# Mathematics

In your transitional kindergarten class, mathematics can be taught—and discovered—in the everyday environment of your young learners. For example, students can learn new concepts and relationships of numbers and quantities as they recite numbers in order, count objects or visually compare groups of objects and express if they are the “same” or “more.” They can learn about measurement by comparing the length, weight or capacity of objects by using words such as bigger, longer, heavier or taller. Young children learn these important foundations of mathematics while engaging in imaginative play, exploring the environment and materials, making discoveries or interacting with teachers or other adults.

“Mathematics learning at this level must be active, rich in natural and mathematical language, and filled with thought-provoking opportunities. Students respond to the challenge of high expectations and mathematics should be taught for understanding rather than around preconceptions around children’s limitations. This does not mean abandoning children’s ways of knowing and representing; rather it is a clear call to create opportunities for young students to learn new, important mathematics in ways that make sense to them.”1

## Elements of Mathematic Instruction

Instructional time in TK should focus on the following content:2

###### Number and Operations
• develop an understanding of whole numbers, including concepts of correspondence, counting, cardinality and comparison. Your TK students should know number names and the count sequence and count to tell the number of objects; and
• represent, compare and order whole numbers and join and separate sets. Students  should compare numbers, understand addition as putting together and adding to and understand subtraction as taking apart and taking from.
 This series of three videos demonstrates complete math lessons in a TK classroom. Each video focuses around using student names in math lessons.
###### Geometry
• identify shapes and describing spatial relationships; and
• describe shapes and space. TK students should analyze, compare, create, and compose shapes.
###### Measurement
• identify measureable attributes and comparing objects by using these attributes. Students should describe and compare measureable attributes; and
• order objects by measureable attributes.

One of the critical components of California’s Common Core State Standards is the Standards for Mathematical Practice. These standards focus on the key aspects of mathematics that teachers ought to focus on when engaging students in mathematics across school levels, and include the following concepts:

• making sense of problems and persevering in solving them;
• reasoning abstractly and quantitatively;
• constructing viable arguments and critiquing the reasoning of others;
• modeling with mathematics;
• looking for and making use of structure;
• using appropriate tools strategically;
• attending to precision; and
• looking for and expressing regularity in repeated reasoning.
 San Francisco Unified School District has developed the above developmentally appropriate number sense activities aligned with the Preschool Learning Foundations Learning Trajectories and the Kindergarten Common Core. These activities are easy to implement and can be used in centers, small group, and whole group settings.

## Mathematics on the Standards Continuum

TK allows you the gift of time to move your students along the standards continuum, preparing them for a successful kindergarten year aheadAs there are no set standards for TK, WestEd and the Child Development Division of the California Department of Education developed a publication that aligns the Preschool Learning Foundations with the Kindergarten Common Core State Standards to help guide developmentally appropriate TK instruction. Find the publication here. The alignment of the foundations and the common core standards illustrates the developmental progression of TK-aged students.

Even though the Foundations and the Common Core Standards are organized somewhat differently, overall, both cover the same key areas in mathematics.

Differences in organization:

• Content related to number sense in the Preschool Learning Foundations is represented in two key areas in the Common Core State Standards: 1) counting and cardinality and 2) operations and algebraic thinking.
• Content in number and operations in base ten of the common core standards is too advanced for it to have corresponding content in the preschool foundations.
• Content related to Classification appears under “algebra and function” in the preschool foundations, and under “measurement and data” in the common core standards.
• The common core standards include differentiated standards in mathematical reasoning and do not include standards related to patterning, subitizing (number sense) and measuring length (measurement).

1 NCTM Principles and Standards for School Mathematics, 2000, p. 77

2 Adapted from NCTM Curriculum Focal Points and Connections for Prekindergarten and Kindergarten