Loudoun County Public Schools

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1 Ludun Cunty Public Schls Department f Instructin Curriculum and Instructin ELL Mathematics Curriculum Guide Office f English Language Learners (ELL) August 2011 Teresa Vignarli, ELL Supervisr Beth Slagle, ELL Specialist 1

2 Ludun Cunty Public Schls ELL Mathematics Curriculum Guide August 2011 Cmmittee Members Svetlana Spencer Jasn Wagner With special thanks t past cmmittee members frm the Office f English Language Learners (ELL) wh helped t write previus curriculum guides. This curriculum guide cntains infrmatin frm varius surces including Virginia Department f Educatin (VDOE), Wrld-Class Instructinal Design and Assessment (WIDA), websites, ther schl divisins and state departments, gvernment dcuments, and publisher s surces. 2

3 Resurces: Pacemaker Basic Mathematics, Lngman Mathematics, Pacemaker Pre-Algebra, (Pearsn) Illustrated Math Dictinary, ELL Fast Math Guide and Placement Tests UNIT 1: WHOLE NUMBERS CONTENT OBJECTIVES / GRADE RELATED SUGGESTED ACTIVITIES (Internet, ActiveStudi Flipcharts, Wrksheets) Identify key math wrds, terms and symbls related t whle numbers: number line, whle number, even numbers, dd numbers, digits, rename, runding, befre, after, psitin, rder, cardinal numbers, rdinal numbers, symbls >, <, =, hw many, estimate. Read and write whle numbers using digits and wrds. Identify numbers n a number line , 1.4 Identify dd and even numbers a. Identify and represent integers; 6.3 b. Order and cmpare integers; 6.3 c. Identify and describe the abslute value f integers. Recgnize place value t thusands. Rename a number t shw the place value f each digit. Write a number given the place value f each digit a. Read, write, and identify the place value f each digit in a three-digit numeral, using numeratin mdels; Vcabulary and definitins (fr Spanish and nn Spanish speakers) Vcabulary matching game Numbers f the Wrld Hw Many? Numbers Number Wrds 1-10 I Have Wh Has..? Matching Number with Wrds (A and B) Cunting by 10s Numbers Writing Number Wrds Practice A Even and Odd Numbers Even and Odd Wrksheet Place Value Matching Activity Place Value Practice t Hundreds 3

4 UNIT 1: WHOLE NUMBERS 2.1 b. Rund tw-digit numbers t the nearest ten; and, 2.1 c. Cmpare tw whle numbers between 0 and 999, using symbls (>, <, r =) and wrds (greater than, less than, r equal t). Recgnize place value t millins. Read and write whle numbers ,000,000 using the place value chart a. Identify rally and in writing place value fr each digit in a whle number expressed thrugh millins; 4.1 b. Cmpare tw whle numbers expressed thrugh millins, using symbls (>, <, r =); and, 4.1 c. Rund whle numbers expressed thrugh millins t the nearest thusand, ten thusand, and hundred thusand. Cmpare whle numbers using the symbls >, < and =. 2.2, Demnstrate multiple representatins f multiplicatin and divisin f fractins a. Name and write fractins (including mixed numbers) represented by a mdel; 3.3 b. Mdel fractins (including mixed numbers) and write the fractins names; and, 3.3 c. Cmpare fractins having like and unlike denminatrs, using wrds and symbls (>, <, r =). Order whle numbers. State the number befre r after given number Demnstrate multiple representatins f multiplicatin and divisin f fractins. Read and say rdinal numbers t 30. Use rdinal numbers first thrugh thirtieth in dates. 4 Place Value Wall Pster Place Value Chart Place Value Practice t Millins Cmparing Numbers Number Line Mre/ Less Greater Than/ Less Than Games Cmparing Numbers Recrding Sheet Cmparing Numbers Practice Greater Than/ Less Than Student Activity Numbers befre, after and between Game t Practice Befre, After and Between Befre, After and Between Explanatin Directins fr Befre, After and Between Numbers That Are Between Befre, After and Between Practice (Larger Numbers) What is My Number? Game Numerical Order (frm least t greatest) Number Review Cardinal and Ordinal Numbers Ordinal Cncentratin Cards. Ordinal Numbers

