ELMWOOD PARK PUBLIC SCHOOLS APPLIES SKILLS SOLVES … · • Identifies cone, sphere, cube, cylinder, prism Probability and Statistics • Gives examples ofcertain and uncertain events

ELMWOOD PARK PUBLIC SCHOOLSBASIC SKILLSMATHEMATICS

GRADE K

By the end of Kindergarten, a student will be competent in the following areas of mathematics.

APPLIES SKILLSComputation

• Counts to 100• Counts sets of objects• Uses objects to show addition and subtraction to ten

Measurement~easurestotheinch

Identifies pennies, nickels, and dimes

Geometry• Names shapes: circle, square, triangle, and rectangle• Sorts geometric shapes

Probability and Statistics• Begins to use tallying as a means of counting

Algebra• Forms three object patterns• Identifies missing numbers in sequences

APPROVED BY BOARD OF EDUCATIONAUGUST 24, 2010ELMWOOD PARK PUBLIC SCHOOLS

SOLVES PROBLEMS• Searches for patterns• Explores strategies

REASONS MATHEMATICALLY• Compares and contrast information• ~akes estimates

COMMUNICATES MATHEMATICAL IDEAS• Uses concrete and pictorial models to demonstrate

understanding

CONNECTS MATHEMATICS TO OTHER SUBJECTSAND LIFE

• Birthday graph• Telephone numbers


GRADE 1

By the end of Grade 1, a student will be competent in the following areas of mathematics.


• Knows place values to hundreds• Adds and subtracts single digits• Shows fractions as equal parts of a whole

Measurement• Measures to inch and centimeter

Tells time to five minutesIdentifies and gives value for pennies, nickels, and dimes

Geometry• Compares two dimensional shapes• Identifies cone, sphere, cube

Probability and Statistics• Uses tallying as a means of counting• Gives examples ofcertain and uncertain events

Algebra• Recognizes and extends patterns of objects and numbers• Reads and writes number sentences• Gives equivalent names for numbers

APPROVED BY BOARD OF EDUCATIONAUGUST 24, 2010

ELMWOOD PARK PUBLIC SCHOOLS

SOLVES PROBLEMS• Searches for and uses patterns• Explores strategies

REASONS MATHEMATICALLY• Compares and contrast information• Makes estimates

COMMUNICATES MATHEMATICAL IDEAS• Uses concrete and pictorial models to demonstrate

understanding


• Money games and activities• Temperature readings, weather charts


GRADE 2



• Counts by twos, fives, and tens• Knows whole number place value to thousands• Adds three addends• Adds and subtracts two digit numerals• Names fractions (1/2, 1/3, 1/4, 1/5) of regions

MeasurementCounts coins to $1.00Tells time to minuteMeasure to half inch, half centimeter

Geometry• Constructs and names line segments• Finds perimeter of simple polygons• Identifies cone, sphere, cube, cylinder, prism

Probability and Statistics• Gives examples of certain and uncertain events• Displays simple data in a tally chart or bar graph

Algebra• Extends patterns of objects and numbers• Solves simple addition and subtraction equations


SOLVES PROBLEMS• Investigates situations• Identifies questions• Explores a variety of strategies

REASONS MATHEMATICALLY• Compares and contrast information• Makes estimates• Checks reasonableness of results

COMMUNICATES MATHEMATICAL IDEAS• Gathers, organizes and shares information• Uses concrete and pictorial models to demonstrate

understanding


• Relates addition and subtraction• Weather Graphing


GRADE 3



• Knows whole number place value to hundred thousands• Solves three digit addition and subtraction• Represents multiplication with arrays• Finds fractions of regions and sets• Applies estimation skills

MeasurementCounts coins to $1.00 and calculates changesEstimates and measures length

Geometry• Identifies and constructs line segments and rays• Recognizes cylinders, prisms, and pyramids

Probability and Statistics• Displays data in a tally chart and bar graph• Finds median in a data set• Conducts simple chance experiments

Algebra• Extends patterns ofobjects and numbers• Understands concepts ofequalityAPPROVED BY BOARD OF EDUCATIONAUGUST 24, 2010


SOLVES PROBLEMS• Investigates situations• Identifies questions• Constructs solutions

REASONS MATHEMATICALLY• Compares and contrast information• Makes estimates• Checks reasonableness of results

COMMUNICATES MATHEMATICAL IDEAS• Gathers, organizes and shares information• Discusses mathematical ideas and asks questions


