# Math Curriculum Guide PK-8

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1 Math Curriculum Guide July 2013 PK-8 Archdiocese of Oklahoma City Department of Catholic Education P.O. Box Northwest Expressway Oklahoma City, Oklahoma

2 PreK through Second Grade Team/Department Outcomes for Math 1. SWBAT identify place value within SWBAT solve problems involving addition and subtraction up to SWBAT apply basic math to everyday situations. 4. SWBAT interpret charts and graphs. 5. SWBAT measure in standard units using the appropriate tools and techniques. 6. SWBAT produce two-dimensional and three-dimensional shapes based on their attributes. 7. SWBAT recognize equal groups of objects to represent multiplication. Pre-K Course Outcomes 1. SWBAT identify basic 2-D and 3-D shapes. 2. SWBAT classify objects in sets by observable attributes. 3. SWBAT describe the difference of 2 objects with measurable attributes in common. 4. SWBAT count in sequence by ones to SWBAT recognize patterns in everyday situations. 6. SWBAT identify numerals 0 to Classifying, Sorting and Patterns 2. Geometric Shapes 3. Numbers & Counting 4. Measurement 5. Writing Numerals Pre-Kindergarten Unit Concepts Pre-Kindergarten Unit Goals 1. SWBAT classify attributes of objects (size, color, shape, pattern). 2. SWBAT identify 2D and 3D shapes (circle, square, triangle, rectangle, cubes/cones, cylinders, spheres). 3. SWBAT name numerals, quantities of sets and rote count to SWBAT identify measurable attributes of objects (weight, length, height). 5. SWBAT write numerals 0 to 10.

3 Kindergarten Course Outcomes 1. SWBAT recognize place values of ones and tens. 2. SWBAT illustrate addition as putting together & adding to and subtraction as taking apart & taking from fluently to the sum of & difference of 5 through verbal explanation with prompts and manipulatives. 3. SWBAT count in sequence by ones, fives and tens to SWBAT classify numbers and objects according to common attributes. 5. SWBAT interpret various forms of information using charts and graphs with scaffolding. 6. SWBAT describe attributes of two & three-dimensional shapes including planes, faces, edges and sides. 7. SWBAT identify measurable attributes by more than one characteristic. 1. Writing Numerals 2. Classifying 3. Counting and Comparing Whole Numbers 4. Adding and Subtracting Whole Numbers 5. Place Value 6. Graphing 7. Geometry-Shapes, Patterning and Symmetry 8. Measurement Kindergarten Unit Concepts Kindergarten Unit Goals 1. SWBAT write numerals recall numbers 0-20 by writing, rote counting, recognition and one to one correspondence. 2. SWBAT classify objects into given categories; count the number of objects in each category and sort the categories into sets. 3. SWBAT compare the relationship between numbers and quantities (more or less); counting sequentially and non-sequentially and connect counting to cardinality and ordinality. 4. SWBAT describe addition as the composition and subtraction as the decomposition of numbers up to 10 using objects, drawings and word problems. 5. SWBAT recognize that numbers are composed or decomposed into ones and tens by using objects, drawings and equations up to 10 (base 10). 6. SWBAT classify information in a variety of graph formats to represent ways to organize information. 7. SWBAT describe two and three-dimensional shapes in a real-world setting. 8. SWBAT describe measurable attributes of objects, such as length or weight of a single object using standard and non-standard forms of measurement (unifix cubes and rulers).

4 1st Grade Course Outcomes 1. SWBAT identify place value to 100 with ones, tens and hundreds. 2. SWBAT add and subtract equations and word problems to 20; fluently to sum and difference of SWBAT record time to the hour and half hour using analog and digital clocks. 4. SWBAT interpret data on graphs and tally charts. 5. SWBAT measure the lengths of objects using standard and non-standard units. 6. SWBAT illustrate 2D and 3D shapes based on their attributes. 7. SWBAT compare groups of objects or numbers using symbols greater than, less than and equal to. 1st Grade Unit Concepts 1. Number Sense 2. Addition and Subtraction to Geometric Shapes 4. Place Value 5. Addition and Subtraction to Time 7. Measurement 8. Charts and Graphs 1st Grade Unit Goals 1. SWBAT write numbers to 50 in order to count and compare values. 2. SWBAT solve addition and subtraction word problems and equations to 10 using multiple strategies and manipulatives. 3. SWBAT illustrate geometric shapes according to defining attributes. 4. SWBAT illustrate that a three-digit number represents hundreds, tens, and ones. 5. SWBAT solve addition and subtraction word problems and equations to 20 using multiple strategies and manipulatives. 6. SWBAT illustrate time to the hour and half hour using analog and digital clocks. 7. SWBAT measure objects lengths using standard and non-standard tools. 8. SWBAT interpret data from tally charts and picture and bar graphs.

