1 PRESCHOOL Mathematics Expectation 1 Children demonstrate ...

Preschool K-3 4-5 6-8 9-12

PRESCHOOL Mathematics Expectation 1 Children demonstrate an understanding of number and numerical operations. K-12 Standard 4.1 Strand A: Number Sense Strand B: Numerical Operations Benchmarks

Grade Specific Concepts/Skills

Student Activities/Evidence

By the end of Preschool at developmentally appropriate levels of increasing complexity and skill, all students should:

By the end of the grade level listed above, children demonstrate their level of competence in the following ways. These examples demonstrate a level of complexity appropriate for a preschooler.

The following are examples of tasks/classroom assessments that provide evidence of a student’s progress toward proficiency:

1. Demonstrate understanding of one-to-one correspondence

Match two sets of items - that go together and have the same number - that are put together as a pair by the child for his/her own reasons

Center Activities: Cups and saucers, dolls and bottles in Dramatic Play; cars in garages in Blocks; acorn tops and bottoms in Discovery, setting tables

Say one word for each item in a set.

CCDC: Logical Thinking Objective 33 GWM: Assessment Tasks in Topics 1, 2, 6, 8, 9

Demonstrate a beginning sense of equivalency in problem solving situations: “the same.” 2. Spontaneously count for own purposes and learn the counting numbers.

Compares groups recognizing “more,” “less” Recites counting words in fixed order up to 10; attempts to rote count in order to 30+ Correctly assigns a number to each item while counting five or fewer items.

3. Discriminate numbers from other symbols in the environment, and recognizes and names some numerals.

Teacher-directed labeling and counting activities

ELAS-M (projected start 2007-08, under NJDOE development) Center Activities: Cups of water into a large container, different colors for painting, snakes made of clay, blocks in a tower, children in a band. Teacher-directed labeling and counting activities

Counts each item in a set up to ten and indicates that the last number is the sum, answering the question, “How many?” Identifies numerals in the environment and distinguishes them from letters.

CCDC: Logical Thinking Objective 34 GWM: Assessment Tasks in Topics 6, 8, 9,12

Begins to read and write numbers for own purposes.

Teacher-directed model writing activities

Reads and matches numerals to quantities through 5 or so.

ELAS-M (projected start 2007-08, under NJDOE development) Center Activities: Cash register, numeral/set puzzles, counting books

CCDC: Logical Thinking Objective 34 GWM: Assessment Tasks in Topic 6, 8, 9, 12, ELAS-M (projected start 2007-08, under NJDOE development)

Reads and writes numerals and connects to quantity through 10 or so. 1

PRESCHOOL Mathematics Expectation 1 Children demonstrate an understanding of number and numerical operations. K-12 Standard 4.1 Strand A: Number Sense Strand B: Numerical Operations Benchmarks






4. Compares numbers in different contexts and estimates an approximate amount.

Begins to compare amounts of items in different Center Activities: Cutting and gluing in Art, bucket balance scale in Discovery contexts using “more”, “less,” and “the same.” Begins to compare groups of items and assigns number to describe different amounts.

Teacher-directed comparison and estimating activities GWM: Assessment Tasks in Topics 6, 8, 9, 10, 12. CCDC: Logical Thinking Objective 28 ELAS-M (projected start 2007-08, under NJDOE development)

5. Adds groups of concrete objects to another group and counts the total, or removes groups of concrete objects from a group and counts the remainder.

Understand there are more when two sets are combined, or less when some are removed.

Center Activities: sharing blocks, making snack mixtures, distributing craft items, sorting counters,

Adds one item to or removes one item from a group of less than 5 to obtain the desired number.

Teacher-Directed Activities: putting together and taking apart activities, paired with counting

Adds one item to or removes one item from a group of 5 or more to obtain the desired number.

CCDC: Logical Thinking Objective 34

GWM: Assessment Tasks in Topics

RESOURCES Department of Early Childhood Preschool Curriculum Guide and Teacher Handbook CC: Creative Curriculum for Preschool, 4th Edition: Chapter 3 - “Number Concepts,” PP.134-135, 140; Chapter 6 - “Blocks,” pp. 243-269; Chapter 8 – “Toys & Games,” pp.295-315; Chapter 12 – “Sand and Water,” pp.403-421; Chapter 14 – “Cooking,” pp.443-469. Section in all Interest Area Chapters: “What Children Learn in the ___ Area: Mathematics,” “How ___ Promotes Development: Cognitive Development,” and “Connecting with Curriculum Objectives: Cognitive Development.” CCDC: Creative Curriculum Developmental Continuum, Individual Child Profile GWM: Growing with Mathematics, PreK: Topics 1, 2, 5, 6, 8, 9, 10, and 12; Concept Book: Grandma’s Special Toy Box, Literature Big Book: The Puppets’ Party; Discussion Book: pp. 20, 21, 44, 45. Pre-K Assessment Book.

