Paragon Prep Mathematics

  by Paragon Math  teachers:  Marilyn McArthur, Mark Hathaway and Bob Cash

  Mathematics at Paragon Prep is designed to be a rigorous, college-preparatory curriculum.  It is assumed that entering students are functioning on or above their grade levels.  The goal of the curriculum is to prepare all Paragon students to be successful in Calculus track high school programs.  This allows Paragon students to have many choices in their high school math courses, as well be prepared for college.

The 5th grade program is designed to help students fine-tune skills on basic operations of arithmetic while further developing algebraic thinking.  Problem solving is stressed to aid students’ development of critical thinking skills. 

  Entering 5th graders should posses the following skills:

bulletBasic facts – students should have committed to quick memory of addition, subtraction, multiplication and division (through 12’s)
bulletStudents should be able to relate and use inverse operations  (check addition with subtraction; multiplication with division).
bulletAddition, subtraction and multiplication operations through 3 digits by 3 digits.
bulletPlace value understanding of whole numbers and decimals through hundredths.
bulletComparisons of numbers (whole numbers, decimals and fractions) by > and <.
bulletChecking reasonableness of solutions by estimation.
bulletRounding to a given place value of whole numbers.
bulletFractions –
bulletConcepts
bulletRecognize equivalent fractions
bulletSimplify fractions to lowest terms
bulletAdd and subtract fractions with like denominators.
bulletAdd and subtract decimals to hundredths place.
bulletGeometry
bulletName basic shapes
bulletFind perimeter of figures
bulletFind area of squares and rectangles.
bulletMeasurement – use rulers metric and English systems.
bulletRecognize arithmetic patterns
bulletIdentify and use properties of mathematics
bulletCommutative property of addition and multiplication
bulletAssociative property of addition and multiplication.
bulletIdentity property of addition
bulletIdentity property of multiplication
bulletDistributive property
bulletBe able to find factors and multiples of numbers.
bulletBe able to construct and read graphs and charts
bulletBar graph
bulletCircle graphs
bulletTwo variable line graphs.

6th grade students study pre-algebra.  Mathematics at this level is offered in two levels of intensity, enabling students to proceed with their comfort functioning level. Entering 6th grade Pre-algebra students are expected to have a strong grasp of arithmetic skills (see 5th grade above).  Students should have quick recall of all basic math facts.  Skills that students should possess upon entering the 6th grade include:

·        All operations, addition, multiplication, subtraction and division with whole numbers, decimals, fractions and integers, including negative numbers.

bulletBe able to apply and use order of operations including grouping and exponents.
bulletPlace value demonstrated by use of expanded notation, i.e., 325.46 = (3 x 102) + (2 x 101) + (5 x 100) + (4 x 10-1) + (6 x 10-2)
bulletRounding to given place value (whole numbers & decimals)
bulletFactors and multiples 
bullet            prime factorization of numbers 
bullet            list factors and multiples of numbers
bullet            find the GCF and LCM of two or more numbers - using lists and prime factorization.
bulletWrite fractions to decimals, fractions to percents, decimals to percent, and vice-versa.
bulletBe able to recognize and use area formulas of basic geometric shapes:  rectangle, parallelogram, triangle, and circle.
bulletBe familiar with geometric terms of parallel and perpendicular.
bulletBe able to calculate the total angle measures of shapes.
bulletClassify triangles and quadrilaterals.
bulletBe able to measure with ruler and protractor.
bulletUnderstand and use angle relationships of supplementary and complementary.
bulletBe able to calculate volume of prisms.
bulletBe able to convert standard English measurements of length, weight and volume
bulletBe able to perform metric conversions.

Upon completion of the 6th grade, students at Paragon should have mastered the pre-algebra skills that will enable them to successfully begin a first year algebra course.  The study of algebra begins at the 7th grade.  Students are scheduled according to their demonstrated ability levels.  One class encompasses the complete study of Algebra I, while the other class begins the first part of Algebra I.

bulletCalculate with integers, fractions and decimals using order of operations.
bulletUnderstand the concept and use of variables.
bulletBe able to systematically solve equations using multiple steps.
bulletHave an understanding of the coordinate number plane.  Be able to locate and identify points on the plane.
bulletHave a firm understanding of the relationship of fractions, decimals and percents, and be able to convert between them.
bulletBe able to recognize and appropriately use of formulas.
bulletKnow, understand and apply the basic properties of mathematics: commutative, associative and distributive.
bulletHave been introduced to graphing lines in the plane, including: 
bulletbe able to determine the equation of line from a series of points
bulletbe able to apply the Equality Property to solve linear equations
bulletbe able to recognize and combine like terms in equations,
bulletbe able to write linear equations from word problems.

8th grade students who have successively completed Algebra I take Geometry.  The remainder of students completes the second portion of Algebra I.

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