This interactive Flash game helps students practice counting, subitizing, and grouping by 10s, as they transport Okta the Octopus and his friends to a safe ocean. The goal is to select given numbers of Oktas as quickly as possible before the timer runs out. Then users count the total number of Oktas "saved" and identify that number on a number line. Students choose from three levels of difficulty, which vary according to time limit, range of target numbers, and whether visual target cues appear. These settings are customizable. Users who count incorrectly are given the option of visual help in recounting.

This interactive pan balance allows students to enter numeric or algebraic expressions and investigate the important concept of equivalence as well as practice arithmetic and algebraic skills. Users place an expression in each of the red and blue pans. These expressions may or may not include the variable x. If the expression is algebraic, a value for x is entered or adjusted by moving the slider. As the value of x changes, the results will be weighed and graphed. Instructions and exploration directions and questions are included.

This Java tool is used to strengthen student understanding of equality and computation of numerical expressions. The applet also helps students understand that equality is a relationship, not an operation. After entering an expression in both the red and blue pan, the pans will move up and down depending on which expression is greater. When the expressions are equivalent, the pans will balance and the full equation will be entered into the Balanced Equations table. Instructions and exploration directions and questions are included.

This Java applet allows children to explore a balancing tool and thus build their algebraic thinking about equivalency. By placing shapes on each side of the balance and finding equivalent sets of weights, students discover the weight of each shape in one of six built-in sets or a random set.

In this unit, students investigate fractional parts of the whole and use translations, reflections, rotations, and line symmetry to make four-part quilt squares. Students have a practical context for using the mathematical terms associated with divisions of the square, transformations, and symmetries. Suggestions for implementation and extensions are included.

This interactive applet lets students create quilting type patterns and explore tessellation possibilities. The applet gives learners a choice of six polygons that can be turned or flipped and fitted together. Suggestions for exploration and five challenge patterns are provided. The tool supports a number of lessons and units including What's So Special About Triangles and Virtual Pattern Blocks (cataloged separately).

This five lesson Illuminations unit gives students an opportunity to create and analyze numeric and geometric patterns with particular emphasis on growing patterns. The lesson titles are respectively, What's Next?, Patterns On Charts, Growing Patterns, Exploring Other Number Patterns and Looking Back And Moving Forward. Each lesson includes learning objectives, material list, instructional plan, linked resources and assessment options.

In this math game, learners attempt to solve a puzzle involving five dice. By deciphering the non-standard pattern in the dice, learners use problem solving and strategy skills. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions. There is an online simulation of the game that is part of this resource.

This interactive Flash animation allows students to explore size estimation in one, two and three dimensions. Multiple levels of difficulty allow for progressive skill improvement. In the simplest level, users estimate the number of small line segments that can fit into a larger line segment. Intermediate and advanced levels offer feature games that explore area of rectangles and circles, and volume of spheres and cubes. Related lesson plans and student guides are available for middle school and high school classroom instruction. Editor's Note: When the linear dimensions of an object change by some factor, its area and volume change disproportionately: area in proportion to the square of the factor and volume in proportion to its cube. This concept is the subject of entrenched misconception among many adults. This game-like simulation allows kids to use spatial reasoning, rather than formulas, to construct geometric sense of area and volume. This is part of a larger collection developed by the Physics Education Technology project (PhET).

In this lesson plan, students are asked to use measurement skills to perform an experiment. The data from the experiment is then recorded in a table and analyzed to determine the median and range. The lesson plan includes a PDF document for data collection and analysis, as well as extension suggestions for higher level thinkers.

In this three-lesson unit students conduct surveys, create graphs, and explore combinations related to pizza toppings. Each lesson plan contains worksheets in PDF format.

In this data collection and analysis activity students investigate the data in connection with recyclable materials and develop plans to help the environment. Through this activity, students explore recycling plastic containers and graph the frequency of different types of recyclable plastics. The lesson includes student worksheets, extension suggestions, and student questions.

In this interactive Flash game learners use their knowledge of coordinates on a grid to move Plotter the penguin and avoid trouble. The game includes three levels of difficulty, a story mode, and a choice of five different games to play. Each game provides instruction as well as in-depth help in linked PDF documents.

In this math activity, learners classify polygons according to more than one property at a time. In the context of a game, learners move from a simple description of shapes to an analysis of how properties are related. This lesson guide includes sample steps in the game and extensions.

In this lesson, students will play the roles of banker and consumers as they learn how to use different combinations of coins to make money amounts up to 25 cents. Students will earn money and save it in their piggy banks until they have the exact amount to purchase an item of their choice. Suggestions for questions and assessment options are included.

This interactive Java application helps students understand the partial quotients algorithm of division in the context of dividing food equally. Students select a character and a type of food as well as the quantities of characters (divisor, 1-50) and food (dividend, 1-500) – or have the applet make selections randomly. The applet creates a story problem and leads users through the algorithm one step at a time, using questions related to the meaning of each step, and displays graphics illustrating the steps. Remainders can be expressed as whole numbers or fractions. An online calculator is available to help with calculations.

In this math meets physics game, learners pretend they are pilots of rescue helicopters and must fly their helicopters to the top of a mountain to rescue lost hikers. Learners first explore the four forces of flight: lift, drag, thrust, and weight. Before playing the game, learners conduct a probability experiment with spinners and record their results in tally tables and bar graphs. They then use their findings to select spinners with the greatest probability of helping them win the game. In a portion of the game, learners use ordered pairs to plot points on the coordinate plane to show their flight path.

In this lesson plan students explore the four forces of flight in order to complete the "Rescue Mission". Students must use their knowledge of probability to choose the spinner that will help them win the game. Students must also use their knowledge of graphing points on a coordinate grid in order to plot the results of each spin. The game board and spinners are included (PDF).

In this lesson plan students must create their own method for keeping track of rubber ducks found around the classroom. Students are then given an opportunity to share their data collection strategies and discuss the benefits and drawbacks of each one. The lesson plan is written to make an easy tie in to language arts by incorporting discussion of the words "in" or "on" when discussing the ducks location. PDF documents for cut out rubber ducks, data collection assessment, and answer key are provided.

In this unit of five lessons from Illuminations, learners begin with a number-line model and extend it to investigate linear relationships with the Distance, Speed, and Time Simulation from NCTM's E-Examples. Students then progress to plotting points and graphing linear functions while continually learning and reinforcing basic multiplication facts. Instructional plan, questions for the students, assessment options, extensions,and teacher reflections are given for each lesson as well as links to download all student resources.