• Relates addition and subtraction• Economics: Shopping Applications


GRADE 4



• Knows whole number place value to millions• Recalls multiplication facts through nine• Multiplies one digit times three digits• Recognizes equivalent fractions• Applies estimation skills

MeasurementKnows and uses units of measure for time, money, length,and area

Geometry• Understands concepts of parallel, perpendicular, and

symmetry• Gives ordered pairs for coordinate points

Probability and Statistics• Investigates uncertain events• Collects, organizes, and displays data in graphs• Finds median and mode in a data set

Algebra• Extends patterns• Represents number patterns• Solves simple equations using addition, subtraction,

multiplication, and division


SOLVES PROBLEMS• Investigates situations• Formulates questions, defines problems• Constructs solutions

REASONS MATHEMATICALLY• Analyzes information• Predicts results, makes inferences• Draws conclusions, verifies results

COMMUNICATES MATHEMATICAL IDEAS• Gathers, organizes, interprets, represents, and shares

information• Explains thinking using mathematical language and'

notation such as models, tables, graphs, and numbers


• Relates multiplication and division• Economics, Geography


GRADE 5

By the end of Grade 5, a student will have command of the following areas of mathematics.


• Understands whole number and decimal place values• Multiplies and divides by two digit numbers• Applies concepts of prime and composite numbers,

divisibility, and factoring• Applies estimation skills

MeasurementFinds area, perimeter, radius, diameter, and volume

Geometry• Measures and uses mathematical terminology to describe

shapes and angles• Plots ordered pairs

Probability and Statistics• Conducts probability experiments and simulations• Finds median, mode, and mean

Algebra• Solves simple single variable equations• Creates and extends two step patterns



REASONS MATHEMATICALLY• Analyzes information• Predicts results, makes inferences• Draws conclusions, verifies results


information• Explains thinking using mathematical language and

notation such as models, tables, graphs, and numbers


• Relates multiplication and division• Economics, Geography, Health, Physical Science


GRADE 6

By the end of Grade 6, students will be competent in the following areas of mathematics


• Applies and extends previous understandings ofmultiplication and division to divide fractions by fractions

• Multiplies and divides multi-digit numbers and findscommon factors and multiples

• Applies and extends previous understandings of numbersto the system of rational numbers

Ratios and Proportional Relationships• Understands ratio concepts and uses ratio reasoning to

solve problemsGeometry

• Selects, understands, and uses tools (protractor, compass)• Understands coordinate geometry• Finds area, perimeter, circumference, radius, diameter, and

volumeProbability and Statistics

• Finds median, mode, and mean• Interprets circle graphs, line graphs, step graphs, and bar

graphs• Determines probability of chance events• Develops understanding of statistical variability• Summarizes and describes distributions

Expressions and Equations• Applies and extends previous understandings of arithmetic

to algebraic expressions


• Reasons about and solves one-variable equations andinequalities

• Represents and analyzes quantitative relationships betweendependent and independent variables

SOLVES PROBLEMS• Attends to precision• Uses appropriate tools strategically• Investigates situations• Formulates questions, defines problems• Constructs solutions• Makes sense of problems and perseveres in solving them

REASONS MATHEMATICALLY• Analyzes information• Looks for and makes use of structure• Looks for and expresses regularity in repeated reasoning• Predicts results, makes inferences• Draws conclusions, verifies results• Reasons abstractly and quantitatively



notation such as models, tables, graphs, and numbersCONNECTS MATHEMATICS TO OTHER SUBJECTSAND LIFE

• Art, Physical Education, Earth Science


GRADE 7



• Applies and extends previous understandings of operationswith fractions to add, subtract, multiply, and dividerational numbers

Ratios and Proportional Relationships• Analyzes proportional relationships and use to solve real

world and mathematical problemsGeometry

• Draws, constructs and describes geometrical figures anddescribe the relationships between them

• Solves real-life and mathematical problems involvingangle measure, are, surface, area, and volume

Probability and Statistics• Uses random sampling to draw inferences about a

population• Draws informal comparative inferences about two

populations• Investigates chance processes and develop, use, and

evaluate probability modelsExpressions and Equations

• Uses properties of operations to generate equivalentexpreSSIOns

• Solves real-life and mathematical problems usingnumerical and algebraic expressions and equations