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PRESCHOOL Mathematics Expectation 2 Child demonstrates emerging knowledge of spatial concepts, measurement and geometry. K-12 Standard 4.2 Strand A: Geometric Properties Strand C: Coordinate Geometry Strand B: Transforming Shapes Strand D: Units of Measurement Benchmarks






1. Identifies basic shapes in the environment

Identifies familiar shapes that are natural parts of the environment - the clock on the wall or a penny as a circle; - the blocks placed on the rug make a rectangle; - the ball on the playground is a sphere; - the napkin as a square. Names circle, square, triangle, cube, and sphere

2. Understand and uses measurement words and some standard and non-standard measurement tools

3. Uses positional and directional words in a functional way

Uses common base tool (such as inch cube, unit block, hands, feet, cups, string) to measure quantity, length, height, weight of objects: - child find out how many unit blocks would line up on the edge of the rug. - uses measurement vocabulary such as long, short; high, low; heavy, light; big, bigger; small, medium, large Makes direct comparisons of materials in the environment in terms of size, length, weight, volume, height or area. Uses vocabulary accurately to describe direction, distance, position, and order: over outside behind off around under front in front of on through inside back bottom up down top - applies ideas about relative position, “I saw the squirrel run over the shed, then up the tree”.

Center Activities: Picture Puzzles, Pattern Blocks. Shape People Teacher Directed Shape Activities: Play-Dough Shapes, Feely Box. GWM: Topic 11 Task 1 CCDC: Logical Thinking Objective 27 ELAS-M (projected start 2007-08, under NJDOE development Center Activities: Full and Empty, Balance the Scales, Bottles: Heavy or Light. Teacher Directed Light and Heavy Activities, More or Less Activities. CCDC: Logical Thinking Objective 28 GWM: Topic 2 Task 1, Task 2, Task 3. Topic 10 Task 1, Task 2, Task 3 ELAS-M (projected start 2007-08, under NJDOE development Center Activities: Beanbag Throw, Bird Puppet, Center Clean-up Teacher Directed Positional Activities: Obstacle Course, Positional Games: “Where’s the Bear?” GWM: Topic 3 Task 1 CCDC: Logical Thinking Objective 32 ELAS-M (projected start 2007-08, under NJDOE development

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PRESCHOOL Mathematics Expectation 2 Child demonstrates emerging knowledge of spatial concepts, measurement and geometry. K-12 Standard 4.2 Strand A: Geometric Properties Strand C: Coordinate Geometry Strand B: Transforming Shapes Strand D: Units of Measurement Benchmarks






4. Makes three-dimensional constructions and models

5. Makes connections between two dimensional and three dimensional forms

Students will explore spatial relationships while:

Center Activities: Shape Sort Activities, Mystery Shapes, Shape Creatures, Sand Table: Wet Sand Shapes

- constructing sculptures of height, depth, width

Teacher Directed Play Dough Shapes

- using blocks in such a way that they enclose a space or bridge a structure.

CCDC: Logical Thinking Objective 27, Representation and Symbolic Thinking Objective 37

Uses either two or three-dimensional shape names such as cube/square, triangle/pyramid.

GWM: Topic 3 Task 3 ELAS-M (projected start 2007-08, under NJDOE development) Center Activities: Library-Shape Books, Block Building with 2-D and 3-D shapes.

