GLEN RIDGE PUBLIC SCHOOLS

Curriculum Guide

Course Title: MATHEMATICS

Subject: Mathematics

Grade Level: Kindergarten

Department/School: Mathematics/Forest and Linden Avenue Schools

Duration: Full year

Number of Credits: N/A

Prerequisite: N/A

Elective or Required: N/A

Authors: Evan M. Kozak and Jodie Schnack

Date Submitted: Summer 2007

Course Description

The Kindergarten Mathematics Program will introduce the students to the world and wonder of mathematics using hands-on discovery and learning covering a range of topics from counting and patterning to algebra and problem solving. Kindergartners will experience mathematical concepts and ideas at work during small group centers and by participating in group topical discussions and explorations.

GLEN RIDGE PUBLIC SCHOOLS

MATHEMATICS MISSION STATEMENT

Mathematics and Computer Science are an integral part of our lives. Students must be actively involved in their mathematics education with problem solving being an essential part of the curriculum. The mathematics and computer science curricula should emphasize thinking skills through a balance of computation, intuition, common sense, logic, analysis and technology. Students will be engaged and challenged in a student-centered learning environment that is developmentally appropriate. Students will communicate mathematical ideas effectively by applying hands-on manipulatives, basic computational skills, mathematical models, and technology in order to solve practical problems.

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.

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

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

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

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

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

Standard 4.1 (Number and Numerical Operations)

A. Number Sense

• Use real-life experiences, physical materials, and technology to construct meanings for numbers
• Demonstrate an understanding of whole number place value concepts.
• Understand that numbers have a variety of uses.
• Count and perform simple computations with coins: amounts up to $1.00 (using cents notation).
• Compare and order whole numbers.

B. Numerical Operations

• Develop the meanings of addition and subtraction by concretely modeling and discussing a large variety of problems: joining, separating, and comparing.
• Develop proficiency with basic addition and subtraction number facts using a variety of fact strategies (such as "counting on" and "near doubles") and then commit them to memory.
• Construct, use, and explain procedures for performing addition and subtraction calculations with: pencil-and-paper, mental math, calculator.

C. Estimation

• Judge without counting whether a set of objects has less than, more than, or the same number of objects as a reference set.
• Explore a variety of strategies for estimating both quantities (e.g., the number of marbles in a jar) and results of computation.

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).
• Describe, identify and create instances of line symmetry.

• 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).

B. Functions and Relationships

• Use concrete and pictorial models of function machines to explore the basic concept of a function.

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).

B. Probability

• Use chance devices like spinners and dice to explore concepts of probability: certain, impossible; more likely, less likely, equally likely.
• Provide probability of specific outcomes: probability of getting specific outcome when coin is tossed, when die is rolled, when spinner is spun (e.g., if spinner has five equal sectors, then probability of getting a particular sector is one out of five); when picking a marble from a bag with three red marbles and four blue marbles, the probability of getting a red marble is three out of seven.

C. Discrete Mathematics--Systematic Listing and Counting

• Sort and classify objects according to attributes: Venn diagrams.
• Generate all possibilities in simple counting situations (e.g., all outfits involving two shirts and three pants).

D. Discrete Mathematics--Vertex-Edge Graphs and Algorithms

• Follow simple sets of directions (e.g., from one location to another, or from a recipe).
• Color simple maps with a small number of colors.
• 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.
• Solve problems that arise in mathematics and in other contexts: open-ended problems; non-routine problems; problems with multiple solutions; problems that can be solved in several ways.
• Select and apply a variety of appropriate problem-solving strategies (e.g., "try a simpler problem" or "make a diagram") to solve problems.
• Pose problems of various types and levels of difficulty.
• Monitor their progress and reflect on the process of their problem solving activity.