REASONS MATHEMATICALLY• Analyzes information• Predicts results, makes inferences• Draws conclusions, verifies results• Reasons abstractly and quantitatively



notation such as models, tables, graphs, and numbers• Constructs viable arguments and critiques the reasoning of

others


• History, Science, Phys. Ed., Music, Art


GRADE 8



• Knows that there are numbers that are not rational andapproximates them by rational numbers

Functions• Defines, evaluates, and compares functions• Uses functions to model relationships between quantities

Geometry• Understands congruence and similarity using physical

models, transparencies, or geometry software

Probability and Statistics• Investigates patterns of association in bivariate data

Expressions and Equations• Works with radicals and integer exponents• Understands the connections between proportional

relationships, lines, and linear equations• Analyzes and solves linear equations and pairs of

simultaneous linear equations

APPROVED BY BOARD OF EDUCAnONAUGUST 24, 2010


SOLVES PROBLEMS• Attends to precision• Investigates situations• Formulates questions, defines problems• Constructs solutions

REASONS MATHEMATICALLY• Analyzes information• Predicts results, makes inferences• Draws conclusions, verifies results• Reasons abstractly and quantitatively• Looks for and makes use of structure• Looks for and expresses regularity in repeated reasoning



notation such as models, tables, graphs, and numbers• Constructs viable arguments and critiques the reasoning of

othersCONNECTS MATHEMATICS TO OTHER SUBJECTSAND LIFE

• History, Science, Economics, Social Sciences, Arts


GRADE 9-12


COMPUTATION• Applies basic mathematical operations

o Adds and subtracts by finding a common denominator,multiplies and divides, reduces and performs long divisionwithout a calculator

o Uses exponents and scientific notationo Understands percents, including percents less than I% and

greater than 100%o Uses ratios and proportions to solve problemso Uses radicals correctlyo Calculates using absolute valueo Finds and uses multiples, factors, and primeso Adds, subtracts, multiplies and divides numbers, and uses

the relationships among these operations including inverse,commutative, associative, and distributive properties

o Knows terminology for complex numbers, integers, rationalnumbers, irrational numbers, and complex numbers

• Knows and carefully records symbolic manipulationso Understands the use of mathematical symbols as well as the

limitations on their appropriate uses (e.g., equal signs,parentheses, superscripts, and subscripts).

• Demonstrates fluency with mathematical notation andcomputation

o Correctly performs addition, subtraction, multiplication, anddivision that includes variables

o Performs appropriate basic operations on sets (e.g., union,intersection, elements of, subsets, and complement)


o Uses alternative symbolic expressions, particularlyalternatives to x (e.g., letters of the Greek alphabet that donot already have specific scientific or mathematicalmeanings)

ALGEBRA• Knows and applies basic algebraic concepts

o Uses the distributive property to multiply polynomialso Knows how to compose and decompose functions and how

to find inverses of basic functionso Simplifies and perfonns basic operations on rational

expressions, including finding common denominatorso Understands exponents, roots, and their propertieso Knows basic theorems of exponents and rootso Understands logarithms (to bases 2, 10 and e) and their

propertieso Divides low degree polynomials (e.g., long division)o Knows basic theorems of logarithmso Factors polynomials (e.g., differences of squares, perfect

square trinomials, differences oftwo cubes and trinomialssuch as x2 + 3x + 2)

• Uses various appropriate techniques to solve basic equations andinequalities

o Solves linear equations and absolute value equationso Solves linear inequalities and absolute value inequalitieso Solves systems of linear equations and inequalities using

algebraic and graphical methods (e.g., substitutionelimination, addition, and graphing)

o Solves quadratic equations using various appropriatemethods while recognizing real solutions

• Factoring• Completing the square• The quadratic formula

• Distinguishes between and among expressions, formulas,equations and functions

o Knows when it is possible to simplify, solve, substitute orevaluate equations and expressions and when it is notpossible

o Understands that the concept of a function has a specificdefinition beyond being a type of algebraic expression

o Represents functions, patterns, and relationships in differentways (e.g., statements, formulas, and graphs)

o Understands the algebraic language and notation forfunctions

o Understands a variety offunctions and properties of each• Understands the relationship between equations and graphs

o Understands basic forms of the equation ofa straight lineand how to graph the line without the aid of a calculator

o Understands the basic shape of a quadratic function and therelationships between the roots of the quadratic and zeroesof the function

o Knows the basic shape of the graph of exponential and logfunctions, including exponential decay

• Applies algebra procedurally and conceptually to a range ofcommon problems

o Recognizes which type of expression best fits the context ofa basic application

