Counting and Cardinality

Compare numbers.

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In this 5-lesson unit primary students identify attributes of buttons and other objects in their classrooms. Throughout the unit students learn to collect data about objects, display the data (Venn diagrams, pictographs, and bar graphs), and analyze the data to determine what this tells us about buttons and/or other objects. Each of the five lesson plans includes necessary student/class worksheets, questions for students, extension ideas, and assessment ideas. Lessons 2 and 3 reference stories that are an important part of the skill development: "The Button Box" by Margarette Reid and "The Elves and the Shoemaker" story. | Lesson Plans, Unit of Instruction Grade Level: K, 1, 2 | |

In this 8-lesson unit students use buttons to explore logical and numerical relationships that form the conceptual basis for understanding addition and subtraction operations. Topics include counting, ordinal numbers (and relative position), classification (attributes), relationships between numbers, addition of sets, commutativity of addition, sums to 10, fact families (including subtraction), three models of subtraction ("take away", comparative, missing addend), and bar graphs. Includes student activity sheets and a link to an online graphing applet. | Activity, Instructor Guide/Manual, Lesson Plans, Unit of Instruction Grade Level: K, 1, 2 | |

This hands-on activity helps students develop spatial sense and scaling concepts. Students use interlocking cubes to build first a chair and then a table of appropriate size for the chair. The student goes on to build two other sets of chairs and tables to make three different sizes in all. The Teachers' Notes page includes suggestions for implementation, discussion questions, and ideas for extension. | Activity Grade Level: K, 1, 2 | |

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). | Activity, Lesson Plans, Unit of Instruction Grade Level: K, 1, 2 | |

This interactive Flash applet supports the exploration of early number. A child or teacher can place a number of objects on the screen and then move the objects to group them, drag them onto a number line or track, into a hoop to create sets of objects, or into a 10 by 10 grid. This applet lends itself well to group work with a projector. Clicking on the info button allows the user to mouse over items to learn how to use them. | Activity, Interactive Media Grade Level: K, 1, 2 | |

This interactive Flash applet supports the exploration of numbers to 100 by simulating a 100-bead string. A teacher or child can move all or some beads to the left or right to add and subtract. The controls allow users to move beads individually or 10 at a time to model different counting and calculation strategies. Users can hide or show the numbers represented by the beads. This applet lends itself well to use on an interactive white board. A pdf guide to this collection of teaching applets is cataloged separately. | Activity, Interactive Media Grade Level: K, 1, 2 | |

In this iOS App students recognize numbers of dots on dominos and identify their value, compare their values, and use their values to complete addition or subtraction equations up to ten. The first four levels of this App are free for calculations with numbers to ten, there are more levels and tasks available for a fee. Within each level of the App there are two buttons in the upper right corner. One is a camera button that will take a picture of a finished sheet and the other is an activity button that opens up more complicated equations with multiple operations. | Activity, Interactive Media Grade Level: K, 1 | |

This 37-page pdf provides background information and teaching activities for developing young children's number sense. The document includes instructions and printable materials for using dot cards, five frames, and ten frames. | Activity, Game, Instructional Strategy, Lesson Plans Grade Level: Pre-K, K, 1 | |

This interactive Flash applet develops early counting skills (1-10), including one-to-one correspondence and subitizing. A group of dots appears on a card, in progressively higher numbers, and the user types the corresponding numeral. The applet provides help for incorrect answers. Setting options include type of pattern (standard or random), timing (on/off and duration), initial range of numbers displayed, and number of correct answers required for each pattern. [Note: If an error message appears at the end of a round, close the window to return to the applet.] | Activity, Interactive Media Grade Level: K, 1 | |

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. | Reference Materials, Article Grade Level: K, 1, 2, 3, 4, 5 |