Download 5-8 Core vs NYS Standards

Core vs NYS Standards
Grade 5
Core
NYS
Operations and Algebraic Thinking -------------------------------------------------------------------------- 5.OA
Write / Interpret Numerical Expressions
Use ( ), [ ], and { } with order of operation
Same
Write numerical expression
given the verbal expression
Same
Create sequences from rules (2)
1 rule
Explain patterns between sequences
Same
Graph ordered pairs
Same
Analyze Patterns / Relationships
Numbers / Operation base 10 ------------------------------------------------------------------------------------ 5.NBT
Generalize Place value
Perform multi-digit Operations
x / ÷ by 10 to move thru place values
New Topic
Use exponents on powers of 10
NT
Relate number of zeros to exponent
when multiplying by 10’s
NT
Relate placement of decimal points
to division by 10’s
NT
Read decimals to thousandths
Same
Write decimals in expanded form
to thousandths
NT
Compare decimals to thousandths
using >, =, <
Same
Round decimals to any place
Nearest hundredth
Fluently with multi-digit multiplication
Same
Divide 4 digit numbers by 2 digit numbers
Same
All four operations on decimals
with division by hundredths
Division to thousandths
© 2011 Questar III, Board of Cooperative Educational Services for Rensselaer • Columbia • Greene Counties – all rights reserved.
November 2011
Numbers and Operations – Fractions ----------------------------------------------------------------------- 5.NF
NOTE: No restrictions on denominators
Equivalent Fractions with + / + / - fractions with unlike denominators
NT
Solve + / - word problems using
fractions with unlike denominators
NT
Estimate reasonableness of fractional answers
using mental math and benchmark fractions
+ / - with like
denominators
Interpret a fraction as division
NT
Multiply fraction by whole number
and fraction by fraction
NT
Area of rectangles with fractions
NT
Interpret integer and fraction multiplication as scaling
NT
Solve word problems with fraction multiplication
NT
Divide unit fractions by whole numbers
NT
Divide whole numbers by unit fractions
NT
Solve word problems with
whole number / fraction division
NT
Multiply and Divide Fractions
Measurement and Data -------------------------------------------------------------------------------------------- 5.MD
Convert Units within a Measurement System
Solve multi-step conversion problems
Same
Interpret line plots of fractional data
NT
Understand volume as an attribute
NT
Recognize that volume is additive
NT
Measure volume by counting cubes
NT
Relate volume to multiplication
NT
Use volume formulas …
V = l x w x h or V = B x h
NT
Represent / Interpret Data
Volume
© 2011 Questar III, Board of Cooperative Educational Services for Rensselaer • Columbia • Greene Counties – all rights reserved.
November 2011
Geometry ---------------------------------------------------------------------------------------------------------------- 5.G
Graph Points in 1st Quadrant
Classify 2-D Figures
Graph points and
use vocabulary of coordinate plane
Same
Solve problems by plotting points
NT
Classify figures based on properties
Same
Understand that subcategories of figures
have the same attributes
NT
Note: No probability concepts are addressed
© 2011 Questar III, Board of Cooperative Educational Services for Rensselaer • Columbia • Greene Counties – all rights reserved.
November 2011
Core vs NYS Standards
Grade 6
Core
NYS
Ratios and Proportional Relationships --------------------------------------------------------------------- 6.RP
Ratios and Rates
Understand ratio and ratio language
Same
Understand rate based on ratio
Same
Solve ratio / rate word problems in drawings
and equations
Same
Use tables and graphs to interpret
ratios / rates
New Topic
Solve unit rate problems
Same
Find the percent of a quantity, find the whole, given part and percent
Same
Use ratio to convert measurement units
Same
Number System --------------------------------------------------------------------------------------------------------- 6.NS
Complete Fraction Division
Divide fraction by fraction
including work with mixed numbers
utilizing visual models and equations
Same
Fluent with division
Same
Fluent with decimal operations
Same
GCF of any 2 numbers ≤ 100
NT
LCM of 2 numbers ≤ 12
NT
Express a sum using the distributive property
Same
Fluency
Factors and Multiples
Rational and Integer Number Systems
Understand the use of negative numbers
to describe real-world context
Same
Understand positives and negatives as opposites
Same
Locate rational numbers and integers
on a number line
Same
Order integers on a number line
Same
Understand absolute value as distance from 0
Same
© 2011 Questar III, Board of Cooperative Educational Services for Rensselaer • Columbia • Greene Counties – all rights reserved.
