Section 4: New Jersey Core Curriculum Standards

New Jersey Core Curriculum Standards

The Mathematics Standards consist of five statements, which describe what is essential to excellent mathematics education, and present a view of mathematics teaching and learning that integrates the processes of mathematical activity, the content of mathematics, and the learning environment in the classroom. The following standards were adopted by the New Jersey State Board of Education.

Text Box: STANDARD 4.1 (NUMBER AND NUMERICAL OPERATIONS) ALL STUDENTS WILL DEVELOP NUMBER SENSE AND WILL PERFORM STANDARD NUMERICAL OPERATIONS AND ESTIMATIONS ON ALL TYPES OF NUMBERS IN A VARIETY OF WAYS. This course will cover the following Core Curriculum Standards:

Descriptive Statement: Numbers and arithmetic operations are what most of the general public think about when they think of mathematics; and, even though other areas like geometry, algebra, and data analysis have become increasingly important in recent years, numbers and operations remain at the heart of mathematical teaching and learning. Facility with numbers, the ability to choose the appropriate types of numbers and the appropriate operations for a given situation, and the ability to perform those operations as well as to estimate their results, are all skills that are essential for modern-day life.

Number Sense

Numerical Operations

Estimation

Text Box: STANDARD 4.2 (GEOMETRY AND MEASUREMENT) ALL STUDENTS WILL DEVELOP SPATIAL SENSE AND THE ABILITY TO USE GEOMETRIC PROPERTIES, RELATIONSHIPS, AND MEASUREMENT TO MODEL, DESCRIBE AND ANALYZE PHENOMENA. Descriptive Statement: Spatial sense is an intuitive feel for shape and space. Geometry and measurement both involve describing the shapes we see all around us in art, nature, and the things we make. Spatial sense, geometric modeling, and measurement can help us to describe and interpret our physical environment and to solve problems.

Geometric Properties

Transforming Shapes

Coordinate Geometry

Units of Measurement

Measuring Geometric Objects

Text Box: STANDARD 4.3 (PATTERNS AND ALGEBRA) ALL STUDENTS WILL REPRESENT AND ANALYZE RELATIONSHIPS AMONG VARIABLE QUANTITIES AND SOLVE PROBLEMS INVOLVING PATTERNS, FUNCTIONS, AND ALGEBRAIC CONCEPTS AND PROCESSES. Descriptive Statement: Algebra is a symbolic language used to express mathematical relationships. Students need to understand how quantities are related to one another, and how algebra can be used to concisely express and analyze those relationships. Modern technology provides tools for supplementing the traditional focus on algebraic procedures, such as solving equations, with a more visual perspective, with graphs of equations displayed on a screen. Students can then focus on understanding the relationship between the equation and the graph, and on what the graph represents in a real-life situation.

Patterns

Functions and Relationships

Modeling

Procedures

Text Box: STANDARD 4.4 (DATA ANALYSIS, PROBABILITY, AND DISCRETE MATHEMATICS) ALL STUDENTS WILL DEVELOP AN UNDERSTANDING OF THE CONCEPTS AND TECHNIQUES OF DATA ANALYSIS, PROBABILITY, AND DISCRETE MATHEMATICS, AND WILL USE THEM TO MODEL SITUATIONS, SOLVE PROBLEMS, AND ANALYZE AND DRAW APPROPRIATE INFERENCES FROM DATA. Descriptive Statement: Data analysis, probability, and discrete mathematics are important interrelated areas of applied mathematics. Each provides students with powerful mathematical perspectives on everyday phenomena and with important examples of how mathematics is used in the modern world. Two important areas of discrete mathematics are addressed in this standard; a third area, iteration and recursion, is addressed in Standard 4.3 (Patterns and Algebra).

Data Analysis

Probability

Discrete Mathematics – Systematic Listing and Counting

Discrete Mathematics – Vertex-edge Graphs and Algorithms

Text Box: STANDARD 4.5 (MATHEMATICAL PROCESSES) ALL STUDENTS WILL USE MATHEMATICAL PROCESSES OF PROBLEM SOLVING, COMMUNICATION, CONNECTIONS, REASONING, REPRESENTATIONS, AND TECHNOLOGY TO SOLVE PROBLEMS AND COMMUNICATE MATHEMATICAL IDEAS. Descriptive Statement: The mathematical processes described here highlight ways of acquiring and using the content knowledge and skills delineated in the first four mathematics standards.