5 2nd Grade Course Outcomes 1. SWBAT illustrate place value using thousands, hundreds, tens and ones. 2. SWBAT solve real world one and two step addition and subtraction with regrouping and non-regrouping. 3. SWBAT interpret time from analog and digital clocks to the nearest five intervals and the value of adding and subtracting money up to a dollar. 4. SWBAT interpret a picture, bar and line graph up to four categories. 5. SWBAT measure lengths using inches, feet, centimeters, meters and yards using appropriate tools. 6. SWBAT produce shapes according to their defining attributes. 7. SWBAT construct equal groups of objects to represent multiplication. 8. SWBAT add and subtract equations fluently to 20. 2nd Grade Unit Concepts 1. Geometric Shapes 2. Place Value through Addition and Subtraction within 100 with regrouping and non. 4. Value of Money 5. Measuring time within 5 minutes 6. Represent and Interpret Data 7. Measuring Length: Standard Units 8. Fractions 9. Modeling Multiplication 2nd Grade Unit Goals 1. SWBAT produce different shapes according to their defining attributes. 2. SWBAT produce knowledge of three digit numbers using hundreds, tens and ones. 3. SWBAT add and subtract within 100 using concrete models and strategies to add and subtract with or without regrouping. 4. SWBAT find the total amount for different denominations of money - coins, bills. 5. SWBAT determine time from analog and digital clocks to the nearest 5 minutes. 6. SWBAT interpret a picture, bar and line graph up to four categories. 7. SWBAT measure lengths of objects using appropriate tools in standard units. 8. SWBAT model how to separate a figure using fraction terminology (halves, thirds etc.). 9. SWBAT create equal groups of objects using repeated addition to prepare for multiplication.

7 4 th Grade Course Outcomes 1. SWBAT represent in a variety of ways (i.e. manipulatives, pictoral, and writing) the relationships among numbers up to the millions place and decimals to the hundredths place. 2. SWBAT solve multi-digit arithmetic and word problems by applying the four operations including decimals and fractions. 3. SWBAT relate whole numbers in terms of factors and multiples, including proficiency of multiplication and division facts up to SWBAT apply rules of equivalence and ordering of fractions, decimals and mixed numbers. 5. SWBAT solve problems involving measurement and measurement conversion. 6. SWBAT organize data by using various graphic representations. 7. SWBAT describe two-dimensional figures using measurements of segments and angles. 4 th Grade Unit Concepts 1. Place Value of Whole Numbers and Decimals 2. Multiple-Digit Addition and Subtraction of Whole Numbers and Money 3. Basic Concepts of Multiplication and Division 4. Multiple-Digit Multiplication of Whole Numbers and Money 5. Multiple-Digit Division of Whole Numbers and Money 6. Fraction Concepts 7. Operations with Fractions: Addition and Subtraction with Like Denominators 8. Geometry 9. Measurement 4 th Grade Unit Goals 1. SWBAT distinguish the values and relationships of whole numbers and decimals in terms of standard, written and expanded forms and in ordering and rounding. 2. SWBAT calculate multi-digit addition and subtraction problems of whole numbers and money with regrouping including word problems. 3. SWBAT apply concepts of multiples, factors, fact families, multiplication properties, algebraic equations, arrays and models of multiplication and division facts to SWBAT solve real-world multi-digit multiplication problems with whole numbers and decimals with regrouping. 5. SWBAT solve real-world problems with whole digit quotients and remainders with up to 4-digit dividends and 1-digit divisors including word problems and money. 6. SWBAT apply concepts of equivalent fractions, simplest form, mixed numbers and improper fractions using models, notation, comparing and ordering. 7. SWBAT solve real-world addition and subtraction problems using fractions with like denominators and multiplication problems using a fraction and whole number, including word problems. 8. SWBAT classify geometric shapes based upon their properties of lines and angles. 9. SWBAT calculate word problems involving measurement and conversion of measurements involving distances, intervals of time, volume, mass and money including area and perimeter formulas for rectangles.

