Adopted June, 2005

Introduction

The study of Mathematics is an important means of exploring the order in our world; therefore it is an integral part of Catholic education. Mathematics contributes to the development of the whole person by enriching life and providing a practical tool for successful daily living.

This mathematics curriculum has been designed for use by member schools of the Archdiocese of Atlanta. Discussion and planning for this curriculum has involved many representatives from our member schools. Groups who worked on this document represented K-2, 5-5, 6-8, pre-algebra and algebra teachers.

According to the National Council of Teachers of Mathematics (NCTM, 2000) quality mathematics programs of study have teacher—generated philosophy, standards, and benchmarks. In addition these programs have the following essential principles.

• Equity which ensures high expectations and strong support for all students
• Curriculum that is coherent, focused and well articulate
• Teaching that requires understanding what students already know and what they need to know
• Learning that actively builds new knowledge from experience, previous knowledge, and new concepts and understandings
• Assessment which supports learning important mathematics and furnishes useful information to teachers, students and parents
• Technology which enhances the mathematics taught and influences student learning.

The standards and benchmarks in this document are consistent across grade levels Kindergarten through Pre-Algebra, but differ for the specific course of Algebra I. Although the benchmarks at each grade level and for Pre-Algebra and Algebra differ, they always represent and are responsive to age-appropriate understandings of the concepts designated.

When Algebra I is taught in the eighth grade, appropriate evaluation of prospective students must be conducted to ensure that they are ready for and likely to be successful in Algebra I. Eligibility requirements for Algebra I are stated immediately prior to the standards for this course. In addition, when Algebra is taken in eighth grade, students must take a standardized end-of-course test prepared and scored by the Educational Testing Service.

Research for this curriculum was based on NTCM Standards (2000), the Quality Core Curriculum of Georgia including The Math Matters research (1999), and Content Knowledge: A Compendium of Standards and Benchmarks for K—12 Education (McRel/ASCD 1997).

Jump to Philosophy of Curriculum

Jump To Goals of Curriculum

Jump To Philosophy of Math Instruction

Jump To Grades K-2 Standards and Benchmarks

Jump To Grades 3-5 Standards and Benchmarks

Jump To Grades 6-8 Standards and Benchmarks

Jump To Algebra Standards and Benchmarks

Jump To Supplemental Resource Materials

Jump To Algebra As Accelerated Study

Philosophy of Curriculum

At the core of education which is Catholic are the beliefs and teachings of the Catholic Church. While curriculum documents can reflect these realities in written form it is the responsibility of all that minister in Catholic schools to bring them to life in themselves and in those whom they teach.

Of great importance to the curriculum are the elements of message, community, service and worship. Through an exploration of each, learners seek to acquire a deeper understanding essential for their own growth and development. Such an approach necessitates a vision of curriculum, which is non-biased and inclusive.

In order for a curriculum series to have validity, it must have the learner as its central focus. Courses which are planned should be developmentally responsive. Instruction should be engaging and cause the learner to be an active participant. Secular subject areas should be represented as well as the universal truths which are reflected by the history and tradition of the Church. In general, subject areas should acknowledge the present, study and reflect on the past, and assume a posture of openness to the future.

hen developing curriculum, the unique features of each school should be taken into consideration. In addition, all professional educators should understand that it is the curriculum, which drives the entire educational process. This document allows teachers to make implementation decisions on a local level for the improvement of educational programs.

Goals of Curriculum

1. Communicate the Gospel message.
2. Engender a sense of responsibility as members of a church community.
3. Empower learners to accept responsibility for the acquisition and use of knowledge.
4. Cultivate a desire for continuous learning through formal and informal education.
5. Engender a sense of responsibility as citizens within a democracy.
6. Empower learners to make informed choices.
7. Use independent and critical thinking.
8. Strive toward connectedness of all learning.
9. Implement instruction, which is developmentally appropriate.
10. Strive toward clear and accurate communication through the development of a variety of skills.
11. Represent all subject areas resulting in comprehensive literacy.
12. Use all available technologies to support instruction.
13. Implement effective prevention programs as early as possible for students who demonstrate learning challenges.
14. To ensure a thorough foundation of knowledge for successful transition into secondary study.

Philosophy of Mathematics Instruction

The study of the mathematics in a Catholic kindergarten through grade eight program ranges from basic skills to higher—level abstract concepts. The specific needs of individual learners vary greatly as they progress through each developmental stage, therefore, it is essential that students be active participants in their learning and that extended instruction be available for both above average and below average performance.

