is a graduate level course on Computational Mechanics of Materials. The primary focus of this course is on the teaching of state-of-the-art numerical methods for the analysis of the nonlinear continuum response of materials. The range of material behavior considered in this course will include: linear and finite deformation elasticity, inelasticity and dynamics. Numerical formulation and algorithms will include: Variational formulation and variational constitutive updates, finite element discretization, error estimation, constrained problems, time integration algorithms and convergence analysis. There will be a strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. At the beginning of the course, the students will be given the source of a base code with all the elements of a finite element program which constitute overhead and do not contribute to the learning objectives of this course (assembly and equation-solving methods, etc.). Each assignment will consist of formulating and implementing on this basic platform, the increasingly complex algorithms resulting from the theory given in class, as well as in using the code to numerically solve specific problems. The application to real engineering applications and problems in engineering science will be stressed throughout.

This unit contains two lessons which help students develop number sense through activities involving collection, representation, and analysis of data. Students also practice reading and writing large numbers and develop estimation skills. In Lesson 1, Every Breath You Take, students estimate the number of breaths taken during a specified time, experiment, and display real-life data. In Lesson 2, Making Your First Millions, students develop the concept of a million by working with smaller numerical units, such as blocks of 10 or 100, and then expanding the idea by multiplication or repeated addition. They analyze situations and identify patterns that will enable them to develop the concept of large numbers. Each lesson includes student activity sheets, an instructional plan, and extensions.

" Welcome to 2.007! This course is a first subject in engineering design. With your help, this course will be a great learning experience exposing you to interesting material, challenging you to think deeply, and providing skills useful in professional practice. A major element of the course is design of a robot to participate in a challenge that changes from year to year. This year, the theme is cleaning up the planet as inspired by the movie Wall-E."

Explore size estimation in one, two and three dimensions! Multiple levels of difficulty allow for progressive skill improvement.

This lesson unit is intended to help you assess how well students are able to: Model a situation; make sensible, realistic assumptions and estimates; and use assumptions and estimates to create a chain of reasoning, in order to solve a practical problem.

In this measurement lesson plan students use their estimation and reasoning skills to develop benchmarks for an ounce and a pound. Students test the accuracy of their estimates using a scale and give themselves a score based on how close they came to the desired weight (an ounce or a pound). This lesson plan includes a student data collection worksheet (PDF).

This applet allows students to individually practice working with relationships among fractions and ways of combining fractions. It is an online, one person game, with immediate feedback on incorrect moves. All instructions for this fun visual game are included and illustrated.

This lesson fosters a student's conceptual fraction sense with proper fractions, improper fractions, and mixed numbers by placing thirty fraction cards in order between given whole numbers on a number line clothesline. Users will visually identify that all proper fractions are grouped between zero and one, and that improper fractions or mixed numbers are all grouped above one. Users also play an estimation game with groups using the same principle. Instructional plan, questions for the students, assessment options, extensions, and teacher reflections are given.

Explore fractions while you help yourself to 1/3 of a chocolate cake and wash it down with 1/2 a glass of orange juice! Create your own fractions using fun interactive objects. Match shapes and numbers to earn stars in the fractions games. Challenge yourself on any level you like. Try to collect lots of stars!

How many small squares of chocolate are in a whole Fruit & Nut bar? Through the use of videos, estimation, and discussion, challenge your students to find out!

In this five lesson unit with overview from Illuminations, student activities explore relationships among fractions through work with the length model. Students construct fraction strips and use fraction bars throughout the unit to make sense of basic fraction concepts, to compare fractions and order fractions and to work with equivalency in fractions. Specific learning objectives, a material list, an instructional plan, questions for the students, assessment options, extensions, and teacher reflections are given for each lesson.

This interactive lesson encourages young students to solve problems by estimating angles and distances. They use an applet to give LOGO-like commands, e.g. forward (length), turn (right or left) to make a path that moves a turtle to a pond. Students can create a Path 1 and Path 2 and try to minimize the total path length. There is a newer applet (Turtle Pond, cataloged separately) that allows for adding or editing the commands and a choice of right angles only, or angles in multiples of 15 degrees. The lesson provides suggestions for implementation and discussion questions.

In this activity students practice measuring techniques by measuring different objects and distances around the classroom. They practice using different scales of measurement in metric units and estimation.

This google slide show will be used by second grade teachers with their students as a numeracy routine. Directions for the teacher are found here. For quarter one, students will estimate using physical objects in a jar. Students should be given time to notice and wonder about each jar of items.

This google slide show will be used by second grade teachers with their students as a numeracy routine. Directions for the teacher are found here. For quarter two, students will estimate using pictures. Students should be given time to notice and wonder about each. Using a number line range is a good technique.

This google slide show will be used by second grade teachers with their students as a numeracy routine. Directions for the teacher are found here. For quarter three, students will estimate using pictures with clues. Students should be given time to notice and wonder about each. Then, students can adjust their estimates as clues are revealed. Using a number line range is a good technique. This resource has been adapted from the work of Steve Wyborney.