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### PK.A Mathematical Thinking

- PK.A.a Number Sense
- PK.A.a.1 Demonstrates understanding of one-to-one correspondence
- PK.A.a.1.a Child demonstrates one-to-one correspondence when counting.
- PK.A.a.1.b Child demonstrates one-to-one correspondence to determine if two sets are equal.

- PK.A.a.2 Shows understanding of how to count and construct sets
- PK.A.a.2.a Child counts sets in the range of 10 to 15 objects.
- PK.A.a.2.b Child constructs sets in the range of 10 to 15 objects.

- PK.A.a.3 Shows understanding by participating in the comparison of quantities
- PK.A.a.3.a Child compares two sets to determine if they are equal.
- PK.A.a.3.b Child compares two sets to determine if one set has more.
- PK.A.a.3.c Child compares two sets to determine if one set has fewer.
- PK.A.a.3.d Child determines one set of objects is a lot more than another set of objects.

- PK.A.a.4 Assigns and relates numerical representations among numerals (written), sets of objects, and number names (spoken) from zero to 10
- PK.A.a.5 Counts and knows the sequence of number names (spoken)
- PK.A.a.5.a Child counts and recognizes number names (spoken) in the range of 10 to 15.
- PK.A.a.5.b Child counts up through 31 by understanding the pattern of adding by one, with teacher support and multiple experiences over time.

- PK.A.a.6 Shows understanding of and uses appropriate terms to describe ordinal positions
- PK.A.a.6.a Child demonstrates the concept of ordinal position with concrete objects (e.g., children or objects).
- PK.A.a.6.b Child names ordinal positions (e.g., first, second, third, fourth, fifth).

- PK.A.a.1 Demonstrates understanding of one-to-one correspondence
- PK.A.b Number and Operations
- PK.A.b.1 Shows understanding of how to combine sets and remove from a concrete set of objects (receptive knowledge)
- PK.A.b.1.a Child indicates there are more when combining (adding) sets of objects.
- PK.A.b.1.b Child indicates there are less (fewer) when removing (subtracting) objects from a set.

- PK.A.b.2 Shows understanding of addition and subtraction using a concrete set of objects (expressive knowledge) or story problems found in everyday classroom activities
- PK.A.b.2.a Child combines sets of objects to equal a set no larger than 10.
- PK.A.b.2.b Child removes objects from a set no larger than 10.
- PK.A.b.2.c Child uses concrete objects (e.g., fingers, blocks) to solve complex problems.

- PK.A.b.3 Begins to develop an understanding of separating a set into a maximum of four parts, with teacher support and multiple experiences over time

- PK.A.b.1 Shows understanding of how to combine sets and remove from a concrete set of objects (receptive knowledge)
- PK.A.c Patterns and Seriation
- PK.A.c.1 Understands characteristics of patterns and non-patterns and begins to reproduce them with at least two elements (e.g., red/blue, red/blue versus a non-pattern like a rainbow)
- PK.A.c.1.a Child recognizes patterns and non-patterns.
- PK.A.c.1.b Child duplicates identical patterns with at least two elements.
- PK.A.c.1.c Child recognizes pattern units (e.g., red/blue is the pattern unit of a red/blue/red/blue/red/blue pattern; dog/cat/cow is the pattern unit of a dog/cat/cow/dog/cat/cow pattern).
- PK.A.c.1.d Child begins to independently produce patterns with at least two elements (e.g., red/blue, red/blue), with teacher support and multiple experiences over time.

- PK.A.c.2 Sorts, orders, compares, and describes objects according to characteristics or attribute(s) (seriation)
- PK.A.c.2.a Child places objects in increasing order of size where the increasing unit is constant (e.g., unit blocks).
- PK.A.c.2.b Child verbalizes why objects were placed in order (e.g., describes process of how and why), with teacher support and multiple experiences over time.

- PK.A.c.1 Understands characteristics of patterns and non-patterns and begins to reproduce them with at least two elements (e.g., red/blue, red/blue versus a non-pattern like a rainbow)
- PK.A.d Geometry
- PK.A.d.1 Understands various two-dimensional shapes, including circle, triangle, square, rectangle, oval, and other less common shapes (e.g., trapezoid, rhombus)
- PK.A.d.1.a Child categorizes (sorts) examples of two-dimensional shapes.
- PK.A.d.1.b Child names two-dimensional shapes.
- PK.A.d.1.c Child constructs examples of two-dimensional shapes.
- PK.A.d.1.d Child identifies the number of sides of two-dimensional shapes.

- PK.A.d.2 Shows understanding that two-dimensional shapes are equivalent (remain the same) in different orientations
- PK.A.d.2.a Child slides shapes, with teacher support and multiple experiences over time.
- PK.A.d.2.b Child flips shapes, with teacher support and multiple experiences over time.
- PK.A.d.2.c Child rotates shapes, with teacher support and multiple experiences over time.

- PK.A.d.3 Understands various three-dimensional shapes, including sphere, cube, cone, and other less common shapes (e.g., cylinder, pyramid)
- PK.A.d.3.a Child categorizes (sorts) examples of three-dimensional shapes.
- PK.A.d.3.b Child names three-dimensional shapes.

- PK.A.d.4 Analyzes and constructs examples of simple symmetry and nonsymmetry in two dimensions, using concrete objects

- PK.A.d.1 Understands various two-dimensional shapes, including circle, triangle, square, rectangle, oval, and other less common shapes (e.g., trapezoid, rhombus)
- PK.A.e Spatial Relations
- PK.A.e.1 Shows understanding of spatial relationships and uses position words (e.g., above, below, next to, beside, on top of, inside, outside)
- PK.A.e.1.a Child shows understanding of positional words (receptive knowledge).
- PK.A.e.1.b Child uses the positional terms verbally (expressive knowledge) (e.g., in front of, behind, between, over, through, under), with teacher support and multiple experiences over time.

- PK.A.e.2 Describes relative position from different perspectives (e.g., “I am on top of the climber and you are below me.”)
- PK.A.e.3 Understands and can tell the difference between orientation terms (e.g., horizontal, diagonal, vertical)
- PK.A.e.4 Uses directions to move through space and find places in space (e.g., obstacle courses, Simon Says, Mother May I?, hopscotch, giving simple directions)

- PK.A.e.1 Shows understanding of spatial relationships and uses position words (e.g., above, below, next to, beside, on top of, inside, outside)
- PK.A.f Measurement
- PK.A.f.1 Engages in activities that explore measurement
- PK.A.f.2 Compares continuous quantities using length, weight, and height
- PK.A.f.2.a Child measures or compares the length of one or more objects using a non-standard reference (e.g., paper clips), with teacher support and multiple experiences over time.
- PK.A.f.2.b Child measures or compares the weight of one or more objects using non-standard reference (e.g., beans), with teacher support and multiple experiences over time.
- PK.A.f.2.c Child measures or compares the height of one or more objects using non-standard reference (e.g., pencils), with teacher support and multiple experiences over time.
- PK.A.f.2.d Child uses measurement vocabulary (e.g., length, weight, height) and comparative terminology (e.g., more, less, shorter, longer, heaviest, lightest), with teacher support and multiple experiences over time.

- PK.A.f.3 Represents and analyzes data
- PK.A.f.3.a Child assists with collecting and sorting materials to be graphed.
- PK.A.f.3.b Child works with teacher and small groups to represent mathematical relations in charts and graphs.
- PK.A.f.3.c Child analyzes, with teacher and small groups, the relationship between items/objects represented by charts and graphs.

- PK.A.f.4 Child predicts the results of a data collection, with teacher support and multiple experiences over time.