This activity promotes algebraic thinking of equivalency as well as giving children practice in addition and subtraction. Since there are many different solutions for the values of the unknowns, learners can focus on the idea of working systematically. Students see two weights on one side of an interactive balance, and are asked to find how many different ways they can hang three weights on the other side for it to be balanced. An easier problem, "Number Balance", (cataloged separately) is linked on the problem page. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support.

This interactive Flash applet helps students develop number sense and fluency with addition and subtraction facts within 10. Okta hides some bubbles under a shell, and then either adds more bubbles or takes some away. Students determine how many bubbles are left under the shell. Users can choose a specific one-digit starting number or let the applet choose randomly. Users can select addition, subtraction or both.

This webpage offers a variety of games which develop strategic thinking, analytical skills, and basic number skills. Three pdfs provide instructions and materials for sets of games played on reusable boards, on consumable sheets, and with number cards. The only other materials required are counters/chips, dice, and pens/pencils. The site also includes instructions for games that require only counters or paper and pencil. A short article describes the rationale for using such games in the classroom and offers suggestions for organizing and managing games and for maximizing their benefits.

In this problem students practice addition and subtraction (and possibly multiplication) while developing systematic work strategies. Given two types of ladybirds, each with either 4 or 7 spots, learners explore ways of combining them to achieve different total numbers of spots. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, and links to related games.

This 5-lesson unit is intended to help children who already understand the meanings of addition to develop fluency with addition facts. The activities and games take advantage of commutativity, the additive identity, doubles, and number patterns to develop operation sense and foster retention. Lessons include student materials, questions for students and teachers, assessment ideas, and links to interactive applets.

In this 6-lesson unit students use pasta shapes to explore the take away model of subtraction in several different contexts (counting, sets, number line, balanced equations, and inverse of addition). They decompose numbers, explore the zero property, act out subtraction situations with objects and pictures, record differences with vertical and in horizontal notation, create fact families, find differences with a calculator, and compose and solve problems involving subtraction. The lessons include student activity sheets (pdf), questions for student discussion and teacher reflection, assessment options, and links to online applets.

This problem uses the context of a growing plant in which to practice doubling and also to develop representation and recording strategies. The Teachers' Notes page offers suggestions for implementation and discussion as well as ideas for extension and support.

This interactive online game for one or two players provides practice with number facts and builds strategic thinking and pattern discovery. Players choose an operation (addition, subtraction or multiplication) and 100 problems appear in a 10 by 10 grid. They then select problems that match given target numbers while attempting to get 5 in a row in the grid. Users have the option of working for 3 in a row on a 5 by 5 board, and of turning the sound off. This game is a good balance of skill and luck.

This problem uses linking cubes as a concrete context for exploring simple multiplication and division, doubling, halves and quarters. The problem displays a rod of 4 cubes and asks students how many cubes are necessary to make rods related to it in a variety of ways. It can be used to introduce key concepts and vocabulary. The Teachers' Notes page offers suggestions for implementation, discussion questions, and ideas for extension and support.