Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
MARLBORO CENTRAL SCHOOL DISTRICT CURRICULUM MAP _________Math 6___________________ Course Title Title or Topics Concepts (Unit (understandings) organizing idea) Purposes of numbers September Number sense in measurement Building Number Concepts October Multiplying whole & decimal numbers November Divide whole numbers, decimals December Geometry January Fraction concept and number theory adding, Subtraction __________Grade 6________________ Grade Levels Skills Major Assessments Time Frame (What students (Tests, projects, etc.) (Number of actually do) weeks) In order of importance - Tests - Homework - Projects 3-4 wks + In order of importance - Tests - Homework - Projects 3-4 wks + In order of importance - Tests - Homework - Projects 3-4 wks + Basic ideas-points, rag, segments, angles etc. angle measurement-Meaning of a degree Polygons – triangles, tiles problem solving by solving a simpler problem Circles-circumferences, area problem solve using logical reasoning Congruent & similar figures, transformations 3 dimensional figures, surface area In order of importance - Tests - Homework - Projects 3 wks + Divisibility rules - Prime & composite numbers Greatest common fracture-Least common multiples Prime factorization comparing & ordering fractions, +- fractions same & differences denominationsEstimating sums & differences Egyptian & Roman numerals-Problem solve – too little or too much information-Mixed numbers, add & subtract In order of importance - Tests - Homework - Projects 3-4 wks + First Quadrant Graphing Number patterns Problem solving-Guide Whole numbers & decimals Number sense Exponent’s & powers Multiplying with multiples of 10 Estimating products Problem solving a) choosing an operation b) using table Multiple decimals Square roots Mental math, estimates Interpret all parts of division, word problem Problem solving – write equation, choosing a strategy, order of operations Name whole & decimal numbers Plot point & ungrid Rounding whole & decimal numbers Estimate add & subtract by a) Rounding to a place b) Finding a range Problem solving using patterns, table, equations Add & subtract whole & decimal numbers Associative, commutative, distributive properties Multiple properties of 1 and 0 Standards & exponent form of a number Expanding using exposure Problem solving . reading a table Estimating using cluster method Ordering decimal numbers Planets = A.U. distances Estimate quotients 1, 2, 3 digit divisions O’s in quotient Decimal & whole numbers division Fractions as decimals Repeating decimals Ordering fractions & decimals Word problems Topics (Unit Title or organizing idea) February Concepts (understandings) See January Using measurement April Relating Geometry & measurement May Ratio, Properties, percent, and relating %, fractions, decimals to each other June Statistic, probability, In ledgers Follow book – homework assignments from book Worksheets from book & teacher made Problem of day – teacher and book generated Some hand on activity simulation Do practice tests, then tests and sometime re-tests Major Assessments (Tests, projects, etc.) Time Frame (Number of weeks) In order of importance Tests Homework Projects 2-3 wks Customary & metric units of length, are, volume – estimating & measuring with ruler-custom & metric weight & capacity, mass conversion – custom & metric problem solve Use data from table In order of importance Tests Homework Projects 3-4 wks Perimeter, circumferences, area of rectangle, squares, circles, paralleling … surface area, volume problem solve: a) Table 2) Use formula In order of importance Tests Homework Projects 3-4 wks % & decimal & fractions Find % of a number Estimations, multiple step problems, Find what % one number is of another, % > than 100% and <1% In order of importance Tests Homework Projects 3-4 wks Mean, median, mole, range, interpreting graphs, circle graphs, probability, counting, choices, making ………..,+ x divide integers, graphing in 4 quadrants. In order of importance Tests Homework Projects 2-3 wks January continued March Skills (What students actually do) MARLBORO CENTRAL SCHOOL DISTRICT CURRICULUM MAP _______Math____________________ Course Title Title or Topics Concepts (Unit (understandings) organizing idea) Large numbers with place value greater September than 1000 Number sense & whole number operations Problem solving strategies October Number sense & whole number operations Problem solving strategies November Decimal concepts & operations December Decimal concepts & operations January Measurement Metric & Customary (some) Geometry Skills (What students actually do) _________Grade 6_______________ Grade Levels Major Assessments Time Frame (Tests, projects, etc.) (Number of weeks) Standard & exponents form Read & write large numbers Compare & order large numbers Sequence large numbers Daily class problems Class disc. Individual response checks Numbers & exponents Factors, multiples Prime & composite numbers Probability Prime factorization Solve problems Least common multiple Greatest common factor Probability Section quizzes Chapter test Write about math Applicable word problems Decimals are ……whole numbers Decimal places can be rounded Decimals can be added, subtracted, multiplied, & divided Round decimals Compare & order decimals Estimate sums, differences, products quotients Daily class problems Class discussion Individual response checks In order of importance Tests Homework Projects Add, subtract, multiple, divide decimals Section quizzes Chapter test Write about math Applicable word problems Metric system Customary system Area, volume, perimeter using above units of measure Measure with metric & customary rulers Liquids & moss measurement metric & Customary Add & subtract units of measure Find area, volume, perimeter Write about math Daily class problems Applicable word problems Class discussion Individual response checks Section quizzes Chapter test Estimate Preparation for mental math Varies about 8 wks Various about 8 wks Varies about 4 wks Topics (Unit Title or organizing idea) February Concepts (understandings) Skills (What students actually do) Fractions as part of a whole Fractions can be compared, sequenced, added or subtracted only with like denominators Multiply by a fraction < 1 gives a product smaller than started Divide by a fraction < 1 gives a quotient larger than the number started with Fractions as part of a whole Fractions can be compared, sequenced, added or subtracted only with like denominators Multiply by a fraction < 1 gives a product smaller than started Divide by a fraction < 1 gives a quotient larger than the number started with Find missing number in equal fractions Reduce fractions to lowest terms Find common denominators Convert between improper fractions and mixed numbers Convert between fractions & decimals Add, subtract, multiply, divide fractions, whole numbers & mixed numbers Write about math Daily class problems Class discussions Individual response checks Section quizzes Chapter test Applicable word problems Find missing number in equal fractions Reduce fractions to lowest terms Find common denominators Convert between improper fractions and mixed numbers Convert between fractions & decimals Add, subtract, multiply, divide fractions, whole numbers & mixed numbers Write about math Daily class problems Class discussions Individual response checks Section quizzes Chapter test Applicable word problems Two quantities can be expressed as a Ratio A proportion is made of two ratios A percent is a ratio that compares to 100 Find missing numbers in equal ratios Test to see if two ratios form a Proportion Solve proportions