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MATHEMATICS
The School Department of the Diocese of Oakland has established the mathematics curriculum. As is age and developmentally appropriate, the curriculum for each grade level encompasses the following components:
· Numbers and Operations
· Measurement and Geometry
· Statistics, Data Analysis, and Probability
· Algebra, Functions, and Graphing
· Reasoning and Proof
Kindergarten
NUMBERS AND OPERATIONS
• Counting and comparing
• Estimation and rounding
• Operations with whole numbers and integers
MEASUREMENT AND GEOMETRY
• Time
• Measurement (ex. comparison of objects in length, weight, capacity)
• Geometry (ex. identify and describe common geometric objects
STATISTICS, DATA ANALYSIS, AND PROBABILITY
• Probability and statistics (ex. collect data, record results using
objects, pictures, picture graphs)
ALGEBRA, FUNCTIONS, AND GRAPHING
• Algebraic concepts (ex. introduce symbols +,-,= )
REASONING AND PROOF
• Reasoning (ex. begin to strategize which approach to use to
solve a problem)
Grade One
NUMBERS AND OPERATIONS
• Counting and comparing (ex. read, write, count, order, and compare whole numbers to 100)
• Place value
• Estimation and rounding
• Operations with whole numbers and integers (ex. add and subtract two-digit number without regrouping (sums to 99)
• Money and decimals
MEASUREMENT AND GEOMETRY
• Time
• Measurement (ex. measure objects in length, weight, and volume through direct comparison and non-standard units)
• Geometry (ex. classify plane and solid objects by common attributes)
STATISTICS, DATA ANALYSIS, AND PROBABILITY
• Probability and statistics (ex. describe, extend, and explain ways to get to the next element in a simple repeating pattern)
ALGEBRA, FUNCTIONS, AND GRAPHING
• Algebraic concepts (ex. extend more complex linear patterns by using manipulatives and drawings; verbalize rule)
REASONING AND PROOF
• Reasoning (ex. use the inverse relationship between addition and subtraction to solve problems)
Grade Two
NUMBERS AND OPERATIONS
• Counting and comparing (ex. use expanded forms to represent numbers up to 999)
• Place value (ex. recognize the place value of whole numbers through the hundreds digit)
• Estimation and rounding (ex. recognize when an estimate is reasonable in measurements to the nearest inch) operations with whole numbers and integers (ex. use repeated addition and subtraction to begin multiplying and dividing)
• Fractions (ex. use physical or visual representation to demonstrate that fractions are part of a whole)
• Money and decimals (ex. solve problems using coins and bills)
MEASUREMENT AND GEOMETRY
• Time (ex. understand relations of time such as minutes in an hour)
• Algebraic concepts (ex. extend more complex linear patterns by using manipulatives and drawings; verbalize rule)
• Measurement (measure using standard and non-standard units)
• Geometry (describe and classify common geometric objects according to the number and shape of faces, edges, and vertices)
STATISTICS, DATA ANALYSIS, AND PROBABILITY
• Probability and statistics (identify range and mode; collect numerical data and record organize, display, and interpret it in systematic ways such as bar graphs, charts)
ALGEBRA, FUNCTIONS, AND GRAPHING
• Algebraic concepts (ex. use the communicative and associative rules to simplify mental calculations and to check results; begin to work with inequalities (<,>) and equalities (=)
REASONING AND PROOF
• Reasoning (ex. set up a problem, justify procedures, check validity)
Grade Three
NUMBER AND OPERATIONS
• Counting and comparing
• Place value
• Estimation and rounding (ex. estimate area and volume of solid objects)
• Operations with whole numbers and integers (memorize multiplication and division fact 0-12)
• Fractions (add and subtract fractions using drawings or concrete objects and then go on to show equivalency of simple fractions)
• Money and decimals (ex. begin to multiply and divide money amounts in decimal notation by using whole number multipliers and divisors)
• Decimals (ex. know and understand that fractions and decimals are two different representations of the same concept)
MEASUREMENT AND GEOMETRY
• Time
• Measurement (ex. begin to estimate length, liquid volume, and weight/mass)
• Geometry (ex. identify, describe, and classify polygons and common geometric solids including those that make up more complex solid objects)
STATISTICS, DATA ANALYSIS, AND PROBABILITY
• Probability and statistics (ex. conduct simple probability experiments, recording and displaying the results using a bar graph or line plot)
ALGEBRA, FUNCTIONS, AND GRAPHING
• Algebraic concepts (ex. represent relationships of quantities in the form of mathematical expressions, equations, or inequalities; use a blank line or a box to stand for any number in simple the equations using addition, subtraction, multiplication, or division)
REASONING AND PROOF
• Reasoning (ex. solve multi-step problems; express solutions in verbal and written language)
Grade Four
NUMBERS AND OPERATIONS
• Counting and comparing (ex. read, write, count, order, and compare whole numbers to millions and decimals to hundredths)
• Place value (recognize the place value of whole numbers through the millions and decimals through the hundredths place)
• Estimation and rounding (estimate the sum or difference of whole numbers and positive decimals to two decimals)
• Operations with whole numbers and integers (explore prime and composite numbers; multiply multi-digit numbers by two digits and divide a multi-digit number by a one-digit number with a remainder)
• Fractions (ex. describe, compare, add, and subtract like fractions and mixed numbers