Developmentally appropriate and responsive standards, benchmarks, and activities drive student growth within a balanced mathematics curriculum. Each area of learning is necessarily dependent on prior knowledge, content, process, problem solving, logical reasoning, and performance standards. Authentic assessment that includes real-world applications is an essential component in every balanced program of study. In order to be successful in the college preparatory secondary school program and be eligible to meet current high school graduation requirements, students in the Catholic K—8 elementary school mathematics program should progress through a program of study that includes pre-algebra instruction.

Mathematics Standards and Benchmarks

Level I (Grades K—2)

STANDARD: Communicating mathematically

 Level I (K—2)

1. Uses the language of math to express mathematical thinking.
2. Organizes and consolidates their mathematical thinking through communication.
3. Expresses math ideas graphically, symbolically, and geometrically.

STANDARD: Number concepts, operations, computation

Level I (K—2)

1. Uses models to represent number concepts to connect number words and numerals to the quantities they represent.
2. Applies the concepts of whole numbers by counting with understanding and recognizing the value of sets.
3. Communicates basic numbers with understanding of ordinal and cardinal numbers and their relationship to one another.
4. Understands that a unit can be divided equally into parts.
5. Understands that a unit can be divided equally into parts.
6. Understands and communicates meanings of the operation of whole numbers and knows the language of basic operations.
7. Uses reasonable estimation.
8. Develops fluency with basic number combinations for addition and subtraction and with an introduction to multiplication.

STANDARD: Problem solving

Level I (K—2)

1. Communicates and shows understanding of problem solving processes.
2. Creates and resolves problems that arise in mathematics and in other contexts.
3. Uses concrete models and symbols to represent a problem and its solution.
4. Uses information from pictures, graphs, and charts to solve problems.
5. Identifies too little or too much information in a problem.

STANDARD: Algebra

Level I (K—2)

1. Sorts, classifies, and orders objects and numbers by similar properties.
2. Recognizes, creates, describes, and extends simple patterns in a variety of contexts.
3. Identifies a variable as a letter or symbol that stands for one or more numbers and is able to solve for the numbers.
4. Understands and applies basic principles and properties of operations, using specific numbers.

STANDARD: Measurement

Level I (K—2)

1. Uses appropriate tools to measure weight, height, temperature, length, width, volume, perimeter, and area in non-standard, standard, and metric systems
2. Tells time using analog and digital clocks.
3. Solves problems with time.
4. Identifies various forms of currency.
5. Counts money.
6. Solves problems with money.

STANDARD: Geometry

Level I (K—2)

1. Identifies and names both 2-dimensional and 3-dimensional shapes.
2. Recognizes and compares planes/faces, corners/vertices, angles, and sides, edges of geometric shapes.
3. Uses simple coordinate geometry.
4. Develops a variety of skills that relate to direction, distance, and position in space.
5. Recognizes and creates symmetrical and congruent shapes.

STANDARD: Statistics, probability, data analysis

 Level I (K—2)

1. Observes, sorts, and classifies objects and/or events.
2. Collects information about objects and/or events.
3. Organizes and displays results using concrete objects, pictures, and graphs.
4. Interprets the information presented on a graph.
5. Applies basic concepts of probability.

Level 2 (Grades 3-5)

STANDARD: Communicating mathematically

 Level II (3—5)

1. Develops an age appropriate oral and written mathematical vocabulary.
2. Utilizes mathematical vocabulary to express mathematical processes and principles.

STANDARD: Number concepts, operations, computation

Level II (3—5)

1. Recognizes and uses place value in numbers from ten-thousandths to billions.
2. Recognizes and applies inverse operations (addition/subtraction and multiplication/division).
3. Expresses numbers in a variety of forms (standard, expanded and word).
4. Estimates and computes using rounding and compatible numbers.
5. Recalls basic facts accurately.
6. Adds, subtracts, multiplies and divides whole numbers, fractions, decimals and integers accurately.
7. Compares and orders fractions, decimals integers and percents.
8. Converts between fractions, decimals integers and percents.
9. Identifies and applies the properties of operations (distributive, commutative, associative and identity properties).

STANDARD: Problem solving

Level II (3—5)

1. Selects and uses appropriate strategies to solve problems.
2. Identifies relevant information in a problem.
3. Chooses the correct operation to solve a problem.
4. Uses estimation to determine if an answer is reasonable.

