Middle School Portal: Math and Science Pathways (MSP2)
M.C. Escher is a widely known and popular artist whose work depicts complex, and often impossible, geometrical patterns. This Web site examines the mathematics behind his drawings. Many examples of Escher's work are given, illustrating mathematical principles such as the shape and the logic of space. Tessellations and polyhedra are common building blocks of the drawings. It is quite interesting to see how basic designs are transformed into the intricacies depicted by Escher. The material is cert
Author(s): Creator not set

Office for Mathematics, Science and Technology Education
The Office for Mathematics, Science, and Technology Education at the University of Illinois at Urbana-Champaign has an impressive collection of Java lessons and curriculum resources for learning about these topics. The office was established to serve as a model-builder for innovative, standards-based, technology-intensive mathematics and science instruction at the K-16 levels. Most of the lessons focus on geometry, statistics, or algebra; but there are also some that cover science concepts. The
Author(s):

Middle School Portal: Math and Science Pathways (MSP2)
This virtual manipulative with an interactive three-circle Venn diagram can be used to model set operations for union, intersection, and subset. For each statement, the student uses an onscreen paint function to find and highlight the region that is the solution. The student can click a button to find out if his or her solution is correct. In addition to the manipulative, there are 13 progressively more difficult logic statements to challenge the student. Instructions for use and a link to the N
Author(s): Utah State University. National Library of Virtual

Middle School Portal: Math and Science Pathways (MSP2)
This manipulative offers an interactive version of the classic logic game of the same name. In this version, the student plays against the computer and has eight chances to guess the colored pattern of four pegs. The student may select to play with a pattern consisting of two to six colors. The site includes instructions for using the applet, a lesson plan, and information for teachers and parents. There is also a link to the National Council of Teachers of Mathematics (NCTM) Standard for Number
Author(s): Utah State University. National Library of Virtual

Middle School Portal: Math and Science Pathways (MSP2)
Using this online activity, students explore the meaning of probability using the pigeonhole principle. The initial question asks students to determine the probability that someone who is not paying attention to what she is doing can put checks into the correct envelopes. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. The solution hint suggests experimenting with the possible outcomes with checks a, b,
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
In this online activity, students analyze predictions made by sportswriters about which basketball teams will win to determine which teams are playing each other. The Getting Started link describes how to set up a table to organize the given information. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. The solution illustrates and explains three different ways to successfully organize information, includ
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
This online challenge activity introduces a gift-counting problem that requires students to organize information in a table and then to draw conclusions. The importance of organizing information for decision making is noted for census takers, librarians, and demographers. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. The solution hint suggests how to organize a useful table. Related questions ask stud
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
This online activity offers students a chance to analyze data stated as percentages to draw conclusions about the similarity of five archeological sites. Students analyze the data by making a table of the differences for each pair of sites by subtracting the smaller percentage from the larger for each of five types of evidence. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. The activity features a solu
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
This online activity offers students a chance to compare soda prices from two stores using data displayed on a scatter plot graph. Students are shown how the line y = x can be used to analyze the data and draw a conclusion. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. The activity contains a solution hint, two different ways to find the solution, questions related to analyzing similar data from other
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
With this online activity, students explore the classic mathematics map-coloring question known as the four-color problem. Students must determine the minimum number of colors needed to color a map so that entities sharing a border have different colors. Initially, students investigate the minimum number of colors necessary to color a map of states west of the Mississippi River. The activity's Getting Started section suggests coloring the states in a specific order. The Solution page uses odd an
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
This activity contains directions and printable pages with diagrams for constructing a pyramid, cube, and octahedron. Each page is decorated with colorful images of the Cyberchase team so that one image appears on each face of the constructed three-dimensional objects. Copyright 2005 Eisenhower National Clearinghouse
Author(s): Public Broadcasting System (U.S.). PBS Kids

Middle School Portal: Math and Science Pathways (MSP2)
This online activity challenges students to think about and use percentages related to television viewing to make comparisons to determine television viewing preferences. The activity is one of 80 mathematical challenges featured on the Figure This! web site emphasizing real-world uses of mathematics. To answer this activity's initial question, the student reads data from a chart, applies a formula, and uses the calculated information to draw a conclusion about TV viewing preferences. Informatio
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
This online activity challenges students to determine which of four different size grape juice cans labeled with the grape juice concentration would have the strongest grape taste. The activity is one of 80 mathematical challenges featured on the Figure This! web site emphasizing real-world uses of mathematics. The Hint suggests forming ratios that are fractions to compare quantities. Two ways of answering the initial question are illustrated with tables. Related questions have students consider
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
In this online activity, students are challenged to reproduce 20 different figures using the seven pieces of the Chinese tangram game. The figure to be reproduced is shown in the upper right corner of the screen. The student points and clicks to rotate and position the tangram pieces to copy the figure. For each figure, the student must use, but not overlap, all seven pieces. Clicking on the hint will put outlines of the tangram pieces on the figure the student is trying to reproduce. Figures in
Author(s): PBS Kids

Middle School Portal: Math and Science Pathways (MSP2)
Given that a square table sits one person per side, this activity challenges students to figure out how many tables would need to be pushed together to seat a party of nineteen. The activity, part of the Figure This! collection of 80 math challenges emphasizing math in the real world, explains how arranging geometric shapes is important to architects, landscapers, and quilters. Students are encouraged to model the problem using squares of paper to represent tables. Related questions ask students
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
This activity challenges students to think about angles as geometric shapes and to find the sizes of the angles between their fingers. It is part of the Figure This! collection of 80 online mathematical challenges emphasizing real world uses of mathematics. For this challenge, the students trace a hand stretched to form an L-shape with the thumb and sketches angles of 90 degrees and 45 degrees between the thumb and index finger. They use the sketches to estimate the angles between their other fi
Author(s): National Action Council for Minorities in Engineer

Middle School Portal: Math and Science Pathways (MSP2)
This web site contains descriptions and links to more than 60 virtual manipulatives, activities designed to function as concept tutorials. The virtual manipulatives, mostly in the form of Java applets, are designed to facilitate grades 6-8 mathematics learning. By encouraging active student exploration with computers, the virtual manipulatives can help students visualize mathematical relationships. They are organized into five categories based on the National Council of Teachers of Mathematics (
Author(s): Utah State University. National Library of Virtual

Middle School Portal: Math and Science Pathways (MSP2)
This activity asks the student to determine the time in Cairo, Egypt, when it is 3:00 p.m. in San Francisco. It includes a map of the world with the time zones marked. The activity, part of the Figure This! collection of 80 math challenges emphasizing math in the real world, explains how to determine the time in different time zones and what the prime meridian and the international date line are. Students see how positive and negative numbers relate to the time zones and are asked to think about
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
This activity opens with a picture that shows two individuals who have each built a patio using different arrangements of the same number of identical concrete tiles. Both patios have the same total area, and students are challenged to figure out the dimensions of a single concrete tile. The activity, part of the Figure This! collection of 80 math challenges emphasizing math in the real world, explains how area is an important concept used by architects, real estate agents, and artists. The Hint
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
This activity challenges students to develop an algorithm to find the day of the week on which they were born. An algorithm is described as a step-by-step routine for solving a problem. The activity, part of the Figure This! collection of 80 math challenges emphasizing math in the real world, notes how algorithms are used by scientists, factory workers, and chefs. The hint shows students that, for any date, the day of the week changes from one year to the next. Students are reminded to consider
Author(s): National Council of Teachers of Mathematics (NCTM)