This Java applet provides opportunities for creative problem solving while encouraging young students to estimate length and angle measure. Using the Turtle Pond Applet, students enter a sequence of commands to help the turtle get to the pond. Children can write their own solutions using LOGO commands and input them into the computer. The turtle will then move and leave a trail or path according to the instructions given. (N.B. the applet is an upgrade of one that supported the Lesson "Get the Turtle to the Pond," cataloged separately.)

The brief video clips on this webpage illustrate the range of number sense exhibited by students in grades Pre K-2. In interviews, Cena and Jonathan, both age 7, and Rudy, age 9, demonstrate different levels of understanding number and place value concepts. The page includes discussion questions for each set of videos as well as concluding reflection questions.

This lesson from Illuminations provides an introduction to the use of variables, and develops students' algebraic thinking. Students create variable machines to discover the value of words by assigning each letter of the alphabet a unique number value. Learning objectives, a materials list, a pdf file of the student worksheet, an instructional plan, questions for the students, assessment options, extensions, and teacher reflections are provided.

This lesson plan provides the teacher with an activity to help students calculate the Greatest Common Factor of two or more positive integers and develop a definition based on their exploration. Students find the prime factorization of two positive numbers using factor trees and Venn diagrams to sort the prime factors. The plan includes learning objectives, materials needed, questions to ask students, assessment options, extensions, teacher self-reflection questions, and further references.

The activities in this Illumination lesson plan deal with patterns and the importance of looking at an object/item from more than a single perspective and reaffirms to learners that numerous reasonable solutions are possible. Students investigate a series of items (a list of class names and a parade of animals) that appear to be ordered in some "obvious" ways and also explore ways of sorting items ( a deck of cards and numbered horses) into two disjoint groups on the basis of some definable characteristic. Activity sheets are included in pdf format.

Companies that manufacture large products, like those provided by Robinson, must find a balance for each job based on human and machine work hours, materials, and available space. A job will often require the knowledge of a process improvement engineer to assist in determining the most reasonable approach to a job. This video shows how someone on the sales team might work with an engineer so that the company can provide its goods to a customer.

This lesson from Illuminations helps students to begin to develop an understanding of area by using a Java applet on the computer. Learners use 12" × 12" paper squares to measure the area of a door and determine whether area increases or decreases as the length or width of their door changes. The lesson includes discussion questions, extensions, and other teacher support. It is supported by the applet IGD: Areas in Geometry (cataloged separately).

In this unit of five lessons from NCTM's Illuminations, students explore the numbers of letters in their names and create bar graphs, pictographs, circle graphs, and glyphs. They also find the range, compute measures of center, and create box-and-whisker plots. Individual lessons link to related tools where appropriate, and include questions for students, assessment options, teacher reflection questions, and sometimes extensions.