STANDARD: Algebra

Level II (3—5)

1. Understands the concept of a variable.
2. Utilizes the order or operations and applies inverse operations to solve for the unknown.
3. Recognizes and extends number patterns in a variety of contexts.
4. Understands the concept of equality in an equation.

STANDARD: Measurement

Level II (3—5)

1. Selects and utilizes an appropriate tool and identifies the appropriate unit to measure time, distance, capacity, money and temperature.
2. Utilizes both metric and customary systems of measurement and converts units within each system.
3. Uses appropriate strategies to estimate measurements.
4. Understands and applies formulas for finding measures of perimeter, area, and volume.

STANDARD: Geometry

Level II (3—5)

1. Selects and uses the appropriate tools for geometric measurement.
2. Recognizes lines, rays, segments, and angles as components of plane geometry.
3. Identifies two and there dimensional figures and their component parts.
4. Calculates area, perimeter, and volume of two and three dimensional objects.
5. Interprets spatial relationships and their variations (symmetry, transformations, flips, rotations, inversions, patterns, tessellations, similarity and congruency).

STANDARD: Statistics, probability, data analysis

 Level II (3—5)

1. Gathers, records, and interprets data in chart/graph forms including tables, lines, circles and bars.
2. Interprets data as presented in various forms, intervals and scales.
3. Calculates mean, median, mode and range of a data set.
4. Plots ordered pairs.
5. Uses a variety of manipulatives to test probability.
6. Determines and expresses probability using mathematical models.

Level III (Grades 6-8)

STANDARD: Communicating mathematically

 Level III (6—8)

1. Uses the language of mathematical ideas precisely in both oral and written form.
2. Analyzes and evaluates mathematical thinking and strategies.
3. Predicts outcomes of real-world situations using various methods.

STANDARD: Number concepts, operations, computation

Level III (6—8)

1. Represents and understand the relationship among fractions, decimals, percents, ratios and proportions.
2. Represents and understands the relationship among exponential (including roots), scientific and calculator notations.
3. Represents and understands the relationship among factors, multiples and prime and composite numbers.
4. Represent and understand integers.
5. Selects and uses appropriate estimation techniques.
6. Computes accurately with all sets of numbers.
7. Performs the correct order of operations with mathematical expressions.
8. Selects and uses appropriate computational methods for a given situation.

STANDARD: Problem solving

Level III (6—8)

1. Applies and adapts a variety of strategies to understand problem-solving situations and processes.
2. Understands and uses inductive, deductive, and logical reasoning.
3. Determines whether solutions are reasonable and appropriate.

 STANDARD: Algebra

Level III (6—8)

1. Develops a conceptual understanding of different algebraic symbols.
2. Identifies and applies algebraic properties with rational numbers.
3. Recognizes and simplifies algebraic expressions.
4. Uses the concept of equality and balance to solve equations and inequalities.
5. Represents, analyzes, and generalizes a variety of patterns, sequences and functions.
6. Uses the coordinate plane to graph ordered pairs, lines, and functions.

STANDARD: Measurement

Level III (6—8)

1. Understands the customary and metric systems of measurement.
2. Selects and uses appropriate units and tools to measure accurately.
3. Understands relationships among units and converts from one unit to another within the same system.
4. Understands the basic concept of rate as a measure.

 STANDARD: Geometry

Level III (6—8)

1. Identifies and defines the properties of two and three dimensional figures.
2. Uses tools to perform basic constructions, draw geometric figures and create transformations and tessellations.
3. Understands the mathematical concepts of similarity, congruency and the Pythagorean relationship.
4. Use formulas to find perimeter, area, circumference, volume and surface area.

STANDARD: Statistics, probability, data analysis

 Level III (6—8)

1. Addresses and solves problems by collecting, organizing and displaying data.
2. Computes and uses measures of central tendency and spread.
3. Analyzes and interprets data displayed in various formats.
4. Explores probability using simulations or experiments.
5. Understands and computes both the experimental and theoretical representations of probability.

Algebra I -- A Course of Study Standards and Benchmarks

For many students Algebra I is considered the beginning course in the high school college preparatory sequence for mathematics. As a gateway course, Algebra I provides students with the tools to deal with quantitative aspects of their environment.

When Algebra I is taught in the eighth grade, appropriate evaluation of prospective students must be conducted to ensure that these students are ready for and likely to be successful in Algebra I. The purpose of such acceleration is to allow capable students to experience more complex mathematics in high school, as all students in the member schools of the Archdiocese of Atlanta will take four courses of mathematics in grades 9-12.