• Linear equation to solve distance/time problems• Quadratic equation to explain the motion of a falling

object• Compound interest as an exponential function

• Demonstrates the ability to work with formulas and symbolsalgebraically

o Knows formal notationo Knows arithmetic and geometric progressions and series

APPROVED BY BOARD OF EDUCATIONAUGUST 24, 2010


GEOMETRY• Understands and uses both basic plane and solid geometry

o Knows properties of similarity, congruence and parallellines cut by a transversal

o Knows how to figure area and perimeter of basic figureso Understands the ideas behind simple geometric proofs

and is able to develop and write simple geometric proofs• Pythagorean theorem• There are 180 degrees in a triangle• The area ofa triangle is half the base times the

heighto Solves problems involving proofs through the use of

geometric constructionso Uses similar triangles to find unknown angle

measurements and lengths of sideso Visualizes solids and surfaces in three-dimensional

spaceo Knows the basic formulas for volume and surface area

for three-dimensional objects• Knows analytical (coordinate) geometry

o Knows geometric properties of lines (e.g., slope andmidpoint of a line segment)

o Knows the formula for the distance between two pointso Solves mathematical and real world problems that

involve the properties of special right triangles with thePythagorean theorem and its converse

o Recognizes geometric translations and transformationsalgebraically

• Understands basic relationships between geometry andalgebra

o Knows that geometric objects and figures can also bedescribed algebraically

o Knows the algebra and geometry of circleso Knows the algebra and geometry of parabolas and

ellipses

PROBABILITY AND STATISTICS• Applies concepts of statistics and data analysis in the social

sciences and natural scienceso Understands data displays including bar graphs and

scatterplotso Finds the mean. median. and mode of a data seto Expresses the probability of an event as a ratio. a decimal, or

a percento Knows whether events are independent or dependent

MATHEMATICAL REASONING• Knows important definitions, why definitions are necessary and

are able to use mathematical reasoning to solve problemso Uses inductive reasoning in basic argumentso Uses deductive reasoning in basic argumentso Uses geometric and visual reasoningo Uses multiple representations to solve problemso Learns to solve multi-step problemso Uses a variety of strategies to revise solution processeso Understands the use of both proof and counterexample in

problem solutions and are able to conduct simple proofso Understands the process of abstracting mathematical models

from word problems. geometric problems and applicationsand are able to interpret solutions in the context of thesesource problems

• Understands work with mathematical notation to solve problemsand to communicate solutions

o Translates simple statements into equationso Understands the role of written symbols in representing

mathematical ideas and the precise use of special symbols ofmathematics

• Knows a select list of mathematical facts and knows how to buildupon those facts

o Pythagorean theoremo Formulas for perimeter. area. volumeo Quadratic formula


•

•

•

•

Estimates successfullyo Converts between decimal approximation and fractionso Uses estimation or approximation in place of an exact

answero Recognizes the accuracy of an estimationo Makes and uses estimations

Understands and uses calculators appropriately yet realizestheir limitations

o Recognizes when the results produced are unreasonable orrepresent misinformation

o Uses calculators for systematic trial-and-error problemssolving

o Plots useful graphsGeneralizes and goes from specific to abstract and abstract tospecific

o Determines the mathematical concept from the context of anexternal problem. solves the problem. and interprets themathematical solution in the context ofthe problem

o Knows how to use specific instances of general facts. aswell as how to look for general results that extend particularresults

Demonstrates active participation in the process of learningmathematics

o Experiments with problems that have multiple solutionmethods

o Demonstrates an understanding of the mathematical ideasbehind the steps of a solution. as well as the solution

o Shows an understanding of how to modify patterns to obtaindifferent results

o Shows an understanding of how to modify solutionstrategies to obtain different results

o Recognizes when a proposed solution does not work,analyzes why and uses the analysis to seek a valid solution

• Recognizes and applies the broad range of applications inmathematical reasoning

o Knows that mathematical applications are used in otherfields

• Carbon dating• Exponential growth• Predator/prey models• Periodic motion• Interactions of waves

o Knows that mathematics has played and continues to play animportant role in the evolution of disciplines as diverse asscience, engineering, music, and philosophy


Documents

ELMWOOD PARK PUBLIC SCHOOLS APPLIES SKILLS SOLVES … · • Identifies cone, sphere, cube, cylinder, prism Probability and Statistics • Gives examples ofcertain and uncertain events