November 2011
Represent points in all quadrants on a plane
Same
Investigate reflections that result from sign changes on points
NT
Find vertical and horizontal distance on a plane
NT
Expressions and Equations -------------------------------------------------------------------------------------- 6.EE
Algebraic Expressions
Write and evaluate whole-number exponents
Same
Read, write, and evaluate expressions
with variables
Same
Use appropriate mathematical algebraic
and operational terms
Same
Order of operation
Same
Use of the distributive property
Same
Identify equivalent expressions
NT
Understand the meaning of an
equation’s / inequality’s solution(s)
NT
Use substitution to check
Same
Use variables to write equations / inequalities
Same
Solve one step equations / inequalities
with positive rational numbers
2-Step equations
Graph solutions to inequalities on a
number line
NT
One Variable Equations / Inequalities
Represent / Analyze 2 variable equations
Write equations in 2 variables
NT
Identify independent / dependent variables
NT
Use graphs and tables to analyze the relationship
between the variables
NT
Geometry ----------------------------------------------------------------------------------------------------------------- 6.G
Area, Surface Area, and Volume
Find area of triangles, quadrilaterals, and
polygons using decomposition
Same
Calculate volume of prisms with
fractional values
NT
© 2011 Questar III, Board of Cooperative Educational Services for Rensselaer • Columbia • Greene Counties – all rights reserved.
November 2011
Calculate area on the plane using
horizontal / vertical distances
NT
Find surface area of solids using their nets
NT
Statistics and Probability ----------------------------------------------------------------------------------------- 6.SP
Statistical Variability
Understand the meaning of statistical variability
Range
Describe statistical distributions using their
shape, centers, and spread
NT
Understand the differences between
centers and spreads
NT
Display data using dot plots, histograms,
and box plots
Histograms
Summarize data with the number of observations
NT
Describe the distribution’s variables and
their units of measure
NT
Find measures of central tendency…
mean and median
Same
Find measures of variability…
range, IQR, and mean absolute deviation
Range
Use distribution shape to choose the most
appropriate descriptive statistics
NT
Distributions
Note: No probability concepts addressed
© 2011 Questar III, Board of Cooperative Educational Services for Rensselaer • Columbia • Greene Counties – all rights reserved.
November 2011
Core vs NYS Standards
Grade 7
Core
NYS
Ratios and Proportional Relationships --------------------------------------------------------------------- 7.RP
Proportional Relationships
Unit rates with fractions
New Topic
Test for proportionality numerically,
in tables, or from a graph
NT
Determine the constant of proportionality
verbally, visually, graphically, and from equations
NT
Represent proportions by equations
Same
From a linear graph of proportionality
explain the meaning of (x,y), (0,0), and
(1, r) if r is the unit rate
NT
Use proportions to solve multistep ratio
and percent problems ( interest, tax, markup,
markdown, tip, commission, % interest )
NT
Number System -------------------------------------------------------------------------------------------------------- 7.NS
Fraction Fluency
Maintain addition, subtraction,
multiplication, and division of fractions
NT
Represent + / - of integers on number line
Same
Define addition of integers
Same
Define subtraction of integers as
“adding the opposite”
Same
Define multiplication and division of integers
Same
Define inverses
Same
Define rational numbers
Same
Convert rational numbers to decimals and
address terminating and repeating
Same
Solve problems with rational numbers
Same
Integers
© 2011 Questar III, Board of Cooperative Educational Services for Rensselaer • Columbia • Greene Counties – all rights reserved.
November 2011
Expressions and Equations -------------------------------------------------------------------------------------- 7.EE
Algebraic Expressions
Add, subtract, factor, and expand
linear expressions with rational coefficient
Same
Read, write, evaluate, and interpret expressions
with variables
Solve multistep problems with positive and
negative rational expressions and equations
Order of operation
Same
Solve 2 step equations
Multistep
Solve 2 step inequalities,
graph on number line, and interpret results
Positive coefficient
1 step
NT
Same
Geometry ----------------------------------------------------------------------------------------------------------------- 7.G
Geometric Figures
Scale Drawings
Same
Construct triangles given angle / side measures
to determine existence
NT
Describe cross-sections of right prisms
or pyramids
NT
Angle Measure, Area, Surface Area, and Volume
Derive the relationship between area and circumference
Same
Know formulas for area and circumference
of circles
Same
Define supplementary, complementary, vertical,
and adjacent angle relationships
NT
Write and solve equations to find unknown
angle measures of figures
NT
Solve area, volume, and surface area problems
Extended
Statistics and Probability ---------------------------------------------------------------------------------------- 7.SP
Sampling
Understand the meaning of a random sample
NT
Generate data from multiple random sample
NT
Examine variability between samples
NT
Using random sampling, compare populations
by using measures of center and spread
NT
Graphically compare populations
NT
Populations
© 2011 Questar III, Board of Cooperative Educational Services for Rensselaer • Columbia • Greene Counties – all rights reserved.