5 UNIT 1: WHOLE NUMBERS Use the calendar. 2.3, 2.18 Tell time using analg and digital clcks. 1.11, 2.16, 3.15, a. Tell time t the nearest minute, using analg and digital clck; and, 3.11 b. Determine elapsed time in ne-hur increments ver a 12-hur perid Identify equivalent perids f time, including relatinships amng days, mnths, and years, as well as minutes and hurs. Slve everyday prblems. Read a table. Make a table t slve a prblem. Rund whle numbers. 2.1, Recgnize and use the inverse relatinships between additin/subtractin and multiplicatin/divisin t cmplete basic fact sentences. TSW use these relatinships t slve prblems. The Apartment Directins fr Paper Strips Paper Strips The Calendar Schl Curse Schedule Hw Much Time? Analg Clck Time 1 Time 2 Digital Clck Digital Clck Practice Time 3 24 Hurs = 1 Day Chsing the Time Using a Number Line t Rund Runding t the Nearest 10 Runding Numbers Let s Rund Runding Prblem Runding With Larger Numbers 5

6 UNIT 2: ADDING WHOLE NUMBERS CONTENT OBJECTIVES / GRADE RELATED Identify key wrds and terms related t adding whle numbers: add, sum, plus, addend, hrizntal, vertical, clumn, slve, regrup, estimate. Write and slve additin prblems in hrizntal and vertical frm using numbers. Zer prperty f additin. 1.8, 4.6, a. Given tw whle numbers whse sum is 99 r less, will estimate the sum; and, 2.6 b. Find the sum, using varius methds f calculatin. Use basic facts t add larger numbers. 2.7 Add numbers with regruping Determine, by cunting, the value f a cllectin f bills and cins whse ttal value is $5.00 r less, cmpare the value f the bills and cins, and make change. SUGGESTED ACTIVITIES (Internet, ActiveStudi Flipcharts, Wrksheets) Vcabulary and definitins (fr Spanish and nn Spanish speakers) Vcabulary Matching Activity Learning abut Additin Writing additin sentences Let s Think! Directins t the activities Cunt On! Cunt On t Find Sums Cunt n With Number Patterns Zer Prperty f Additin Additin With Zer Sums t 10 Ten and Mre Additin Strategies Summary Adding Tw-Digit Numbers Ready t Regrup 2-digit additin Let s Add Sme Mre! Fun With Additin Recall additin facts with sums t 20 r less and the crrespnding subtractin facts. Estimate sums. Find an answer that is clse t an exact ne. 6 Estimatin explanatin. Exact r Estimate? Runding Estimates

7 UNIT 2: ADDING WHOLE NUMBERS Determine, by cunting, the value f a cllectin f bills and cins whse ttal value is $5.00 r less, cmpare the value f the bills and cins, and make change. Practice with Runding a. Determine cmmn multiples and factrs, including least cmmn multiple and greatest cmmn factr. 4.5 b. Add and subtract fractins having like and unlike denminatrs that are limited t 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fractins, using cmmn multiples and factrs. 4.5 d. Slve single-step and multistep practical prblems invlving additin and subtractin with fractins and with decimals Given tw whle numbers, each f which is 99 r less, a. Estimate the difference; and, b. Find the difference, using varius methds f calculatin. Recgnize and use the cmmutative and the assciative prperties f additin a. Mdel additin, subtractin, multiplicatin, and divisin f integers; and, 7.3 b. Add, subtract, multiply, and divide integers. The Cmmutative Prperty Explanatin The Cmmutative Prperty The Assciative Prperty explanatin Gruping with the Assciative Prperty Prblem Slving and Extensin Activities Let s G Shpping 7

