May, 2008
2008
Diocesan Elementary and High School Committee
Bev Kincaid Notre Dame High School
Karen Kercher Reading Central High School
Sister Ida Reading Central High School
John Bordick Pius X High School
Cheryl Genteel Pius X High School
Lynn Sabol Nativity High School
Janice Little Bethlehem Catholic High School
Fran McGouldrick Allentown Central High School
Sr. Catherine Danielle St. Catharine of Siena Elementary
Ed Tray St. Stephen Elementary
Maureen Thorley Notre Dame of Bethlehem Elementary
Alice Miller St. Jerome Elementary
Deb DNardo Holy Family Elementary
William Kocher St. Michael the Archangel Elementary
John Gallery St. Jane Frances de Chantal Elementary
Sister Anita Patrick Gallagher, IHM Diocesan Office
Overview
The mathematics curriculum for the schools of the Diocese of Allentown has been carefully developed to reflect the Principles and Standards for School Mathematics established by the National Council of Teachers of Mathematics.
After a year of Articulation between the elementary and high school Honors Algebra teachers, an Elementary/Secondary Committee was formed to standardize the Honors Algebra I course of studies in the elementary and high schools.
It had been determined by the Elementary/Secondary Committee that there was a definite need to make the Honors Algebra I curriculum and assessment, standard in order that that the elementary schools can better instruct and prepare students for the high school math curriculum.
Care had to be taken that students being instructed in the Honors Algebra I program in the elementary school would have adequately completed all levels of mathematics prior to beginning the Honors Algebra course and that they would have adequate time to complete the program in eighth grade.
Accelerated Math Program
An officially recognized Accelerated Math program meets the following criteria:
· Students meet the criteria for admission to the program;
· The pacing of the program is in keeping with those suggested in these guidelines;
· Students are being given adequate mathematics instructional time
· Honors Algebra I is completed at the conclusion of the program and students take the standardized Honors Algebra I end-of-course test approved by the Office of Education.
· Those programs which do not meet the criteria set forth for Honors Algebra I in these guidelines are considered enrichment programs rather Honors Algebra Programs.
Criteria for Admission
General Recommendations
Third, fourth and fifth grade Math marks should be considered
Students being admitted to the Elementary Accelerated Math Program should meet the following criteria:
1. Consistent scores of 90% or above in Math Scores for the Iowa Tests in Concepts, Problem Solving and the Composite (National Percentiles used.)
2. Evidence of above average performances on Mathematics Level Mastery Tests. Students admitted from other programs/schools should be tested using back copies of the level tests. “above average performance” is interpreted as a score of 90 or above.
3. Consistent grades of 90 or above in Mathematics on the report card.
4. CoGat scores in 3rd and 5th grade in the non verbal and quantitative scores 114 or above.
5. Recommendation of Mathematics Teacher.
Continuation in the Accelerated Math Program is based on meeting the above criteria annually.
Identification of Students for Accelerated Math
Students are identified as potential candidates for Accelerated Math at the end of grade 4 or 5. The program is begun at grade 5 or 6 (depending on circumstances in the individual school) to insure that the students have had a sufficient amount of time to master the skills necessary to complete the Honors Algebra I course in the eighth grade.
CURRICULUM
The curriculum used for the Elementary Accelerated Math Program is not a separate curriculum other than that which is used for Mathematics instruction in the elementary school of the Diocese of Allentown.
The plan of the program is to provide for a vertical progression of skills following an accelerated pace as outlined elsewhere in these guidelines.
The Approved Diocesan Math Curriculum takes into consideration the recommendations made by the National Council of Teachers of Mathematics as well as the recommendations of the Department of Education of the State of Pennsylvania.
Students are taught to reason and communicate mathematically, to use concrete and technological aids in developing mathematical reasoning skills and to integrate mathematics skills with those of other curricular areas and with real life situations.
The Approved Diocesan Math Curriculum allows for flexibility, permitting the teacher to arrange the order for teaching skills at each level as it best meets the needs of the class, with the end of teaching all the math skills prescribed at each level.
