Core vs NYS Standards Grade 5 Core NYS Operations and Algebraic Thinking -------------------------------------------------------------------------- 5.OA Write / Interpret Numerical Expressions Use ( ), [ ], and { } with order of operation Write numerical expression given the verbal expression Analyze Patterns / Relationships Create sequences from rules (2) Explain patterns between sequences Graph ordered pairs 1 rule Numbers / Operation base 10 ------------------------------------------------------------------------------------ 5.NBT Generalize Place value x / by 10 to move thru place values Use exponents on powers of 10 Relate number of zeros to exponent when multiplying by 10 s Relate placement of decimal points to division by 10 s Read decimals to thousandths Write decimals in expanded form to thousandths Compare decimals to thousandths using >, =, < Round decimals to any place New Topic Nearest hundredth Perform multi-digit Operations Fluently with multi-digit multiplication Divide 4 digit numbers by 2 digit numbers All four operations on decimals with division by hundredths Division to thousandths
Numbers and Operations Fractions ----------------------------------------------------------------------- 5.NF NOTE: No restrictions on denominators Equivalent Fractions with + / - + / - fractions with unlike denominators Solve + / - word problems using fractions with unlike denominators Estimate reasonableness of fractional answers using mental math and benchmark fractions + / - with like denominators Multiply and Divide Fractions Interpret a fraction as division Multiply fraction by whole number and fraction by fraction Area of rectangles with fractions Interpret integer and fraction multiplication as scaling Solve word problems with fraction multiplication Divide unit fractions by whole numbers Divide whole numbers by unit fractions Solve word problems with whole number / fraction division Measurement and Data -------------------------------------------------------------------------------------------- 5.MD Convert Units within a Measurement System Solve multi-step conversion problems Represent / Interpret Data Interpret line plots of fractional data Volume Understand volume as an attribute Recognize that volume is additive Measure volume by counting cubes Relate volume to multiplication Use volume formulas V = l x w x h or V = B x h
Geometry ---------------------------------------------------------------------------------------------------------------- 5.G Graph Points in 1 st Quadrant Graph points and use vocabulary of coordinate plane Solve problems by plotting points Classify 2-D Figures Classify figures based on properties Understand that subcategories of figures have the same attributes Note: No probability concepts are addressed
Core vs NYS Standards Grade 6 Core NYS Ratios and Proportional Relationships --------------------------------------------------------------------- 6.RP Ratios and Rates Understand ratio and ratio language Understand rate based on ratio Solve ratio / rate word problems in drawings and equations Use tables and graphs to interpret ratios / rates Solve unit rate problems Find the percent of a quantity, find the whole, given part and percent Use ratio to convert measurement units New Topic Number System --------------------------------------------------------------------------------------------------------- 6.NS Complete Fraction Division Fluency Factors and Multiples Divide fraction by fraction including work with mixed numbers utilizing visual models and equations Fluent with division Fluent with decimal operations GCF of any 2 numbers 100 LCM of 2 numbers 12 Express a sum using the distributive property Rational and Integer Number Systems Understand the use of negative numbers to describe real-world context Understand positives and negatives as opposites Locate rational numbers and integers on a number line Order integers on a number line Understand absolute value as distance from 0
Represent points in all quadrants on a plane Investigate reflections that result from sign changes on points Find vertical and horizontal distance on a plane Expressions and Equations -------------------------------------------------------------------------------------- 6.EE Algebraic Expressions Write and evaluate whole-number exponents Read, write, and evaluate expressions with variables Use appropriate mathematical algebraic and operational terms Order of operation Use of the distributive property Identify equivalent expressions One Variable Equations / Inequalities Understand the meaning of an equation s / inequality s solution(s) Use substitution to check Use variables to write equations / inequalities Solve one step equations / inequalities with positive rational numbers Graph solutions to inequalities on a number line 2-Step equations Represent / Analyze 2 variable equations Write equations in 2 variables Identify independent / dependent variables Use graphs and tables to analyze the relationship between the variables Geometry ----------------------------------------------------------------------------------------------------------------- 6.G Area, Surface Area, and Volume Find area of triangles, quadrilaterals, and polygons using decomposition Calculate volume of prisms with fractional values
Calculate area on the plane using horizontal / vertical distances Find surface area of solids using their nets Statistics and Probability ----------------------------------------------------------------------------------------- 6.SP Statistical Variability Distributions Understand the meaning of statistical variability Describe statistical distributions using their shape, centers, and spread Understand the differences between centers and spreads Display data using dot plots, histograms, and box plots Summarize data with the number of observations Describe the distribution s variables and their units of measure Find measures of central tendency mean and median Find measures of variability range, IQR, and mean absolute deviation Use distribution shape to choose the most appropriate descriptive statistics Range Histograms Range Note: No probability concepts addressed