The same content standards must be used to guide Algebra I as a course of study no matter in which grade students take this course. In addition, Archdiocesan minimum standards for placement must be demonstrated for each student engaged in the Algebra program. This does not preclude providing students in middle grades mathematics the opportunity to explore algebraic topics and content in a variety of pre-algebra contexts.

STANDARD: Arithmetic operations and simplify expressions

1. Apply the laws of exponents to evaluate expressions.
2. Rewrite numbers into scientific notation from decimal form and vice versa.
3. Compute percents and have a basic understanding of the relationship to everyday mathematics.
4. Compute ratios, proportions and have a basic understanding of their relationship to trigonometry.
5. Apply the order of operations to simplify numerical expressions.
6. Evaluate absolute value expression.
7. Identify subsets of real numbers, such as natural numbers, whole numbers, integers, rational and irrational numbers.

STANDARD: Algebraic operations and simplify expressions

1. Apply the distributive property and combine like terms.
2. Simplify radical expressions including rationalizing a denominator.
3. Factor polynomials.
4. Evaluate scientific notation expressions using the laws of exponents.
5. Add, subtract, multiply, and divide rational expressions.

STANDARD: Solutions of equations and inequalities

1. Solve one and two step linear equations and linear inequalities.
2. implify, and then solve linear equations and linear inequalities.
3. Solve linear equations and linear inequalities with variable on both sides of the mathematical symbol.
4. Solve systems of linear equations in two variables.
5. Write and solve linear equations and linear inequalities expressed as a word problem.
6. Solve absolute value equations and inequalities.
7. Solve polynomial equations using the zero product property and quadratic formula.
8. Solve radical equations.

STANDARD: Equations and inequalities on a coordinate plane

1. Identify the parts of a coordinate plane.
2. Graph ordered pairs in the form of scatter plots, determine line of best fit and derive equation.
3. Graph linear equations and inequalities using two points, the x and y—intercepts, table of values, and slope and y—intercept.
4. Find the slope of a line algebraically and graphically.
5. Find the distance and midpoint of two points and the area to apply the Pythagorean Theorem.
6. Identify, graph and solve linear, quadratic, exponential and absolute value equations and inequalities.
7. Write the equation of a line given the slope and y—intercept, two points, the x and y—intercepts and the slope and one point.

STANDARD: Fundamentals of relations and functions

1. Identify a relation as a function.
2. Determine the domain and range of a function.
3. Evaluate a function.
4. Utilize direct and indirect variation.
5. Find the zeros of a polynomial function.

Appendices

Instructional Time Allocations for Mathematics Instruction

Archdiocese of Atlanta Policy 6130

“Schools shall provide class schedules that will most effectively serve the essential components of instruction within that school, namely the needs of the students, the school’s mission, philosophy and goals and the programs that flow from them.”

PreK – K For a 6.5 hour school day: 50 min. Math

For a 7.0 hour school day: 60 min Math

Grades 1 – 5 For a 6.5 hour school day: 60 min. Math For a 7.0 hour school day: 60 min. Math

Grade 6-7-8 For a 6.5 hour school day: 50 min. Math For a 7.0 hour school day: 50 min. Math

A1
Suggested Supplemental Resource Materials

Textbook selection, including supplemental resource materials, is the responsibility of the school principal. The final decision about purchasing core content materials should be made after consulting with teachers and utilizing other available resources. Standards and Benchmarks established by the Office of Catholic Schools should be followed unless there is a compelling and significant reason to deviate from those recommendations.

PreK – K

A large variety of appropriate math manipulatives are an essential component of an
appropriate pre-school mathematics program

• Mathematics tasks utilizing paper and pencil activities are not appropriate for
  pre-kindergarten students
• Use of a consumable textbook or individual worksheets is recommended for
  kindergarten students
• Math Big Book Library and display rack
• Attribute blocks and other grouping manipulatives
• Pattern blocks or tiles
• Sequencing objects
• Basic shapes sets
• Counting objects
• Sorting sets
• Beads to sort and string
• Wooden Puzzles
• Number lines
• Dominos
• Coins for counting
• Telling time materials
• Calendars
• Trade books about number concepts, counting and size, measurement, telling time and money
• Appropriate early learning software
  • Examples: Stickybear’s Numbers Deluxe PK-1
  • Bugs in a Box
  • Franklin Learns Math

A2.1

Grades 1 and 2

A large variety of appropriate math manipulatives are an essential component of an appropriate early grades mathematics program