using cross Write about math Daily class problems Class discussions Individual response checks Section quizzes Chapter test Varies about 4 wks Classify lines Names, describe angles Measure angles Classify polygons Identify quadrants Find area, volume, perimeter Write about math Daily class problems Class discussion Individual response checks Section quizzes Chapter test Varies about 4 wks Geometry Lines, segments, rays Angles’ measured in degrees Line symmetry Definition of volume, are, perimeter June Use graphs to compare numbers over time + as parts of a whole Use graphs to organize & display Information Construct bar, line, pie graphs Calculate mean, median, mode Write about math Daily class problems Class discussions Individual response checks Section quizzes Chapter test Varies about 4 wks Fraction concepts & operations March Fraction concepts & operations April Ration, proportion, percent May Graphing Major Assessments (Tests, projects, etc.) Time Frame (Number of weeks) Varies about 8 wks MARLBORO CENTRAL SCHOOL DISTRICT CURRICULUM MAP _______Math 7_______ Course Title Title or Topics (Unit organizing idea) September Order of operations Evaluating expressions Math terminology Solving 1 step & 2 step equations Problem solving October Decimals Fractions (a little bit) Problem solving Number theory November Fractions Problem solving Coordinate Geometry December Geometry Problem solving January (Measurement) Customary units Metric units Problem solving __________Grade 6__________ Concepts (understandings) Skills (What students actually do) Grade Levels Major Assessments Time Frame (Tests, projects, etc.) (Number of weeks) PEMDAS Understanding variables & solving for the variable Math language Ex.) addition, sum, plus, total…etc. Subtraction – decreased by, Difference Write expressions using variables Translate words into mathematical Sentences Write & solve equations Graded homework Classroom test Quiz . Assessment questions 3-4 wks Place value Changing decimals to fractions Changing fractions to decimals Rules for divisibility Exponents Prime & composite GCF, LCM Factor tree Use divisibility rules to find the quotient Distinguish between prime & composite Numbers Find the LCM for 2 numbers Add, subtract, multiply, divide decimals Graded homework Classroom test Assessment questions Quiz 3-4 wks Equal fractions Improper fractions, mixed numbers Comparing Estimation Adding, subtracting, multiplying, dividing fractions Plotting points, setting up y & x axis Understand basic operations with Fractions Understand fractions in real world Plot points on graph Graded homework Classroom test Assessment questions Quiz 3-4 wks Definitions (points, lines, planes, etc.) Angles (types, measurement) Triangles classification Polygons Congruent & similar Circles Quadrilaterals Corresponding parts Translations Classify & describe lines Name & describe angles Measure angles Classify triangles Classify polygon Classify quadrilaterals Graded homework Classroom test Assessment questions Quiz 3-4 wks Customary units of length, capacity, Mass Metric units length, capacity, mass Metric table Conversions Time Compare measurements of both customary & metric Using the appropriate measurement to Measure Graded homework Classroom test Assessment questions Quiz 3-4 wks Topics (Unit Title or organizing idea) February Ratio & proportions Problem solving March Percents Problem solving Measurement of shapes April Probability Problem solving May Statistics Problem solving June Negative numbers Problem solving Review Concepts (understandings) Skills (What students actually do) Major Assessments (Tests, projects, etc.) Time Frame (Number of weeks) Setting up ratios Writing ratios Setting up proportions Word problems (setting up proportion) (in order to solve) Similar figures Solving percent w/proportions) Scale drawings Find what % of one number is of another number Writing & solving proportions Tests Graded homework Assessment questions Quiz 3-4 wks Percents & decimals Percents & fractions Finding a % of a number Interest Estimation Multiple step Area & volume of figures Surface area Circumference Sample space Combinations, permutations Chance events Finding what % of one number is of another number Finding interest in real life situation Tests Graded homework Assessment questions Quiz 3-4 wks Construct experiments to determine Probabilities (use of manipulatives) Made predictions and compare results Tests Graded homework Assessment questions Quiz 3-4 wks Histograms Data collection Frequency tables Stem & leaf plots Mean, median & mode Use of mean, median & mode Read & construct displays of data using graphs Tests Graded homework Assessment questions Quiz 3-4 wks Operations with negative numbers Solving equations Number sense Using basic operations with negative Numbers Solving equations with negative numbers Tests Graded homework Assessment questions Quiz 3-4 wks MARLBORO CENTRAL SCHOOL DISTRICT CURRICULUM MAP _________Math 8 - Regular_______________ Course Title Title or Topics Concepts (Unit (understandings) organizing idea) Review whole numbers (operative) September Patterns Order of operations: whole numbers Integer Review: addition & subtraction Number line theory: = > < October Fractions (Addition & subtraction) Decimals (All operations) Rates, ratios, proportions November Problem solving December Geometry Basic Polygons – area – volume January Geometry continued Skills (What students actually do) ____________Grade 8__________ Grade Levels Major Assessments Time Frame (Tests, projects, etc.) (Number of weeks) Graded homework Classroom tests Assessments questions Take home tests Textbook exams Workbook problems 2-3 ongoing Tables Word problems Test – homework assignments Teacher supplements – dottos Sample assessment questions Drill review exercises; Cumulative reviews and practice Board and seat work Multiples/factors Primes & composite Round – estimates Ruler measurement Cost – products (%) basic Text – homework assignments Teacher supplements – dottos Sample assessment questions Drill review exercises Cumulative reviews and practice Board and seat work Graded homework Classroom tests Assessments questions Take home tests Textbook exams Workbook problems 2+ Making diagrams View diagrams Make a list (patterns) Pick out facts (table) Text – homework assignments Teacher supplements – dottos Sample assessment questions Drill review exercises Cumulative reviews and practice Board and seat work Graded homework Classroom tests Assessments questions Take home tests Textbook exams Workbook problems 2+ Name polygons – def. Properties also Basic formulas Variables usage Text – homework assignments Teacher supplements – dottos Sample assessment questions Drill review exercises Cumulative reviews and practice Board and seat work Graded homework Classroom tests Assessments questions Take home tests Textbook exams Workbook problems 3+ Volume of polyhedrons Idea of polygons Perimeter revisit Measurement (side & angles) Angle identify fractions Text – homework assignments Teacher supplements – dottos Sample assessment questions Drill review exercises Cumulative reviews and practice Board and seat work Graded homework Classroom tests Assessments questions Take home tests Textbook exams Workbook problems 2+ Topics (Unit Title or organizing idea) February Percents (+, >, < 100%) March Pythagorean: theorem April Solving Equations (one variable) Graphing (coordinate) Algebra May Probability June General Review Concepts (understandings) Skills (What students actually do) Major Assessments (Tests, projects, etc.) Time Frame (Number of weeks) Pictures – rates, ratios Revisit rates –ratios proportions % key on