mathematics curriculum guidelines · comparing and ordering iodd and even numbers. one mdigit. two...

DIOCESE OF ROCKFORD, ILLINOIS

MATHEMATICS

CURRICULUM

GUIDELINES

2014

Acknowledgments

Michael M. Kagan, Assistant Director of Educational Services, Superintendent of Schools

Margo J. Shifo, Assistant Superintendent of Schools

Chairperson:

Karen Behrns, Principal Our Lady of Good Counsel School

Aurora, Illinois William Anderson, Teacher Cori Gendron, Principal

St. Anne School St. Edward School Dixon, Illinois Rockford, Illinois

Abbie Miller, Teacher Bianca Sutherland, Teacher Our Lady of Good Counsel School St. Rita School

Aurora, Illinois Rockford, Illinois

Barbara Villont, Curriculum Director Marian Central Catholic High School

Woodstock, Illinois

Editing Staff Cori Gendron Beth Heitkamp Richard Reynolds St. Edward School St. Bernadette School Cathedral of Peter School Rockford, IL Rockford, IL Rockford, IL

ii

PreSchool

DATE COMPLETEDCount, recognize, read, and write numbers 0‐20. MCount, recognize, read, and write numbers 0‐100. IDemonstrate one‐to‐one correspondence 0‐20. I/DCount backwards from 10. I/D

Recognize and illustrate one‐half, whole. I

Identify penny, nickel, dime, quarter, and dollar. I

Count by 2's to 20. ICount by 5's to 50. ICount by 10's to 100. I

More than. ILess than. IEqual to. I

Compute sums to 9 using manipulatives. I/DCompute differences from 9 using manipulatives. I/D

Use charts, graphs, and tables . ISort, classify, and use patterns . IPredicting patterns. I

Know months, days of the week. ISequence of events and timelines. ICompare and order objects (i.e. length, height, weight). I

Above, below, before, after, between. I/DInside, outside, nearest, farthest. I/D

NUMBER SENSE AND NUMERATION Whole Numbers

Fractions

Money

Skip Counting

To identify objects by location

Compare Sets, Numbers

Perform operations using whole numbers

Problem solving

Measurement

Geometry and Spatial Sense

I=Introduce M=Mastery m=maintainD=Develop I/D=Intro/Dev

PreSchool Page 1

PreSchool I=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevLeft, right. I

Triangles. MSquares, rectangles. MPentagon, octogon. ICircle. MHalf‐circle. I/DOval. I

Teaching PointsCounting on from any number 0‐20Estimate reasonable quantitiesIdentify morning, afternoon, nightAsk how and why questionsIdentify top/bottom, front/backDiscuss yesterday, today, tomorrow

Identify and name plane figures

PreSchool Page 2

DATE COMPLETEDSequence numbers to 100.* MRecognize, read and write numbers to 100.* MRecognize number words, zero to ten. MRecognize, read and write numbers to 1000.* ISkip count by 10's. MSkip count by twos and fives. IUse decade words. ICount on from any number to 100.* IUse ordinal numbers to identify location.* MUse 1:1 correspondence.* IIdentify a specific object in a collection ‐ to count on.* ICount backward from 10. MConnect ordinal number to cardinal number ‐ first through tenth. MConnect ordinal number to cardinal number ‐ eleventh through twentieth. IRecognize, read and write place value: to the left of the decimal point ‐ by one digit. MRecognize, read and write place value: to the left of the decimal point ‐ by two digits. IEstimate ‐ adding and subtracting. IApply Commutative property of addition. IUse mental math ‐ addition and subtraction. I

Identify 'more than',' less than' and 'equal to'.* MEqualize sets.* I

Use signs of equality and inequality, <, >, ≠ =.* I

Identify "Set." ICompute sums to 10 using manipulatives ‐ adding and subtracting.* M

Represent addition and subtraction using the number line. I

KindergartenNUMBERS AND OPERATIONS

Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1‐20, count out that many objects.

Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g. claps), acting out situations, verbal explanations, expressions or equations.


Kindergarten Page 1

Kindergarten I=Introduce M=Mastery m=maintainD=Develop I/D=Intro/Dev

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem*

I

Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5=2+3 and 5=4+1).

I

Master facts to 5 ‐ addition and subtraction.* MCompute sums to 19 using manipulatives ‐ adding and subtracting.* IIntroduce facts to 12 ‐ addition and subtraction. I

Demonstrate knowledge of 1/2, 1/3, 1/4. ICalculate equal parts of a whole. I

ALBEBRA

By observing, describing, comparing and creating. IBy sorting and classifying by characteristics. IBy predicting what comes next, identifying the missing element. IBy distinguishing between growing and repeating patterns. IBy representing information numerically, graphically and verbally. IBy discussing and analyzing change. IBy measuring and comparing quantities. IBy using tables and graphs I

Measure geometric figures by: comparing, ordering objects without measuring tools.* DDescribe and compare length and height.* DDescribe and compare weight.* DDescribe and compare distance, capacity, mass. DCompare objects using nonstandard units (i.e. length, weight, capacity, etc.). M

MEASUREMENT AND DATA Describe and compare measurable attributes:

Fractions

Use algebraic and analytical methods to understand patterns and relationships:

Kindergarten Page 2

Kindergarten I=Introduce M=Mastery m=maintainD=Develop I/D=Intro/Dev Time

Recognize, read and write: months, days of the week. IRecognize, read and write: hour, half hour. IRecognize and read digital, analog time. ICreate and interpret sequence of events, timelines. IRecognize elapsed time without changing units. IRecognize, tell, and count money: penny nickel, dime, dollar. ITo determine proper tool use of measurement: ruler, thermometer. I

Read, write, and count money in dollars and cents. I

GEOMETRY Identify and describe shapes.

Above, below, before, after, between. MInside, outside, nearest, farthest. MLeft, right, north, south, east, west. IInvestigate and predict the result of: slide, turn, flip. IChanging shapes. IDescribe, model, draw, and classify: point. I

Triangles. MSquares, rectangles. MPentagons, hexagons, octagons. IEllipse (oval). MCircle. MSemi‐circle. M

Cube, cylinder, sphere, cone. IDescribe symmetry, congruency. I

Describe, model, draw and classify:

Analyze, compare, create, and compose shapes:*

Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

Identify objects by location:

Money

Kindergarten Page 3

Kindergarten I=Introduce M=Mastery m=maintainD=Develop I/D=Intro/Dev

Construct convincing arguments and proofs to solve problems using geometric figures and shapes.

I

Collect and describe data. IOrganize and construct data. I

Identify, draw, label and analyze:Real graph (using actual objects). IPicture graph, bar graph. IVenn diagram. IProbability ‐ single event. IFormat questions; conduct experiments, surveys. IDemonstrate data collection methods. IClassify objects into given categories; count the number of objects in each category and sort the categories by count.

I

PROBLEM SOLVINGAnalyze and plan the problem determining the appropriate strategy by:

Drawing a picture. ICreating original problems. IDetermining if information is sufficient to solve. IUsing tables, charts, graphs and diagrams. ITrial and error. IWorking backwards. ISorting, classifying and using patterns. IUsing estimation. IChoosing correct operation. IChecking reasonableness. IDraw logical conclusions and communicate reasoning: using simple materials. IUse technology to draw conclusions and solve problems. I

STATISTICS AND PROBABILITY

Compose simple shapes to form larger shapes, For example, "Can you join these two triangles with full sides touching to make a rectangle?"

Kindergarten Page 4

Date Completed

Recognize, read, and write numbers 120.* mRecognize, read, and write numbers to 1000. DUnderstand natural counting. D

One half, one third, one fourth. DFifths through tenths. IInequalities. I

Money in dollars and cents. DNumber words zero to ten. DNumber words zero to twenty. IDecade words. D

Count by ones: to 100 m to 1000. ICount from any given number to 100. MCount backward from 10. mCount backward from 20. ICount backward from any given number up to 100. I

By tens. MBy twos and fives. DBy hundreds. IUse ordinal numbers to identify location. m

Connect ordinal number to cardinal number: First through tenth. m Eleventh through twentieth. MCount on. M

Identify a specific object in a collection

Skip count from any given number:

Sequence numbers (counting skills):

Grade 1NUMBERS AND OPERATIONS Extend the counting sequence.

Recognize, read, and write decimals:

Recognize, read, and write numbers in fractions:


Grade 1 Page1

Date CompletedGrade 1 I=Introduce M=Mastery m=maintainD=Develop I/D=Intro/Dev

Using 1:1 correspondence. MTo identify "more than," "less than," and "equal to". MTo equalize sets. M

= D<, >, not = IComparing and ordering odd and even numbers. I

One digit. mTwo digits. MThree digits. Icomparisons with the symbols >, =, and < I

Estimate. D

Compute sums to 9 using manipulative. mCompute sums to 18 using manipulatives. MMaster facts to 5. mMaster facts to 12. MDevelop facts to 18. DDefine addend and sum. I

3 addends, 1 digit numbers. D4 or more addends, 1 digit numbers. I

2 or more 2 digit numbers. IDollar and cents. IUsing the number line. MUsing commutative property. DUsing mental math. D

Recognize, read, understand and write place value*: Understand place value

Use signs of equality and inequality:

Compare sets, numbers:

Perform operations using whole numbers and integers.

