Use the resources in this collection to encourage your students to talk about the math they use to play the game or solve the problem. Encourage them to share their thoughts and describe their strategies to one another as they figure out the best moves or steps in a process. Provide students with opportunities to demonstrate their work and explain their reasoning using the language of mathematics. Listen carefully as your students interact with one another to exchange ideas, organize their thoughts, present their arguments and consider the suggestions of their classmates. These resources provide you with starting points that engage students in mathematical thinking and communication.

ResourceTitle/DescriptionGrade Level

K, 1

This activity helps students become familiar with positional words and develop systematic thinking. Students use the clues provided to arrange six colored squares in an array, either on paper or with the interactive Flash applet that is provided. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support and a printable sheet (doc). Students may be asked to create a similar problem for others to solve.

3, 4, 5, 6+

This web site, which is part of the NCTM Illuminations project, allows students to challenge themselves or opponents from anywhere in the world by playing games that are organized around content from the upper elementary and middle grades math curriculum. The games allow students to learn about fractions, factors, multiples, symmetry, as well as practice important skills like basic multiplication and calculating area.

1, 2

This activity uses Cuisenaire Rods to develop flexibility and fluency with addition facts and to encourage systematic thinking. Several different challenges are posed, all involving making equivalent trains using a given number of rods of different colors. An interactive Flash Cuisenaire applet is provided as an alternative to using real rods. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and a link to a related activity, Cuisenaire Counting (cataloged separately).

1, 2, 3

This series of activities can be used to introduce number sequences and patterns and to reinforce parity (even and odd numbers) and its application in addition. The resources are intended for use on an interactive whiteboard but may also be used individually or in small groups. They can be accessed online or downloaded (zip) to a local computer. The pack includes teacher notes, background information on the content, and a student worksheet.

2, 3, 4, 5

This interactive problem provides an opportunity for children to become familiar with Venn diagrams, while reinforcing knowledge of number properties. Students must place the numbers from 1 to 40 into a Venn diagram of two sets with an intersection. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support.

1, 2, 3, 4, 5

This Nim-like interactive Flash game provides an opportunity to practice basic addition and subtraction while developing strategic thinking through generalization and by applying knowledge of factors and multiples. It can be played against the computer or a friend. Players take turns adding a whole number from 1 to 4 to a running total. The player who hits the target of 23 wins. Computer settings allow changing the target number, the range of numbers to add, who goes first, and whether the player reading the target wins or loses. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for support, and links to related games.

This set of two interactive challenges from the Annenberg Teachers' Lab helps learners develop reasoning skills with number patterns by looking systematically at specific examples, and then by making predictions and generalizations. In "How Many Valentines", students try to figure out the number of valentines sent by an entire class. In "Mystery Operation", solvers try to determine what the computer's mystery operation is by entering a pair of numbers and studying the outputs. Background discussion, a rationale, grade-level information, connections to standards, and solvers' comments are included for each activity.

3, 4, 5

This Java applet game allows children to think strategically in an engaging context: the goal is for the two frogs and two toads to change places on the lily pads. The challenge is to do this in as few slides and jumps as possible. Students will need to work very systematically and may also want to develop their own recording system.

3, 4, 5, 6+

This Java applet activity allows students to explore the various situations described in "The Chairs Around the Table" lesson (cataloged separately). The user can select Exploration mode, in which the number of chairs needed for a particular arrangement of tables is displayed; or Guess, in which the user is able to construct an arrangement and then predict the number of chairs. There are two types of tables to choose from and two different table arrangements. Instructions and exploration question are provide.

This Java applet activity allows students to visually identify more number patterns in Pascal's Triangle by coloring numbers that have the same remainder when divided by the number rolled, thereby practicing division and remainders. A learner rolls a random number, which can be from 1 to the number of rows of the triangle, or enters his/her own choice. There is an auto-color button that will automatically color the correct entries and the number of rows of Pascal's triangle can be increased or decreased. Separate tabs to access information for the learner, the instructor and to seek help are provided.

3, 4, 5, 6+

This Java applet activity allows the learner to visually identify number patterns in Pascal's triangle as they color multiples of a given number. The user can also click on an auto-color button that will automatically color the multiples of the given number. The number of rows of Pascal's triangle can be increased or decreased. There are separate tabs to access information for the learner, the instructor and to seek help.