calculator Text – homework assignments Teacher supplements – dottos Sample assessment questions Drill review exercises Cumulative reviews and practice Board and seat work Graded homework Classroom tests Assessments questions Take home tests Textbook exams Workbook problems 3-4 + Squares (proportion) Square root (calculator) Area – Plane figure P………………… Coordinate…….. Text – homework assignments Teacher supplements – dottos Sample assessment questions Drill review exercises Cumulative reviews and practice Board and seat work Graded homework Classroom tests Assessments questions Take home tests Textbook exams Workbook problems 2+ Equations/Inequalities Balance equations ………………….. Text – homework assignments Teacher supplements – dottos Sample assessment questions Drill review exercises Cumulative reviews and practice Board and seat work Graded homework Classroom tests Assessments questions Take home tests Textbook exams Workbook problems 2-3+ Outcomes Tree design Multiply principal (counting) In dept. (dept meeting) Graded homework Classroom tests Assessments questions Take home tests Textbook exams Workbook problems Graded homework Classroom tests Assessments questions Take home tests Textbook exams Workbook problems 2+ Graded homework Classroom tests Assessments questions Take home tests Textbook exams Workbook problems Graded homework Classroom tests Assessments questions Take home tests Textbook exams Workbook problems 3+ MARLBORO CENTRAL SCHOOL DISTRICT CURRICULUM MAP _______Math 8________________ Course Title Title or Topics (Unit organizing idea) September Problem solving Patterns October Number and numeration Algebraic November Geometry December Probability January Statistics & Data Analysis Concepts (understandings) _______Grade 8____________ Grade Levels Skills Major Assessments Time Frame (What students (Tests, projects, etc.) (Number of actually do) weeks) Develop and apply strategies to solve a wide variety of problems extending to multi-step and non-routine problems 5 steps to problem solving Strategies include: . patterns, diagrams . trial and error . simpler but related problems . work backwards Problems of the week Presentation of Pow’s Test Homework Problem based learning projects 4 wks Review basic operations with whole Numbers Integers Rational numbers Patterns Functions Order of operations Using a problem solving foundation In/our tables Weekly problems of the week In/out of class assessments 1-Patterns 2-Probability & s… game of Pig 4 wks Consecutive sums Using a counter example Angle sums in polygons Types of angles Diagonals of a polygon Measuring angles with protractor Constructing regular polygons with protractor and straightedge Weekly problems of the week In/out of class assessments 1-Patterns 2-Probability & s… game of Pig 4 wks Use experimental and theoretical probability to represent and solve problems involving uncertainty Frequency histograms Game strategies Conduct/predict outcomes of Experiments Students ………… Titanic WebQuest 4 wks Combinations/permutations Probability modeling Circle graphs Sample space Tree diagrams Exponents Mean/median/mode Student …. For outcomes Excel 4 wks Topics (Unit Title or organizing idea) February Concepts (understandings) Skills (What students actually do) Major Assessments (Tests, projects, etc.) Indirect measurement Pythagorean …. Area/perimeter Square roots Locating points on coordinates grid Perpendicular/parallel links Find height of school building, flag pole Using – proportions Trig ratios Ratio/similar triangles Proportional reasoning Trig ratios (…………..) Measure the height of building/flagpole +/-/x/÷ Equations Two step equations Write variable expressions Problem solving Modeling equations Using tiles Graphing calculator to explore lines, slopes, system or equations Graphing in computer lab 2 quizzes 4 wks Graphing equations Slope intercepts Systems of equations Inequalities with one variable Inequalities with two variables Battleship using points & lines Graphing in computer lab 2 quizzes 1 unit test 4 wks Graphing Coordinate plane June Transformational geometry Symmetry Modeling transactions, rotations, dilations, reflections 1 quiz 1 project – Ana-m….. art 4 wks Geometry Measurement -direct -indirect March Measurement April Equations May Transformational Geometry Review Outside measurements Performance Assessment on indirect Measures Time Frame (Number of weeks) 6 wks 6 wks MARLBORO CENTRAL SCHOOL DISTRICT CURRICULUM MAP _________Pre-Sequential___________ Course Title Title or Topics Concepts (Unit (understandings) organizing idea) Addition September Subtraction Whole numbers Decimals October Fractions November Decimals <-> Fractions Percents December Integers Basic Algebra January Equation solving Skills (What students actually do) _______Grade 9_________ Grade Levels Major Assessments Time Frame (Tests, projects, etc.) (Number of weeks) Students can: . add, subtract, multiply, divide whole numbers . write and read whole numbers, decimal and place values . round-off whole numbers, decimal . whole numbers problem solve decimals – money problems Students can: . add, subtract, multiply, divide fractions . change mixed <-> Improper . compare using number line . find % of number . apply proportions and % . w.p. finding/using sales tax 2 tests Homeworks Worksheets Quizzes 2 3 tests Homeworks Worksheets Quizzes 4 Compare and order decimals Conversions of % <-> Decimals <-> fractions Ratios Percent of numbers Sales tax word problems Students can: . convert % -decimal –fraction . problem solve with % . find % of number . apply proportion and % . w.p. finding/using sales tax 3 tests Homeworks Worksheets Quizzes 2 Add/subtract/multiply/divide using number lines Absolute value Variables and expressions Order of operations Combining like terms Substitutions, distributive properties Students can: . add-subtract-multiply-divide INT . use number line to compare integers . use absolute value . build vocabulary . understand PEMDAS . be able to combine like terms . be able to distribute Students can: . solve one operation linear equation . solve two operation linear equation . understand balance and opposite 2 tests Homeworks Worksheets Quizzes 2 2 tests Homeworks Worksheets Quizzes 4 Multiplication Division Read & write Rounding word problems Add/subtract/multiply/divide Mix <-> Improper Compare and order fractions Word problems Single operation equation Double operation equation 2-3 2-3 2 Topics (Unit Title or organizing idea) February Equation solving II March Exponents April Writing Algebraic Expressions & Equations May Inequalities Review June Review Concepts (understandings) Skills (What students actually do) Combining like terms within equations Variables on both sides of the equation Distributive property within equation Solving Students can: . solve equation with parenthesis, variables on both sides, and combining . understand balance/opposite 2-3 tests Homeworks Worksheets Quizzes 4 Bases, exponents and powers Evaluating exponents Multiplying & dividing like bases Power to power Students can: . understand exponent and concepts . expand exponents . multiply-divide like base . multiply power to power . build vocabulary 2 tests Homeworks Worksheets Quizzes 3-4 Translating verbal phrases into mathematical expressions Translating verbal sentences into mathematical sentences Students can: . identify variables in word problems . build computation vocabulary . write expressions and equations from words 2 tests Homeworks Worksheets Quizzes 3-4 Number line Graphing solution sets to single variable inequalities Students can: . build vocabulary . use a number line to show inequalities . use rules of inequalities . find solution sets of inequality 2 tests Homework Quizzes Worksheets 2 Final exam 1-2 Review Major Assessments (Tests, projects, etc.) Time Frame (Number of weeks) 2-3 MARLBORO CENTRAL SCHOOL DISTRICT CURRICULUM MAP _________Sequential 1A______________ Course Title Title or Topics Concepts (Unit (understandings) organizing idea) September Integers Basic Algebra’s October Basic Algebra Exponents November Solving equations December Inequalities January Writing expressions and equations from words Skills (What students actually do) _______________Grade 9 – 10_________ Grade Levels Major Assessments Time Frame (Tests, projects, etc.) (Number of weeks) Add/subtract/multiply/divide Number line Absolute value Order of operations Combining like terms Distributive property Variables and substitutions Students can: . add, subtract, multiply, divide all integers . use number line . use and understand absolute value . build vocabulary . understand and use PEMDAS . use variables and substitutions . distributive and combine 2 tests Homework Quizzes Worksheets 2 Evaluating expressions Bases, exponents, powers Evaluation in exponential form Multiplying/dividing like bases Power to power Negative exponents Scientific notation Students can: . like terms . understand exponent concepts expanded notation both positive and negative exponents . multiply – divide like bases and power to power . apply uses of scientific notation . recognize the whole number vs. decimal Exponential terms . solve equations with single and multisteps . Understand the concept of balance and opposite . use checks to verify solution 3 tests Homework Quizzes Worksheets 2 3 tests Homework Quizzes Worksheets 4 Number line Graphing solution sets to single variable inequalities Solution of inequalities with graph Properties of inequalities Graphing and shading inequalities Students can: . show how number lines indicate inequalities . solve, work and graph are inequalities . understand the principles of operation within inequalities 2 tests Homework Quizzes Worksheets 2-3 Translating verbal phrases into mathematical expressions Translating verbal sentences into mathematical sentences Students can: . build vocabulary . identify variables in word problems . write expressions and equation from words . Problem solve forming equations 2 tests Homework Quizzes Worksheets 3-4 Preparation and set up Solution of one and multi-step Operations Combining like terms Variables on both sides Distributive property Word problems 2 3 Topics (Unit Title or organizing idea) February Polynomials March Polynomials April Quadratics Graphing May Graphing Probability Statistics June Ratio Proportions Percents Review Concepts (understandings) Skills (What students actually do) Major Assessments (Tests, projects, etc.) Time Frame (Number of weeks) Classify … polynomials Basic operation of polynomials Multiplying binomials FOIL Students can: . identify polynomials by classification and term . add-subtract-multiply-divide polynomial . use FOIL method for multi binomials . divide by monomial/binomial 2-3 tests Homework Quizzes Worksheet 4 Finding a common monomial factor Factoring the difference of binomial Squares Basic trinomial factoring Complete factorization Students can: . find common monomial factor . recognize and factor trinomial . recognize and factor difference of binomial sequence 2-3 tests Homework Quizzes Worksheet 4 Standard form Solution by factoring Points or coordinate plan Basic graphing, T-table X, Y intercept Slope Plotting by points Systems of equations Using graphing Mean, median, mode range Simple probability Writing & evaluating Probability using and/or Predicting outcomes Permutations combination factorial Students can: . solve quadratics by factoring and then check . find point on coordinate plane . recognize and use graph of linear equation in any method 2 tests Homework Quizzes Worksheet 1-2 Students can: . graph equation and find solution set at intersection . identify, estimate and find mean, median, mode . find simple compound probability by ratio factoring 2-3 tests Homework Quizzes Worksheet 1-2 Forming a ratio Forming a proportion Forming percents from fractions and Decimals Percent and percentage problems Students can: . problem solve using permutations and combinations . compare and describe ratio . form proportions . find % . recognize and set proportion for % problems . use decimal equivalent for % to problem solve 1 test Homework Final exam 1-2 2 3-4 1-2 MARLBORO CENTRAL SCHOOL DISTRICT CURRICULUM MAP _____Sequential Math I – Course I_________ Course Title Title or Topics Concepts (Unit (understandings) organizing idea) Set theory September Number line – coordinates/graphing Skills (What students actually do) ___________Grade 9_________ Grade Levels Major Assessments Time Frame (Tests, projects, etc.) (Number of weeks) Graphing on number line Operations involving rationals/signed Numbers Identify properties Problems of day (POD) Teacher prepared quiz (TPQ) Teacher prepared test (TPT) Homework (HW) Board presentation (BP) 1-4 5-6 2 wks 2 wks Numbers and operations Operations – signed numbers Rational numbers Order of operations Properties October Statements Rules of logic Tautologies/contradictions Converse, inverse, contra positive Evaluating algebraic expressions Basic equation solving Complete truth tables To apply order of operations rules to algebraic expressions POD PPQ TPT HW BP 1-4 2 ½ wks 5-6 1 ½ wks Equations containing parenthesis/fractions Translation process Integer problems Perimeter problems Solve equations Solve simple word problems POD PPQ TPT HW BP 1-2 1 ½ wks 3-4 1 ½ wks Word problems involving inequalities Ordered pairs, etc. Graphing – table/slope intercept Solve inequality word problems Graph linear equations POD PPQ TPT HW BP 1 1 wk 2, 3______ POD PPQ TPT HW BP 1, 2 3, 4 Logic Equation solving November Solving equations Introduction to word problems December Solving literal equations Solving inequalities Graphing systems of linear equations January Graphing continued Basic concepts of Geometry Lines parallel to axis Graphing systems of linear inequalities Points/lines/planes Distance/line segments/rays Graph “special lines” Graph inequalities Name sets of points Short Month Rest of December 1 ½ wks 1 ½ wks Regular week Topics (Unit Title or organizing idea) February Concepts (understandings) Skills (What students actually do) Major Assessments (Tests, projects, etc.) Time Frame (Number of weeks) Angle measures – special angles Parallel lines – trans……… Classification of triangles Angles of a triangle Polygons Congruent triangles Isosceles triangles Recognize various types of angles Find angles for onerous polygons POD PPQ TPT HW BP 1, 2, 3 4, 5, 6, 7 Area formulas Volume Circumference/area of circle Experiments/tree diagrams Exponents/factoring Monomial operations Polynomial operations Factoring algebraic expressions Determine area Determine volume Factor POD PPQ TPT HW BP 1, 2, 3 4 5-8 Polynomials/factoring continued Introduction to statistics Quadratic equations Word problems – quad ratio equations Charts/graphs Measures of central tendency Quartiles/percentiles Solve quadratic word problems Deal with statistics POD PPQ TPT HW BP 1 1 wk 2 1 wk 3, 4, 5 remainder of month May Simplifying radicals Operations involving radicals Complete operations with radicals POD PPQ TPT HW BP 1 wk for each entry POD PPQ TPT HW BP 2 weeks to finish topics listed – review built in also Geometry continued March Geometry continued Probability Polynomials/Factoring April Solving systems of linear equations – algebraically Rationals, irrationals June Ratio and similarity Pythagorean theorem Transformations