Compute with regrouping:

Compute, no regrouping:

Find sums (of whole numbers):

Add.

Use place value understanding and properties of operations to add and subtract.

To the left of the decimal point:

Grade 1 Page2


Estimate. D

Compute differences from 9 using manipulative. mCompute differences from 18 using manipulatives. MMaster facts to 5. mMaster facts to 12. MMaster facts to 18. DDefine subtrahend, minuend, difference. ICompute multi‐digit numbers with no regrouping.* DUsing the number line. MUsing mental math. D

Equal parts of a whole. D

ALGEBRA

Using simple materials. DUsing technology. D

By observing, describing, comparing, and creating. DBy sorting and classifying by characteristics. DBy predicting what comes next and identifying the missing element. DBy distinguishing between growing and repeating patterns. DBy representing information numerically, graphically, and verbally. DBy discussing/analyzing change. DTo identify patterns. D

MEASUREMENT

Use manipulative materials to model concepts of measurement. D

Compare, order objects without measuring tools. MMeasure distance, length, and height. MMeasure capacity, weight. M

Measure geometric figures*:

Draw logical conclusions and communicate reasoning:

Understand patterns and relations:

Measure lengths indirectly and by iterating length units.

Recognize, read, and write Fractions

Find differences (of whole numbers):

Subtract.

Grade 1 Page3


Measure mass. MCompare objects using nonstandard units (i.e.. Length, weight, capacity, etc.). m

U.S. customary system.Length: inch, 1/2 inch, 1/4 inch. ILength: foot, yard. MCapacity (cup, pint, quart, gallon). IWeight (ounce, pound, ton). IConversions within system. ITemperature Fahrenheit. I

Length: millimeter, centimeter, decimeter, meter. ITemperature Celsius. I

Ruler. MThermometer. M

Time

Months, days of the week. MHour, half hour.* MHalf past, quarter past, quarter to. IFive minute intervals. IDigital, analog time. DSequence of events, timelines. DElapsed time, duration without changing units. D

Money

Penny, nickel, dime, dollar. MQuarter, half dollar. IFive and ten dollar bill. IMake change. I

Recognize, tell, and count money:

Recognize, read, and write time:

Determine proper tool for use of measurement:

Metric system

Compare and/or order objects using appropriate units:

Grade 1 Page4


GEOMETRY

Above, below, before, after, between. MInside, outside, nearest, farthest. MLeft, right, North, South, East, West. D

Slide, turn. DChanging shapes. MFlip. DDescribe, model, draw, and classify point. D

Triangles. mQuadrilaterals I square, rectangles. mPentagons, hexagons, octagons. DEllipse (oval). mCircles. MIdentify semicircle (half circle). m

Cube, cylinder, sphere, cone. DSymmetry, congruency. D


By measuring and comparing quantities. DBy using tables and graphs. DCollect and describe data. D

Real graph (using actual objects). DPicture graph, bar graph. DVenn Diagram. D

Identify and describe shapes* Identify objects by name and location:*

Discuss and analyze change:

Construct convincing arguments and proofs to solve problems using geometric figures and patterns.

Identify solid figures:

Describe, model, draw, and classify plane figures*

Investigate and predict the result of:

Organize and construct data. Identify, draw, label, and analyze:

Grade 1 Page5


Single event. DPermutations, combinations. I

Conduct experiments, surveys. DDemonstrate data collection methods. D

PROBLEM SOLVING

Drawing pictures. DCreating original problems. DDetermining if sufficient information present to solve. DUsing tables, charts, graphs, and diagrams.* DUsing Trial and error. DWorking backwards. DSorting, classifying, and using patterns. DEstimation. DChoosing correct operation. DChecking reasonableness. D

Analyze and plan the problem determining the appropriate strategy by:

Format Questions.

Determine the probability of:

Grade 1 Page6

Grade 2 DATE COMPLETED

Recognize, read, and write whole numbers to 1000.* MRecognize, read, and write natural numbers. DRecognize, read, and write number words, zero to twenty. MRecongnize, read, and write decade words. MRecognize, read, and write Roman Numerals. IRecognize, read and write numbers to describe "set". DConnect ordinal number to cardinal number, eleventh through twentieth. mCount on from any given number to 100. mCount backward from 20.* MCount backward from any given number up to 100. DSkip count from any given number by 10's.* mSkip count from any given number by 5's.* MSkip count from any given number by 100's.* MSkip count from any given number by 1000's. IRead and write numbers to 1000 using base‐ten numerals, number names, and expanded form. I

Add using the number line. mSubtract using the number line. M

Estimate addition using whole numbers. DCompute sums to 9 using manipulatives. mCompute sums to 18 using manipulatives. mMaster addition facts to 12. mMaster addition facts to 18.* MDefine addend and sum. MCompute, no regrouping, 3 or more addends, 1 digit. DEstimate subtraction using whole numbers. DCompute differences from 18 using manipulatives. mMaster subtraction facts to 12. mMaster subtraction facts to 18.* MDefine subtrahend, minuend, difference. D

NUMBERS AND OPERATIONS

Represent and solve problems involving addition and subtraction.

Add and subtract within 20.


Second Grade Page1

Grade 2 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/Dev

By two digits.* mBy three digits.* M

Compute with regrouping, 2 or more 2 digit numbers.* MAdd with regrouping, 2 or more 3 digit numbers.* I/DAdd with regrouping, 2 or more 4 digit numbers.* I/DSubtract multi‐digit numbers with no regrouping.* MSubtract with regrouping, two 2‐digit numbers.* MSubtract with regrouping, two 3‐digit numbers. IMentally add 10 or 100 to a given number 100‐900, and mentally subtract 10 or 100 from a given number 100‐900,* DExplain why addition and subtraction strategies work, using place value and the identity, commutative, and associative properties of addition.* D

Estimate multiplication. ICompute products with factors up to 5x5, with or without manipulatives.* I

Master multiplication facts through 12. IMultiply 2‐digit by 1‐digit numbers. ICommutative Property of Multiplication. IMultiply using mental math. I

Master division facts through 12. I

Recognize and demonstrate 1/2, 1/3, 1/4 MRecognize and demonstrate fifths through tenths. DRecongize and demonstrate Inequalities. DCalculate: Equal parts of a whole. D

Divide.

g f q g halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Fractions

Work with equal groups of objects to gain foundations for multiplication.

Use place value understanding and properties of operations to add and subtract.

Recognize, read, and write place value: To the left of the decimal point:

Multiply.

Second Grade Page2


Determine inequalities. DIdentify more than, less than, equal to. mEqualize sets. m

= M ≠, <, > DCompare and order odd and even numbers. D

ALGEBRA

Using simple materials. DUsing technology. D

By observing, describing, comparing, and creating. DBy sorting and classifying by characteristics. DBy predicting what comes next and identifying the missing element. DBy distinguishing between growing and repeating patterns. DBy representing information numerically, graphically, and verbally. DBy discussing/analyzing change. DTo identify patterns. DSolve simple equations informally. I

Use manipulative materials to model concepts of measurement. D

Length: inch, 1/2 inch, 1/4 inch. DLength: 1/8 inch, 1/16 inch. ILength: foot, yard. MLength: mile. ILength: millimeter, centimeter, decimeter, meter. DCapacity: cup, pint, quart, gallon. M

Draw logical conclusions and communicate reasoning:

Understand patterns and relations:

Understand inequalities.

Use signs of inequality:

Measure (or estimate), compare, and/or order objects using appropriate units:

MEASUREMENT

Second Grade Page3

Grade 2 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevWeight: ounce, pound, ton. MMake conversions within English system. DTemperature: Fahrenheit. MTemperature: Celsius. DMeasure an object twice, using different appropriate units for the two measurements; describe how the two measurements relate to the size of the unit chosen.* I/D

Months, days of the week. mHour, half hour. mHalf past, quarter past, quarter to. MFive minute intervals. DMinutes before and after. IAM and PM. IDigital, analog time. DSequence of events, timelines. DElapsed time, duration, without changing units. D

Sequence of events, timelines. DElapsed time, duration, without changing units. D

Recognize, read, and write numbers to describe dollars and cents. MAdd with dollars and cents. MRecognize and count penny, nickel, dime, dollar. mRecognize and count quarter, half‐dollar. MRecognize and count five and ten dollar bills. MRecognize and count $20, $50, and $100 bills. IMake change. D

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and c symbols appropriately*:

Recognize, read, and write time:*

Solve problems involving time:

Second Grade Page4


Triangles. mQuadrilaterals. mSquares, rectangles. mPentagons, hexagons, octagons. DIrregular shapes. ISolid figures: cube. D

Perimeter. IArea (Square, Rectangle). ICircumference. IVolume. I

Above, below, before, after, between. mInside, outside, nearest, farthest. mLeft, right, North, South, East, West. M

Slide, turn. DChanging shapes. mFlip. D

Plane elements: point. DEllipse (oval). mCircles, semicircles. m

Cylinder, sphere, cone. DPrisms (triangular, rectangular). IPyramid. IDetermine symmetry, congruency. D

Using simple materials. DUsing diagrams. I

Reason with shapes and their attributes.GEOMETRY

Construct convincing arguments and proofs to solve problems using geometric figures and patterns:

Describe, model, and classify solid figures:

Describe, model, draw, and classify:



Define, compare, demonstrate, and calculate:

Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.*

Second Grade Page5

Grade 2 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevUsing technology. D

By measuring and comparing quantities. DBy using tables and graphs. DBy collecting and describing data. D

Read and create a real graph (using actual objects). MInterpret and create picture graph, bar graph, line plot. DInterpret and create Venn diagram. D

Conduct experiments, surveys. DDemonstrate data collection methods. D

Single event. DPermutations, combinations. D

PROBLEM SOLVING

Drawing pictures. DCreating original problems. DDetermining if sufficient information present to solve. DUsing tables, charts, graphs, and diagrams.* DUsing Trial and error. DWorking backwards. DSorting, classifying, and using patterns. DEstimation. DChoosing correct operation. DChecking reasonableness. D


Format Questions.