November 2011
Probability
Define probability, P(E) as
0 ≤ P(E) ≤ 1
Same
Distinguish between theoretical
and empirical probabilities
Same
Calculate probabilities
Same
Represent the sample space for
compound events numerically,
in tables or trees
Same
Calculate compound probabilities
Same
Use simulations to determine frequencies
for compound events
NT
© 2011 Questar III, Board of Cooperative Educational Services for Rensselaer • Columbia • Greene Counties – all rights reserved.
November 2011
Core vs NYS Standards
Grade 8
Core
NYS
Number System -------------------------------------------------------------------------------------------------------- 8.NS
Irrational Numbers
Define an irrational number
New Topic
Find decimal approximations of irrational
numbers
NT
Locate irrationals on a number line
NT
Convert repeating decimals to fraction form
NT
Expressions and Equations -------------------------------------------------------------------------------------- 8.EE
Exponents
Lines and linear equations
Equations
Operate and evaluate integer and zero exponents
Same
Estimate using powers of 10 for very
small and large quantities
NT
Scientific notation
NT
Operations with scientific notation
NT
Know simple perfect squares and cubes
NT
Solve equations using square roots or
cube roots
NT
Unit rate as slope
Same
Equations forms of y = mx and y = mx + b
Same
Explain that slope is constant
using similar triangles
NT
Solve multistep equations with rational coefficients
using distributive property and variables
on both sides
Same
Solve equations with one, no, or infinite solutions
NT
Define the solution of a system of equations
as a point
Same
Solve systems of equations both algebraically
and graphically
Graphically
Solve systems with one, no, or infinite solutions
NT
Solve system word problems
NT
© 2011 Questar III, Board of Cooperative Educational Services for Rensselaer • Columbia • Greene Counties – all rights reserved.
November 2011
Functions ---------------------------------------------------------------------------------------------------------------- 8.F
Define Functions
Model Functions
Function as a rule assigning one input
to exactly one output
Same
Function as a set of ordered pairs
Same
Interpret and compare functions in multiple forms…
tables, graphs, equations, and verbally
Same
Know if functions are non-linear
Same
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
Angle Measure
Pythagorean Theorem
Same
Define dilations, rotations, reflections,
and translations using coordinates
Same
Define transformations that
preserve distance, angle measure, and parallels
NT
Define congruence using transformations
NT
Define similarity using dilations
NT
Define similarity by A-A similarity
NT
Sum of the interior angles of a triangle
NT
Exterior angles of a triangle
NT
Angle formed by parallel lines
cut by a transversal
Same
Prove the Pythagorean theorem and converse
NT
Solve a right triangle using Pythagorean theorem
NT
Solve real-world problems in 2 and 3-dimensions
using the Pythagorean theorem
2-dimensions
© 2011 Questar III, Board of Cooperative Educational Services for Rensselaer • Columbia • Greene Counties – all rights reserved.
November 2011
Volume
Use Pythagorean theorem to find distance
between 2 points
NT
Know and use formulas for volume of cones,
cylinders, and spheres
NT
Statistics and Probability ----------------------------------------------------------------------------------------- 8.SP
Bivariate Data
Categorical Bivariate Data
Plot and interpret bivariate data
NT
Describe data patterns of clusters, outliers,
+ / - association, linear / nonlinear association
NT
Lines of Best Fit
NT
Write the equation of a Best Fit line
NT
Interpret the meaning of slope / y-intercept
in problem context
Same
Use two-way tables to show frequencies
and relative frequencies of bivariate
categorical data
NT
Look for patterns of association in
bivariate categorical data
NT
Note: No probability concepts addressed
© 2011 Questar III, Board of Cooperative Educational Services for Rensselaer • Columbia • Greene Counties – all rights reserved.
November 2011