Review Ratios Proportions Similar polygons Pythagorean triples Complete simple word problems of type Indicated Work with Pythagorean theorem Pass Regents 2 wks 2 wks 1 wk 1 wk 2 wks 2 remaining weeks – extra time if needed MARLBORO CENTRAL SCHOOL DISTRICT CURRICULUM MAP ______Sequential Math Course 1B______ Course Title Title or Topics Concepts (Unit (understandings) organizing idea) General technique for solving problems September 6. problem solving strategies Students can solve problems by: . guess & check . simpler problem . working backward . discovering pictures . drawing pictures . making lists and charts 1 test 2 quizzes Student authored problem With scenario & solution Homework Oral assessment Board problems 2 ½ wks Sets and subsets Union and intersection Identify set and subset Perform union & intersection 1 test, 1 quiz, oral, homework 1 ½ wks Sentences, statements, and truth values Negation, conjunction, disjunction, Conditional Compound statements, converse, inverse, contra-positive Bi-conditional, tautologies Students can: . judge the truth value of a statement . construct a truth table . determine truth value of a compound statement by simplifying truth values . identify tautologies 1 test homework 2 quizzes oral assessment Truth tables on board Student prepared overheads “Logic Bingo” Notebook check 3 wks Identify set and subset Perform union & intersection Students can: . identify natural, whole, integer, rational & irrational numbers Students can: . identify point, line, plane, line segment, midpoint, perpendicular bisector, angle . Use complementary and supplementary relationships . Use congruent angle relationships, and exterior angles of triangles 1 test 2 quizzes 1 ½ wks 1 test 2 quizzes Cooperative Group Activity Homework Peer Assessment Self-assessment Student generated test questions 4 wks Define geometric figures Congruent Triangles: ASA, SSS, SAS Quadrilaterals Line reflections & line symmetry Point reflection & point symmetry Translations Rotations Students can: . define and identify polygons, regular polygons . show that two triangles are congruent by ASA, SSS, SAS . reflect in a line or in a point . translate a figure in plane . rotate about a point 1 test 2 quizzes Homework Oral assessments “Party Paper” activities Board demonstrations by students Notebook check 4 wks Ratios Rates Word problems involving ratio Proportion Direct variation Percent and percentage problems Students can: . express ration, continued ratio . determine equivalent ratios . determine rate . solve problems using ratios and proportions . calculate constant of variation . calculate percents & percentages 1 test 2 quizzes Homework Oral assessments Board problems Review relay game 3½ Problem solving Sets October Logic Real Numbers November Angle Measure in Geometry December Congruence and transformations January Ratio and Proportion Skills (What students actually do) __________Grade 10-12_____________ Grade Levels Major Assessments Time Frame (Tests, projects, etc.) (Number of weeks) Points, lines, planes Angles, angle measure, Perpendicularity Pairs of angles Angles and parallel lines Triangles and angles Triangles with congruent angles homework oral assessment Topics (Unit Title or organizing idea) February Concepts (understandings) Skills (What students actually do) Similar polygons Similar triangles Dilations Ratio of perimeters of similar polygons Ratio of areas of similar polygons Students can: . use proportions to find measures of similar polygons & triangles . identify corresponding parts of similar figures . use A.A. Theorem to show triangles are similar . dilate a figure & determine constant of dilation . use ratios of area & perimeter Students can: . Find area and perimeter of any parallelogram or trapezoid . find area and perimeter of triangle and reg. Polygons . use formulas to problem solve . find areas of shaded regions . use Pythagorean Theorem to find lengths needed to find areas . calculate volumes Students can: . find principle square roots . solve for variable by taking square root - exact values and approximately values . 4 basic operation with square root radicals 1 test homework 2 quizzes Board problems Oral assessment Worksheet Review relay game Notebook check 4 wks 1 test 2 quizzes Board problems homework Oral assessment Student generated problems & solutions Notebook check 4 wks 1 test Worksheets Oral assessment Homework 4 quizzes 3 wks Frequency tables & histograms Cum. Freq. tables & cum. Histograms Mean, Media, Mode, Percentiles Students can: . construct freq. Table, freq. As histogram, cum. Freq. Table, cum. Freq. Histogram . calculate mean, median, mode and percentile 1 test 2 quizzes Music survey – Record Homework Display Analyze Oral assessment 3 wks Simultaneous equations Review graphic solutions Algebraic solutions . solve systems by elimination . solve systems by substitution June Test taking strategies Practice testing Students can: . use test taking strategies . improve performance on practice exams Similarity March Geometric Formulas April Operations with Radicals May Statistics Regents Review Area and perimeter formulas for Polygons Area of circle and circumference Terms and definitions for circle Problem solving with area, perimeter or Circumference Areas of shaded regions Pythagorean Theorem Volume formulas Radicals with rational or irrational Numbers Finding principle square roots Simplifying square root radicals Adding and subtracting radicals Multiplying and dividing square root Radicals Major Assessments (Tests, projects, etc.) Time Frame (Number of weeks) 2 wks 1 test strategies Oral assessment Board presentation 3 ½ wks MARLBORO CENTRAL SCHOOL DISTRICT CURRICULUM MAP _____________Math 2_____________ Course Title Title or Topics Concepts (Unit (understandings) organizing idea) Operations – signed numbers September Rational numbers Numbers and operations Polynomial Review October Polynomial review continued Review factoring November Factoring continued Review equation solving December Algebraic fractions Complex fractions January Review Algebraic fractions Word problems Equation solving revisited Skills (What students actually do) __________Mixed Grade___________ Grade Levels Major Assessments Time Frame (Tests, projects, etc.) (Number of weeks) Operations involving rationals/signed Numbers Complete basic algebraic tasks Problem of Day (POD) Teacher Prepared Quiz (TPQ) Teacher Prepared Test (TPT) Homework (HW) Board Presentation (BP) 1-3 4-6 1 ½ wks 2 ½ wks Power of a power Multiplying polynomial by monomial Multiplying polynomial by polynomials Division of monomials Division of polynomial by monomial Greatest common factor Complete more difficult algebraic tasks Factor Problem of Day (POD) Teacher Prepared Quiz (TPQ) Teacher Prepared Test (TPT) Homework (HW) Board Presentation (BP) 1-3 2-4 5-7 1 wks 1 ½ wks 1 ½ wks Difference of 2 squares Trinomial squares Factoring trinomials – co-efficient of quadratic term is one Factoring trinomials – co-efficient of quadratic term not equal to one Factoring completely Equations with parenthesis Equations with fractional co-efficients Factor Complete the solutions for more difficult Equations Problem of Day (POD) Teacher Prepared Quiz (TPQ) Teacher Prepared Test (TPT) Homework (HW) Board Presentation (BP) 1-5 6, 7 Reduction Multiplication Division Addition/Subtraction Simplification of complex fractions Operations involving Algebraic fractions Problem of Day (POD) Teacher Prepared Quiz (TPQ) Teacher Prepared Test (TPT) Homework (HW) Board Presentation (BP) 1-4 2 ½ wks 51 wk Short month Integer problems Ratio problems Literal equations Word problems Solving equations – involving