
PPreKindergarten Standards
Top Mathematicians

Number and Operations

P.NO.1
Shows understanding of how to combine sets and remove from a concrete set of objects (receptive knowledge)


P.NO.1.a
Child indicates there are more when combining (adding) sets of objects.


P.NO.1.b
Child indicates there are less (fewer) when removing (subtracting) objects from a set.


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


P.NO.2.a
Child combines sets of objects to equal a set no larger than 10.


P.NO.2.b
Child removes objects from a set no larger than 10.


P.NO.2.c
Child uses concrete objects (e.g., fingers, blocks) to solve complex problems.


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


P.NO.1

Number Sense

P.NS.1
Demonstrates understanding of onetoone correspondence


P.NS.1.a
Child demonstrates onetoone correspondence when counting.


P.210

P.35

P.45

P.510

P.610

P.710

P.810

P.920

P.1010


P.NS.1.b
Child demonstrates onetoone correspondence to determine if two sets are equal.


P.115

P.125


P.NS.2
Shows understanding of how to count and construct sets


P.NS.2.a
Child counts sets in the range of 10 to 15 objects.


P.510

P.610

P.710

P.810

P.920

P.1010

P.1310


P.NS.2.b
Child constructs sets in the range of 10 to 15 objects.


P.510


P.NS.3
Shows understanding by participating in the comparison of quantities


P.NS.3.a
Child compares two sets to determine if they are equal.


P.115

P.125


P.NS.3.b
Child compares two sets to determine if one set has more.


P.NS.3.c
Child compares two sets to determine if one set has fewer.


P.NS.3.d
Child determines one set of objects is a lot more than another set of objects.


P.NS.4
Assigns and relates numerical representations among numerals (written), sets of objects, and number names (spoken) from zero to 10


P.1310

P.155


P.NS.5
Counts and knows the sequence of number names (spoken)


P.NS.5.a
Child counts and recognizes number names (spoken) in the range of 10 to 15.


P.1310

P.1610


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.


P.NS.6
Shows understanding of and uses appropriate terms to describe ordinal positions


P.NS.6.a
Child demonstrates the concept of ordinal position with concrete objects (e.g., children or objects).


P.NS.6.b
Child names ordinal positions (e.g., first, second, third, fourth, fifth).


P.NS.1

Patterns and Seriation

P.PS.1
Understands characteristics of patterns and nonpatterns and begins to reproduce them with at least two elements (e.g., red/blue, red/blue versus a nonpattern like a rainbow)


P.PS.1.a
Child recognizes patterns and nonpatterns.


P.175


P.PS.1.b
Child duplicates identical patterns with at least two elements.


P.175


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).


P.175


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.


P.PS.2
Sorts, orders, compares, and describes objects according to characteristics or attribute(s) (seriation)


P.PS.2.a
Child places objects in increasing order of size where the increasing unit is constant (e.g., unit blocks).


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.


P.PS.1

Geometry

P.G.1
Understands various twodimensional shapes, including circle, triangle, square, rectangle, oval, and other less common shapes (e.g., trapezoid, rhombus)


P.G.1
Shows understanding of spatial relationships and uses position words (e.g., above, below, next to, beside, on top of, inside, outside)


P.G.1.a
Child shows understanding of positional words (receptive knowledge).


P.255

P.265

P.275

P.285


P.G.1.a
Child categorizes (sorts) examples of twodimensional shapes.


P.G.1.b
Child names twodimensional shapes.


P.185

P.195


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.


P.255

P.265

P.275

P.285


P.G.1.c
Child constructs examples of twodimensional shapes.


P.G.1.d
Child identifies the number of sides of twodimensional shapes.


P.205

P.215


P.G.2
Describes relative position from different perspectives (e.g., "I am on top of the climber and you are below me.")


P.G.2
Shows understanding that twodimensional shapes are equivalent (remain the same) in different orientations


P.G.2.a
Child slides shapes, with teacher support and multiple experiences over time.


P.G.2.b
Child flips shapes, with teacher support and multiple experiences over time.


P.G.2.c
Child rotates shapes, with teacher support and multiple experiences over time.


P.G.3
Understands various threedimensional shapes, including sphere, cube, cone, and other less common shapes (e.g., cylinder, pyramid)


P.G.3
Understands and can tell the difference between orientation terms (e.g., horizontal, diagonal, vertical)


P.G.3.a
Child categorizes (sorts) examples of threedimensional shapes.


P.G.3.b
Child names threedimensional shapes.


P.225


P.G.4
Analyzes and constructs examples of simple symmetry and nonsymmetry in two dimensions, using concrete objects


P.235

P.245


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)


P.G.1

Measurement and Data

P.MD.1
Engages in activities that explore measurement


P.MD.2
Compares continuous quantities using length, weight, and height


P.MD.2.a
Child measures or compares the length of one or more objects using a nonstandard reference (e.g., paper clips), with teacher support and multiple experiences over time.


P.MD.2.b
Child measures or compares the weight of one or more objects using nonstandard reference (e.g., beans), with teacher support and multiple experiences over time.


P.MD.2.c
Child measures or compares the height of one or more objects using nonstandard reference (e.g., pencils), with teacher support and multiple experiences over time.


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.


P.295

P.305

P.315

P.325


P.MD.3
Represents and analyzes data


P.MD.3.a
Child assists with collecting and sorting materials to be graphed.


P.MD.3.b
Child works with teacher and small groups to represent mathematical relations in charts and graphs.


P.MD.3.c
Child analyzes, with teacher and small groups, the relationship between items/objects represented by charts and graphs.


P.3410

P.355


P.MD.4
Child predicts the results of a data collection, with teacher support and multiple experiences over time.


P.MD.1