Matches three-dimensional shapes; twodimensional shapes; three-dimensional shapes to two-dimensional shapes

Teacher Directed Shape Walk

Sees top of can and identifies it as a circle

ELAS-M (projected start 2007-08, under NJDOE development)

CCDC: Representation and Symbolic Thinking Objective 37

Decides which piece will fit into a puzzle space RESOURCES Department of Early Childhood Preschool Curriculum Guide and Teacher Handbook CC: The Creative Curriculum for Preschool: Chapter 3: “Geometry and Spatial Sense,” pp. 136-137, 141. Chapter 6 “Blocks,” pp.243-269. Chapter 8: “Toys and Games,” pp.295-315. Chapter 9: “Art,” pp. 317-349. Chapter 11: “Discovery,” pp. 381-401. Chapter 12: “Sand and Water,” pp. 403421. CCDC: Creative Curriculum Developmental Continuum, Individual Child Profile GWM: Growing with Mathematics Discussion Book pp. 12-13; Math Big Book: Wayne’s New Shape; Topic Booklet: Circle Time Song p. 3-15; Storybook Time p. 3-16, Picture Chat p. 3-18, Shape Sort p. 3-21, Copy Me p. 3-21, Introducing Balance Scales p. 10-11, More or Less Sand p.10-20

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PRESCHOOL Mathematics Expectation 3 Children understand patterns, relationships and classification. K-12 Standard 4.3 Strand A: Patterns Strand B: Functions and Relationships Strand C: Modeling Benchmarks



By the end of preschool at developmentally appropriate levels of increasing complexity and skill, all students should:



1. Sort objects into groups and by classifying them into subgroups by one or more attributes

2. Describes an object by characteristic it does or does not possess

Categorizes objects into broad groups; food, clothes, animals

Center Activities: “Balloon Match” GWM 1-13; “Button Sort” GWM 4-13; Feely Box

Sorts a group of objects by one attribute, then by another(color, shape, size, function, use) - in the block area, stacks blocks according to shape prior to placing on the shelf - sorts objects into groups/subgroups and can state reason

Teacher Directed Matching and Sorting Activities: “Ribbon Sort” GWM 4-12; “Sorting Patterns” GWM 7-20;

Identify object given tactile, visual or verbal clues. Notices similarities and differences. - “This button doesn’t have holes.”

ELAS-M (projected start 2007-08, under NJDOE development)

Uses comparative words related to number, size, shape, texture, weight, color, speed, volume. - “This bucket is heavier than that one.” - “Now the music is going faster.”

Teacher Directed Matching and Sorting Activities “Helping Wilbur” GWM 4-20; “Sorting Patterns” & “Finding Patterns” GWM 7-20

CCDC: Logical Thinking Objective 27 GWM: Topic 4 Task 1, Task 2

Center Activities: Matching and Sorting Activities: “Card & Super Sort” GWM 4-21

GWM: Topic 4 Task 3 CCDC: Logical Thinking Objective 28 ELAS-M (projected start 2007-08, under NJDOE development)

3. Seriate a set of four objects according to various properties including size, length, heaviness, texture or loudness

Notices when one object in a series is out of place. - removes the one measuring spoon that is out of place and tries to put it in the right place; Figures out a logical order for a group of objects. - arranges a group of rocks from smallest to largest, and largest to smallest

Center Activities: Seriate: “Lids in Lids” GWM 5-13; “Arrange the Ribbons” GWM 5-13 Teacher Directed: “Taller? Tallest? Shorter? Shortest?” GWM 5-12; “Over & Under” GWM 7-12 CCDC: Logical Thinking Objective 29 GWM: Topic 5 Task 1, Task 2, Task 3. ELAS-M (projected start 2007-08, under NJDOE development)

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PRESCHOOL Mathematics Expectation 3 Children understand patterns, relationships and classification. K-12 Standard 4.3 Strand A: Patterns Strand B: Functions and Relationships Strand C: Modeling Benchmarks






4. Identify patterns in the environment.

Notices and imitates patterns - repeats a teacher’s simple clapping pattern - “Look at the rug. It has a circle, then a number, then a letter…”

Center Activities: “Wilbur’s Fashions”

GWM 7-21; “Natural Patterns” GWM 11-22 Teacher Directed: “Finding Patterns” GWM 7-20; “Hidden Magnets” GWM 11-20 CCDC: Logical Thinking Objective 30 GWM: Topic 11 Task 2

5. Represent patterns in a variety of ways.

Extends given patterns or creates simple patterns of own design: - on computer, says, “Square, circle, square, circle” after copying the pattern on a pattern card; Creates complex patterns of own design or by copying: - stringing beads: red/green/blue/red/green/blue

Demonstrates understanding that patterns can continue indefinitely RESOURCES Department of Early Childhood Preschool Curriculum Guide and Teacher Handbook