Organize and construct data:

Discuss and analyze change: Represent and interpret data*.

Determine the probability of:


Second Grade Page6


Decimals to tenths, hundredths. IMoney in dollars and cents. mNumber words zero to twenty. mDecade words. mRoman numerals. D "Set." D

Whole numbers to 999. mWhole numbers to six digits. MNatural, counting numbers. M

Count by ones to 999. mCount backward from 20. mCount backward from any given number, up to 100. MUse skip counting from any given number by 2's, 5's, 10's, and 100's. mUse skip counting from any given number by thousands. M

To the left of the decimal point by one, two, and three digits. mTo the left of the decimal point through six digits. ITo the right of the decimal point by one digit. I

To the nearest ten, hundred. MTo the nearest thousand. ITo the nearest dollar. I

use = muse ≠, >, < M

Recognize, read, and write place value:

Compare sets, numbers: Use signs of equality and inequality:

Round numbers:


Sequence numbers (counting skills):

Recognize, read, and write numbers to describe:

Recognize, read, and write numbers to describe:


Third Grade Page 1


Numbers beyond 1000. IOdd and even numbers. M

Estimate. DMaster facts to 18. mDefine addend and sum. mCompute, no regrouping (4 or more one digit addends). M

2 or more 2‐digit numbers. m2 or more 3‐digit and 4‐digit numbers. MApply Commutative property of addition. MApply Associative property of addition. DAdd using mental math. D

Estimate. DMaster facts to 18. mDefine subtrahend, minuend, difference. MCompute multi‐digit numbers with no regrouping. mCompute with regrouping two 3‐digit numbers. MCompute with regrouping, any two numbers. ISubtract with dollars and cents. ISubtract using a number line. mSubtract using mental math. D

Interpret products of whole numbers within 100, e.g., interpret 5x7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5X7.* MInterpret whole‐number quotients of whole numbers, e.g., interpret 56/8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56/8.* M

Add.

Compute, with regrouping:

Subtract.

Compare and order:

Represent and solve problems involving multiplication and division.*

Third Grade Page 2

Grade 3 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevUse multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.* D

Apply Associative property of multiplication. 3x5x2 can be found by 3x5=15, then 15x2=30. * DApply Commutative Property of Multiplication. 5x3=15 and 3x5=15.* MApply Distributive Property. Knowing that 8x5=40 and 8x2=16, one can find 8x7 as 8x(5+2) = (8x5)+(8x2)=40+16=56. * I

Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 25x2=50, one knows 50/2=25) or properties of operations.* MCompute products with factors up to 5x5. MDefine multiplier, multiplicand, product, factor. MKnow from memory facts through 10.* MCompute with no regrouping, 2‐digit x 1‐digit. MCompute with no regrouping, 2‐digit x 2‐digit, 3‐digit x 2‐digit. ICompute with regrouping, 2x1‐digit, 2‐x2‐digit, 3‐x2‐digit. IWrite numbers using expanded notation IDefine divisor, dividend, quotient, remainder. IMaster division facts through 12. DCompute with no remainder, 2‐x1‐digit, 3‐x1‐digit. I

One‐half, one‐third, one‐fourth. mFifths through tenths. M2/3, 2/4, 3/4, and tenths. IDenominators and numerators, like fractions. ICalculate fractions as equal parts of a whole. DCompare and solve inequalities involving fractions. D

Estimate and use mental math with addition, subtraction, multiplication. DEstimate and use mental math with division. I

Recognize, read, write, and apply numbers to describe:

Use estimation skills appropriately:

Understand properties of multiplication and the relationship between multiplication and division*.

Multiply and divide within 100*.

Fractions:

Third Grade Page 3


ALGEBRADetermine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8x?= 48, 5=_/3, 6x6=?* I

To understand patterns and relationships. DTo identify unknown quantities, algebraic phrases. DTo identify patterns. DTo solve simple equations informally. D

Inch, 1/2 inch, 1/4 inch. M1/8 inch, 1/16 inch. DCapacity (Volume) using milliliter, liter, kiloliter. I/DWeight/Mass using gram, kilogram. I/D

Length: Foot/yard. mLength: Mile. MLength: Millimeter, centimeter, decimeter, meter. DLength: Kilometer. ICapacity: cup, pint, quart, gallon. mWeight: ounce, pound, ton. mTemperature: Fahrenheit. mTemperature: Celsius. D

Five minute intervals. MMinutes before and after. DAM and PM. DDigital, analog time. MElapsed time, duration, without changing units. D

Use algebraic and analytical methods:

Comparing and Ordering objects using appropriate units: Length:

Measurement & Data

Recognize, read, and write time (including solving word problems)*:

Compare and/or order objects using appropriate units:

Third Grade Page 4

Grade 3 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevElapsed time, duration, with changing units. ISequence of events, timelines. DSchedules. I

All coins. mOne‐, five‐, and ten‐dollar bills. m$20, $50, and $100's. MMake change. D

GEOMETRY

Point. MRight angles. ISquares, rectangles. mCube, cylinder, sphere, cone. DPrisms, triangular and rectangular. DPyramid. DSymmetry, congruency. DPentagons, hexagons, octagons. D

Area of a square, rectangle. DCircumference. DPerimeter. DVolume. D

Left, right, North, South, East, West. m

Slide, turn, flip. D

Draw conclusions and communicate reasoning using simple materials, diagrams, technology. D



Describe, model, draw, and classify:

Construct convincing arguments and proofs to solve problems using geometric figures and patterns.


Recognize, tell, and count money:

Third Grade Page 5


Conduct experiments, surveys. DDemonstrate data collection methods. DDesign data collection methods. I

Identify, draw, label, analyze real graph. mIdentify, draw, label, analyze picture graph, bar graph, Venn Diagram. DIdentify, draw, label, analyze tables, circle graph, solid line graph. I

By measuring and comparing quantities. DBy using tables and graphs. D

Drawing pictures, creating original problems, determining if information is sufficient to solve. DUsing tables, charts, graphs, and diagrams, trial and error, working backwards, using patterns. DEstimating, and choosing the correct operation. DCheck reasonableness. D

Discuss and analyze change:

Format Questions.

PROBLEM SOLVING Analyze and plan the problem determining the appropriate strategy by:

Organize and construct data.


Third Grade Page 6


Use signs of equality and inequality ‐ not equal, <, >. mCompare and order whole numbers to 6 digits. mCompare and order whole numbers to 9 digits. IUse Natural counting. mCompare and order decimals. D

Use place falue understanding to round multi‐digit whole numbers to any place:Round numbers to the nearest ten, hundred, thousand. MRound numbers to the nearest thousand. IRecognize, read and write place value 6 digits to the left of the decimal point. MRecognize, read and write place value 9 digits to the left of the decimal point. IRecognize, read and write place value to the right of the decimal point by one digit. MRecognize, read and write place value to the right of the decimal point by two digits, three digits. I

Compute, no regrouping 3 addends, 1 digit. mCompute, no regrouping 4 or more addends, 1 digit. mCompute with regrouping 2 or more 3 digit numbers. mCompute with regrouping 2 or more 4 digit numbers. mAdd with negative numbers. IApply commutative property. DApply associative property. DAdd using mental Math. D

Estimate. DDefine subtrahend, minuend, difference. mCompute with regrouping two 3 digit numbers. mCompute with regrouping any 2 numbers. MSubtract using mental Math. D

Estimate. DCompute products with factors up to 5X5. mDefine multiplier, multiplicand, product, factor. mMaster facts through 12. M

Subtract.


Use place value understanding and properties of operations to perform multi‐digit arithmetic. Add.

Multiply.


Fourth Grade Page 1

Grade 4 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevMultiply by 10, 100, 1000. ICompute with no regrouping ‐ 2X1 digits. mCompute with no regrouping ‐ 2X2 digits, 3X2 digits. MCompute with regrouping ‐ 2X1 digit, 2x2 digits/3x2 digits. MMultiply 4x3 digits, more digits. ICheck by division. IIdentify common multiple, least common mulitple of two or more numbers. IApply commutative property. DApply associative property. IUse mental math. D

Estimate. DDefine divisor, divident, quotient, remainder. MMaster facts through 12. MCompute with no remainder ‐ 2X1 digit, 3X1 digit. MCompute with no remainder ‐ 3X2 digits, more digits. MDivide by 10, 100, 1000. I

2X1 digit, 3X1 digit. D4X2 digits, 5X2 digits. I6X3 digits, more digits. ICheck with multiplication. IDivide using mental math. DDivide using expanded notation. D

Fractions

Fractions ‐ calculate equal parts of a whole. DIdentify unlike fractions. IRecognize, read and write mixed numbers. MRewrite franctions in simplest form. IIdentify proper and improper fractions. MSolve fraction inequalities. DCompare and order fractions. D

Divide.

