In this Illuminations lesson plan students explore the use of variables as they solve for the weights of objects using information presented in pictures. Learners model situations that involve adding and subtracting whole numbers, using objects, pictures, and symbols. A student activity sheet is available and downloadable (pdf).

In this 6-lesson unit, students explore 5 models of subtraction (counting, sets, number line, balanced equations, and inverse of addition) using connecting cubes. The lesson activities focus on the comparative mode of subtraction as children investigate the relationship between addition and subtraction, write story problems in which comparison is required, and practice the subtraction facts. The lessons include printable student activity sheets, a bibliography of children's counting books, questions for student discussion and teacher reflection, assessment options, extensions, and links to online applets (cataloged separately).

This interactive 100 grid has a variety of open-ended uses. Users can "make" as many counters as they choose from among three different kinds, and then drag them onto the grid, allowing any number to be covered by up to 3 different markers at one time. An Ideas page offers possible tasks and games suited to the applet.

This game from the BBC reinforces doubling and mental addition for a range of abilities. Students attempt to reach a target score by placing darts on the correct sections of a dartboard. The first level of the game provides practice doubling with a single number. Levels 2 and 3 increase the challenge level by involving two and three addends. Teachers and parents can control the starting level and the optional timing feature.

This interactive Flash applet models the difference meaning of subtraction. A child or teacher can compare two rows of beads and analyze the calculation they represent. Once a user sets up the two rows of beads (up to 30 each), the applet provides a series of animations which represents the rows with two number lines and then as a single number line with the difference indicated by a "jump". This applet works well with an interactive white board. A teacher's guide to this series of applets is cataloged separately.

This interactive Java applet provides students with practice in subtraction and pattern recognition. Starting with four numbers in the corners of an outside square, students find the differences (larger minus the smaller) between the pair of numbers on each side of the square. After correctly completing each square, they repeat the process for the next inner square, until all squares are complete. Students can explore the patterns that emerge as they work toward the center square. Users can choose to work with whole numbers, integers, fractions, decimals, or money. They may also create their own problems by selecting the four starting numbers for the outside square.

In this 6-lesson unit, students use dominoes to explore four models of addition: counting, number line, sets, and balanced equations. They learn about the commutative property, the relation between addition and subtraction, the result of adding 0, and the concept of doubles. Students write story problems which involve the operation of addition and begin to memorize the addition facts. They represent addition in pictures. The various models of addition help students develop a rich conceptual schema for addition. Included are a Bibliography of Counting Books, student materials, questions for student and teacher reflection, assessment and extension ideas. [Suggestion: Use the alternate applet, Pan Balance - Numbers, listed as a Related Resource, rather than Pan Balance - Shapes, in Lesson 4.]

This web page describes several games and puzzles that build number sense, fact and computational fluency, flexibility, and reasoning. Each activity uses an ordinary set of double-6 dominoes. After describing dominoes generally, the page provides rules for the basic domino game and a variation, and proposes several other challenges involving addition, multiplication and prime numbers. The page includes a link to an interactive Dominoes Environment (cataloged separately).

This interactive Flash applet provides a customizable set of dominoes that users can manipulate to play games or solve puzzles. It can be used with an interactive whiteboard to facilitate group work. Users can determine the size of a set (up to double-9), remove individual dominoes, rotate and move them, and change their size. The Teachers' Notes page includes a link to page containing domino games and challenges (cataloged separately).

This narrative document describes the progression of Counting and Cardinality and Operations and Algebraic Thinking across the K-5 grade band. It is informed both by research on children's cognitive development and by the logical structure of mathematics. The document discusses the most important goals for elementary students that of understanding and using numbers. The focus is on the basic operations—the kinds of quantitative relationships they model and consequently the kinds of problems they can be used to solve as well as their mathematical properties and relationships.