ELAS-M (projected start 2007-08, under NJDOE development) Center Activities: “Penguin Parade” GWM 7-21; Sand table “Patterns in Sand” GWM 7-22 “Copy

the Pattern” GWM 11-21. Teacher Directed: “Pretty Patterns” GWM 11-20; CCDC: Logical Thinking Objective 30 GWM: Topic 11 Task 3 ELAS-M (projected start 2007-08, under NJDOE development)

CC: The Creative Curriculum for Preschool: Chapter 3: “Patterns and Relationships,” p. 136, 140. Chapter 6: “Blocks,” pp. 243-269. Chapter 8: “Toys and Games,” pp.295-315. Chapter 11: “Discovery,” pp. 381-401. Chapter 16: “Outdoors,” pp. 493-522. CCDC: Creative Curriculum Developmental Continuum, Individual Child Profile GWM: Growing with Mathematics Discussion Book pp.40, 41; Math Big Book The Dancing Dragons, Pretty Patterns, Topic Booklet: People and Shoe Patterns p. 7-11, Circle Time Song p. 7-15, Design Match p. 7-17, Bow Tie Patterns p. 7-19, Sorting Patterns p. 7-20, Penguin Parade p. 7-21, Picture Chat p. 11-16, Storybook Time p. 11-17, Hoop Patterns p. 11-18, Rolling a Pattern p. 11-19. 6

PRESCHOOL Mathematics Expectation 4 Children develop knowledge of sequence of events and temporal awareness. K-12 Standard 4.4 Strand A: Data Analysis Strand C: Discrete Mathematics-Systematic Listing and Counting Strand D: Discrete Mathematics-Vertex-Edge Graphs and Algorithms Benchmarks






1. Start and stop on a signal

Freezes in position when the music stops Moves to a designated place on a signal

Center Activities, Music Activities Teacher Directed Large Motor Activities GWM: Moving to Music GWM 5-5 CCDC: Logical Thinking Objective 32 ELAS-M (projected start 2007-08, under NJDOE development)

2. Describe the sequence of the daily routine and demonstrates understanding of basic temporal relations

Student uses words to describe passage of time, such as morning, shorter time, longer time. Uses past and future tenses appropriately. - “We will go outside after snack time.” Associates events with time-related concepts. - “Tomorrow is Saturday so there is no school.”

Center Activities: Day and night Picture Collages GWM 5-20; Growth Cycles GWM 5-19. Teacher Directed Sequence Cards GWM 5-20. GWM: Picture Sequence GWM 5-20; Identifying the sequence of a day’s events GWM 5-17. CCDC: Logical Thinking Objective 31 ELAS-M (projected start 2007-08, under NJDOE development)

3. Arranges pictures of events in temporal order and explains which came first, second, and third (ordinal numbers)

Student describes series of events or directions: - Child puts on smock, fills paint cup, paints pictures, hangs picture to dry - arranges 3 photos in correct order, a photo of the child eating breakfast, a photo of the child walking in the school, a photo of the child in the classroom. Child states, which came first, second, third.

Center Activities: “Trucks in Order” GWM 12-21, “Order and Check” GWM 12-21 Teacher Directed: “Ordering Numbers” GWM 1220; “Money Order” GWM 12-20 GWM: Topic 12 Task 1 CCDC: Logical Thinking Objective 31 ELAS-M (projected start 2007-08, under NJDOE development)

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PRESCHOOL Mathematics Expectation 4 Children develop knowledge of sequence of events and temporal awareness. K-12 Standard 4.4 Strand A: Data Analysis Strand C: Discrete Mathematics-Systematic Listing and Counting Strand D: Discrete Mathematics-Vertex-Edge Graphs and Algorithms Benchmarks






RESOURCES Department of Early Childhood Preschool Curriculum Guide and Teacher Handbook CC: The Creative Curriculum for Preschool: Chapter 2: “Daily Events,” pp. 82-92, “Using a Calendar,” p. 85, “The Daily Schedule,” pp.92-97; Chapter 3: “Measurement,” pp. 137-138, 141, “People and the Past,” p. 149, 151. CCDC: Creative Curriculum Developmental Continuum, Individual Child Profile GWM: Growing with Mathematics Discussion Book pp. 18-19, Topic Booklet: Circle Time Song p. 5-15, Picture Chat p. 5-17, How Things Grow p. 5-19, Picture Sequence p. 5-20, Before and After p. 5-21.

