Overview Link to this section
Mathematics is a natural part of the preschool environment. Young children actively construct mathematical knowledge through everyday interactions with their environment, whether inside or outside. When building in the block area or sorting blocks by shape, children explore geometry in the real world. When measuring two cups of flour and three spoons of sugar in a cooking activity, they learn principles of measurement. Climbing in and out of cardboard boxes, crawling through a tunnel, or riding a bike helps children develop a sense of spatial relationships (e.g., on, under, over). Mathematics learning grows naturally from children’s curiosity and enthusiasm to learn and explore their environment. Teachers should encourage children’s natural enthusiasm and interest in doing mathematics and use it as a vehicle for supporting the development of children’s mathematical concepts and skills.
Priority Standards Link to this section
What students will know, what students will do, and what thinking skills students will develop to apply and transfer mathematical understandings that endure within the discipline, leverage deeper understandings, and/or support readiness for success at the next grade level.
In Pre-K, we focus on these critical areas:
Counting
Counting concepts include learning the verbal sequence of numbers, understanding the one-to-one principle, and developing a sense of quantity by putting groups of physical counters together and taking them apart.
Geometry
In geometry, students learn the names of shapes, and identify shapes in the classroom and in the world beyond. They learn that a shape is defined by the number of sides and the number of angles/corners. They will describe and construct basic shapes such as circles, rectangles, triangles and squares.
Addition and Subtraction
Children build on counting concepts, learn how numbers can be combined and taken apart and learn how adding one more or one less changes the quantity in predictable ways.
Measurement
Children learn height and length by comparing the size of one object to another object, and order objects by size (seriation) using relative vocabulary such as long, longer, and longest as well as high, higher, and highest.
Classification
Children classify materials by attributes, demonstrating important systematic thinking. They share their mathematical thinking with others, explaining where things go and why they belong together.
Patterns
Children learn repeating sequences, and then create and extend patterns.
Instruction: Signature Elements Link to this section
Below are signature elements of SFUSD Math instruction that students should experience regularly throughout Pre-K as they develop as mathematicians.
Practice with shapes
This Making Shapes activity in Seesaw, designed by an SFUSD teacher, can both give students an opportunity to explore and play with shapes; it can also introduce students to Seesaw’s drawing tools. (Make sure to model the activity first).
Encourage inquiry and exploration to foster problem solving and mathematical reasoning
Mathematical reasoning and problem solving are natural to all children as they explore the world around them. The most powerful mathematics learning for preschool children often results from their own explorations. Teachers should maintain an environment that nurtures children’s inquiry and exploration of mathematical ideas and that values problem solving. They should ask children questions to stimulate mathematical conversations and encourage mathematical reasoning through everyday interactions.
Introduce mathematical concepts through intentionally planned experiences
In addition to the meaningful mathematics that preschool children acquire spontaneously through play and everyday activities, teachers should provide carefully planned experiences that focus children’s attention on particular mathematical concepts, methods, and the language of math. Mathematical experiences planned in advance would allow teachers to present concepts in a logical sequence and forge links between previously encountered mathematical ideas and new applications.
Materials
Below are items you should have to support your students' math instruction. If you are missing anything from the list, please first contact your site administrator. If they are unable to resolve the issue, please contact the SFUSD Early Education Department.
- 5 and 10 Frames
- Various Math Counters
- Number Path
- Two- color Counters
- Attribute Shapes
- Dice
- Sidewalk Chalk
- Dry erase markers and Dry Erase Sheet Protectors
Reflection Questions Link to this section
- How are students' developmental needs, communities, and experiences being reflected and honored, or how could they be?
- What opportunities do you see for developing equitable access & demand, inquiry, collaboration, and assessment for learning?
- What are the implications for your own practice? What strengths can you build upon? What will you do first?
Want more?
CA PTKLF Mathematics - The Preschool and Transitional Kindergarten Learning Foundations (PTKLF) provide guidance on the wide range of mathematics knowledge and skills that children age three to five and a half typically attain when attending a high-quality early education program.
Operation Videos: Addition, Subtraction Division and Multiplication in PK
This page was last updated on May 2, 2025