8 UNIT 3: SUBTRACTING WHOLE NUMBERS CONTENT OBJECTIVES / GRADE RELATED Identify key wrds related t subtracting whle numbers: subtract, difference, minus, regrup, inverse, brrw, take all, take nthing. Write and slve subtractin prblems in vertical and hrizntal frms using numbers Determine, by cunting, the value f a cllectin f bills and cins whse ttal value is $5.00 r less, cmpare the value f the bills and cins, and make change Create and slve ne- and tw-step additin and subtractin prblems, using data frm simple tables, picture graphs, and bar graphs Slve prblems by cmpleting numerical sentences invlving the basic facts fr additin and subtractin. TSW create stry prblems, using the numerical sentences. Subtract larger numbers withut regruping. 8 SUGGESTED ACTIVITIES (Internet, ActiveStudi Flipcharts, Wrksheets) Vcabulary and definitins (fr Spanish and nn Spanish speakers) Zer Facts Instructins Take All Take Nthing All r Nthing One Less Than / Tw Less Than Mre Than / Less Than Subtracting with 10 A difference f 10 Practice Activities Subtracting Tw-Digit Numbers Additin and Subtractin Practice

9 UNIT 3: SUBTRACTING WHOLE NUMBERS 3.8, 4.6 Subtract numbers with regruping Determine, by cunting, the value f a cllectin f bills and cins whse ttal value is $5.00 r less, cmpare the value f the bills and cins, and make change. Regruping when subtracting frm zeres Determine, by cunting, the value f a cllectin f bills and cins whse ttal value is $5.00 r less, cmpare the value f the bills and cins, and make change. Use clue wrds t add r subtract t slve wrd prblems b. Identify and describe the characteristics f even and dd numbers Recgnize and describe the related facts that represent and describe the inverse relatinship between additin and subtractin. 9 Subtractin With 2-Digit Numbers Mre Practice With Subtractin Subtractin With 3-Digit Numbers Tricky Regruping Subtracting Acrss Zeres Clue wrds fr Additin and Subtractin Prblem Slving and Extensin Activities The Sccer Game Prblem Slving With Subtractin Using Data Frm a Chart t Slve Prblems Basketball Tickets A Schl

10 UNIT 3: SUBTRACTING WHOLE NUMBERS Use inverse peratins t find missing numbers Estimate slutins t and slve single-step and multistep prblems invlving the sum r difference f tw whle numbers, each 9,999 r less, with r withut regruping. Use calculatrs t slve additin and subtractins prblems. Musical Think additin t subtract Number Families Wrds, Numbers, Calculate! Prblem Slving With Calculatrs 10

11 UNIT 4: MULTIPLYING WHOLE NUMBERS CONTENT OBJECTIVES / GRADE RELATED Identify key math wrds, terms and symbls related t multiplying numbers: multiplicatin, multiply, factrs, prduct, partial prduct, times Write multiplicatin prblems in hrizntal and vertical frm using numbers. Use a multiplicatin table t find basic prducts. 3.9 Recgnize and use symbls t represent multiplicatin. 4.7 Recgnize and use the cmmutative, assciative, multiplicative identity, and distributive prperties f multiplicatin a. Mdel additin, subtractin, multiplicatin, and divisin f integers; and, 7.3 b. Add, subtract, multiply, and divide integers a. Investigate the identity and the cmmutative prperties fr additin and multiplicatin; 3.20 b. Identify examples f the identity and cmmutative prperties fr additin and multiplicatin b. Investigate and describe the assciative prperty fr additin and multiplicatin Investigate and recgnize the distributive prperty f multiplicatin ver additin TSW apply the fllwing prperties f peratins with real numbers: a. The cmmutative and assciative prperties fr additin and multiplicatin; b. The distributive prperty; c. The additive and multiplicative identity prperties; d. The additive and multiplicative inverse prperties; and, 11 SUGGESTED ACTIVITIES (Internet, ActiveStudi Flipcharts, Wrksheets) Vcabulary and definitins (fr Spanish and nn Spanish speakers) Equal Grups Wrking With Equal Grups. Mre wrk with grups Multiplicatin Practice All Abut Multiplicatin Multiplicatin Using Arrays Explanatin What is an Array? Wrking With Arrays Building Arrays Using Arrays With Multiplicatin and Divisin Cmmutative Prperty Explanatin What s the Order? Let s Change Places Zer Prperty Explanatin Identity Prperty Explanatin Multiplying With Zers and One Mre Practice With 0 and 1 Multiplicatin Dubles Multiplicatin With Fives Assciative and Distributive Prperties Explanatin Three Factrs and the Assciative Prperty The Distributive Prperty f Multiplicatin Practice With the Distributive Prperty Practice With Multiplicatin Prperties Multiplicatin Prperties Wall Pster