• Money and decimals (ex. show proficiency in all types of money problems, including finding unit cost)
• Decimals (order fractions, decimals, and mixed numbers on a number line)
MEASUREMENT AND GEOMETRY
• Time
• Measurement (ex. area of rectangle using English and metric systems; carry out unit conversions within a system of measurement)
• Geometry (ex. describe, identify, define, and make models of the building blocks of geometry [solid and plane figures, parallel and perpendicular lines, types of angles, types of triangles, types of quadrilaterals, radius and diameters of circles])
STATISTICS, DATA ANALYSIS, AND PROBABILITY
• Probability and statistics (ex. formulate survey questions, systematically collect, represent, and interpret numerical and categorical data, and clearly communicate findings)
ALGEBRA, FUNCTIONS, AND GRAPHING
• Algebraic concepts (ex. use a letter to represent an unknown number in simple equations; begin to use and interpret formulas)
REASONING AND PROOF
• Reasoning (ex. solve multi-step problems; continue to develop previously learned skills to solve more complex problems, e.g. use a variety of methods such as words, numbers, symbols, charts, graphs, tables, diagrams, and models to explain mathematical reasoning)
Grade Five
NUMBERS AND OPERATIONS
• Counting and comparing (identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers)
• Place value
• Estimation and rounding (ex. estimate, round, and manipulate very large numbers (e.g. millions) and very small numbers (e.g. thousandths)
• Operations with whole numbers and integers (ex. identify prime factors of all numbers through 50 and write numbers as a product of their prime factors; use exponential notation for factorization of positive integers and evaluate exponential expressions)
• Fractions (ex. add and subtract unlike fractions and mixed numbers; convert common fractions to decimals and percents)
• Money and decimals
• Decimals (ex. add, subtract, multiply, and divide with decimals)
• Percents (convert percents to decimals and convert percents to decimals)
MEASUREMENT AND GEOMETRY
• Time
• Measurement (ex. measure and compute the volume of solid objects using standard and metric systems)
• Geometry (ex. derive and use formulas to compute the area and perimeter of triangles, quadrilaterals, and irregular shapes, including problems that require conversion of units)
STATISTICS, DATA ANALYSIS, AND PROBABILITY
• Probability and statistics (ex. compute and compare mean, median, mode; organize and display data, selecting appropriate graphs and representations)
ALGEBRA, FUNCTIONS, AND GRAPHING
• Algebraic concepts (ex. write and evaluate simple algebraic expressions in one variable by substitution; use parentheses to indicate which operations to perform first when using simple operations)
• Graphing (ex. begin to identify and graph ordered pairs in the four quadrants of the coordinate plane)
REASONING AND PROOF
• Reasoning (ex. begin to identify the properties used to evaluate expressions (associative, commutative))
Mathematics instruction in grades six, seven, and eight is taught in levels. Results of a variety of assessments are used to place students in either the regular strand or the accelerated strand. Classes are small (12-15 students), allowing for small group work and individualized instruction as well as whole group instruction.
Grade Six
The sixth grade curriculum continues with all of the previous strands, expanding for readiness for pre-algebra. Mastery of previously learned skills is expected as is the ability to integrate and apply skills for more complex mathematical problems.
NUMBERS AND OPERATIONS
• Counting and comparing (ex. order and compare signed integers on a number line as well as decimals, fractions, and mixed numbers)
• Estimation and rounding (ex. use estimation to verify the reasonableness of a result)
• Operations with whole numbers and integers (ex. show proficiency with the four basic arithmetic operations with whole numbers and integers)
• Fractions ( show proficiency with the four basic arithmetic operations with fractions; solve problems involving ratios and proportions including using the means-extremes principle)
• Decimals (ex. show proficiency with the four basics arithmetic operations with decimals)
• Percents (ex. convert percents to fractions and decimals)
MEASUREMENT AND GEOMETRY
• Measurement (ex. compare and convert weights, capacities, geometric measures, time and temperatures within a measurement system)
• Geometry (ex. use the properties of complementary and supplementary angles and the sum of the measures of the angles of a triangle to solve problems)
STATISTICS, DATA ANALYSIS, PROBABILITY
• Probability and statistics (ex. compute range, mean, median, and mode of data sets and understand how additional date may affect these computations of measures of central tendency; understand how outliers affect these measures)
ALGEBRA, FUNCTIONS, GRAPHING
• Algebraic concepts (ex. begin to write and evaluate an algebraic expression for a given situation using up to three variables; understand that in a two-variable equation, one variable is a function of the other)
• Graphing (ex. draw the points corresponding to linear relationships on graph paper)
REASONING AND PROOF
• Reasoning (ex. justify the steps used in evaluating expressions (including the distributive property)) and begin to apply the process of solving equations (properties of equality)\
Grade Seven
Students in grade seven have a full course of pre-algebra.
Grade Eight
Eighth grade students placed in the regular strand of math complete pre-algebra and begin their study of algebra. Students placed in the accelerated strand complete a full year of algebra.
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