formulas Problem of Day (POD) Teacher Prepared Quiz (TPQ) Teacher Prepared Test (TPT) Homework (HW) Board Presentation (BP) 1, 2 3 Order of operations Adding/subtracting monomials Adding/subtracting polynomials Multiplying monomials 2 ½ wks 1 ½ wks Regents week 1 wk 1 ½ wks Topics (Unit Title or organizing idea) February Absolute valve Inequalities Quadratic equations March Real number system rationals/irrationals Radicals continued Quadratic equations revisited April Quadratic equations continued Solving systems of linear equations algebraically May Graphing systems of linear equations Graphing expanded Introduce imaginary numbers June Review for final examination Concepts (understandings) Skills (What students actually do) Major Assessments (Tests, projects, etc.) Time Frame (Number of weeks) Derived equations Solving inequalities Solutions to quadratic equations – by Factoring Work with absolute valve Solve quadratic equations Problem of Day (POD) Teacher Prepared Quiz (TPQ) Teacher Prepared Test (TPT) Homework (HW) Board Presentation (BP) 1 2, 3 1 wk 2 wks Roots/Radicals Simplifying radicals Rationalize denominators Operations involving radicals Rationalize binomial radical Denominators Solve by factoring Complete operations involving radicals Solve quad equations Problem of Day (POD) Teacher Prepared Quiz (TPQ) Teacher Prepared Test (TPT) Homework (HW) Board Presentation (BP) 1-5 6 Quadratic formula Irrational roots Fractional co-efficients Quadratic formula Applied to quadratics of various difficulty levels Problem of Day (POD) Teacher Prepared Quiz (TPQ) Teacher Prepared Test (TPT) Homework (HW) Board Presentation (BP) 3 wks Scope/intercept Parabolas – axis of symmetry, etc. Parabolas/imaginaries Graph linear equations Graph quadratic equations Problem of Day (POD) Teacher Prepared Quiz (TPQ) Teacher Prepared Test (TPT) Homework (HW) Board Presentation (BP) 2 weeks graphing 1 ½ wks imaginary numbers Review for final examination Pass final Teacher prepared final Remaining time for review 3 wks 1 wk Short month MARLBORO CENTRAL SCHOOL DISTRICT CURRICULUM MAP _________Math II__________ Course Title Title or Topics (Unit organizing idea) September The Real Number System October Operations on Polynomials November Factoring and Operations on Rational Expressions December First-Degree Equations and Inequalities January First-Degree Equations and Inequalities (cont.) Begin Linear Relations and Functions Concepts (understandings) Sets, Subsets, Union, Intersection Subsets of Real Numbers Solution sets of open sentences -one variable Properties of Real Numbers Properties of Equality Proof in algebra _____________________________ Grade Levels Skills Major Assessments Time Frame (What students (Tests, projects, etc.) (Number of actually do) weeks) Students can: -create sets and subsets -perform union & intersection -graph solution sets of open sentences one variable -identify properties of real numbers & equality -use properties to prove truth of solutions -subsets of Real Numbers Students can: -evaluate expressions and formulas -add, subtract, multiply & divide two monomials, a monomial and polynomial, two polynomials -use properties of reals to simplify operations on polynomials 1 test Homework Board problems Oral assessment 2 quizzes 4 wks 1 test Homework Board problems Oral assessment 2 quizzes 4 wks Factoring polynomials Transforming Rational Expressions into Equivalent Expressions Simplifying Rational Expressions 4 operations on Rational, Complex Fractions Expressions Rational Equations Students can: -factor polynomials -change algebraic fractions to equivalent fractions -simplify rational expressions -perform 4 basic operations on 2 rational expressions -solve rational equations 1 test 2 quizzes Homework Board problems Oral assessment Algebra-Tile Geometric Activity 5 wks Literal Equations First-Degree Inequalities in one variable Problem solving with Literal Equations and First-Degree Inequalities Students can: -solve literal equations -solve first-degree inequalities -solve “word problems” involving literal equations and first-degree inequalities 1 test 2 quizzes Algebra “Proof” Students Authored Test Questions Homework Oral assessments Board problems 3 wks Absolute value equation Absolute value inequalities Students can: -solve absolute value equations and inequalities -graph the results 1 Quiz Homework Oral assessment Board problems 1 ½ wks Finding solution sets of open sentences in two variables Students can: -find the solution set of an open sentence when domain is real numbers -find the solution set of an open sentence when the domain is other than TR 1 Quiz Homework Oral assessment 1 ½ wks Evaluation algebraic expressions and Formulas 4 operations for monomials and polynomials Applying properties of Real Numbers to simplify polynomials Topics (Unit Title or organizing idea) February Linear Relations and Functions March More Linear Relations and Functions April Real Numbers and Radicals May Quadratic Equations and Functions June Concepts (understandings) Review graphing ordered pairs Review graphing lines using table, x and y intercepts, slope – intercept form Slope Writing equations for lines Major Assessments (Tests, projects, etc.) Time Frame (Number of weeks) Students can: -graph ordered pairs -graph lines using 3 methods -choose the best method -find slope of a line -write an equation for a line a) given M and A b) given M and ordered pair c) given two ordered pairs Students can: -graph inequalities -graph inequalities using other replacement sets -graph systems of inequalities -solve systems of equations algebraically -solve problems using systems 1 test 3 quizzes Cooperative Learning Activity Peer Evaluation Self-evaluation Graphing Calculator Activity 4 wks 1 test 3 quizzes Homework Oral assessment Student Prepared overheads Board problems 4 wks Students can: -Perform 4 operations on irrational numbers -Rationalize radical denominators -Perform 4 operations on polynomials with radicals -Rationalize binomial radical denominators -Solve irrational equations Students can: -graph parabolas -solve quadratic equations by factoring and formula -connect solutions of equations to xintercepts of function -solve quadratic-linear systems graphically and algebraically 1 test 3 quizzes Homework Oral assessment Board problems 4 wks 1 test 2 quizzes Homework Oral assessment T1-92 graphing calculator project Board problems Overhead presentation 4 wks Laws of Exponents Students can: -perform 4 basic operations on positive, negative, and 0 exponents 1 test 1 quiz Homework Oral assessment Board problems 1 ½ wks Review of Final Examination Students can: -Do everything! Worksheets Calculator activities 1 ½ wks Inequalities in Two Variables Comparing Inequalities Using Different Replacement Sets Systems of Equations Systems of Inequalities Problem Solving Roots and Radicals 4 Operations on Radicals Rationalizing Radical Denominators Polynomials with Radicals Rationalizing Binomial Radical Denominator Irrational Equations Quadratic Functions Quadratic Equations Relating Quadratic Function to Quadratic Equation Quadratic – Linear Systems Exponents Review Skills (What students actually do) MARLBORO CENTRAL SCHOOL DISTRICT CURRICULUM MAP _____Intermediate Sequential Course III___ Course Title Title or Topics Concepts (Unit (understandings) organizing idea) Sets September Math Systems Rational Numbers Rational Expressions October Relations Functions Irrational Numbers Radical EQ November Imaginary & complex numbers Equations with complex roots Graphing Parabola Quadratic Inequalities December Finis conic section Invwerse & composition of functions Basic transformations January