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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Pre-K Through 12 Mathematics Curriculum

 Pre-K Kindergarten Primary Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Pre-algebra 1.5 years Grade 6/7 Pre-Algebra 1 yr Grade 6/7 Algebra 1 Grade 7/8 Geometry Advanced Algebra FST PDM ADDITIONAL COURSES: AP Calculus AB, AP Calculus BC, AP Statistics, Linear Algebra Time & Money Intro to telling time: analog and digital; on the hour; intervals; identify coins-by name and value Count groups of coins by 1s, 2s, 5s, 10s Money: identify, sort, count coins; add coins up to 50 cents; analog & digital clocks (1/2 hour intervals) Counting money; making change; telling time Review, assess, reteach time & money concepts Money operations; time Money operations; time Integrated into problemsolving; I=prt; Stock Market (7th gr) Integrated into problemsolving Word problems;exponential growth Stock project, word problems, exponential growth Exponential growth of money Counting Counting orally: dice, calendar, games Recognizing events happening in sequential order; counting by 2’s, 5’s, 10’s; Mathland Counting forward and backwards 2’s, 5’s, 10’s Counting by 2’s, 5’s, 10’s (count 1-120) Skip counting; counting by 3’s, 4’s, 10’s, 20’s Skip counting; multiplication Skip counting; Number systems: roman numerals,binary numbers Decimals; square roots GCF, LCM, prime factorization, multiples, decimals; square roots GCF, LCM, prime factorization, multiples, decimals; square roots Multiples & factors Introduction to complex numbers Complex numbers Proofs involving integers Number Sets Computation Addition & subtraction (including computations with 10); doubling numbers; square roots; ratio & proportion; Begin to use equations to describe a math operation Addition & subtraction to 10; open equations; skip counting Subtraction, addition; skip-counting; place-value & regrouping addition Plus & minus; placevalue; multiplication by repeated addition; Addition up to 4 digit numbers; subtraction with re-grouping; multiplications facts to 10; concept of division 4-digit addition & subtaction with borrowing and carrying; multiplication: different methods; mental math Multiplication and long division; fraction & decimal operations Operations for whole numbers; math facts; money operations; adding & subtracting on number line; order of operations; operations with negative numbers; exponents, powers of 10 and of negative numbers Operations for whole numbers; & fractions; math facts; adding & subtracting on number line; order of operations; operations with negative numbers; exponents, powers of 10; absolute value Basic computation; order of operations; operations with fractions; square roots; exponents Positive & negative numbers; order of operations; absolute value on number line; simplifying radicals; exponents Side measures; angles, area, perimeter, Square roots;absolute value; rational functions; complex numbers Complex numbers; combinatorics Reading, Writing, Understanding, Numbers Number recognition; write numerals 1-10 How to write (draw) numerals Understand the meaning of two digit numbers, i.e. a digit’s placement determines its value, intro to three digit numbers Number recognition; odd & even; place-value: 1, 10, 100 Place value Place value Reading large numbers & decimal numbers Writing numbers like millions Writing numbers like millions; Associative, commutative, distributive, transitive properties Associative, commutative, distributive, transitive properties Associative, commutative, distributive, transitive properties Associative, commutative, distributive, transitive properties; proofs; conditional statements; logic Associative, commutative, distributive, transitive properties Solving and factoring over different number sets Mathematical induction Axioms, Properties, Theorems, Proofs Number Sense Estimate number of objects in container; 1-1 correspondence 1-1 Correspondence used for counting; comparing height, weight, shapes; pre-adding; number appearance; arrangement of objects Compare and contrast numbers; explore greater than, less than, equal to through estimation activities, counting games, etc. Determine number in a group; more vs. less vs. equal; fast vs. slow Predicting and estimating; compare & order numbers Great than; lesser than; equal to; estimating Estimates Place value, estimation, negative numbers Number sense; scientific notation Number sense; scientific