8 5 th Grade Course Outcomes 1. SWBAT illustrate the values of digits ranging from thousandths to millions. 2. SWBAT solve problems using addition, subtraction, multiplication and division for multi-digit whole numbers, decimals through thousandths, and fractions with like and unlike denominators. 3. SWBAT organize data using various graphic representations. 4. SWBAT apply formulas using proper units of measurement to solve problems. 5. SWBAT classify complex geometric figures based on properties. 5 th Grade Unit Concepts 1. Place Value and Adding and Subtracting Whole Numbers and Decimals 2. Multiply and Divide Whole Numbers 3. Multiply and Divide Decimals 4. Fraction Concepts 5. Add and Subtract Fractions 6. Multiply and Divide Fractions 7. Geometry 8. Geometric Measurement 9. Probability and Statistics 5 th Grade Unit Goals 1. SWBAT calculate multi-digit decimal equations using computation, rounding and estimation (millions - thousandths). 2. SWBAT solve real world multi-digit multiplication equations and divide with 2-digit divisors. 3. SWBAT solve real world multiplication and division equations with decimals to the thousandths. 4. SWBAT apply prime factorization, greatest common factors, and least common multiples to find common denominators and simplify fractions. 5. SWBAT solve real world addition and subtraction equations with fractions containing like and unlike denominators (including mixed numbers). 6. SWBAT solve real world multiplication equations with fractions and mixed numbers. 7. SWBAT classify two-dimensional figures based on attributes (angles, measurement, congruent, similar figures). 8. SWBAT calculate perimeter, area, and volume using metric units. 9. SWBAT represent and interpret tables, charts, and graphs displaying range, median, mean, and mode.

9 Sixth through Eighth Grade Team/Department Outcomes for Math 1. SWBAT manipulate rational and irrational numbers. 2. SWBAT analyze with scaffolding real world and mathematical problems using numerical and algebraic expressions, linear equations, and inequalities. 3. SWBAT model functional relationships in tables, graphs, and equations. 4. SWBAT apply proportional relationships to solve real world and mathematical problems. 5. SWBAT apply probability and statistical concepts to interpret real world and hypothetical events. 6. SWBAT apply properties of angle relationships, transformations, and geometric formulas to two and three dimensional figures. 6 th Grade Course Outcomes 1. SWBAT perform mathematical operations with decimals, fractions, percents and integers. 2. SWBAT apply the properties of ratios, rates, proportions and basic probability to solve real-world problems. 3. SWBAT solve one-step equations and inequalities using algebraic processes. 4. SWBAT solve real world and mathematical problems involving perimeter, area, surface area and volume of geometric figures. 5. SWBAT interpret data sets by applying measures of central tendency. 6 th Grade Unit Concepts 1. Operations with Decimals 2. Representing Statistical Variability 3. Characteristics of Data Sets 4. Operations with Fractions 5. Algebraic Expressions 6. One Step Equations and Inequalities 7. Ratios, Unit Rates, Percentages and Proportions 8. Geometry: Area, Surface Area, Volume, and Perimeter 9. Understanding Integers 6 th Grade Unit Goals 1. SWBAT perform operations with decimals. 2. SWBAT create a display of statistical data in appropriate format in order to draw conclusions. 3. SWBAT calculate measures of central tendency and variation. 4. SWBAT perform operations with fractions. 5. SWBAT apply properties of operations to write and simplify algebraic expressions. 6. SWBAT solve one variable equations and inequalities using algebraic processes. 7. SWBAT apply ratio concepts to solve real-world and mathematical problems. 8. SWBAT solve real-world and mathematical problems involving perimeter, area, surface area, and volume (2-D: square, rectangle, triangle & parallelogram; 3-D: cube & rectangular prism). 9. SWBAT perform basic operations using integers (number line, coordinate plane).

