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.

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.

This mobile app (available for both iOS and Android devices) was developed by the National Council of Teachers of Mathematics with funding from Verizon Foundation. The app is based on the Decimal Maze from the popular lesson "Too Big or Too Small". The goal is to help Okta reach the target (maximum, minimum, or a specific value) by choosing a path from the top of the maze to the bottom — adding, subtracting, multiplying and dividing as the player goes. Seven levels with seven puzzles in each level test the player's skills with operation with powers of ten, negative numbers, fractions, decimals, and exponents.

This instructional guide (PDF) is for the mobile app Pick-a-Path (both iOS and Android platforms). The guide provides professional development by discussing the math in each level of the game, giving suggestions for classroom use, and recommending related resources from Illuminations. The Pick-a-Path app is cataloged separately and listed as a related resource.

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 online version of the popular card game, students combine five given number cards, using the four arithmetic operations (addition, subtraction, multiplication, division), to arrive at a target number. This version uses the numbers 1–10 only. Users may ask for a hint or view a possible solution, although there are often multiple solutions.

This interactive game for one or two players develops students' fluency with multiplication facts, understanding of the relationship between factors and products, and strategic thinking. Players take turns moving markers on a factor list and claiming their products on a board displaying all the products of the numbers 1-9. The first player to claim four in a row wins the game. The factors and number needed to win are customizable. The resource includes links to related lessons.

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 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.

In this 5-lesson multi-media unit, students will explore various real-world applications of different forms of measurement, including time and distance. They will make estimations and calculations. Throughout the unit, students will be using online resources to familiarize themselves with coral reefs, the nation of Belize, and to plan a pretend scuba diving trip. Activity sheets (pdf), links to online resources, assessment options and other commentary are provided.

This interactive tool allows a user to create many geometric shapes. Squares, triangles, rhombi, trapezoids and hexagons can be created, colored, enlarged, shrunk, rotated, reflected, sliced, and glued together.

In this Illuminations lesson, students apply their knowledge of addition equations to investigate the equivalence of two numeric expressions using the "Pan Balance-Numbers" applet (cataloged separately). An instructional plan, questions for the students, assessment options, extensions, and teacher reflections are given for the lesson as well as links to the applet and a student activity sheet(word format).

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.

In this month-long interdisciplinary project students collect weather data, determine the best visual representation for displaying it, and discuss the patterns and implications of their findings. This resource includes extension and assessment suggestions and guiding questions.

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.

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).