The Honors Algebra I curriculum developed for use in the Elementary Accelerated Math Program is consistent with the curriculum in use in the secondary schools of the diocese. Students unable to complete a full year of Honors Algebra I at the elementary level are admitted to a course designed to meet the needs of these students.
Monitoring of the program is essential to insure that the students have followed an adequately thorough program.
Scheduling
· Two or more math classes
· Separate math personnel
· One class of each grade that is self contained
· Students are not to be expected to complete a level of Math on their own over the summer.
If you do not have an Accelerated Math Program in place and would like to establish one or if you would like to improve your accelerated math program please contact Sr. Anita for more information.
Communication
Good communication is essential to the success of the program:
· A Parent Information session should be held at the program’s inception in the school and thereafter, periodically, to increase parents’ awareness of the program specifics.
· Frequent communication between parents and teachers should be maintained throughout the program, and especially when there is a concern related to the child’s placement in the program.
· Frequent communication between teachers and administration should be maintained throughout the program.
THIS IS A SCOPE OF THE MATERIAL TAUGHT, it is not sequential
1. PROPERTIES OF EQUALITY
Closure Property
Commutative Property
Associative Property
Properties of Equality: Reflexive, Symmetric, and Transitive
Identity Properties
Inverse Properties
Multiplicative Property of Zero
Distributive property
Property of Opposites in Products
Definition of Subtraction
Definition of Division
2. REAL NUMBER SYSTEM
Definition Real Number System:
Rational Numbers, Irrational Numbers, Integers, Whole Numbers, and Natural Numbers (Counting Numbers)
Set and set notation
Operations with real numbers
Order of Operations
Evaluate Expressions
Translate Expressions into Symbols
Definition of Absolute Value
3. SOLVE SINGLE VARIABLE EQUATIONS
Transformation by: Addition, Subtraction, Multiplication, and Division
Transformation of multi – step equations and equations with variables on both sides
Linear equations and problems solving:
e.g. consecutive integers, money, age, mixture, number, angles, perimeter, area, uniform motion
Transformation of Formulas and problem solving
Absolute Value Equations
4. SOLVE SINGLE VARIABLE INEQUALITIES
Properties of order
Solve inequalities
Solve combined inequalities
Solve absolute value inequalities
Graph solution sets of inequalities
Use inequalities to solve word problems:
5. POLYNOMIALS
Classification of Polynomials (different types)
Characteristics of Polynomials (degree, decreasing and increasing order)
Law of exponents - including zero, negative exponents and scientific notation
Add and Subtract Polynomials
Multiply monomials, powers of monomials FOIL
Multiply polynomials
Divide Polynomials by monomials
Divide Polynomials by polynomials
6. FACTORING
Factor Monomials: GCF and LCM
Factor Monomials from Polynomials
Factor Special Polynomials: Difference of Two Squares, Perfect Square Trinomials, Sum and Difference of Two Cubes
Factor Quadratic Trinomials:
Factor by Grouping
Solve Polynomial Equations by Factoring (Zero product property)
7. LINEAR EQUATIONS IN TWO VARIABLES
The Coordinate Plane
Plot Points in the Coordinate Plane
Solve open sentences in two variables
Graph Linear Equations in Two variables
Use table, slope intercept, and x and y intercepts
Graph Linear Inequalities in Two variables
Determine the Slope of a Line
Given 2 points
Given the equations of a line
Given a graph
Equation of a line: given a point and a slope, given 2 points
Slope intercept form, Point slope form, standard form
Write the equation of parallel and perpendicular lines
Direct Variation
Relations and Functions
- Domain and Range
- Define by rule
- Composite function
8. RATIONAL EXPRESSIONS
Simplify Rational Expressions
Multiply and divide rational expressions
Add and subtract rational expressions (like and unlike denominators)
Simplify complex fractions
Solve fractional equations
9. RADICALS
Rational Square Roots
Irrational Square Roots
Simplify numerical square roots
Multiply square roots
10. SOLVE SYSTEMS OF LINEAR EQUATIONS (optional) by
substitution
linear combinations
graph
The high schools are responsible for testing eighth grade Honors Algebra 1 students for high school placement. The Diocese has developed and approved several standardized tests that will be used for this purpose.
“The laws of nature are but
the mathematical thoughts of God” - Euclid