10 7 th Grade Course Outcomes 1. SWBAT perform mathematical operations with rational numbers. 2. SWBAT solve multi-step, real-life, mathematical problems using numerical and algebraic expressions and equations. 3. SWBAT apply proportional reasoning to solve multi-step problems involving rates, ratios, percents and dimensional analysis. 4. SWBAT analyze statistical data to create and interpret appropriate representation. 5. SWBAT solve real-problems involving angle measure, area, surface area, and volume for regular and composite figures. 6. SWBAT apply the principles of probability to real world and hypothetical populations. 1. Integer Operations 2. Rational Numbers 3. Expressions and Equations 4. One and Two Step Inequalities with Graphing 5. Ratios and Proportions and Percents 6. Two Dimensional Shapes 7. Three Dimensional Shapes 8. Probability 9. Displaying and Analyzing Data 7 th Grade Unit Concepts 7 th Grade Unit Goals 1. SWBAT apply all operations using integers. 2. SWBAT apply all operations and properties to problems using rational numbers. 3. SWBAT solve real-world and mathematical problems using numerical and algebraic expressions and equations. 4. SWBAT solve inequalities and graph the results on a number line. 5. SWBAT analyze real world and mathematical problems using ratios, rates and proportions. 6. SWBAT solve real world and mathematical problems involving angles, area, perimeter, and circumference of two-dimensional figures (regular & complex). 7. SWBAT solve real world and mathematical problems involving surface area and volume of threedimensional figures (prisms, cones, spheres). 8. SWBAT apply the principles of probability to real-world applications. 9. SWBAT apply information to create and to interpret complex graphs and charts.

11 7 th /8 th Pre-Algebra Course Outcomes 1. SWBAT compare and contrast rational and irrational numbers in different representations. 2. SWBAT apply operations to real world scenarios using rational numbers. 3. SWBAT solve multi-step equations and inequalities with one variable. 4. SWBAT analyze linear equations and inequalities. 5. SWBAT apply transformations, relationships and geometric formulas to two and three-dimensional figures. 6. SWBAT interpret by modeling the correlations of two variable sets of data. 7 th /8 th Pre-Algebra Unit Concepts 1. Rational/Irrational Numbers 2. One, two, multi-step Equations & Inequalities with Integers 3. Fractions, Decimals, Percents (including equations) 4. Linear Equations & Inequalities (including graphing systems of equations) 5. Applications of Linear Equations & Inequalities 6. Data Interpretation (scatter plots, relationships b/w two sets of data) 7. Transformations 8. Formulas 7 th /8 th Pre-Algebra Unit Goals 1. SWBAT organize rational and irrational numbers in different representations. 2. SWBAT solve multi-step equations and inequalities with integers. 3. SWBAT manipulate fractions, decimals, and percents, including equations of each. 4. SWBAT graph linear equations and inequalities. 5. SWBAT generate linear equations, inequalities and graphs of real world problems. 6. SWBAT interpret by modeling the correlations between two variable sets of data. 7. SWBAT apply principles of congruence and similarity to transformations and transversals, using models and geometry software, if available. 8. SWBAT apply appropriate formulas and tools to calculate perimeter, area of 2-D figures, surface area and volume of 3-D figures, and to apply the Pythagorean Theorem.

12 8 th Algebra Course Outcomes 1. SWBAT apply operations on integers, rational and irrational numbers. 2. SWBAT model real-world problems using equations, inequalities, and system of equations. 3. SWBAT apply basic operations to exponents and rational exponents. 4. SWBAT analyze polynomials by graphing and solving equations containing polynomials. 5. SWBAT interpret functions, including evaluating and building functions that model a given scenario. 6. SWBAT analyze varieties of expressions and functions through simplifying and solving. 8 th Algebra Unit Concepts 1. Real Numbers: Language, Operations, and Properties 2. Functions/Linear Equations and Inequalities 3. Graphing Linear Equations and Inequalities 4. Systems of Linear Equations and Inequalities 5. Exponents and Polynomials (Basic Operations) 6. Factoring Polynomials 7. Rational Expressions and Equations 8. Radicals and Rational Exponents 9. Solving Quadratic Equations 8 th Algebra Unit Goals 1. SWBAT apply appropriate mathematical language, algebraic properties, and order of operations to simplify and evaluate expressions. 2. SWBAT analyze conceptually and mathematically the general characteristics of functions and their applications to linear equations and inequalities. 3. SWBAT graphically model linear equations. 4. SWBAT solve systems of linear equations and inequalities. 5. SWBAT simplify expressions involving exponents and polynomials. 6. SWBAT factor polynomial expressions (with GCF, grouping, trinomials with leading ones and non-leading ones, and binomials including difference of squares, sum of cubes, and difference of cubes). 7. SWBAT apply appropriate techniques to simplify and solve rational expressions and equations. 8. SWBAT apply appropriate techniques to manipulate radicals and compute expressions with rational and negative exponents. 9. SWBAT solve quadratic equations by factoring, graphing, completing the square & applying the quadratic formula.

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