# 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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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)] |
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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 |
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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 |
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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 |
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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 |
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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 |
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Conics | Parabolas | Circles | (Regular): parabolas; (honors): parabolas, ellipses, hyperbolas |
Parabolas | Parabolas, ellipses, hyperbolas; rotations in parametric, rectangular, and polar form |
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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 |