Counting - Cardinality unit planning framework
Young learners

Overview

This page provides a sequences of activities to facilitate counting and the conceptualization of cardinality. Activities to find the quantity and value of objects and create a procedure to count groups of objects, which will eventually lead to the development of cardinality:

Cardinality - Counting objects results in a cardinal result (numbered value). Beginning learners will repeat or emphasize the last word in a sequence to mean the total value of a set of objects. one two three four five six seven = seven (x x x x x x x)

Mathematics content - mathematical discoveries

Includes enduring understanding, big ideas, land marks, structure, concepts, and generalizations for mathematical content (number value and operations, algebra, geometry, measurement, data analysis and probability).

Supporting ideas from unpacking the big idea (facts, concepts, generalizations) to include as concepts and outcomes when teaching counting can be selected from the following sources depending on the abilities of the learners. A general outcome like:

Seems fairly simple. However, if it is unpacked to include accurate representation and cardinality, then it requires many supporting ideas like the ones identified below:

Processes - how mathematicians know

Includes enduring understanding, big ideas, land marks, structure, concepts, and generalizations for mathematical processes (problem solving, representation, communication, connections, reasoning and proof). Mathematical knowledge base

Use of reasoning and proof to verify mathematical ideas.

Problem solving is a way of understanding and communicating ideas.

Use of representation to understand mathematical ideas.

Communication of mathematical ideas

Connections of mathematical ideas

Habits of Mind - how mathematicians think better

Includes enduring understanding, big ideas, land marks, structure, concepts, and generalizations for a state of mind that encourages and assists in doing mathematics (mathematizing). Examples of attitudes, dispositions, values, ... concepts in the mathematical knowledge base.

Resources and materials

Pencil, sequence of numbers, objects to count, activities, math notes, worksheets

Pedagogical ideas

Focus questions

Exploration

Invention

Exploration, discovery, application, extension

Vocabulary

Activity sequence

While these are sequenced, to add structure, the order isn't meant to imply one process or skill needs to be mastered before moving to the next. Learners will construct structures and procedures for each of these ideas simultaneously and some interaction of differnt ideas, evne if inaccurate, is helpful in the eventual development of counting and cardinality. Since this is a framework see also specific activities, plans, and materials.

Classification

Counting

Number recognition

Subitizing

Beyond Ten

Numbers to 100

Skip Counting

Counting Backwards

One-to-one correspondence

See more activities, plans, and materials.

Assessment

Provide students with a problem and score their work with the Cardinality scoring guide.

Recording materials or scoring guides

Need to add more scoring guides with levels for other dimensions or categories like cardinality.

Student work sheets

See specific activities, plans, and materials.

 

Dr. Robert Sweetland's notes
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