• The use of a consumable textbook or individual worksheets is recommended.
• Trade books about number concepts, estimating, counting and size, measurement, telling time, money and geometry
• Attribute blocks and other grouping manipulatives
• Pattern blocks or tiles
• Base ten blocks
• Cuisenaire rods classroom kit
• Geoboards
• Wooden geometric solids
• Dominos
• Coins for counting
• Calendars
• Graphing mats
• Number lines
• Fraction circles
• Beginning rulers
• Spinner sets
• Dice
• Measuring spoons and cups and jars
• Thermometers
• Clocks
• Technology items accompanying selected textbook purchases
• Primary calculator
• Appropriate early learning software
  • Examples: Math Blaster ages 6-9
  • The Graph Club
  • Mighty Math Zoo Zillions

A2.2

Grades 3-5

• A textbook is required
• Workbooks are optional but recommended for reinforcement and/or enrichment
• A large variety of appropriate math manipulatives continue to be an essential component of an effective intermediate level mathematics program.
• Balance and weights
• Pattern blocks
• Geoboards, double sided
• Measuring tapes
• Rulers
• Fraction circles, squares, cubes
• Fraction activity cards
• Decimal modules
• Relational attribute blocks
• Color and number spinners
• Metric measuring spoons, cups and jars
• Base ten units, rods, flats and cubes
• Money kits
• Calendar math activities
• Cash register activity kits
• Mental math activities
• Tangrams
• · Technology items accompanying selected textbook purchases
• Explorer Calculator
• Overhead projector and appropriate teacher materials
• Appropriate intermediate level software
  • Examples: Math Blaster Ages 6-9
  • Math Blaster Ages 9-12
  • Math Munchers Deluxe
    

A2.3
Grades 6-8

• A textbook is required
• A scientific calculator is required at 6th and 7th grade level
• A graphing calculator is required for students taking Algebra I
• Compass
• Protractor
• Balances and Scales
• Graph Paper
• Solid Figures
• Spinners
• Clocks, calendars and maps for exploring time
• Technology items accompanying selected textbook purchases are essential at this level
• Overhead projector and appropriate teacher materials
• Appropriate middle grades, pre-algebra and algebra software where appropriate
  • Examples: Building Perspective
  • Math Blaster Mystery
  • Alge-Blaster Plus
  • Interactive Mathematics
  • Mathematics Toolbox

A2.4
Algebra as Accelerated Study
Adopted February, 2000

Middle school students who engage in the study of Algebra as their mathematics requirements must meet the same standards as do high school students who study algebra.

The Georgia Department of Education requires:
1. 150 hours of instruction annually
2. Curriculum based on an approved course of study

Additionally, the Office of Catholic Schools requires:
1. Secondary mathematics certification OR Middle grades certification with thirty (30) hours of college-level mathematics courses exclusive of education coursework. These credits may be at the undergraduate level.

Parents wishing their student(s) to study algebra will need to take the following into consideration when making this decision:
1. Students who meet the entrance criteria, and achieve within the appropriate range may be granted a first course exemption at whatever high school they attend whether it be public, private, or parochial.
2. Students may be asked to complete an exit exam at the completion of their elementary school coursework. *
3. Students who achieve a passing score on the exit exam (as determined by the Office of Catholic Schools) may be accelerated into the next level of study in mathematics upon admission to the high school.
4. To meet high school graduation requirements from a member school of the Archdiocese of Atlanta, each student will take four (4) courses of mathematics in high school.

· This exam will be required for at least two (2) consecutive years commencing 2000-2001 to allow for program validation. Once the Office of Catholic Schools validates each individual elementary program of study, this exam may no longer be required.

A3.1
Eligibility Requirements:

For Seventh Grade Pre-Algebra Placement:

• No grade below 80 in 6th grade math at the end of any quarter; score of 85th percentile on the Math Total and no math subtest score below 80 on the Iowa Test of Basic Skills: consistent completion of homework.
• Teacher recommendation based on ability and performance of student.
• An acceptable score on Form I, Iowa Algebra Aptitude Test (as determined by the Office of Catholic Schools)

For Eighth Grade Algebra Placement:

• Completed Pre-Algebra study with no grade below 80 at the end of any quarter, score of 85th percentile on the Math Total and no math subtest score below 80 on the Iowa Test of Basic Skills (or another measure); consistent completion of homework.
• Teacher recommendation based on ability and performance.
• An acceptable score on Form II, Iowa Algebra Aptitude test (as determined by the Office of Catholic Schools).