12 UNIT 4: MULTIPLYING WHOLE NUMBERS e. The multiplicative prperty f zer. Multiply large numbers withut regruping. 4.7 Multiply with regruping. 4.7 Multiply whle numbers by 10, 100, Multiply by numbers that have zer as a digit. 4.7 Recgnize clue wrds fr multiplicatin Slve wrd prblems using multiplicatin. Use calculatrs t slve multiplicatin prblems. Tw-Digit Multiplicatin Practice Mre Tw-Digit Multiplicatin Practice Mdel and Multiply Multiplying 2-Digit Numbers Multiplicatin/Clumns Prblem 1 Stay in Line Name That Prduct Multiplying Large Numbers Multiplicatin Madness Multiplying by Pwers f 10 Wall Pster Practice With Tens! Multiply by 10, 100, r 1,000 Mental Math Shrtcuts Let s Multiply With Zers! Find the Missing Digit Name This Page 12

13 UNIT 5: DIVIDING WHOLE NUMBERS CONTENT OBJECTIVES / GRADE RELATED Identify key wrds and terms related t dividing whle numbers: divisin, dividend, divisr, qutient, remainder Use math terms and clue wrds t find ut hw many times ne number cntains anther. 3.9 SUGGESTED ACTIVITIES (Internet, ActiveStudi Flipcharts, Wrksheets) Vcabulary and definitins (fr Spanish and nn Spanish speakers) All Abut Divisin Operatin Relatinships Reading Reading Practice Let s Read Fact Families With Multiplicatin and Divisin Write and slve divisin prblems. Use divisin tables 4.7, Divisin I Divisin II Divisin Practice Mre Practice With Divisin Patterns f Divisin

14 UNIT 5: DIVIDING WHOLE NUMBERS Patterns f Divisin II Patterns Practice Patterns f Divisin III Mental Math/ Divisin Mental Math/ Divisin Practice Practicing Mental Math/ Divisin Divide with remainders a. Find the sum, difference, prduct, and qutient f tw numbers expressed as decimals thrugh thusandths (divisrs with nly ne nnzer digit); and, 5.5 b. Create and slve single-step and multistep practical prblems invlving decimals. Step by step divisin f large numbers a. Find the sum, difference, prduct, and qutient f tw numbers expressed as decimals thrugh thusandths (divisrs with nly ne nnzer digit); and, 5.5 b. Create and slve single-step and multistep practical prblems invlving decimals. Check answers t divisin prblems using multiplicatin. 3.4 Remaining Numbers Divisin, Divisin, Divisin! Divisin Cmputatin Divisin Delight Hw t Check Hw t Check Divisin Use clue wrds r their equivalent t slve divisin wrd prblems a. Identify and describe the characteristics f prime and cmpsite numbers 14 The Sweater Stre Divisin Practice Qutients and

15 UNIT 5: DIVIDING WHOLE NUMBERS Remainders Class Prblems Let s Write Divide by tw-digit numbers a. Find the sum, difference, prduct, and qutient f tw numbers expressed as decimals thrugh thusandths (divisrs with nly ne nnzer digit); and, 5.5 b. Create and slve single-step and multistep practical prblems invlving decimals. 2-Digit Divisin I Time t Divide 2-Digit Divisin II Mre Dividing Divide by placing a zer in the qutient a. Find the sum, difference, prduct, and qutient f tw numbers expressed as decimals thrugh thusandths (divisrs with nly ne nnzer digit); and, 5.5 b. Create and slve single-step and multistep practical prblems invlving decimals. Divide by 10, 100, and a. Find the sum, difference, prduct, and qutient f tw numbers expressed as decimals thrugh thusandths (divisrs with nly ne nnzer digit); and, 5.5 b. Create and slve single-step and multistep practical prblems invlving decimals. Use calculatrs t slve divisin prblems. Practice Multiplying and Dividing by Pwers f 10 Multiplying and Dividing by Pwers f 10 Pster Language and Writing 15