Exponential Function Skills (What students actually do) ______Grade 10-11__________ Grade Levels Major Assessments Time Frame (Tests, projects, etc.) (Number of weeks) Identify properties of sys Classify elements as Mem of sets Factor Perform oper w/rat exp Simp complex fract Solve fractional EQ Written tests (WT) Homework (HWK) Oral Assessment (OA) Board Problems (BP) Student Seat Work (SSW) Sets of systems 1 wk Relation Domain Range Functions Absolute Value = < > Review Radicals Radical = Classify Rotation as Function or NonFnct. Iden Domain/Range Eval. Funct for specific element Solve equations & iner with absd value simp rad Written tests (WT) Homework (HWK) Oral Assessment (OA) Board Problems (BP) Student Seat Work (SSW) Week per topic Imaginary numbers Powers of I Quad eq with imag roots Parabola …../prod roots Solving Quad < > Diff between imag & complex Evaluate powers of I Solve Quad EQ with complex roots Draw graph of parabola Ident if mat min Solve ineq w/quad Written tests (WT) Homework (HWK) Oral Assessment (OA) Board Problems (BP) Student Seat Work (SSW) Imag & compl 1 wk Graphing 1 + wk Ineq 1 wk Conic Sections Circle Hyperbola Eclipse Revisit fract Inverse, composition Basic transformations Identify graph from EQ Draw resp graph Write inv. Of fnct Oper with composition Review transformation Written tests (WT) Homework (HWK) Oral Assessment (OA) Board Problems (BP) Student Seat Work (SSW) Conic sect 1.5 wks ino & comp wk trans wk Exponential functions Fractional & neg exp Exponential EQ Perform operations in exp form Eval exp with fractional & neg exp Solve equations w/ exp Written tests (WT) Homework (HWK) Oral Assessment (OA) Board Problems (BP) Student Seat Work (SSW) Exp 1 wk Exp EQ 1-2 wks Number Prop. Factoring Polynomial Rational Exp Division Reduce +, -, x, ÷ Complex Fr Fract EQ Rat Exp 2 wks Topics (Unit Title or organizing idea) February Logarithmic functs Statistics March Probability & Binom Them Geography of 0…….. Radian meas April Initial trig functions Trig graphs May Trig applications Trig equations & identities Solving June Review for Regents Concepts (understandings) Skills (What students actually do) Major Assessments (Tests, projects, etc.) Time Frame (Number of weeks) Logs des …… Use for computations Use to solve exp EQ Stat. Mean, median mode Range variance Standard dev normal curve Review ….prob Exactly R outcomes in N trials At least, at mort Bionomial expansion Circle ………………….? Convert expression log <-> exp Use logs to compute ans to problems Draw graph of log functs Compute mean, med mode Use normal curve to eval outcomes Written tests (WT) Homework (HWK) Oral Assessment (OA) Board Problems (BP) Student Seat Work (SSW) Convert < 1 wk Log comp & graph 1-2 wks Stat 1 wk Complete prob of outcomes of stated events Find indicated term of a binomial to given power Compute lengths of …. In 0 ralations Written tests (WT) Homework (HWK) Oral Assessment (OA) Board Problems (BP) Student Seat Work (SSW) Prob 1 wk Binom exp 1 wk & app ) xs sag 1 wk radian < 1 wk ARC length Basic ……………………? Inverse fncts …………? Unit 0, stand pos Angles any size Res A Trig graphs amp freq period State trig ratios Iden reciprocal & inv Relations compute trig value of any size Use trig ret to find missing lengths use trig to solve…………? Draw graphs Written tests (WT) Homework (HWK) Oral Assessment (OA) Board Problems (BP) Student Seat Work (SSW) Basic rel 1 wk Graphs < 1 wk Comp 1-2 wks Rect c…………? Inverse trig Trig equations 1st degree 2nd degree 1 & 2 variable Law sines cosinos …………………case? Vector prob Trig identities Regents Review prob Solve eq with trig functs Linear & Quad single & dual fncts Written tests (WT) Homework (HWK) Oral Assessment (OA) Board Problems (BP) Student Seat Work (SSW) 1 wk per topic Regents quad from previous yrs Homework (HWK Board Problems (BP) Oral Assessment (OA) Student Seat Work (SSW) 2 wks MARLBORO CENTRAL SCHOOL DISTRICT CURRICULUM MAP _____Intermediate Sequential Course II_______ Course Title Title or Topics Concepts (Unit (understandings) organizing idea) Algebra Review September Equations Inequalities Algebra Review Quadratic EQ Factoring October Systems of EQ Irrational numbers Quad Formula Basic Graphing November Graphic soln to system Rational Expressions December Coord Geo Slope, Dist. Mdpt Write EQ for line January Probability & Math Systems Skills (What students actually do) _________Grade 9-10__________ Grade Levels Major Assessments Time Frame (Tests, projects, etc.) (Number of weeks) Solve 1st Deg EQ in one Var Factor polynomials Solve Quad EQ by factoring Written Test (WT) Homework (HWK) Oral Assessment (OA) Board Problems (BP) Student Seat Work (SSW) Review wk Oper wk Factoring 1-2 wks Solve EQ Quad Linear Sys Irrational numbers +, -, x, ÷ Radicals Quadratic Formula Discrim & nature of roots Review Graph Line Graph Parabola Solve sys of EQ in 2 variables algebraically Perform operations with radicals Use Quad Formula to solve 2nd deg EQ Written Test (WT) Homework (HWK) Oral Assessment (OA) Board Problems (BP) Student Seat Work (SSW) Systems Radicals Quad Form Graph Graphic soln to Quad/Linear system Soln of Quad EQ from GR Rational Exp (underlined) Reduce, mul, div Add & subtract Fract EQ Use graphs to solve systems of EQ Use Factoring to simp rat exp Perform operations / rat ex Written Test (WT) Homework (HWK) Oral Assessment (OA) Board Problems (BP) Student Seat Work (SSW) Systems Rat exp Coord slope ??????? Parallel & perpend lines Write EQ of line Pythag thrm review Dist forumula Midpoint Use slopes to determine if lines are “ or 1 Write EQ of line Given slope & ??????? Slope & point 2 pts. Use pythag thrm (dist Form) to find length Written Test (WT) Homework (HWK) Oral Assessment (OA) Board Problems (BP) Student Seat Work (SSW) One topic Flows to other Time month Probability Permutations combinations Prob with perm & comb Math systems Closure, ident. Inverse Comm Assoc Group Compute prob of stated event Diff between comb & ?????????? Compute number of comb perm under stated cond. State profs of math system Ident diff elementary Written Test (WT) Homework (HWK) Oral Assessment (OA) Board Problems (BP) Student Seat Work (SSW) Prob (basic P……….. Prob Systems Operations with polynomials (+, -, x, ÷) Factoring Solve Quad EQ by factoring wk wk wk wk wk 2 wks wk wk wk Topics (Unit Title or organizing idea) February Math Systems Logic March Geometry Basic Terms Introduce Proof Relations Relations Parallel & perp lin….. April Polygons Congruent & other polygons Propertied of Quads May Similar poly Right trib Constructions Locus June Review Concepts (understandings) Skills (What students actually do) Major Assessments (Tests, projects, etc.) Time Frame (Number of weeks) Finish math systems Logic Rules of Inf 2 col ded proof Inverse, converse etc Use T.T. to establish logical EQ & Kaws if Ubs Ident conn inv & contra Pos of conditional Use laws of ind for a formal proof Written Test (WT) Homework (HWK) Oral Assessment (OA) Board Problems (BP) Student Seat Work (SSW) TT wk Law of inf wk Proofs 1-2 wks Begin Geo Basic def, lines, segs Angle relations Relations Parallel & lines & Converses Use proper notation to ident geo elem Solve probelsm using relations discussed Supply reasons for ded proof Written Test (WT) Homework (HWK) Oral Assessment (OA) Board Problems (BP) Student Seat Work (SSW) Basic terms wk Proofs wk Relations 1-2 wks Lines 1-2 wks Polygons Reg polygons Sides & relations Quadrilaterals Ident diff types of poly Compute sc……. & ???? of each int Proofs for Use to estab prop of QUAD Written Test (WT) Homework (HWK) Oral Assessment (OA) Board Problems (BP) Student Seat Work (SSW) Poly Similar poly Right triangle