B. Communication

• Use communication to organize and clarify mathematical thinking: reading and writing; discussion, listening, and questioning.
• Communicate mathematical thinking coherently and clearly to peers, teachers, and others, both orally and in writing.
• Analyze and evaluate the mathematical thinking and strategies of others.
• 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.
• Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards).
• Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

D. Reasoning

• Recognize that mathematical facts, procedures, and claims must be justified.
• Use reasoning to support their mathematical conclusions and problem solutions.
• Select and use various types of reasoning and methods of proof.
• Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of their problem solutions.
• Make and investigate mathematical conjectures: counterexamples as a means of disproving conjectures; verifying conjectures using informal reasoning or proofs.
• 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 calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).
• Use computer software to make and verify conjectures about geometric objects.

Curriculum Description

UNIT I:

Objectives:

After completion of this unit, students will be able to:

1. Explore measurements by comparing lengths. (4.2)

2. Use measurement comparison. (4.2)

3. Identify and describe shapes. (4.2)

4. Explore pattern blocks. (4.2)

5. Count objects, sounds, and taps. (4.1)

6. Count backwards by ones. (4.1)

7. Recognize and understand zero as a number for “none.” (4.1)

8. Represent numbers with concrete objects. (4.1)

9. Use one-to-one correspondence to count objects. (4.1)

10. Recognize and represent numbers with groups of objects. (4.1)

11. Identify attributes and find ways to sort objects using a variety of attributes. (4.2, 4.4)

12. Experiment with and compare volumes and develop awareness of relative size. (4.2)

13. Construct a bar graph and a moveable graph. (4.4)

14. Make comparisons and answer simple questions based on data from the graph. (4.4)

15. Create and extend patterns with: sounds, motions, and color. (4.2)

16. Describe patterns. (4.2)

17. Notice coin features and differences among coins. (4.1)

18. Sort coins according to various attributes. (4.2, 4.4)

19. Count numbers in sequence. (4.1)

20. Represent numbers with claps or taps. (4.1)

21. Make pictorial representation of class data. (4.4)

22. Compare heights of objects. (4.2)

23. Count up to 10 objects. (4.1)

24. Practice reading numerals through 10. (4.1, 4.5)

25. Recognize numbers as “5 and some more.” (4.1)

Approximate duration: 14 lessons, One Month (September)

Suggested Activities:

- Play the game: Give the next number.

- Read the story: Changes, Changes Pat Hutchins (Section 1-2)

- Read the story: Five Little Monkeys Jumping On the Bed Eileen Christelow (Section 1-4)

- Read the story: Emily’s First 100 Days of School Rosemary Wells (Section 1-5)

- Read the story: The Button Box Margarette S. Reid (Section 1-6)

- Read the story: The Flower Garden Even Bunting (Section 1-8)

- Read the story: Where’s My Teddy? Jez Alborough (Section 1-13)

UNIT II:

Objectives:

After completion of this unit, students will be able to:

1. Find and sort shapes. (4.2)

2. Identify and name shapes. (4.2)

3. Describe attributes of shapes. (4.2, 4.4)

4. Explore, recognize, and identify shapes by feel. (4.2, 4.5)

5. Describe attributes of shapes. (4.2, 4.5)

6. Use spatial vocabulary and concepts in everyday situations. (4.2, 4.5)

7. Count and move between 1 and 10 spaces on a game board. (4.1)

8. Read numbers 1-10. (4.1, 4.5)

9. Notice and describe patterns in surroundings. (4.2, 4.3)

10. Extend patterns. (4.2, 4.3)

11. Practice oral counting forward by ones. (4.1, 4.5)

12. Identify numbers. (4.1)

13. Develop stroke formation skills to prepare for writing numbers. (4.1, 4.5)

14. Compare numbers of coins. (4.1)

15. Consider the likelihood of outcomes on a toss of a money cube. (4.5)

16. Recognize and match pictures of coins with actual coins. (4.1)

17. Identify coin features and begin to use coins by name. (4.1, 4.5)

18. Count objects using one-to-one correspondence. (4.1)

19. Represent numbers with concrete materials. (4.1, 4.5)

20. Discove