Counting - Cardinality Sequence

Overview
Mathematics content - (number value and operations, algebra, geometry, measurement, data analysis and probability)
Process - (problem solving, representation, communication, connections, reasoning and proof)
Resources and materials
Pedagogical ideas
Definitions
Activity sequence
Lessons and activities detail
Scoring guide

Overview

Finding the value - students will practice counting groups of objects.

Cardinality - Counting objects can result in a cardinal result (numbered value). Students will repeat or emphasize last word 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 - (enduring understanding, big ideas, land marks, structure, generalizations)

Cardinality - Counting objects can result in a cardinal result (numbered value). Students will repeat or emphasize last word 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)

Supporting ideas from unpacking the big idea (facts, concepts, generalizations)

Processes - how mathematicians knows

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.

Habits of Mind - how mathematicians think better

 

Resources and materials

Pencil,

Pedagogical ideas

Focus questions - How do we know how many?

Exploration - Demonstration and questioning.
Invention - Teacher modeling and student demonstration of explanation of solutions.
Bridges - Matching concrete examples (objects of different valued sets) with numerals (orally - saying 1, 2, ..., visually writing or showing a card with numerals 1, 2, ...) by physically putting them side by side or pointing to show one-to-one correspondence.
Discovery, application, extension - Repeated activities with larger number values.

Need to insert detailed plans for dimensions beyond number value here or below in sequence plan

Definitions

Activity sequence - While these are sequenced as adding structure the order isn't meant to imply that one needs to be mastered before moving to the next. Students can constructing structure for each of these ideas simultaneously.

Classification

Counting

Number recognition

Subitizing

Beyond Ten

Numbers to 100

Skip Counting

Counting Backwards

One-to-one correspondence

Assessment

Insert assessment instructions

Provide students with a problem (insert examples) 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

References

Dr. Robert Sweetland's notes