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Back to Learning Progressions

Back to Infant/Toddler

Age: Kindergarten 

Learning Progression:


Preschoolers typically like math. They have a natural understanding of informal mathematics and are often curious about the world around them and how things work. This curiosity coupled with the activities and routines of daily living provide the ideal environment in which to build mathematical understanding.


As parents, care givers, and early learning teachers, we can foster mathematical development of young children by providing opportunities to explore, make choices, and build confidence. Through play, observation, and interactions with others, parents and teachers can provide meaningful learning experiences for children by building upon their understanding of a child’s interests, family, language, and cultural experiences.

Many preschoolers have already learned some counting words and readily compare small groups of objects, understanding which group contains more. During these early years, preschoolers develop their mathematical knowledge about number, quantity, comparisons, shape, size, and space. High quality preschool mathematical experiences are the foundation for future mathematical learning and success and should be integrated into many activities throughout the day. 


Play is at the center of preschool aged children’s learning. Through play, preschoolers discover interests, develop their growing attention span, and learn about their capabilities and creativity. Play provides an important context for thinking, understanding the world, solving problems, and relating to others. 


Preschoolers make use of all of their senses with new experiences and situations. They compare new ideas and discoveries with those that are familiar and create new meaning and understanding. Parents and teachers can support preschoolers learning by recognizing and taking advantage of the learning opportunities in unexpected situations:


  • Building with blocks may provide an opportunity to sort the blocks by shape.

  • Helping parents with cooking allows a child to explore measurement.

  • Riding a tricycle or making a fort from cardboard boxes allows a child to expand his or her understanding of spatial relationships. 

Play provides an important context for thinking, understanding the world, solving problems, and relating to others.

Teachers can make children feel welcome by ensuring that all children have access to the learning environment through thoughtful organization of materials and space and by establishing a climate of respect for all of the children and families within the preschool setting.

Learning Progressions:

Transitional Kindergarten (TK)

Preschool children who are 4 years of age and will turn 5 between September 2 and December 2 are age eligible to attend a transitional kindergarten (TK) program.


TK curriculum is aligned with the California Preschool Learning Foundations


Developmentally, those enrolled in a TK program are still considered preschool aged children. For information on preschool aged children within the mathematical learning progression, go here:

Starting with the 2012-13 school year, local education agencies (i.e. school districts, county offices of education, and charter schools)  began offering transitional kindergarten programs.

The California Mathematics Framework includes a chapter for TK. This framework includes California Preschool Learning Foundations and California content standards for kindergarten. TK is, therefore, a bridge between preschool and the kindergarten year.

Find the entire TK chapter of the Mathematics Framework on the CDE website here: This chapter includes a side-by-side alignment of the Preschool Learning Foundations with the California Common Core State Standards for Mathematics for Kindergarten.


When developmentally appropriate, TK is a good time to introduce children to the kindergarten standards without the expectation of mastery. For this reason, information and resources within the TK/K section include both the Preschool Learning Foundations and kindergarten standards.


Students in preschool and transitional kindergarten programs who have been exposed to important mathematical concepts—such as representing, relating, and operating on whole numbers and identifying and describing shapes—will be better prepared for kindergarten mathematics and for later learning.

For more information on Transitional Kindergarten, go to the California Department of Education's website:

According the California Mathematics Framework, a high-quality mathematics education for TK includes the following:


  • A mathematically rich environment

  • Frequent opportunities for mathematical discourse

  • Engaging and meaningful mathematics activities

  • Explicit instruction

  • Modeling of mathematical thinking

  • Nurturing of students’ mathematical explorations

Learn more about the Math Domains related to your child's age:

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