Compute with whole numbers, decimals, fractions, remainders

Understand a fraction a/b with a >1 as a sum of fractions 1/b Understand addition and subtraction of fractions as joining and separating parts referrning to the same whole.

Fourth Grade Page 2

Grade 4 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevCalculate equivalent fractions, simplest form. IIdentify the least common denominator. IIdentify the greatest common factor. IAdd fractions with like denominators. IAdd fractions with unlike denominators. IAdd mixed numbers. IAdd improper fractions. IAdd and subtract decimals, aligning decimal points. IAdd fractions using mental math. ISubtract fractions with like denominators. ISubtract fractions with unlike denominators. ISubtract with mixed numbers. ISubtract with improper fractions, proper fractions. ISubtract using mental math. IMultiply with fractions ‐ Fraction X fraction. IMultiply with fractions ‐ Fraction X whole number. IMultiply using mental math. I

Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5x(1/4), recording the conclusion by the equation 5/4=5x(1/4).

Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3x(2/5) as 6x(1/5), recognizing this product as 6/5. (in general, nx(a/b)=(nxa/b). Solve word problems involving multiplcation of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party with 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g. by using a visual fraction model. Examples: 3/8=1/8+1/8+1/8; 3/8=1/8+2/8; 2 1/8= 1+1+1/8= 8/8+8/8+1/8 Add and suntract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Fourth Grade Page 3


Round to the nearest whole number. IConvert decimal to percent and percent to decimal. IConvert fractions to decimals and decimals to fractions. IConvert fraction to percent and perent to fraction. IUnderstand decimal notation for fractions, and compare and order decimal fractions.* M

ALGEBRAUsing algebraic and analytical methods to understand patterns and relationships:By observing, describing, comparing and creating. DBy sorting and classifying by characteristics. DBy predicting what comes next and the missing element. DBy distinguising between growing and repeating patterns. DBy representing information numerically, graphically and verbally. DBy discussing, analyzing change. DTo idenfity unknown quantities, algebraic phrases. DTo identify patterns. DTo solve simple equations. MUsing a variable as a place holder. IBy discussing/analyzing change by measuring and comparing quantitites. DBy discussing/analyzing change by using tables and graphs. DRecognize, read, and write ratios. ISolve word problems using the Distance formula: Distance = Rate X Time. ISolve word problems involving unit pricing. I

Compare and/or ordering objects using appropriate units of: Length: 1 inch, 1/2 inch, 1/4 inch. mLength: 1/8, 1/16. DLength: Mile. mMake conversions within systems. DLength: Metric system, Length ‐ millimeter, centimeter, decimeter, meter. DLength: Dekameter, hectometer. ILength: Kilometer. D

MEASUREMENT AND DATA Solve problems involving measurement and conversion of measurements.

Decimals

Fourth Grade Page 4

Grade 4 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevCapacity: milliliter, liter, kiloleter. D Weight, mass. DMake conversions within systems. ITemperature: Celcius. D

Money and TimeSubtract dollars and cents. MMultiply dollars and cents. IDivide dollars and cents. IRound numbers to the nearest dollar. MRecognize, tell and count money ‐ $20, $50 and $100. mMake change. MUse manipulative materials to model concepts of measurement. DRecognize, read and write time in 5 minute intervals. mRecognize, read, and write minutes before and after. MIdentify AM and PM. MRecognize, read, and write digital, analog time mRecognize, read, and write sequence of events, timelines. MCompute elapsed time, duration ‐ without changing units. DCompute elapsed time, duration ‐ with changing units. DRead and create schedules. DRecognize time zones. I

GEOMETRY

Determine proper tool for measurement ‐ protractor. IUse compass properly. IDefine, compare, demonstrate and calculate perimeter of square, rectangle. DDefine, compare, and calculate Circumference. DDefine, compare, and calculate Volume of a rectangular prism. DExplain scale drawings. IConstruct scale drawings. IUse geometry and spatial sense to investigate and predict the result of slide, turn, flip. D

Describe, model, draw, and classify:Point. mStraight line. I

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Fourth Grade Page 5

Grade 4 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevIntersecting line. IRay, segment. IAngle measurement. IRight angle. DAcute, obtuse, straight angles. IQuadrilaterals. IParallelograms, rhombuses, trapezoids. IPentagons, hexagons, octagons. DCenter, chord, diameter, Pi, radius. IIrregular shapes. DCube, cylinder, spehere, cone. MTriangular, rectangular prisms. DPyramid. DAnalyze symmetry, congruency. D

Construct convincing arguments and proofs to solve geometric figures and patterns.Using simple materials. DUsing diagrams. DUsing technology. D

STATISTICS AND PROBABILITYCollect and describe data. DInterpret, and create picture graph, bar graph. MInterpret and create tables. DInterpret and create circle graph. DInterpret and create Line graph solid. DInterpret and create Line graph broken. IInterpret and create Venn diagram. DIdentify or compute Mean, medium, mode, range. ICompute probability ‐ single event. DCompute probability ‐ permutations, combinations. DFormat questions ‐ conduct experiments, surveys. DFormat questions ‐ demonstrate data collection methods. DFomat questions ‐ design date collection methods. DDraw conclusions. ICommunicate results. I

Fourth Grade Page 6

Grade 4 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevMake decisions, predictions. I

PROBLEM SOLVING Analyze and plan the problem, determining the appropriate strategy by:

Drawing pictures. DCreating original problems. DDetermining if information is sufficient to solve. DRelating to an easier problem. IUsing tables, charts, graphs and diagrams. DUsing trial and error. DWorking backwards. DSorting, classifying and using patterns. DEstimating. DChoosing correct operation. DSolve problems involving percents less than, greater than 100%. ISolve fraction and decimal word problems. ISolve word problems with two statements of equality. ISolve problems to check reasonableness. DFormulate, develop and communicate logical arguments. I

Fourth Grade Page 7


Recognize, read, and write numbers to describe whole numbers to nine digits. MRecognize, read, and write numbers to describe whole numbers to twelve digits. IExplain patterns when multiplying and/or dividing a number by powers of 10*. When you multiply 8X10=80 and 8x1,000=8,000.

I

Numbers beyond one thousand. mDecimals. DFractions. D

To the nearest ten, hundred, and thousand. mTo the nearest ten thousand. MTo the nearest cent. ITo the nearest dollar. m

Fractions.Recognize, read, and write fractions of 2/3, 2/4, 3/4, and Tenths. mIdentify denominators and numerators. mIdentify like fractions. mIdentify mixed numbers. mIdentify unlike fractions. MIdentify and compute equivalent fractions. MCompute the simplest form of a fraction. MIdentify the reciprocal of a number or fraction. MKnow equal parts of a whole. DIdentify and compute with mixed numbers, proper and improper fractions. DIdentify inequalities. DIdentify the Least Common Denominator of two or more fractions. DIdentify the Greatest Common Factor of two or more numbers. D

DecimalsRecognize, read, and write numbers to describe decimals to tenths, to hundredths, and thousandths.

m

Recognize, read, and write decimals to thousandths and beyond using base‐ten numerals, number names, and expanded form*.

D

Recognize, read, and write numbers to compare and order decimals. D

Understand the place value system.

Compare and order numbers:

Round numbers:

NUMBERS AND OPERATIONSI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/Dev

Fifth Grade Page 1

Grade 5 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevRound decimals to any place value. MRecognize, read, and write repeating decimals. IRename decimals as fractions and fractions as decimals. IChange decimals to percent and percent to decimals. MChange fractions to decimals and decimals to fractions. MChange fractions to percents and percents to fractions. MRecognize, read, and write numbers to the left of the decimal point through six digits. mRecognize, read, and write numbers to the left of the decimal point through nine digits. MRecognize, read, and write numbers to the right of the decimal point by one digit. mRecognize, read, and write numbers to the right of the decimal point by two and three digits. MRecognize, read, and write numbers to the right of the decimal point through six digits and beyond. IRecognize, read, and write Roman numerals. DRecognize, read, and write real numbers. IIdentify prime and composite numbers. I

Master facts through 12. mMultiply by ten, one hundred, and one thousand. MCompute, with or without regrouping ‐ 2 X 2 digits and 2 X 3 digits. mCompute, using regrouping ‐ 4 X 3 and higher digits. MUse mental math. DIdentify products of prime numbers. IIdentify and apply distributive property. DIdentify and apply associative property. DIdentify and apply commutative property. MIdentify common multiples and least common multiples. MCheck multiplication by dividing. MMultiply using dollars and cents. M

Divide whole numbers, decimals, fractions, and remainders using 6 or more digit numbers by 3 digits.M

Divide with dollars and cents. DDivide a decimal by a whole number. I

Use equivalent fractions as a strategy to add and subtract fractionsAdd and subtract fractions with unlike denominators, including mixed numbers*. M

Estimate and solve word problems using addition and subtraction of fractions and mixed numbers.D

Perform operations with multi‐digit whole numbers and with decimals to hundredths.