notation; estimation & reasonableness Square roots; estimation & reasonableness Scientific notation; exponents; estimation; radicals Estimation; nth terms Asymptotic behavior; Estimation Asymptotic behavior; Estimation; conceptualizing infinity Conceptualizing infinity; Asymptotic behaviour; estimation Reasoning & Problem-solving Logical thinking: concept of 1 more; sorting; distinguishing between groups; more vs. less Explore a variety of math story problems; practice problem solving strategies i.e. draw pictures, diagrams, lists, etc. Story problems involving addition & subtraction; reading & following directions; sorting treasures by 1 or 2 attributes Problem-solving strategies; logical thinking; classification and sorting; making groups Strategies such as: Make a list; Draw a picture or diagram; logical thinking; working backwards Story problems; Math Olympiads Math Olympiads; logic problems Recognizing key words; logic puzzles, Math Olympiads Recognizing key words; logic puzzles, Math Olympiads Problem-solving; writing verbal models; interpret word problems into algebraic equations Problem-solving strategies; growth & decay (exponents); word problems Logic puzzles; problemsolving strategies Problem-solving strategies; direct and inverse variation Problem-solving strategies Problem-solving strategies; logic, truth tables Patterns, Sequences, Series Recognize, create, extend patterns Build, repeat and extend patterns in two and three dimensions. Explore patterns in our base ten number system, counting by 2’s, 5’s, 10’s Patterns on the 100- board: create and label Pattern & sequences; extending and transforming patterns Skip counting Patterns & sequences Sequences Sequences; perfect squares; fractals; Fibonacci Fibonacci series; triangular numbers; perfect numbers Exponential patterns Inductive logic; basic sequences; nth term Series Arithmetic and geometric; sequences (honors) Sequences & series Measuring Explore non-standard and standard measurement; linear, solids and liquids through real life projects, i.e. cooking, arts and crafts, etc. Explore non-standard and standard measurement; linear, solids and liquids through real life projects, i.e. cooking, arts and crafts, etc. Measurement: length, weight Area, perimeter, volume, length as it relates to fractions Length, weight, temperature Inches, cm, temperature Customary unit conversion Dream Backyard Project; area; perimeter; volumev Area; perimeter Area, length, angles, perimeter Distance, magnitude; 2D representation Fractions & Decimals Intro to fractions through measurement explorations and use of decimal in money Introduction to basic fractions & decimals in money Fractions: 1/2, 3/4, 1/3, 1/4 Explore fractions Adding and subtracting fractions Fractions, decimals, percents (how they relate); the four operations Ratios; rates Ratios; rates; computation; place value; converting computation, place value, converting Fractions: order, compuations Similar triangles; ratios Simplifying rational expressions; complex fractions; rational functions Rational functions Partial fractions Rational Functions Graphing Intro to data collection and how to record data on a simple bar graph Intro to data collection and how to record data on a simple bar graph Bar graphs, plot graphs How to record/interpret data on a graph 4 quadrants; types of graphs Graphing Line plots, bar graphs, scatter plots; coordinate graphing Line plots, bar graphs, scatter plots; coordinate graphing Graphs & solving; graphing inequalities Graphing shapes; parallel & perpendicular lines Graphing quadratics;absolute value functions, piecewise functions; systems of linear inequalities; parent functions all elementary functions; parent functions; parametric equations (honors) Trigonometric, polar, polynomial functions; parametric equations Transformations Explore symmetry in art and nature Introduction to concept of symmetry Congruency, symmetry Identify symmetrical objects, lines of symmetry Flip, slide, & rotational transformations Graphing lines Transformations Transformations; parent functions Transformations; parent functions Transformations; parent functions Statistics & Probability Collect, sort and interpret data using graphs and charts Gathering, organizing, reporting data; drawing conclusions; games of chance; dice, coins, spinners; simple probability Collection, analysis, interpretation graphing data (bar & plot graphs); probability Probability; predicting results Probability; data collection; predicting