New Jersey

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).

  • Count pictures - up to 3 (P-A.3)
  • Count dots - up to 3 (P-A.4)
  • Count shapes - up to 3 (P-A.5)
  • Represent numbers with pictures - up to 3 (P-A.9)
  • Count pictures - up to 5 (P-B.3)
  • Count dots - up to 5 (P-B.4)
  • Count shapes in rows - up to 5 (P-B.5)
  • Represent numbers with pictures - up to 5 (P-B.12)
  • Count pictures - up to 10 (P-C.3)
  • Count dots - up to 10 (P-C.4)
  • Count shapes in rows - up to 10 (P-C.5)
  • Represent numbers - up to 10 (P-C.13)
  • Count pictures - up to 20 (P-D.2)
  • Count dots - up to 20 (P-D.3)
  • Count shapes - up to 20 (P-D.4)
  • Represent numbers - up to 20 (P-D.7)
  • Ordinal numbers (1-A.29)

• 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").

  • More (P-E.1)
  • Fewer and more - compare by counting (P-E.4)
  • Fewer and more - compare in a mixed group (P-E.5)
  • Fewer, more, and same (K-H.4)

• 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

    • Different (P-G.1)
    • Same (P-G.2)
    • Same and different (P-G.3)
    • Classify shapes by color (P-G.4)

  • PK.4.1.4.b Spontaneously count for own purposes.

    • Count pictures - up to 3 (P-A.3)
    • Count dots - up to 3 (P-A.4)
    • Count shapes - up to 3 (P-A.5)
    • Represent numbers with pictures - up to 3 (P-A.9)
    • Count pictures - up to 5 (P-B.3)
    • Count dots - up to 5 (P-B.4)
    • Count shapes in rows - up to 5 (P-B.5)
    • Represent numbers with pictures - up to 5 (P-B.12)
    • Count pictures - up to 10 (P-C.3)
    • Count dots - up to 10 (P-C.4)
    • Count shapes in rows - up to 10 (P-C.5)
    • Represent numbers - up to 10 (P-C.13)
    • Count pictures - up to 20 (P-D.2)
    • Count dots - up to 20 (P-D.3)
    • Count shapes - up to 20 (P-D.4)
    • Represent numbers - up to 20 (P-D.7)

  • PK.4.1.4.c Recognize a number of objects (up to four) without counting.

    • Represent numbers with pictures - up to 3 (P-A.9)
    • Represent numbers with pictures - up to 5 (P-B.12)

• 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!").

    • Add with pictures - sums up to 5 (K-J.6)
    • Addition sentences up to 5 - which model matches? (K-J.7)
    • Add with pictures - sums up to 10 (K-K.8)
    • Addition sentences up to 10 - which model matches? (K-K.9)

  • PK.4.1.5.b Separating ("I have four carrot sticks. I'm eating one! Now I have 3!").

    • Subtract with pictures - numbers up to 5 (K-L.3)
    • Subtraction sentences up to 5 - which model matches? (K-L.4)
    • Subtract with pictures - numbers up to 10 (K-M.3)
    • Subtraction sentences up to 10 - which model matches? (K-M.4)

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).

  • Inside and outside (P-F.1)
  • Left and right (P-F.2)
  • Left, middle, and right (P-F.3)
  • Top and bottom (P-F.4)
  • Above and below (P-F.6)

• PK.4.2.2 Explore and talk about basic shapes in the environment (e.g., circle, square, triangle).

  • Squares (P-K.4)
  • Circles, squares, and triangles (P-K.6)

• PK.4.2.3 Explore three-dimensional shapes by building with blocks and other materials.

  • Name the solid shape (P-L.2)

• PK.4.2.4 Explore connections between two- and three-dimensional forms (e.g., sphere and circle).

  • Identify shapes traced from solids (K-X.8)

• PK.4.2.5 Identify symmetry during play (e.g., building with blocks).

  • Introduction to symmetry (K-W.15)
  • Identify pictures with symmetry (K-W.16)

• 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.

