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PPre-Kindergarten Standards
Top Mathematicians
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Patterns and Seriation
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P.PS.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)
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P.PS.1.a
Child recognizes patterns and non-patterns.
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P.175
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P.PS.1.b
Child duplicates identical patterns with at least two elements.
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P.175
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P.PS.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).
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P.175
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P.PS.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.
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P.PS.2
Sorts, orders, compares, and describes objects according to characteristics or attribute(s) (seriation)
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P.PS.2.a
Child places objects in increasing order of size where the increasing unit is constant (e.g., unit blocks).
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P.PS.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.
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P.PS.1
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Geometry
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P.G.1
Shows understanding of spatial relationships and uses position words (e.g., above, below, next to, beside, on top of, inside, outside)
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P.G.1
Understands various two-dimensional shapes, including circle, triangle, square, rectangle, oval, and other less common shapes (e.g., trapezoid, rhombus)
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P.G.1.a
Child shows understanding of positional words (receptive knowledge).
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P.255
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P.265
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P.275
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P.285
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P.G.1.a
Child categorizes (sorts) examples of two-dimensional shapes.
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P.G.1.b
Child names two-dimensional shapes.
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P.185
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P.195
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P.G.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.
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P.255
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P.265
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P.275
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P.285
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P.G.1.c
Child constructs examples of two-dimensional shapes.
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P.G.1.d
Child identifies the number of sides of two-dimensional shapes.
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P.205
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P.215
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P.G.2
Describes relative position from different perspectives (e.g., "I am on top of the climber and you are below me.")
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P.G.2
Shows understanding that two-dimensional shapes are equivalent (remain the same) in different orientations
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P.G.2.a
Child slides shapes, with teacher support and multiple experiences over time.
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P.G.2.b
Child flips shapes, with teacher support and multiple experiences over time.
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P.G.2.c
Child rotates shapes, with teacher support and multiple experiences over time.
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P.G.3
Understands various three-dimensional shapes, including sphere, cube, cone, and other less common shapes (e.g., cylinder, pyramid)
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P.G.3
Understands and can tell the difference between orientation terms (e.g., horizontal, diagonal, vertical)
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P.G.3.a
Child categorizes (sorts) examples of three-dimensional shapes.
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P.G.3.b
Child names three-dimensional shapes.
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P.225
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P.G.4
Analyzes and constructs examples of simple symmetry and nonsymmetry in two dimensions, using concrete objects
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P.235
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P.245
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P.G.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)
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P.G.1
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Measurement and Data
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P.MD.1
Engages in activities that explore measurement
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P.MD.2
Compares continuous quantities using length, weight, and height
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P.MD.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.
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P.MD.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.
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P.MD.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.
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P.MD.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.
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P.295
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P.305
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P.315
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P.325
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P.MD.3
Represents and analyzes data
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P.MD.3.a
Child assists with collecting and sorting materials to be graphed.
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P.MD.3.b
Child works with teacher and small groups to represent mathematical relations in charts and graphs.
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P.MD.3.c
Child analyzes, with teacher and small groups, the relationship between items/objects represented by charts and graphs.
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P.3410
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P.355
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P.MD.4
Child predicts the results of a data collection, with teacher support and multiple experiences over time.
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P.MD.1
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Number Sense
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P.NS.1
Demonstrates understanding of one-to-one correspondence
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P.NS.1.a
Child demonstrates one-to-one correspondence when counting.
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P.210
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P.35
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P.45
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P.510
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P.610
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P.710
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P.810
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P.920
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P.1010
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P.NS.1.b
Child demonstrates one-to-one correspondence to determine if two sets are equal.
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P.115
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P.125
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P.NS.2
Shows understanding of how to count and construct sets
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P.NS.2.a
Child counts sets in the range of 10 to 15 objects.
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P.510
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P.610
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P.710
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P.810
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P.920
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P.1010
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P.1310
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P.NS.2.b
Child constructs sets in the range of 10 to 15 objects.
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P.510
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P.NS.3
Shows understanding by participating in the comparison of quantities
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P.NS.3.a
Child compares two sets to determine if they are equal.
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P.115
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P.125
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P.NS.3.b
Child compares two sets to determine if one set has more.
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P.NS.3.c
Child compares two sets to determine if one set has fewer.
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P.NS.3.d
Child determines one set of objects is a lot more than another set of objects.
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P.NS.4
Assigns and relates numerical representations among numerals (written), sets of objects, and number names (spoken) from zero to 10
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P.1310
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P.155
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P.NS.5
Counts and knows the sequence of number names (spoken)
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P.NS.5.a
Child counts and recognizes number names (spoken) in the range of 10 to 15.
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P.1310
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P.1610
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P.NS.5.b
Child counts up through 31 by understanding the pattern of adding by one, with teacher support and multiple experiences over time.
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P.NS.6
Shows understanding of and uses appropriate terms to describe ordinal positions
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P.NS.6.a
Child demonstrates the concept of ordinal position with concrete objects (e.g., children or objects).
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P.NS.6.b
Child names ordinal positions (e.g., first, second, third, fourth, fifth).
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P.NS.1
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Number and Operations
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P.NO.1
Shows understanding of how to combine sets and remove from a concrete set of objects (receptive knowledge)
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P.NO.1.a
Child indicates there are more when combining (adding) sets of objects.
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P.NO.1.b
Child indicates there are less (fewer) when removing (subtracting) objects from a set.
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P.NO.2
Shows understanding of addition and subtraction using a concrete set of objects (expressive knowledge) or story problems found in everyday classroom activities
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P.NO.2.a
Child combines sets of objects to equal a set no larger than 10.
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P.NO.2.b
Child removes objects from a set no larger than 10.
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P.NO.2.c
Child uses concrete objects (e.g., fingers, blocks) to solve complex problems.
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P.NO.3
Begins to develop an understanding of separating a set into a maximum of four parts, with teacher support and multiple experiences over time
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P.NO.1