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### PK.4.1 Children demonstrate an understanding of numbers and numerical operations.

- PK.4.1.1 Demonstrate emergent understanding of numbers (for counting: at least through 20; for ordinals: first through fifth, including the last).
- PK.4.1.2 Recognize and name some one-digit written numerals.
- PK.4.1.2.a Begin to write one-digit numerals.
- PK.4.1.2.b Discriminate numbers from other symbols in the environment (e.g., street signs, license plates, room number, clock).

- PK.4.1.3 Compare groups of objects (e.g., using the terms “more,” “less,” “same”).
- PK.4.1.4 Demonstrate understanding of one-to-one correspondence (e.g., put one placemat at each place, give each child one cookie, place one animal in each truck, hand out manipulatives to be shared with a friend, saying “One for you, one for me.”).
- PK.4.1.4.a Match sets
- PK.4.1.4.b Spontaneously count for own purposes.
- PK.4.1.4.c Recognize a number of objects (up to four) without counting.

- PK.4.1.5 Explore the meanings of addition and subtraction by using concrete objects.
- PK.4.1.5.a Joining (e.g., “Three blue pegs, three yellow pegs, six pegs altogether!”).
- PK.4.1.5.b Separating (“I have four carrot sticks. I’m eating one! Now I have 3!”).

### PK.4.2 Children develop knowledge of spatial concepts (e.g., shapes and measurement).

- PK.4.2.1 Use and respond to positional words (e.g., in, under, between, down).
- PK.4.2.2 Explore and talk about basic shapes in the environment (e.g., circle, square, triangle).
- PK.4.2.3 Explore three-dimensional shapes by building with blocks and other materials.
- PK.4.2.4 Explore connections between two- and three-dimensional forms (e.g., sphere and circle).
- PK.4.2.5 Identify symmetry during play (e.g., building with blocks).
- PK.4.2.6 Use simple shapes to make designs, patterns, and pictures (e.g., tangrams).
- PK.4.2.7 Explore the use of nonstandard objects for measurement.
- PK.4.2.8 Compare and order objects according to measurable attributes (e.g., length, weight).
- PK.4.2.9 Demonstrate understanding of basic temporal relations (e.g., the sequence of the daily routine).

### PK.4.3 Children understand patterns, relationships, and classification.

- PK.4.3.1 Describe patterns in the environment.
- PK.4.3.2 Represent patterns in a variety of ways.
- PK.4.3.3 Begin to represent data in pictures and drawings.
- PK.4.3.4 Show awareness of the attributes of objects through sorting, ordering, and classifying.

### PK.4.4 Children use mathematical knowledge to represent, communicate, and solve problems in their environment.

- PK.4.4.1 Learn mathematics through problem solving, inquiry, and discovery and use emergent mathematical knowledge as a problem-solving tool.
- PK.4.4.2 Solve problems that arise in mathematics and in other contexts.
- PK.4.4.3 Use communication to organize and clarify mathematical thinking by discussing, listening, and asking questions during activities.
- PK.4.4.4 Recognize that mathematics is used in a variety of contexts in all disciplines, and apply mathematics in practical situations and other disciplines.
- PK.4.4.5 Use technology to reinforce concrete mathematical information (e.g., to explore patterns and shapes).