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PRESCHOOL Mathematics Expectation 5 Children use mathematical knowledge to represent, communicate and solve problems in their environment. K-12 Standard 4.5 Strand A: Problem Solving Strand C: Connections Strand E: Representations Strand B: Communication Strand D: Reasoning Strand F: Technology Benchmarks






1. Uses mathematical terms when conversing with others

2. Uses emergent mathematical knowledge as a problem-solving tool

Student engages in many individual and smallgroup conversations throughout the day (e.g., center time, lunch-time, playground, while preparing for rest time), with emphasis on mathematical terms: - “My building is taller than yours.” - “I have more sand in my bucket.”

Center Activities: Math Center “Animal Numbers” GWM 9-21; “My Vehicle Graph” GWM 9-21.

Participates in making and discussing graphs with self, real objects, or pictures to represent an activity or experience (types of shoes, preferences for lunch)

GWM: Topic 1 Task 1, Task 2, Task 3; Topic 2 Task 1, Task 2 Task 3; Topic 3 Task 1, Task 2; Topic 4 Task 3, Topic 6 Task 1; Topic 7 Task 2; Topic 10 Task 1, Task 2

Student uses mathematical knowledge as a problem-solving tool when asked open-ended questions and or asked for target information (e.g., "Tell me about what you did." "Would you use the same number again?" "What shape did you use?" "What size could you use that will make it stand up better?"). - Jorge decides to fill his bucket by using small cups of water when he realizes that he cannot fit the bucket under the faucet.

Teacher Directed: “Checking” GWM 9-20; “Toss the Cube” GWM 9-20. CCDC: Logical Thinking Objective 28 and 34 Learning and Problem Solving Objectives 23 and 26

ELAS-M (projected start 2007-08, under NJDOE development) Center Activities: Math Center “Trucks in Order” GWM 12-21; “Order and Check” GWM 12-21. Teacher Directed: “Ordering Numbers” GWM 1220; “Money Order” GWM 12-20. CCDC: Logical Thinking Objective 28 and 34 Learning and Problem Solving Objectives 23 and 26 GWM: Topic 1 Task 3; Topic 3 Task 3; Topic 6 Task 3; Topic 12 Task 4. ELAS-M (projected start 2007-08, under NJDOE development)

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PRESCHOOL Mathematics Expectation 5 Children use mathematical knowledge to represent, communicate and solve problems in their environment. K-12 Standard 4.5 Strand A: Problem Solving Strand C: Connections Strand E: Representations Strand B: Communication Strand D: Reasoning Strand F: Technology Benchmarks






3. Describes how he/she solved mathematical problems in his/her own way.

Children make connections between mathematics and other content areas and reallife situations:

Center Activities: Art Center: “Natural Patterns” GWM 11-22; “Number Collage” GWM 12-26

- “My name is longer than Sam’s because it has more letters,” - “We go on the same bus, Number 14.”

CCDC: Logical Thinking Objective 28 and 34 Learning and Problem Solving Objectives 23 and 26

Teacher Directed: “Let’s Eat!” GWM 12-12

GWM: Topic 11 Task 3 ELAS-M (projected start 2007-08, under NJDOE development)

RESOURCES Department of Early Childhood Preschool Curriculum Guide and Teacher Handbook CC: The Creative Curriculum for Preschool: Chapter 3: “Mathematics,” pp. 134-141, “Process Skills,” pp. 161-162; Chapter 6: “Blocks,” pp. 243269; Chapter 8: “Toys and Games,” pp. 295-315; Chapter 11: “Discovery,” pp. 381-401; Chapter 12: “Sand and Water,” pp. 403-421; Chapter 13: “Music and Movement,” pp. 423-441. CCDC: Creative Curriculum Developmental Continuum, Individual Child Profile GWM: Growing with Mathematics Discussion Book pp. 18-19, Math Big Book: Buster the Balloon, Topic Booklet: Storybook Time p. 5-8, Bigger or Smaller? P. 5-9, Taller or Shorter? P. 5-12, Heavy and Heavier p. 8-10, Light and Lighter p. 9-10, Size and Weight p. 10, Balance the Scales p. 1013, Bottles, Bottles p. 10-13, Circle Time Song p. 10-15, Pour Some More p. 10-16.

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