Scope and Sequence Mathematics Kindergarten through Twelfth Grade

Transcription

1 Scope and Sequence Mathematics Kindergarten through Twelfth Grade Topic/Subtopic K WHOLE NUMBER OPERATION Writing numbers using digits Writing numbers - using words Ordering single digit numbers Ordering two-digit numbers Ordering 3-digit numbers Adding single digit numbers Adding two-digit numbers Adding 3-digit numbers Subtracting single digits Subtracting two-digit numbers Subtracting 3-digit numbers Multiplying by single digits Multiplying by 2-digit numbers Multiplying by 3-digit numbers Multiplying by ten Multiplying by multiples of 10 Multiplying by powers of 10 Dividing by single digit numbers Dividing by 2-digit numbers Dividing by 3-digit numbers Division with remainder Division with no remainder Dividing by powers of 10 Dividing by multiples of 10 Arithmetic Sequences Geometric sequence Counting money Operations with money Making change Writing checks Identify odd and even numbers Missing parts in operations Squares/ square roots Roman numerals Prime and composite numbers Order of operations Divisibility Place value Multiples Least common multiple Factors Pg. 1 Rev. 12/20/11

2 Greatest common factor Prime factorization REAL NUMBER OPERATION Adding fractions like denominators. Adding fractions unlike denominators. Subtracting fractions like denominators. Subtracting fractions unlike denominators Pg. 2 Rev. 12/20/11 Multiplying fractions Dividing fractions Adding pos/neg. numbers Multiplying/dividing pos/neg numbers Operations with mixed numbers Exponents as whole numbers Exponents - as fractions Exponents negative numbers Identify parts of a whole Reading fractions and mixed numbers Writing fractions using numbers Writing fractions using words Equivalent fractions Improper fractions Rounding to nearest place value Rounding to nearest whole number Rounding to nearest decimal place Reducing fractions Adding decimals Subtracting decimals Multiplying decimals Dividing decimals Reciprocals Reading decimal numbers Writing decimal numbers using digits Writing decimal numbers using words Operations with mixed numbers Dividing with a repetitive remainder Scientific notation Converting decimals to fractions Fractional part of a number Decimal part of a number Percent of a number Commutative property Associative property Distributive property Identifying numbers as whole/integer/rational/irrational

3 Absolute value Adding/subtracting radicals Multiplying/dividing radicals Simplifying radicals Inequality statements Ratios/proportions Probability possible outcomes Estimation Expanded forms Averaging Percents to decimals Mean/median/mode Powers and roots of fractions Roots of negative numbers GEOMETRY SHAPES AND FORMULAS Naming/identifying simple polygons(square,rectangle) Naming/identifying more advanced polygons (Trapezoid, octagon) Identifying geometric solids Slopes of parallel/perpendicular lines Parallel lines Perpendicular lines Intersecting lines Skew lines Lines of symmetry Area of polygon Area of a circle Radius and diameter of a circle Area of a triangle Area of a rectangle Area of a parallelogram Area of a trapezoid Area of a rhombus Congruent and similar shapes Introduction to volume Volume of a right solid Surface area Perimeter Lines, rays, segments Types of angles Using rulers/protractors/compass Properties of triangles Properties of quadrilaterals Circumference and pi Semicircles Pg. 3 Rev. 12/20/11

4 Pythagorean theorem Classifying triangles Convex and concave polygons Proofs in geometry Postulates and theorems True/false statements Logic tables Constructions with compass Special right triangles GRAPHING/GRAPHS Identifying most and fewest on a graph Create and read a Pictograph Create and read a bar graph Create and read a venn diagram Solve for missing part of venn diagram Creating and read line graphs Create and read a circle graph Maps Temperature Calendar Tallying Drawing time on a clock Telling time Number a clock face Locating points on a coordinate graph Labeling a number line Graphing inequalities line graph Graphing linear inequalities coordinate graph Finding slope of a line Finding distance between 2 points Using distance formula Finding the equation of a line Slope intercept form Finding midpoint of 2 points Graphing circles Graphing ellipses Graphing hyperbolas Graphing parabolas Graph absolute value functions Max/min problems - graphing Reflecting graphs symmetry Periodic functions stretching graphs Inverse functions Sine and cosine curves Graphing polynomials Pg. 4 Rev. 12/20/11

5 Finding slope of a curve Polar graphing MEASUREMENTS Non-standard measurements Linear English system Linear metric system Weight English system Weight metric system Liquid English system Liquid metric system Linear conversion Weight conversion Liquid conversion Units of time Adding mixed measures Converting unit multipliers WORD PROBLEMS Addition Subtraction Multiplication Division Fractions Multiple operations Determining relevant information Ratios/rate Distance rate time Work rate time Distance rate time with variables Work rate time with variables Age problems with variables Digit problems with variables Coin and mixture problems with variables Motion problems with variables Max/min problems Translating English to algebraic Percent with variables Consecutive integer Perimeter and angle measure Direct/inverse variation Navigation and aviation EQUATIONS / POLYNOMIALS Pg. 5 Rev. 12/20/11

6 One step equations Two-step equations Variables on both sides Part of a whole Algebraic phrases Absolute value Two variable two equations Three linear equations Combining like terms Multiplying/dividing rational expressions Combining polynomials Multiplying binomials Factoring trinomials Solve equations by factoring Solve Quadratic equations Quadratic formula Completing the square Synthetic substitution Sums and products of roots Radical equations The Discriminant The number e Inverse functions Finding roots of polynomial Exponential equations Trigonometric ratios Applications of trigonometry Solving trigonometric equations Adding vectors Logarithms Matrices Solving functions Periodic functions Complex numbers Law of sine/cosine Limits/series Permutations/combinations Sigma notation Pg. 6 Rev. 12/20/11

7 Pg. 7 Rev. 12/20/11

8 Pg. 8 Rev. 12/20/11

9 Pg. 9 Rev. 12/20/11

10 Pg. 10 Rev. 12/20/11

11 Pg. 11 Rev. 12/20/11

12 Pg. 12 Rev. 12/20/11

13 Pg. 13 Rev. 12/20/11