Fifth Grade Page 2


Multiply a fraction by a fraction. DMultiply a fraction by a whole number. DMultiply, using whole and mixed numbers. IMultiply fractions using the canceling method. IMultiply fractions using mental math. DInterpret multiplication as scaling (resizing), using whole numbers, fractions, and mixed numbers *. I

Estimate in addition. DAdd with negative numbers. DApply the commutative property of addition. MApply the associative property of addition. MAdd using mental math. DEstimate in subtraction. DSubtract any two numbers. mSubtract with dollars and cents. mSubtract using mental math. DEstimate in multiplication. DEstimate in division. DDefine divisor, dividend, quotient, and remainder. mMaster division facts through 12. mCompute with no remainder. mDivide by ten, one hundred, one thousand. MUse mental math. DRead and writer numbers using expanded notation. D

Estimate addition and subtraction of fractions. IAdd and subtract fractions with like denominators. MAdd and subtract mixed numbers. DAdd and subtract improper fraction and proper fractions. DUse correct decimal alignment when adding and subtracting decimals. DAdd and subtract decimals using mental math. DEstimate multiplication of fractions. DDivide a fraction by a fraction. I

Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word Apply and extend previous understandings of multiplication and division.

Perform operations using whole numbers and integers.

Fractions an Decimals

Fifth Grade Page 3

Grade 5 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevDivide using whole and mixed numbers. IMultiply fractions using the canceling method. IMultiply and divide using mental math. I

Write and interpret numerical expressions.Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols*.

D

Correctly apply order of operations. ISolve fraction and decimal word problems. D

ALGEBRARecognize, explain, and compute ratios. DRecognize, explain, and compute proportions. IIdentify unknown quantities, algebraic phrases. MUse a variable as a place holder. DSolve simple equations and expressions informally. m

Identify and form ordered pairs consisting of corresponding terms and graph the ordered pairs on a coordinate plane*.

I/D

Understand patterns and relationships by observing, describing, comparing, and creating. DSort and classify by characteristics. DPredict what comes next and looking at missing elements. DDistinguish between growing and repeating patterns. DRepresent information numerically, graphically, and verbally. DDiscuss and analyze change. DIdentify and compute ratios and proportions. IIdentify inequalities. MDefine "Set." DSolve word problems with two statements of equality. DSolve word problems by applying the Distance formula: Distance = rate X time. DSolve word problems involving unit pricing. D

Make conversions of measurment units within a system. DDetermine length using 1/8, 1/6 inch. D

MEASUREMENT AND DATA

Analyze patterns and relationships.

Fifth Grade Page 4

Grade 5 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevDetermine length using millimeter, centimeter, decimeter, meter, decameter, hectometer, kilometer. DDetermine capacity using milliliter, liter, kiloliter. DDetermine weight, mass using gram,kilogram. DDetermine temperature using Celsius. D

Recognize, read, and write minutes before and after the hour. mRecognize, read, and write AM and PM. mRecognize, read, interpret, and create a sequence of events/timelines. mSolve problems involving elapsed time with and without changing units. MRecognize, read, interpret, and create schedules. DRecognize, read, and interpret time zones. D

Make change. m

Explain and construct scale drawings. M

Use a protractor to correctly measure and create angles. mUse a compass correctly. mCompute the circumference of a circle. MCompute the surface area of a prism. I

Define, compare, measure, and calculate volume of a triangular and rectangular prism in various units. M

Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.*

I

Define, compare, measure, and calculate perimeter and area of a square, rectangle, triangle, parallelogram, trapezoid.

M

Investigate and predict the results of slide, turn, and flip. DRecognize and create straight, intersecting, parallel, and perpendicular lines. DIdentify the angle vertex. IDetermine angle measurement. DIdentify a right angle. MIdentify acute, obtuse, and straight angles. DIdentify congruent angles. D

GEOMETRY

Time

Money

Fifth Grade Page 5

Grade 5 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevIdentify adjacent angles. IIdentify types of triangles ‐ isosceles, scalene, acute, obtuse, equilateral, and right. IIdentify the base and height of a triangle. DIdentify quadrilaterals, parallelograms, rhombuses, trapezoids. DIdentify pentagons, hexagons, octagons. DIdentify the center, chord, diameter, Pi, and radius of a circle. DIdentify and measure the degrees and arc of a circle. IIdentify irregular shapes. DIdentify solid figures ‐ cubes, cylinders, sphere, cones. mIdentify pyramids. DDetermine symmetry. D

Using simple materials. MUsing diagrams. DUsing technology. DDevelop, formulate, and communicate logical arguments. D

STATISTICS AND PROBABILITYCollect and describe data. DInterpret and create picture and bar graphs. mInterpret and create tables. DInterpret and create circle graphs. DInterpret and create Venn diagrams. DIdentify and label dependent and independent variables. IDetermine or compute mean, median, mode, range. DCompute probability: permutations, combinations, single events. DConduct surveys, experiments, demonstrate and design data collections methods. DMake inferences by drawing conclusions, communicating results, and making decisions/predictions. D

Discuss and analyze change by measuring and comparing quantities. D

Discuss and analyze change by using tables and graphs. D


Fifth Grade Page 6


Create a line plot to display a data set.* D

Read and create solid line graphs. M

Read and create broken line graphs. M

Use a coordinate system to represent real world and mathematical problems using the first quadrant. I/D

Drawing pictures. D

Creating original problems. D

Determining if information is sufficient to solve. D

Relating to an easier problem. D

Using tables, graphs, and diagrams. D

Relating to an easier problem. D

Using tables, charts, graphs, and diagrams. D

Using trial and error. D

Working backwards. D

Sorting, classifying, and using patterns. D

Using estimation. D

Choosing the correct operation. D

Solve problems involving percents both less than and greater than 100%. D

Check reasonableness of solutions. D


Represent and interpret data

Graph points on the coordinate plane to solve real‐world and mathematical problems.

PROBLEM SOLVING

Fifth Grade Page 7


Whole numbers to nine digits. mWhole numbers to twelve digits. MNatural counting numbers. mIntegers. IRational numbers. DWrite, interpret, and explain a rational number as a point on the number line. mWrite, interpret, and explain ordering and absolute value of rational numbers. DDecimals to tenths, to hundredths. MDecimals to thousandths, and beyond. MRepeating decimals. MRoman Numerals. DIdentify irrational numbers. IIdentify real numbers. DIdentify prime and composite numbers. M

Use positive and negative numbers together to describe quantities having opposite directions or values . M

Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line. MIdentify inequalities. MInterpret statements of inequality as statements about the relative position of two numbers on a number line diagram in a real‐world context. D

Identify denominators and numerators. mIdentify and compute like fractions. m Identify unlike fractions. mIdentify and compute equivalent fractions. mIdentify mixed numbers. mCompute the simplest form of a fraction. mIdentify proper and improper fractions. mSolve inequalities with fractions. m Identify reciprocals. m Identify the least common denominator of two or more fractions. M

NUMBERS AND OPERATIONS Recognize, read, and write numbers to describe:

Fractions


Sixth Grade Page 1

Grade 6 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevIdentify the greatest common factor of two or more whole numbers less than or equal to 100. M

Compute equivalent decimals, inequalities. MRename decimals as fractions and fractions as decimals. MChange fraction to percent and percent to fraction. m Round decimals: To the nearest billionth M To the nearest whole number. m

Decimals. MFractions. MCombinations of decimal, fraction, percent. MComparing sets, numbers. MUse ≤ , ≥ I

To the left of the decimal through nine digits. m To the right of the decimal, through 6 digits and beyond. m

To ten thousand. m To the nearest cent. M

Apply and extend previous understandings of numbers to the system of rational numbers. M

Estimate addition. MAdd using negative numbers. DApply the communative property of addition. m Apply the associative property of addition. m Use mental math. D

Estimate. MSubtract using negative numbers. IUse mental math. D

Estimate. M

Decimals

Compare and order numbers:

Recognize, read, and write place value:

Round numbers:

Perform operations using whole numbers and integers:

Add.

Subtract.

Multiply.

Sixth Grade Page 2

Grade 6 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevMultiply by 10, 100, 1000. mCompute with regrouping 4 times 3 digits, more digits. mCheck with division. mMultiply with dollars and cents. mIdentify common multiple, least common multiple of two or more numbers. mApply commutative property of multiplication. mApply associative property of multiplication. MApply distributive property of multiplication. DIdentify the factors of prime numbers. MUse mental math. DCompute using exponents and roots. IRecognize, read, and write numbers using expanded notation. M

Estimate. MFind quotients (of whole numbers). DDivide by ten, one hundred, one thousand. m Compute whole numbers, decimals, fractions with remainders. m Divide 2 by 1 digit, 3 by 1 digit. m Divide 4 by 2 digits, 5 by 2 digits. m Fluently divide multi‐digit numbers. MDivide 6 by 3 digits, more digits. DCheck by multiplication. m Divide using dollars and cents. MUse mental math. D

Compute with fractions and decimals.Compute fluently with multi‐digit numbers and find common factors and multiples. MCalculate using mixed numbers, proper and improper fractions. MFluently add, subtract, multiply, and divide multi‐digit decimals. M

ALGEBRAIdentify numbers in a "Set." DCalculate ratios. MFind a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.* I

Divide.