  • Long and short (P-I.1)
  • Tall and short (P-I.2)
  • Wide and narrow (P-I.3)
  • Light and heavy (P-I.4)
  • Holds more or less (P-I.5)
  • Compare size, weight, and capacity (P-I.6)

• PK.4.2.8 Compare and order objects according to measurable attributes (e.g., length, weight).

  • Long and short (P-I.1)
  • Tall and short (P-I.2)
  • Wide and narrow (P-I.3)
  • Light and heavy (P-I.4)
  • Holds more or less (P-I.5)
  • Compare size, weight, and capacity (P-I.6)

• PK.4.2.9 Demonstrate understanding of basic temporal relations (e.g., the sequence of the daily routine).

  • A.M. or P.M. (K-Q.5)
  • Times of everyday events (K-Q.6)
  • Seasons (K-Q.7)

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

• PK.4.3.1 Describe patterns in the environment.

  • Shape patterns (K-I.3)

• PK.4.3.2 Represent patterns in a variety of ways.

  • Shape patterns (K-I.3)
  • Complete a pattern (K-I.5)
  • Find the next row in a growing pattern (K-I.8)

• PK.4.3.3 Begin to represent data in pictures and drawings.

  • Which picture graph is correct? (K-S.1)

• PK.4.3.4 Show awareness of the attributes of objects through sorting, ordering, and classifying.

  • Different (P-G.1)
  • Same (P-G.2)
  • Same and different (P-G.3)
  • Classify shapes by color (P-G.4)
  • Long and short (P-I.1)
  • Tall and short (P-I.2)
  • Wide and narrow (P-I.3)
  • Light and heavy (P-I.4)
  • Holds more or less (P-I.5)
  • Compare size, weight, and capacity (P-I.6)

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.

  • More (P-E.1)
  • Fewer and more - compare by counting (P-E.4)
  • Fewer and more - compare in a mixed group (P-E.5)
  • Different (P-G.1)
  • Same (P-G.2)
  • Same and different (P-G.3)
  • Classify shapes by color (P-G.4)
  • Count pennies (P-J.4)
  • Add with pictures - sums up to 5 (K-J.6)
  • Addition sentences up to 5 - which model matches? (K-J.7)
  • Add with pictures - sums up to 10 (K-K.8)
  • Addition sentences up to 10 - which model matches? (K-K.9)
  • Subtract with pictures - numbers up to 5 (K-L.3)
  • Subtraction sentences up to 5 - which model matches? (K-L.4)
  • Subtract with pictures - numbers up to 10 (K-M.3)
  • Subtraction sentences up to 10 - which model matches? (K-M.4)

• PK.4.4.2 Solve problems that arise in mathematics and in other contexts.

  • More (P-E.1)
  • Fewer and more - compare by counting (P-E.4)
  • Fewer and more - compare in a mixed group (P-E.5)
  • Inside and outside (P-F.1)
  • Left and right (P-F.2)
  • Left, middle, and right (P-F.3)
  • Top and bottom (P-F.4)
  • Above and below (P-F.6)
  • Different (P-G.1)
  • Same (P-G.2)
  • Same and different (P-G.3)
  • Classify shapes by color (P-G.4)

• 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.

  • Long and short (P-I.1)
  • Tall and short (P-I.2)
  • Wide and narrow (P-I.3)
  • Light and heavy (P-I.4)
  • Holds more or less (P-I.5)
  • Compare size, weight, and capacity (P-I.6)
  • Pennies and nickels (P-J.1)
  • Dimes and quarters (P-J.2)
  • Pennies, nickels, dimes, and quarters (P-J.3)
  • Count pennies (P-J.4)
  • A.M. or P.M. (K-Q.5)
  • Times of everyday events (K-Q.6)
  • Seasons (K-Q.7)

• PK.4.4.5 Use technology to reinforce concrete mathematical information (e.g., to explore patterns and shapes).