Core vs NYS Standards Grade 7 Core NYS Ratios and Proportional Relationships --------------------------------------------------------------------- 7.RP Proportional Relationships Unit rates with fractions Test for proportionality numerically, in tables, or from a graph Determine the constant of proportionality verbally, visually, graphically, and from equations Represent proportions by equations From a linear graph of proportionality explain the meaning of (x,y), (0,0), and (1, r) if r is the unit rate Use proportions to solve multistep ratio and percent problems ( interest, tax, markup, markdown, tip, commission, % interest ) New Topic Number System -------------------------------------------------------------------------------------------------------- 7.NS Fraction Fluency Integers Maintain addition, subtraction, multiplication, and division of fractions Represent + / - of integers on number line Define addition of integers Define subtraction of integers as adding the opposite Define multiplication and division of integers Define inverses Define rational numbers Convert rational numbers to decimals and address terminating and repeating Solve problems with rational numbers
Expressions and Equations -------------------------------------------------------------------------------------- 7.EE Algebraic Expressions Add, subtract, factor, and expand linear expressions with rational coefficient Read, write, evaluate, and interpret expressions with variables Solve multistep problems with positive and negative rational expressions and equations Order of operation Solve 2 step equations Solve 2 step inequalities, graph on number line, and interpret results Multistep Positive coefficient 1 step Geometry ----------------------------------------------------------------------------------------------------------------- 7.G Geometric Figures Scale Drawings Construct triangles given angle / side measures to determine existence Describe cross-sections of right prisms or pyramids Angle Measure, Area, Surface Area, and Volume Derive the relationship between area and circumference Know formulas for area and circumference of circles Define supplementary, complementary, vertical, and adjacent angle relationships Write and solve equations to find unknown angle measures of figures Solve area, volume, and surface area problems Extended Statistics and Probability ---------------------------------------------------------------------------------------- 7.SP Sampling Populations Understand the meaning of a random sample Generate data from multiple random sample Examine variability between samples Using random sampling, compare populations by using measures of center and spread Graphically compare populations
Probability Define probability, P(E) as 0 P(E) 1 Distinguish between theoretical and empirical probabilities Calculate probabilities Represent the sample space for compound events numerically, in tables or trees Calculate compound probabilities Use simulations to determine frequencies for compound events
Core vs NYS Standards Grade 8 Core NYS Number System -------------------------------------------------------------------------------------------------------- 8.NS Irrational Numbers Define an irrational number Find decimal approximations of irrational numbers Locate irrationals on a number line Convert repeating decimals to fraction form New Topic Expressions and Equations -------------------------------------------------------------------------------------- 8.EE Exponents Lines and linear equations Equations Operate and evaluate integer and zero exponents Estimate using powers of 10 for very small and large quantities Scientific notation Operations with scientific notation Know simple perfect squares and cubes Solve equations using square roots or cube roots Unit rate as slope Equations forms of y = mx and y = mx + b Explain that slope is constant using similar triangles Solve multistep equations with rational coefficients using distributive property and variables on both sides Solve equations with one, no, or infinite solutions Define the solution of a system of equations as a point Solve systems of equations both algebraically and graphically Solve systems with one, no, or infinite solutions Solve system word problems Graphically
Functions ---------------------------------------------------------------------------------------------------------------- 8.F Define Functions Model Functions Function as a rule assigning one input to exactly one output Function as a set of ordered pairs Interpret and compare functions in multiple forms tables, graphs, equations, and verbally Know if functions are non-linear Write a function rule from tables, graphs, or data Explain the meaning of a function s slope and y-intercept Describe / explain if linear functions are increasing, decreasing, or non-linear Geometry ---------------------------------------------------------------------------------------------------------------- 8.G Congruent and Similar Figures Define dilations, rotations, reflections, and translations Define dilations, rotations, reflections, and translations using coordinates Define transformations that preserve distance, angle measure, and parallels Define congruence using transformations Define similarity using dilations Define similarity by A-A similarity Angle Measure Pythagorean Theorem Sum of the interior angles of a triangle Exterior angles of a triangle Angle formed by parallel lines cut by a transversal Prove the Pythagorean theorem and converse Solve a right triangle using Pythagorean theorem Solve real-world problems in 2 and 3-dimensions using the Pythagorean theorem 2-dimensions
Volume Use Pythagorean theorem to find distance between 2 points Know and use formulas for volume of cones, cylinders, and spheres Statistics and Probability ----------------------------------------------------------------------------------------- 8.SP Bivariate Data Categorical Bivariate Data Plot and interpret bivariate data Describe data patterns of clusters, outliers, + / - association, linear / nonlinear association Lines of Best Fit Write the equation of a Best Fit line Interpret the meaning of slope / y-intercept in problem context Use two-way tables to show frequencies and relative frequencies of bivariate categorical data Look for patterns of association in bivariate categorical data Note: No probability concepts addressed