Problem Solving Reasoning

Communication Representations

Connections Technology

Scope and Sequence

The following components of the Core Curriculum will be introduced during the Pre-K school year.

Standard: 4.1 (Number and Numerical Operations)

A.	Number Sense
	· Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 2 pertain to these sets of numbers as well): whole numbers through hundreds; ordinals; proper fractions denominators of 2, 3, 4, 8, 10).
	· Understand that numbers have a variety of uses.
	· Compare and order whole numbers.

Standard: 4.2 (Geometry and Measurement)

A.	Geometric Properties
	· Identify and describe spatial relationships among objects in space and their relative shapes and sizes: Inside/outside, left/right, above/below, between; smaller/larger/same size, wider/narrower, longer/shorter; congruence (i.e., same size and shape).
	· Use concrete objects, drawings, and computer graphics to identify, classify, and describe standard three-dimensional and two-dimensional shapes: vertex, edge, face, side; 3D figures--cube, rectangular prism, sphere, cone, cylinder, and pyramid; 2D figures--square, rectangle, circle, triangle, relationships between three- and two-dimensional shapes (i.e., the face of a 3D shape is a 2D shape).
	· Recognize, describe, extend and create designs and patterns with geometric objects of different shapes and colors.
B.	Transforming Shapes
	· Use simple shapes to make designs, patterns, and pictures.
	· Combine and subdivide simple shapes to make other shapes.
C.	Coordinate Geometry
	· Give and follow directions for getting from one point to another on a map or grid.
D.	Units of Measurement
	· Directly compare and order objects according to measurable attributes: attributes--length, weight, capacity, time, temperature.
	· Recognize the need for a uniform unit of measure.
	· Select and use appropriate standard and non-standard units of measure and standard measurement tools to solve real-life problems: Length--inch, foot, year, centimeter, meter; Weight--pound, gram, kilogram; Capacity--pint, quart, liter; Time--second, minute, hour, day, week, month, year; Temperature--degrees Celsius, degrees Fahrenheit.
	· Estimate measures.

Standard: 4.3 (Patterns and Algebra)

A.	Patterns
	· Recognize, describe, extend, and create patterns: using concrete materials (manipulatives), pictures, rhythms, and whole numbers; descriptions using words and symbols (e.g., "add two" or "+2"); repeating patterns; whole number patterns that grow or shrink as a result of repeatedly adding or subtracting a fixed number (e.g., skip counting forward or backward).
C.	Modeling
	· Recognize and describe changes over time (e.g., temperature, height).

Standard: 4.4 (Data Analysis, Probability, and Discrete Mathematics

A.	Data Analysis
	· Collect, generate, record, and organize data in response to questions, claims, or curiosity: data collected from students' everyday experiences; data generated from change devices, such as spinners and dice.
	· Read, interpret, construct, and analyze displays of data: pictures, tally chart, pictograph, bar graph, Venn diagram; smallest to largest, most frequent (mode).
C.	Discrete Mathematics--Systematic Listing and Counting
	· Sort and classify objects according to attributes: Venn diagrams.
D.	Discrete Mathematics--Vertex-Edge Graphs and Algorithms
	· Follow simple sets of directions (e.g., from one location to another, or from a recipe).
	· Play simple two-person games (e.g., tic-tac-toe) and informally explore the idea of what the outcome should be.

Standard 4.5 (Mathematical Processes)

A.	Problem Solving
	· Learn mathematics through problem solving, inquiry, and discovery.
B.	Communication
	· Communicate mathematical thinking coherently and clearly to peers, teachers, and others, both orally and in writing.
	· Use the language of mathematics to express mathematical ideas precisely.
C.	Connections
	· Recognize recurring themes across mathematical domains (e.g., patterns in number, algebra, and geometry).
	· Recognize that mathematics is used in a variety of contexts outside of mathematics.
	· Apply mathematics in practical situations and in other disciplines.
D.	Reasoning
	· Recognize that mathematical facts, procedures, and claims must be justified.
	· Use reasoning to support their mathematical conclusions and problem solutions.
	· Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of their problem solutions.
	· Evaluate examples of mathematical reasoning and determine whether they are valid.
E.	Representations
	· Create and use representations to organize, record, and communicate mathematical ideas: concrete representations (e.g., base-ten blocks or algebra tiles); pictorial representations (e.g., diagrams, charts, or tables); symbolic representations (e.g., a formula); graphical representations (e.g., a line graph)
	· Select, apply, and translate among mathematical representations to solve problems.
	· Use representations to model and interpret physical, social, and mathematical phenomena.
F.	Technology
	· Use computer software to make and verify conjectures about geometric objects.
	· Use computer-based laboratory technology for mathematical applications in the sciences.