Sixth Grade Page 3

Grade 6 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevUse ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.* IRecognize, read, and write ratios and use language to describe a ratio relationship between two quantities. DCalculate proportions. IWrite, interpret, and explain signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane. M

Distance, length, and height. m Capacity, weight. m Mass. m

Determine proper tool for measurement, i.e. ruler, thermometer, scale, protractor M

Length using inch, half inch, quarter inch, foot, yard, mile. m Length using 1/8, 1/ 16 inch. MCapacity using cup, pint, quart, gallon. mWeight using ounce, pound, ton. mTemperature using Fahrenheit. m Make conversions within system. M

Capacity using milliliter, liter, kiloliter. DWeight, mass using gram, kilogram. DTemperature using Celsius. DMake conversions within system. D

Metric systemLength using millimeter, centimeter, decimeter, meter, dekameter, hectometer, kilometer.


U.S. customary system Comparing and/or ordering objects using appropriate units:

Comparing and ordering objects without measuring tools: Measure geometrice figures by:

Solve real‐world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Sixth Grade Page 4


Without changing units. m With changing units. m Interpret and creat schedules. DInterpret time zones. M

Point m Line: 1) Straight M 2) Intersecting, parallel, perpendicular I Ray, segment (sides) M

Vertex. MMeasurement. D

Right. m Acute, obtuse, straight. MCongruent. MAdjacent. DSupplementary, complementary. I

Triangles. m Isosceles, scalene, acute, obtuse, equilateral, right triangles. DIdentify base/ height (altitude) of a triagnle. I

Squares, rectangles, pentagons, hexagons, octagons. MParallelograms, rhombuses, trapezoids. m Heptagons and beyond. IIdentify convex, concave polygons. I

Calculate elapsed time, duration:

Identify types of angles:

Identify, draw, and classify quadrilaterals:

Identify, draw and classify:

GEOMETRY Describe, model, draw, and classify: Plane elements:

Angles:

Sixth Grade Page 5


Ellipse (oval), circles, semicircle (half‐circle). m Center, chord, diameter, Pi, radius. MDegrees of a circle. D

Cube, cylinder, sphere, cone. m Triangular, rectangular, multi‐sided, prisms. MPyramid. MExplain symmetry, congruency. M

Slide, turn, flip. DChanging shapes. m

Perimeter and area of a square, rectangle. MPerimeter and area of a triangle. MPerimeter and area of a parallelogram, trapezoid. MCircumference of a circle. IVolume of a rectangular prism. MSurface area of a rectangular prism. IExplain and construct scale drawings. MFind the area of triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes. D

Find the volume of a triangular and/or rectangular prism with fractional lengths. MDraw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. D

Represent three‐dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures.

I

Using simple materials. mUsing diagrams. MUsing technology. IUsing geometric relationships. IUsing models. I




Identify, draw and classify solid figures:

Identify, draw and classify:

Sixth Grade Page 6


Collect and describe data. D

Real graph (using actual objects). mPicture graph, bar graph. mTables. DCircle graph. DLine graph, solid or broken. mVenn Diagram. DIdentify and label dependent and independent variables. M

Identify or calculate mean, median, mode, range (average). M

Single event. DPermutations, combinations. D

Conduct experiments, surveys. DDemonstrate data collection methods. DDesign data collection methods. D

Draw conclusion. DCommunicate results. DMake decisions, predictions. D

PROBLEM SOLVINGAnalyze and plan a problem determining the appropriate strategy by: drawing pictures, creating original problems, determining if information is sufficient to solve, relating to an easier problem, using tables, charts, graphs, and diagrams, trial and error, working backwards, sorting classifying and using patterns, estimation, choosing correct operation.

D


Organize and construct data. Identify, draw, label, and anyalyze:

Make inferences.

Format Questions.

Calculate the probability of:

Read, calculate, and interpret data.

Sixth Grade Page 7

DATE COMPLETEDNUMBERS AND OPERATIONS

Recognize, read, and write numbers to twelve digits. mRecognize, read, and write integers. DRecognize, read, and write rational numbers. MIdentify least common denominators, greatest common factor of two or more numbers. mRecognize, read, and write decimals to thousandths and beyond. mIdentify equivalent decimals and inequalities. mRename decimals as fractions and fractions as decimals. mRound numbers to nearest billionth, round repeating decimals. mRecognize, read, and write Roman numerals. DRecognize, read, and write Irrational numbers. DRecongize, read, and write Real Numbers. MIdentify prime and composite numbers. m

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

Describe situations in which opposite quantities combine to make 0.

Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real‐world contexts.

Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real‐world contexts.

Apply properties of operations as strategies to add and subtract rational numbers.

Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real‐world contexts.

Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non‐zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real‐world contexts.

Grade 7 I=Introduce M=Mastery m=maintainD=Develop I/D=Intro/Dev

Seventh Grade Page 1

DATE COMPLETEDGrade 7 I=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevIdentify opposites of any number. MIdentify a "Set." DUse signs of equality and inequality, =, ≠ ,< , > . MUse signs of equality and inequality <, > . ICompare and order decimals, fractions, combinations of decimals and fractions, percentages. mIn terms of set notation, identify elements. MIn terms of set notation: identify subsets, domain and range. IRecognize, read, and write place value to the right of the decimal place through six digits and beyond. mRound numbers to the nearest cent. mPerform operations using whole numbers and integers: estimating addition, subtraction, multiplication, mAdd: Compute with regrouping: negative numbers. MAdd: Compute with regrouping: using mental math. DSubtract: Compute with regrouping: with negative numbers and using mental math. DMultiply: check by division with negative numbers. IMultiply: check by division with associative property, and product of prime numbers. mMultiply: check by division with distributive property. MMultiply: check by division with mental math. DDivide: check by multiplication with dollars and cents. mDivide: check by multiplication with negative numbers. IDivide: check by multiplication using mental math. DCalculate using exponents/roots. DRecognize, read, and write numbers using expanded notation. mFractions, decimals, percents: calculate equal parts of a whole, equivalent fractions, simplest form, mixed numbers, proper and improper fractions, ratios, inequalities, reciprocals, least common denominator, and greatest common factor.

m

Fractions, decimals, percents: addition by estimation, unlike denominators, mixed numbers, improper/proper fractions, decimal alignment. m

Add fractions, decimals, percents by combining fractions, decimals and/or whole numbers. MAdd,subtract, multiply, divide fractions, decimals, percents with negative numbers. IAdd, subtract, multiply, divide fractions, decimals, percents using mental math. DSubtract fractions, decimals, percents using estimation, unlike denominators, mixed numbers, mMultiply fractions, decimals, percents: using estimation, with fractions: fraction times fraction, whole mMultiply: decimal placement, decimal times decimal. MMultiply: combinations of fractions, decimals and/or whole numbers. MDivide fractions, decimals, percents: estimation, with dollars and cents, with fractions (fraction/fraction), m


DATE COMPLETEDGrade 7 I=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevRecognize division by zero as impossible. IDivide: combination of fractions, decimals, and/or whole numbers. MApply the correct order of operations. MSolve problems involving: percent less than, greater than 100%. MSolve problems involving percent of increase or decrease. DSolve problems involving simple interest. MSolve problems involving compound interest. ISolve problems involving mark up/down, commission/profit. MSolve problems involving unit pricing. m

Solve real‐life and mathematical problems using numerical and algebraic expressions and equations.

Use variables to represent quantities in a real‐world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1,r) where r is the unit rate.

EXPRESSIONS AND EQUATIONS Use properties of operations to generate equivalent expressions.

Represent proportional relationships by equations.

ALGEBRA Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.


DATE COMPLETEDGrade 7 I=Introduce M=Mastery m=maintainD=Develop I/D=Intro/Dev

Rename numbers using Base Conversion. IRecognize, read, calculate, and write ratios and proportions. MIdentify and apply symbols of inclusion parentheses ( ) during computation. mIdentify and apply symbols of inclusion brackets [ ], braces { }, insertion of symbols during computing. MApply opposite and multiple signs to numbers, within and outside of grouping symbols. IRecognize, read, write, and calculate using exponential notation. MRecognize, read, write, and calculate using negative exponents. IRecognize the result of an exponent of "0". MMultiply exponential expressions. ICalculate exponents with negative bases. MCalculate Roots: square roots‐rational. DRecognize irrational square roots: estimate, other roots (cubed root, fourth root, etc.), products of Square Root Theorem, signed roots. I

Estimate irrational square roots: with calculator. MRecognize, read, and write numbers using Scientific notation. MPerform operations with scientific notation. DIdentify like terms and polynomials. IIdentify unknown quantities, algebraic phrases and patterns. DEvaluate algebraic expressions using order of operations with integers, rational numbers, irrational numbers, with zero exponents and in function form. I

Evaluate algebraic expressions using order of operations with positive exponents. DSimplify expressions: combine like terms, use distributive property, with exponents. ISimplify rational expressions, radical expressions, and polynomials. ISolve simple equations using a variable as a place holder. mSolve simple equations using a variable as a changing quantity. DSolve more complicated equations with: fractional parts, mixed numbers, decimal part, percentage; using substitution; with variables in the denominator; using systems of equations involving graphic solutions with and without technology.

