A web page and interactive applet showing the ways to calculate the area of a trapezoid. The user can drag the vertices of the trapezoid and the other points change automatically to ensure it remains a trapezoid. A grid inside the shape allows students to estimate the area visually, then check against the actual computed area. The text on the page gives three different ways to calculate the area with a formula for each. The applet uses one of the methods to compute the area in real time, so it changes as the trapezoid is reshaped with the mouse. A companion page is http://www.mathopenref.com/trapezoid.html showing the definition and properties of a trapezoid. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

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.

Data tables should ideally include values that were acquired in a consistent fashion. However, sometimes instruments fail and gaps appear in the records.

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.

In this lesson, students use the real-world application of insect monitoring to practice their fluency with addition and subtraction.

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!

In this Cyberchase video segment, the CyberSquad must estimate the measurements of Spout the Whale in order to find a cage that will fit him.Ű_í_

In this example, students learn how to read a topographic map and understand map contours. 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.

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.
From its beginnings in 1970, the 2.007 final project competition has grown into an Olympics of engineering.  See this MIT News story for more background, a photo gallery, and videos about this course.

Franklin works with Laverne to create a budget for a job painting a room, in this video segment from TV 411.

This lesson unit is intended to help teachers assess how well students are able to: estimate lengths of everyday objects; convert between decimal and scientific notation; and make comparisons of the size of numbers expressed in both decimal and scientific notation.

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.

Harry estimates how long it will take him to get to the front of a long ticket line in this Cyberchase video segment.

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.

Match shapes and numbers to earn stars in this fractions game. Challenge yourself on any level you like. Try to collect lots of stars! The main topics of this interactive simulation include fractions, equivalent fractions, and mixed numbers.

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!

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.

The sizes and distances of things in space are awe-inspiring, but hard to fathom. Things that are unimaginably massive can look tiny to us from Earth, and things that appear very large to us may be among the smallest in the sky. Although students can learn names and features of objects in the night sky, scale is one of the biggest stumbling blocks they need to overcome to actually understand what they’re looking at and to understand astronomy in general. But students have lots of daily life experience with bigger things looking smaller because of relative distance (and visa versa). How Big & How Far takes this experience of observing relative sizes and distances here on Earth and challenges students to apply it to night sky objects.

In this Night Sky Activity, the group measures how many fists tall a volunteer is. Then, students scatter and measure again, this time with outstretched fists and with much smaller and varied measurements. Students discuss how the distance you are from an object can make it appear larger or smaller. This activity sets them up to apply this idea afterwards as they observe night sky objects and attempt to better understand the actual sizes of the objects they see.

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.