Curriculum Description

UNIT 1

Objectives:

After completion of this section, students will have the skills to:

1. Recognize numbers 0 to 5. (4.1)

2. Perform rote counting 1 to 5. (4.1)

3. Count 1 to 5 objects, actions, or sounds. (4.1)

4. Arrange groups of objects in one-to-one correspondence. (4.1)

5. Form groups of 0 to 5 objects. (4.1)

6. Identify and describe the similarities and differences between objects. (4.3, 4.5)

7. Locate objects using position and direction words. (4.2, 4.5)

8. Explore the purpose and use of calendars. (4.2)

9. Collect data such as age and birthday months using a graph. (4.4)

10. Identify quantity by using the sense of touch. (4.1)

11. Count backwards from 5 to 0. (4.1)

12. Recognize and understand the number zero. (4.1)

13. Understand the concept of patterns through rhymes and songs. (4.3)

14. Recognize and sort coins. (4.1)

15. Identify various shapes by exploring outdoors. (4.2)

Approximate duration: September, October

Suggested Activities:

- Use pattern blocks to make designs and become familiar with various shapes such as hexagon, square and triangle.

- Play a Hide and Seek game using words such as behind, next to, and below.

- Use a monthly calendar to learn the days of the week and months of the year.

- Use a class graph to count and tally the ages of children in the class.

- Use small snacks by eating to understand subtraction and the concept of zero.

- Make a class caterpillar number line by adding the number of the school day as a daily activity.

- Count backwards from 5 to 0 while singing the song: There Were Five Little Bears.

- Use building blocks to match the height and length of structures.

- Sort coins into muffin tins to make a “bank.”

- Make a tissue collage while comparing more and less.

- Play Simon Says while asking children to perform each action a specific number of times.

- Use a “Feely” bag or box so children can count objects without looking.

- Take a walk outdoors and explore the different shapes in nature.

- Play computer games that reinforce numbers, patterns and shapes.

UNIT II

Objectives:

After completion of this section, students will have the skills to:

1. Recognize numbers 0 to 10. (4.1)

2. Perform rote counting 1 to 10. (4.1)

3. Sort and classify objects by their attributes. (4.3)

4. Recognize and copy patterns. (4.3)

5. Recognize geometric shapes. (4.2)

6. Compare objects by size, weight, height, and length using comparison words. (4.2, 4.5)

7. Understand the concept of volume. (4.2)

8. Understand the concept of float and sink. (4.3)

Approximate Duration: November, December

Suggested Activities:

- Create shape pictures using circles and triangles.

- Play the counting game Five Hungry Frogs using plastic insects.

- Make a collage using pieces of material such as buttons, cotton balls, and paper shapes.

- Explore attribute blocks and discuss shape, color and size.

- Play a matching coin game.

- Experiment with volume using sand, water, and dried beans.

- Sort objects that sink or float using a water table.

- Use a rocker balance to compare weights using a collection of objects.

- Make pictures using a specific number of wooden craft sticks.

UNIT III

Objective:

After completing this section, students will have the skills to:

1. Count 1 to 10 objects, actions, or sounds. (4.1)

2. Form groups of 0 to 10 objects. (4.1)

3. Match correct numbers to groups of 0 to 10 objects. (4.1)

4. Compare groups of objects to determine more, less, or same/equal to. (4.1)

5. Extend patterns by showing what shape comes next. (4.3)

6. Identify and describe 2 dimensional shapes. (4.2, 4.5)

7. Understand the concept of symmetry. (4.2)

8. Understand the concept of subtraction. (4.1)

Approximate Duration: January, February

Suggested Activities:

- Use templates to draw shapes.

- Play the circle game Do the Hokey Pokey.