results; displaying data, graphs Statistics: data collection, displays & analysis; mean, median & mode Line plots, bar graphs, scatter plots; probability Line plots, bar graphs, scatter plots; probability; Counting Principle; permutations; mean, median, mode, range Line plots, bar graphs, scatter plots; probability; Counting Principle; permutations; mean, median, mode, range Exploring data;picture graphs, pie charts, scatter plots; linear equations from points; matrices (arrays); mean, median, mode Regression, scatter plots, data analysis Descriptive & inferential statistics; probability; central tendency, variance; distributions; hypothesis testing; [research design; density curves; chi-square (honors)] Equations & Inequalities Intro on how to write equations; vertically and horizontally Cover each number in a simple equation and solve for it; writing equations using + and -; equations with 2 or 3 terms added Equations Basic equation solving; multi-operation equations Fact families; prealgebra (variables) Equations with 2 or 3 terms added Basic equation solving Basic equation solving; solutions of inequalities Equations & inequalities, 2 step, variables on both sides Solving equations; systems of equations; solving inequalities; expression vs. equation Translating shapes to equations Radical equations; rational equations Solving and graphing linear & quadratic inequalities Systems of equations; linear programming Geometry Reorganizing geometric shapes Explore two and threedimensional shapes: i.e. squares vs. cubes, circle vs. spheres, etc. Identify basic two-dimensional shapes; square, rectangle, triangle, diamond, circle, oval, etc. Record 2D patterns on grid paper; classification of geometric shapes by number of sides Geometric shapes, definitions, concrete modeling, 3D shape comparison Geometric investigations: shapes, symmetry; patterns in fractions: rhombus, trapezoid, hexagon Classifiying shapes; build polyhedra; division, avg, area, perimeter Polygons, angles, tesselations, circles; shapes classified by number of sides; perimeter, area, volume Angles, lines, perimeter, area, volume; Pythagorean Theorem; identifying shapes Angles, lines, perimeter, area, volume; Pythagorean Theorem; identifying shapes Pythagorean theorem; geometric constructions; polyhedra Angles: measures, properties; congruence; similarity; construction; perspective; area, volume, distance; Pythagorean Theorem; circles & arcs;parallel line relationships; right triangle trigonometry Distance with line segments; magnitude Right triangle & circular trigonometry; trigonometic functions & graphs; unit circle; identities;solving trigonometric equations; Law of Sine & Cosines Analytic geometry, 3D; polar equations; right triangle & circular trigonometry; trigonometric functions & graphs; unit circle; identities; Law of Sines and Cosines; Vectors Trigonometry Functions Function tables Function tables Introduction to functions; domain & range Linear and beginning quadratic functions Functions; domain, range; parent functions; transformations Domain, range, operations, inverses; all elementary functions Parametric equations Lines basic linear equations linear equations Line equation forms: slope-intercept, pointslope, standard; find equation of line through two points Linear equations; parallel & perpendicular lines; distance, midpoint, slope Linear programming; linear functions; linear approximations Linear functions, systems of equations (honors) Systems of equations, linear programming Quadratic & polynomial functions Quadratics; multiplying polynomials; factoring quadratics Factoring; roots of quadratic equations; polynomials; quadratic approximations Polynomials: long division, synthetic division; Fundamental Theorem of Algebra Exponential & logarithmic functions Square numbers Scientific notation; squares and cubes Rules of exponents; basic graphs Review rules of exponents; exponential & logarithmic functions Review exponential & logarithmic functions Conics Parabolas Circles (Regular): parabolas; (honors): parabolas, ellipses, hyperbolas Parabolas Parabolas, ellipses, hyperbolas; rotations in parametric, rectangular, and polar form Matrices Basic addition, subtraction, multiplication; data entry Matrix operations; determinants, solving systems by matrix inverse method Honors: Matrix operations; determinants, solving systems by matrix inverse method Review of Matrix operations; determinants, solving systems by matrix inverse method