The National Council of Teachers of Mathematics advocates for high-quality mathematics teaching and learning for each and every student. Find research and resources related to preschool here.

This web page provides instructions for a basic form of Nim, an ancient game that develops strategic thinking. Starting with a total of 7 counters, two players take turns removing one or two at a time. The player who takes the last counter wins. The game of Nim is very adaptable. This page includes questions that encourage players to generalize a winning strategy as well as a link to another page describing several of variations.

This problem provides an opportunity for students to practice counting and to represent and record findings in different ways: "Noah saw 12 legs walk by into the Ark. How many creatures did he see?" Multiple solution possibilities encourage students to be systematic in their strategies. The Teachers' Notes page offers suggestions for implementation, discussion questions, and an idea for extension.

This activity helps children become more familiar with horizontal and vertical number lines (0 through 10) and how to use them for addition. It can be used to introduce subtraction as the inverse of addition and the use of an unknown number. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, printable number lines (pdf), and a link to a related game, Incey Wincey Spider (catalogued separately).

The author of this one-page article discusses the importance of developing a "sense of ten" as a foundation for place value and mental calculations. She suggests teaching strategies using ten-frames to promote this sense, including instructions for simple games. The article includes a list of references and a link to a related article, "Developing Early Number Sense" (cataloged separately).

The author of this one-page article discusses early number sense and how it develops. She provides research background and suggests teaching strategies that promote early number sense, including instructions for simple games using dot cards. The article includes a list of references and a link to a follow-up article, "A Sense of 'ten' and Place Value" (cataloged separately).

Count as you are carrying out daily routines.While counting, stop often to ask what number comes next.  Ask what number comes after or before a given number.

Students learn the connection between the counting sequence and experience from their daily lives in this daily activity. It also helps give students a sense of how "many" each number is.

Children will listen to and recite a rhyme as the adult points out the words.  Allow children to help point out the words as they are ready. 

Open Middle tasks provide opportunities for student to approach a mathematical task using different strategies and representations. They can be used as a warm-up/closing activity, as a formative assessment, or to facilitate discourse and discussion and get insite into student thinking and problem solving. These tasks provide a great opportunity for student to engage with the Standards for Mathematical Practice.

Open Middle tasks provide opportunities for student to approach a mathematical task using different strategies and representations. They can be used as a warm-up/closing activity, as a formative assessment, or to facilitate discourse and discussion and get insite into student thinking and problem solving. These tasks provide a great opportunity for student to engage with the Standards for Mathematical Practice.

Open Middle tasks provide opportunities for student to approach a mathematical task using different strategies and representations. They can be used as a warm-up/closing activity, as a formative assessment, or to facilitate discourse and discussion and get insite into student thinking and problem solving. These tasks provide a great opportunity for student to engage with the Standards for Mathematical Practice.

Open Middle tasks provide opportunities for student to approach a mathematical task using different strategies and representations. They can be used as a warm-up/closing activity, as a formative assessment, or to facilitate discourse and discussion and get insite into student thinking and problem solving. These tasks provide a great opportunity for student to engage with the Standards for Mathematical Practice.

Open Middle tasks provide opportunities for student to approach a mathematical task using different strategies and representations. They can be used as a warm-up/closing activity, as a formative assessment, or to facilitate discourse and discussion and get insite into student thinking and problem solving. These tasks provide a great opportunity for student to engage with the Standards for Mathematical Practice.

In this task students compare numbers less than 100 to benchmark numbers and learn to build an understanding of the relative magnitude of numbers.

In this problem students practice counting by twos as they explore the natural phenomenon that legs on creatures always come in pairs, laying the foundation for doubling and halving. A set of cards can be downloaded (pdf) and matched. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, an expanded set of cards (pdf), and links to related activities (Noah and Number Tracks, both cataloged separately).

This three-act math task utilizes videos and questioning to help students explore counting.

In this video segment from Cyberchase, the CyberSquad learns how to read a thermometer as they try to keep their chocolate sculpture from melting.

The focus of the Recognize Small Quanitities without Counting (Subitizing) intervention is strategies for recognizing quantities one to three objects without counting.

This problem provides an opportunity to increase familiarity with negative and positive numbers on a number line. The vertical number line is presented as black markings every one meter all the way up a lighthouse and on the underwater support going down to the sea bed, with sea level being "0". In answering the nine questions, children begin to calculate with negative numbers in the context of the distances between the sea creatures. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and a link to a related resource, Swimming Pool (cataloged separately).