prop Special ratios 30-60-90, 45,45,90 RG & Trib sin cos tan Constructions locus Use prop sin to solve prob Use prop to derive phthag thrm Use pythag therm for special r………. Solve related prob Written Test (WT) Homework (HWK) Oral Assessment (OA) Board Problems (BP) Student Seat Work (SSW) Wk Pythag therm & app 2-3 wks Review Use Previous Regents Exams to review years work Written Test (WT) Homework (HWK) Oral Assessment (OA) Board Problems (BP) Student Seat Work (SSW) 2 wks 1wk Wk Prop Quads 1-2 wks MARLBORO CENTRAL SCHOOL DISTRICT CURRICULUM MAP ________Sequential Math III_______ Course Title Title or Topics Concepts (Unit (understandings) organizing idea) Factoring polynomials September Add, Multiple, divide Real Numbers Polynomials Polynomial Fractions October Real Numbers Irrational Numbers November Imaginary Numbers December Conic Sections Exponents January Logarithms Statistics Skills (What students actually do) ________Grade 11_________ Grade Levels Major Assessments Time Frame (Tests, projects, etc.) (Number of weeks) Operations on polynomials Review activities Work sheets Board Work Tests 3 wks Solve & graph inequalities Simplify radicals Add, subtract, multiple, divide Rationalize radicals Solving quadratic inequalities Operations on radicals Review activities Worksheets Board Work Tests 4 wks Add, subtract, multiply, divide, powers of complex numbers Solve Quadratics Def, types composite inverse of Functions Operations on complex numbers Composition of functions Review activities Worksheets Board work Tests 4 wks Circle, eclipse Parabola, hyperbola Properties of exponent Scientific notation Exponential Equations Identify and graph conic sections and exponential equations Review activities Worksheets Board work Tests 4 wks Logarithmic and exponential notation Properties of logarithms Graph exp and log functions Sigma notation Mean, median, mode Standard deviation Graph, multiply, divide and do powers with logarithms Mean, median, mode standard deviation Review activities Worksheets Board work Tests 5 wks Polynomial Fractions Simplify complex fractions Topics (Unit Title or organizing idea) February Statistics Probability Geometry of the Circle March Trigonometry April Right triangles Scalene and obtuse triangles Vectors May Trigonometric Identities June Review Concepts (understandings) Skills (What students actually do) Major Assessments (Tests, projects, etc.) Time Frame (Number of weeks) Permutations, combinations Binomial expansion Probabilities from binomial expansion Find measure of various arcs, chords, and angles of the circle and tangents and secants to the circle Find mean and standard deviation Make a frequency distribution Review activities Worksheets Board work Tests 4 wks Sine, cosine, and tangent values and Graphs Radian and degree measure Reciprocal, Quotient, co-functions Draw trig ???? Construct trig table Review activities Worksheets Board work Tests 4 wks Law of sines Law of cosines Ambiguous case Resolution of forces Area of triangle Solve triangle problems Review activities Worksheets Board work Tests 5 wks Deprive identities Solve trigonometric equations Prove identities Inverse variation Prove identities Solve equations Review activities Worksheets Board work Tests 4 wks Review for Regents Practice for Regents Review activities Worksheets Board work Tests 3 wks MARLBORO CENTRAL SCHOOL DISTRICT CURRICULUM MAP _______Pre-Calculus A____________ Course Title Title or Topics Concepts (Unit (understandings) organizing idea) Linear Equations September Complex numbers Pre-requisite topics Quadratics Matrices October Matrix algebra Math induction Sequences and series November Binomial Expansion Vectors December Polar coordinates January Trigonometry Skills (What students actually do) _________Grade 12__________ Grade Levels Major Assessments Time Frame (Tests, projects, etc.) (Number of weeks) Solve polynomial and high degree equations Write Quadratic equations Review activities Work sheets Board work Tests 4 wks Row-reduction Cramer’s Rule Determinants Inductive proofs Arithmetic and geometric Solve system of equations by various Techniques Review activities Work sheets Board work Tests 4 wks Sequences and series Terms of expansion DOT product 3 dimensional vectors Cross product Equation of a plane Sketch vectors and perform vector Operations Review activities Work sheets Board work Tests 5 wks Rectangular and polar coordinates Multiply, divide polar coordinates De Moivre’s theorem Graphing Polar coordinates Review activities Work sheets Board work Tests 4 wks Graphs, tables, proofs, equations Law of sines Law of cosine Translating Graphs Proving identities Solving equations Review activities Work sheets Board work Tests 3 wks Quadratics Long Division synthetic Division Rational Root theorem Systems of Equation MARLBORO CENTRAL SCHOOL DISTRICT CURRICULUM MAP ___________Pre-Calculus B___________ Course Title Title or Topics Concepts (Unit (understandings) organizing idea) Graphs: Bar, component, histogram September Ogive, pie Statistics October Hypothesis testing Logic November Computer project Matrices December Compile numbers January Review Skills (What students actually do) ___________Grade 12_________ Grade Levels Major Assessments Time Frame (Tests, projects, etc.) (Number of weeks) Graph and design histogram Review activities Work sheets Board work Tests 4 wks Frequency distribution Normal curve Z-Table Student T-test Laws of Logic Logical Proofs Boolean Disjunctive form Logic circuits Karnaughn maps Conduct large sample hypothesis test Conduct small sample hypothesis test Review activities Work sheets Board work Tests 4 wks Graph with excel Row reduction Cramer’s Rule Add, multiply matrices Inverse of a matrix Construct logical proofs Design logical circuits Review activities Work sheets Board work Tests 5 wks Polar coordinates Rectangular coordinate DeMoivre’s theorem Polar graphs Solve system of equations Graphing in polar coordinates Review activities Work sheets Board work Tests 4 wks Review all topics Pre-calculus A And pre-calculus B for calculus Solve Quadratics Use synthetic Division Rationalize Quadratic Review activities Work sheets Board work Tests 3 wks Mean, median, mode, standard Deviation MARLBORO CENTRAL SCHOOL DISTRICT CURRICULUM MAP _______Calculus________________ Course Title Title or Topics (Unit organizing idea) September Graphs Limits October Derivatives November Derivatives December Derivatives Integrals January Integrals Concepts (understandings) Skills (What students actually do) _________Grade 12_______________ Grade Levels Major Assessments Time Frame (Tests, projects, etc.) (Number of weeks) Graph polynomial functions Graph rational functions Limits by Direct Substitution, algebraic manipulation, near infinity Difference Quotient Define limit Limit theorems Review activities Work sheets Board work Tests 4 wks Derivative by: ∆ x process X a process, power race continuity Product and quotient rules Chain rule Continuous & discontinuous functions Rules for differentiation Review activities Work sheets Board work Tests 4 wks Higher order derivatives Velocity, acceleration Derivative of trig f…. Implicit differentiation Logs and Exponents Applications of the chain rule Implicit differentiation Review activities Work sheets Board work Tests 5 wks Curve tracing Applications Optimization Exponent and logarithm functions Indefinite integrals Finding max and mins Critical points and points of inflection Optimization Review activities Work sheets Board work Tests 4 wks General power rule Word problems Definite Integrals Area and volume Application of techniques Review activities Work sheets Board work Tests 3 wks