I

Solve word problems leading to equations of the form px + q= r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. Solve word problems leading to inequalities of the form px +q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.


DATE COMPLETEDGrade 7 I=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevRead, write, and solve algebraic word problems. ISolve inequalities using: additive property of inequality; multiplicative property of inequality, absolute value of inequality. I

Factor polynomials using greatest common factor. IExplore linear relationships with and without technology by identifying coordinates and graphing. MSolve problems by graphing three points or identifying the slope intercept. IExplore linear relationships symbolically by using the distance formula. IDiscuss/analyze change by measuring and comparing quantities; using tables and graphs; using equations with constant rate of change and nonlinear relationships D

MEASUREMENT & DATAUse manipulatives materials to model concepts of measurement. DCompare and/or order objects using appropriate units of U.S. customary system with length: 1/8, 1/16.

m

Make conversions within U.S. customary system. mCompare and/or order objects using appropriate units of the metric system: millimeter, centimeter, decimeter, meter; dekameter, hectometer; kilometer; milliliter, liter, kiloleter; gram, kilogram; conversions within system; temperature in Celsius.

M

Recognize, read, and write time schedules. DRecognize, read, and write time zones. m

Define, compare, demonstrate, and calculate: perimeter, area (of square, rectangle, triangle, parallelogram, trapezoid), circumference, volume. m

Calculate the area of a circle. MCalculate the surface area of a prism. DExplain and construct scale drawings. mInvestigate and predict the result of slide and turn. MInvestigate and predict the result of flip. D

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

GEOMETRY Draw construct, and describe geometrical figures and describe the relationships between them.


DATE COMPLETEDGrade 7 I=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevDescribe, model, draw and classify lines that are straight, intersecting, parallel, perpendicular; rays and segments; angle vertex; acute, obtuse, straight and congruent angles. m

Use facts about supplementary, complementary, vertical, and adjacent angles in a multi‐step problem to write and solve simple equations for an unknown angle in a figure. M

Identify corresponding, alternate interior/exterior, vertical and bisector angles. IIdentify triangles: isosceles, scalene, acute, obtuse, equilateral and right. MIdentify right Triangle parts: hypotenuse and leg, Pythagorean Theorem, 30‐60‐90, 45‐45‐90. IIdentify triangles: base/height (altitude). mIdentify quadrilaterals: parallelograms, rhombuses, trapezoids; pentagons, hexagons, octagons. mIdentify quadrilaterals: heptagons, nine‐sided and beyond convex, concave. DIdentify parts of circles: center, chord, diameter, Pi, radius. mIdentify degrees, arc of a circle, inscribed circles. MIdentify irregular shapes. MIdentify solid figures: prisms (triangular, rectangular); pyramid; symmetry, congruencey. mIdentify complex prisms (with multi‐sided bases). DConstruct convincing arguments and proofs to solve problems using geometric figures and patterns using diagrams. m

Draw logical conclusions and communicate reasoning: using technology; formulate, develop, and communicate logical arguments; develop and solve problems using geometric relationships, using models and using technology.

D

Collect and describe data using random samplings*. DOrganize and construct data by identifying, drawing, labeling and analyzing tables. DAnalyze data via circle graph. MAnalyze and create Venn diagram. DIdentify and label dependent and independent variables. mRead, calculate, and interpret data: mean, median, mode, range. mRead, calculate, and interpret data: quartiles. ICalculate probability: single event; permutations, combinations. DCalculate probability: independent events, dependent events. IFormat questions: Conduct experiments/surveys. DDemonstrate data collection methods. DDesign data collection methods. DMake inferences: draw conclusions, communicate results, make predictions. D



DATE COMPLETEDGrade 7 I=Introduce M=Mastery m=maintainD=Develop I/D=Intro/Dev


D

Solve fraction and decimal word problems, word problems with two statements of equality, distance=rate X time. D

Check reasonableness of solution. DUnderstand patterns and relationships by observing, comparing and creating; sorting and classifying by characteristics; predicting what comes next and identifying the missing element; distinguishing between growing and repeating patterns; representing information numerically, graphically, and verbally; discussing analyzing change.

D



Recognize, read, write integers. MRecognize, read, write rational numbers: ratios and proportions. mRecognize, read, write Roman numerals. DRecognize, read, write irrational numbers. MIdentify Real numbers, opposites. mIdentify members of a "Set." DUse signs of equality and inequality =, <, >. mUse signs of equality and inequality < > ≠. MRecognize, read, and write, in terms of notation: elements. mIdentify subsets. DIdentify domain and range. MAdd using negative numbers. mAdd, subtract, multiply, divide using mental math. DSubtract, multiply, divide using negative numbers. MMultiply using distributive property. mIdentify consecutive odd, even integers. ISolve fraction/decimal word problems. MAdd fraction combinations, decimals, and/or whole numbers. mAdd,subtract,multiply, divide with negative fractions and decimals. MAdd,subtract, multiply, divide fractions and decimals using mental math. DUnderstand fraction/decimal division by zero is irrational. D

Recognize, read, write, and calculate numbers using exponential notation. mRecognize, read, write, and calculate using negative exponents. DRecognize the result of a zero exponent. mMultiply exponential expressions. MRecognize, read, write, and calculate exponential numbers with negative bases. mCalculate Exponents/roots; base conversion. DCalculate rational square roots. MEstimate irrational square roots. DCalculate estimations of irrational square roots with a calculator. mCalculate other roots (cubed root, fourth root, etc.); products of Square Root Theorem; signed roots (radical expressions).

M


ALGEBRA


Eighth Grade Page 1

Grade 8 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevRecognize, read, and write numbers using scientific notation. mPerform operations with numbers in scientific notation. DCalculate proportions. mSolve problems involving: percent of increase/decrease. MSolve problems involving compound interest. DCalculate by applying Order of operations, symbols of inclusion [ ], { }, insertion of symbols. mApply opposite and multiple signs, within and outside symbols of inclusion. MSolve word problems with two statements of equality. DSolve word problems using the distance formula: Distance= rate x time. MCheck reasonableness of solution. DUnderstand patterns and relationships by observing, describing, comparing and creating; sorting and classifying by characteristics; predicting what comes next and identifying the missing element; distinguishing between growing and repeating patterns; representing information numerically, graphically, and verbally; discussing/analyzing change.

D

Identify greatest common factor of algebraic expressions and least common multiple of algebraic expressions.

I

Identify like terms, polynomials, unknown quantities, algebraic phrases, and patterns. D

Evaluate algebraic expressions using order of operations with integers, rational and irrational numbers.D

Evaluate algebraic expressions using order of operations with positive exponents. MEvaluate algebraic expressions using order of operations with zero exponents. DEvaluate algebraic expressions using order of operations with negative and variable exponents. ISimplify expressions: combine like terms; using distributive property; with exponents. DSimplify rational expressions; radical expressions; polynomials. DSolve simple equations using a variable as a changing quantity. DSolve more complicated equations with fractional parts, mixed numbers, a decimal part, and percentage.

M

Solve more complicated equations using substitution, and with variables in the denominator. DSolve more complicated equations with variables on both sides, by factoring, by isolating a variable in terms of other variables.

I

Solve problems using systems of equations involving graphic solutions with and without technology.D

Read, write and solve algebraic word problems. DSolve inequalities using additive property of inequality; multiplicative property of inequality; absolute value of inequality.

M

Eighth Grade Page 2

Grade 8 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevUse graphing technology. IFactor polynomials using greatest common factor. DFactor polynomials using grouping, FOIL. IExplore linear relationships with and without technology by identifying coordinates. mExplore linear relationships with and without technology by identifying and calculating slope; by identifying intercepts.

I

Explore linear relationships by solving and graphing three points. MExplore linear equations by solving and graphing using slope intercept. D

Solve linear equations by graphing point‐slope, parallel and perpendicular, horizontal and vertical.I

Explore linear relationship symbolically by writing equations of lines given two points; the graph; slope and y‐intercept; point and slope; x and y intercept.

I

Explore linear relationships symbolically by using distance formula. DDiscuss/analyze change by measuring and comparing quantities; by using tables and graphs; by using equations with: a constant rate of change and non‐linear relationships.

D

Analyze and plan the problem determining the appropriate strategy by: drawing pictures; creating original problems; determining if information is sufficient to solve; relating to an easier problem; using tables graphs and diagrams; trial and error; working backwards; sorting, classifying, and using patterns; estimation; choosing correct operation.

D

Analyze and solve pairs of simultaneous linear equations.* D

Evaluate algebraic expressions using order of operations in function form. D

Use manipulative materials to model concepts of measurement. DRecognize, read, write time schedules. M

Measure using the Metric system: millimeter, centimeter, decimeter, meter; dekameter, hectometer; kilometer; milliliter, liter, kiloliter; gram, kilogram; conversions within system; temperature: Celsius.

m

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).


Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Define, evaluate, and compare functions.

