In this math lesson, learners use two colors of beads to form two different percent mixes, and then form a final mix using scoops from the two mixes. From this, learners will develop and use a formula to determine the final percent mix from two source mixtures. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

This 4-lesson unit assumes student understanding of multiplication; it uses patterns, properties of the operation, and games to develop fact fluency. The unit included student recording sheets, questions for students and teachers, links to online applets, and suggestions for assessment and extension.

Students decompose 2-digit numbers, model area representations using the distributive property and partial product arrays, and align paper-and-pencil calculations with the arrays. The lessons provide conceptual understanding of what occurs in a 2-digit multiplication problem. Partial product models serve as transitions to understanding the standard multiplication algorithm.

This Illuminations brainteaser activity promotes algebraic thinking and reasoning skills. Each letter of the alphabet has been assigned a numerical value. Solvers use given sums of the letter values of 29 names to deduce the individual values. Solvers are asked to find the value of their own names and may use an interactive applet to test their solutions.

In this six lesson unit, students recognize and explore the relationships among pennies, nickels, dimes, and quarters. They estimate and count sets of mixed coins, create equivalent sets, write story problems that involve money, and use coins to make patterns. Within the unit there is a link to US Mint. http://www.usmint.gov/kids/teachers/

In this Illuminations unit (three lessons), students formulate and refine questions that can be addressed by categorical data (Lesson 1) and numerical data (Lesson 2). They then collect, organize, and display with bar and circle graphs relevant data to answer those questions. They recognize the differences in analyzing categorical and numerical data. In the final lesson students identify examples of each type of data by looking at the question asked and discover the type of data collected determines the type of data display that is the most appropriate way of representing it. Students work with partners to collect data and create graphs for both types of data using the Data Grapher (cataloged separately).

This math meets ecology lesson provides hands-on experiences with mixing oil and water, provides surface area information about the 2010 oil spill in the Gulf of Mexico, and gives learners opportunities to estimate small oil spills of their own making. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

This math meets ecology lesson provides hands-on experiences with mixing oil and water, provides surface area information about the 2010 oil spill in the Gulf of Mexico, and gives learners opportunities to estimate small oil spills of their own making. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

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.

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.

"Each student creates parallelograms from square sheets of paper and connects them to form an octagon. During the construction, students consider angle measures, segment lengths, and areas in terms of the original square" (from NCTM's Illuminations).