All things Kindergarten Math

Unit 3: Introducing and Developing Numbers 0-10 and Reciting Numbers to 60

This unit bundles student expectations that address the foundational skills for developing an understanding of numbers 0 – 10, counting forward and backward 1 – 10, cardinality, subitizing, conservation of set, comparing numbers and sets of objects using comparative language, and generating numbers or set of objects less than or greater than a given amount. This unit also includes the student expectation that addresses reciting numbers up to 60 by ones beginning with any number.

During this unit, students are introduced to the numbers 0 – 10. They use sets of objects up to 10 to develop an understanding of the concepts of cardinality, meaning that the

last number said when counting a set of objects names the number of objects, hierarchical inclusion, meaning each prior number in the counting sequence is included in the set as the set increases, and conservation of set, meaning if the same number of objects are counted and then rearranged, the quantity of objects in the set does not change. Students apply cardinality, hierarchical inclusion, and conservation of set as they begin to grasp the true meaning of numbers. Students count forward and backward to 10 with and without objects, as well as read, write, and represent the numbers. Students also compose and decompose numbers up to 5 using objects and pictures which parallels the development of subitizing, meaning instantly recognizing the number being represented by a small quantity of objects in random and organized arrangements. Students apply all of these skills as they consider magnitude, or relative size, to compare sets of objects up to 10 and generate a set of objects and pictures that is more than, less than, or equal to a given number. Students use comparative language to describe the comparison of numbers represented using objects, pictures, or numerals. When given a

number up to 10, students are expected to generate a number that is one more than or one less than a given number. Along with the investigation of number and quantity,

students are expected to recite numbers up to 60 by ones beginning with any number. Practice with rote reciting of numbers and learning the correct sequence of numbers

aids in developing the foundation for meaningful counting strategies.

After this unit, in Unit 6 and 8, students will continue to develop the foundations of numbers as they extend their number set to include 11-15 and 16-20 and extend reciting numbers up to 100.

by ones beginning with any number.

Have a Number Talk

Of all the things I have seen so far for math, I think that a Number Talk will give you the most “bang for your buck.” In other words, you can get big results with a small amount of time. A Number Talk is a whole group activity that takes 5-10 minutes. It can be done at the beginning of the math lesson, or during some other time of the day. The purpose of a Number Talk is to help students develop computational fluency as well as number sense.

Ideas for Number Talks:

*Dots (Back of Book 1 of Developing Number Concepts by Kathy Richardson and from the blackline masters found at

*Lines pictures from Developing Number Concepts by Kathy Richardson


*Large Dice

*Unifix trains with two colors

*Ten Frame (blackline masters found at

*Greg Tang books

Subitize 5-10
Ten Frame 1-10
10 Frames for Kindergarten Kids Adding Counting Using Ten Frames
Subitizing - Number Fluency

Counting Principles and Teaching Them

Introducing the Counting Principles
Teaching the One-to-One Counting Principle
Teaching the Stable-Order Counting Principle
Teaching the Cardinal Counting Principle
Teaching the Order-irrelevance Counting Principle