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. 1

Eighth Grade Page 3


GEOMETRYDefine, compare, demonstrate, and calculate area of a circle. mCalculate surface area of a prism. MInvestigate and predict result of slide, turn. mInvestigate and predict result of flip. DDescribe, model, draw and classify angle measurement. mIdentify adjacent, supplementary, and complementary angles. mIdentify corresponding, alternate interior, alternate exterior and vertical angels; angle bisectors. MIdentify Polygons: isosceles, scalene, acute, obtuse, equilateral and right triangles. mIdentify parts of a right triangle: hypotenuse, leg; pythagorean theorem; 30‐60‐90, 45‐45‐90. MIdentify quadrilaterals: heptagons, nine‐sided and beyond; convex, concave. MIdentify and measure circles: degrees, arc, inscribed circles. mIdentify irregular shapes. mIdentify solid figures: multi sided prism. MIdentify sine, cosine, tangent. IConstruct convincing arguments and proofs to solve problems using geometric figures and patterns using technology; formulate, develop and communicate logical arguments; develop and solve problems using geometric relationships, using models and using technology.

D

Collect and describe data. DOrganize and construct data using tables. DOrganize and construct data using a circle graph. mAnalyze and create a Venn Diagram. DRead, calculate and interpret data quartiles. DCalculate probability of a single event, permutations, and combinations. DCalculate probability of independent events, dependent events. MFormat questions: Conduct experiments and surveys. DDemonstrate data collecting methods. DDesign data collection methods. D


Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Eighth Grade Page 4

Grade 8 DATE COMPLETEDI=Introduce M=Mastery m=maintainD=Develop I/D=Intro/DevMake inferences: Draw conclusions. DCommunicate results. DMake decisions, predictions. D


D

Solve fraction and decimal word problems, word problems with two statements of equality, distance=rate X time. D

Check reasonableness of solution. DUnderstand patterns and relationships by observing, comparing and creating; sorting and classifying by characteristics; predicting what comes next and identifying the missing element; distinguishing between growing and repeating patterns; representing information numerically, graphically, and verbally; discussing analyzing change.

D

Eighth Grade Page 5

DATE COMPLETED

Translate verbal expressions into mathematics expressions. MWrite an expression containing identical factors as an expression using exponents. MUnderstand and apply the rules for order of operations to evaluate expressions. MApply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.*

M

Solve open sentences by performing arithmetic operations. M

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.*

M

Solve multi‐step mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals). Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.*

M

Recognize and use the distributive property, commutative, and associative properties to simplify expressions.

M

Translate verbal expressions into equations and formulas. MExplore problem situations by asking and answering questions. MRepresent mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.*

D

Graph integers on a number line. MAdd and subtract integers with and/or without using a number line. MMultiply and divide integers. MFind the absolute value of a number. MCompare, order, and understand absolute value of rational numbers. MWrite inequalities for graphs on number lines. MGraph inequalities. DIdentify rational and irrational numbers. MFind a number between two rational numbers. DAdd, subtract, multiply and divide rational numbers. DSolve multi‐step mathematical problems that contain rational numbers. DSimplify expressions that contain rational numbers. D

Define variables and write equations and inequalities for problems that contain rational numbers D

Write verbal problems from equations. D

Introduction to Algebra I=Introduce M=Mastery m=maintainD=Develop I/D=Intro/Dev

Algebra Page 1

DATE COMPLETEDIntroduction to Algebra I=Introduce M=Mastery m=maintainD=Develop I/D=Intro/Dev

Solve linear equations by using addition, subtraction, multiplication and division. MSolve problems working backwards. DSolve equations involving more than one operation. MSolve equations with the variable on both sides. MSolve equations containing grouping symbols, fractions, or decimals, more that one variable. D

Solve proportions. MSolve percent problems and mixture problems. DSolve problems involving simple interest, percent of increase or decrease, discount or sales tax. MSolve problems by making a table or chart. MSolve problems involving uniform motion by using the formula d=rt. DSolve problems involving direct and inverse variations. D

Solve inequalities by using addition, subtractions, multiplication, and division. MSolve inequalities involving more than one operation. MSolve problems by making a diagram. DSolve compound inequalities and graph their solution sets. DSolve problems that involve compound inequalities. DSolve open sentences involving absolute value and graph the solutions. DCreate equations and inequalities in one variable and use them to solve problems.* DSolve linear equations and inequalities in one variable, including equations with coefficients represented by letters.*

D

Explain each step in solving a simple equation. Construct a viable argument to justify a solution method.*

D

Solve problems by looking for a pattern. DMultiply monomials. MSimplify expression involving powers of monomials. ISimplify expressions containing negative exponents. DExpress numbers in scientific and decimal notation. DFind products and quotients of numbers expressed in scientific notation. IFind the degree of a polynomial. MInterpret parts of an expression, such as terms, factors, and coefficients.* M

Polynomials

Equations

Applications of Rational Numbers

Inequalities

Algebra Page 2


Arrange the terms of polynomials so that the powers of a certain variable are in ascending or descending order.

D

Add and subtract polynomials. MSimplify expressions involving polynomials. MIdentify and use the FOIL method of multiply two binomials. MMultiply any two polynomials by using the distributive property. MKnow and apply the patterns for (a+b)2,(a‐b)2, and (a+b)(a‐b). M

Find the prime factorization of an integer. MFind the greatest common factor (GCF) for a set of monomials. MUse the GCF and the distributive property to factor polynomials. MUse grouping techniques for factor polynomials with four or more terms. ISolve problems by using guess and check. IFactor quadratic trinomials. IIdentify and factor polynomials that are the differences of squares. IIdentify and factor perfect square trinomials. IFactor polynomials by applying the various methods of factoring. IUse the zero product property to solve equations. I

Simplify, multiply, divide rational expressions. MDivide polynomials by binomials. IAdd and subtract rational expressions with like and unlike denominators. MSolve problems by making an organized list of the possibilities. ISimplify mixed expressions and complex fractions. MSolve rational and radical equations in one variable.* ISolve problems involving work and uniform motion. ISolve formulas for a specified variable and those that involve rational expressions. I

Graph ordered pairs on a coordinate plane. MIdentify the domain, range, and inverse of a relation. ISolve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.

I

Show relations as sets of ordered pairs and mappings. DSolve linear equations for a specific variable, a given domain. D

Factoring

Rational Numbers and Expressions

Functions and Graphs

Algebra Page 3


Graph linear equations and inequalities on a coordinate plane. MUnderstand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.*

I

Know and understand the definition of a function and determine whether a given relation is a function. ICalculate functional values for a given function. IWrite an equation to represent a relation, given a chart of values. ISolve problems by using bar and line graphs. MFor a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features.*.

D

Understand the correspondence between algebra and coordinate geometry (i.e. graph). M

Find the slope of a line, given the coordinates of two points on the line. MWrite a linear equation in standard form given the coordinates of a point on the line and the slope of the line; given the coordinates of two points on the line.

M

Write an equation in slope‐intercept form given the slope and y‐intercept. MDetermine the x and y intercept of a graph. MGraph linear equations using the x and y intercept of the slope and the y‐intercept. MGraph linear and quadratic functions and show intercepts, maxima, and minima. IWrite a linear equation in slope intercept form given the slope of a line and the coordinates of a point of the line, given the coordinates of two point on the line.

M

Write an equation of a line that passes through a given point and is parallel or perpendicular to the graph of a given equation.

I

Find the coordinates of a midpoint of a line segment in the coordinate plane given the coordinates of the end points.

I

Solve problems by using pictograph, circle graphs, and comparative graphs. D

Solve problems after checking for hidden assumptions. ISolve simple rational and radical equations in one variable.* MSolve system of equations by graphing, the substitution method, elimination method using addition and subtraction, elimination method using multiplication and addition.

M

Solve system of equations of inequalities by graphing. IDetermine whether a system of equations has one solution, no solution, or infinitely many solutions by graphing.

I

Solve problems by using a table. DRadical Numbers and Expressions

Graphing Linear Equations

System of Open Sentences

Algebra Page 4


Simplify rational square roots and cube roots. MFind the approximate values for square roots. DUse the Pythagorean Theorem. DIdentify irrational numbers. DRewrite expressions involving radicals and rational exponents using the properties of exponents.* DSimplify rational expressions involving addition and subtraction. MSolve radical equations. MFind the distance between two points in the coordinate plane. I

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the quadratic function.

I

Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

I

Graph quadratic functions. IFind the roots of a quadratic equation by graphing. ISolve problems by identifying subgoals. ISolve quadratic equations by completing the square, using the quadratic formula. IEvaluate the discriminant of a quadratic equation to determine the nature other roots of the equation. ISolve problems that can be represented by quadratic equations. IFind the sum and product of the roots of a quadratic equation. IWrite a quadratic equation given its roots. I

Interpret numerical data from a table. MRepresent and interpret statistical data on a line plot, on a stem‐and‐leaf plot. MCalculate and interpret the mean, median, mode, range, quartiles, and interquartile range of a set of data.

M

Represent and interpret statistical data on a box‐and‐whisker plot. MGraph and interpret pairs of numbers on a scatter plot. MFind the probability and/or odds of a simple event. MConduct and interpret probability experiments. DSolve problems by first solving a simpler but related problem. DFind the probability of a compound event.B14 D

Quadratics


Algebra Page 5

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Multiplication Rational numbersproduct Irrational numbersfactorof

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