16 UNIT 6: NUMBER THEORY CONTENT OBJECTIVES / GRADE RELATED Identify key wrds and terms related t number thery: divisible, factrs, greatest cmmn factr (GCF), multiples, least cmmn multiple, prime number, cmpsite number, expnent, square, square rt. Identify patterns in number sequences. Multiples f 2, 5, and 10. Use the divisibility tests fr 2, 5, and 10. Multiples f 3, 6, and 9. Use divisibility tests fr 3, 6, and 9. Use divisibility test fr 4. Find the factrs f a number. Find the greatest cmmn factr a. Identify and represent integers; 6.3 b. Order and cmpare integers; 6.3 c. Identify and describe the abslute value f integers. SUGGESTED ACTIVITIES (Internet, ActiveStudi Flipcharts, Wrksheets) Vcabulary and definitins (fr Spanish and nn Spanish speakers) Vcabulary matching game Number Patterns Instructins Writing Number Patterns Lk fr a Pattern Multiples Wall Pster Multiples f 2, 5, and 10 Instructins Discvering the Multiples f 2, 5, and 10 Multiples f 2, 5, and 10 Divisibility Wall Pster Practice with Divisibility Divisibility Puzzle Prblem Slving with Divisibility Language Activity Factrs and Prducts Finding Factrs Find the GCF The Factrs Game Rules fr Playing the Factrs Game Thinking abut Numbers Review Find the multiples f a number. Find the least cmmn multiple a. Identify and represent integers; 16 LCM Instructins Multiples Multiples and Factrs Bard All Abut Multiples

17 6.3 b. Order and cmpare integers; 6.3 c. Identify and describe the abslute value f integers. Identify prime and cmpsite numbers. Write the prime factrizatin f a number a. Identify and represent integers; 6.3 b. Order and cmpare integers; 6.3 c. Identify and describe the abslute value f integers. Find the value f expressin cntaining expnents Investigate and describe cncepts f psitive expnents and perfect squares. Evaluate numerical expressins using the rder f peratins (PEMDAS). 7.2 Find squares and square rts a. Determine whether a given number is a perfect square; and, 8.5 b. Find the tw cnsecutive whle numbers between which a square rt lies. Prime Numbers Finding the primes Finding Prime Factrizatin: Tw Methds Prime Factrizatin Practice w/answer key Prime Factrizatin Triple Match w/answer key Factrs/Multiples/Primes/Cmpsites Wall Pster Review f Factrs, Multiples, Primes, and Cmpsites Vcabulary Review Expnential Frm Ten Chart Take Ten Expnential Frm Example 2 Expnent Extravaganza Instructins t Order f Operatins Cmparing Expressins Order f Operatins Dear Aunt Sally Evaluating Expressins Order Cunts Practicing Order f Operatins Squares and Square Rts Wall Pster Explring Square Rt and Sample Prblems Writing abut Perfect Squares and Square Rts Wrking with Perfect Squares and Square Rts Table f Perfect Squares and Square Rts Square Rt Activity Sheet Square and Square Rts Chart Squared Away! 17

18 UNIT 7: FRACTIONS AND MIXED NUMBERS CONTENT OBJECTIVES / GRADE RELATED Identify key wrds and terms related t fractins: fractin, numeratr, denminatr, equivalent fractins, lwest terms, highest terms, like fractins, unlike fractins, prper fractins, imprper fractins, mixed number. Name fractins and their parts. Read and say fractins. Write fractins with wrds a. Recgnize and name fractins in their equivalent decimal frm and vice versa; and, 5.2 b. Cmpare and rder fractins and decimals in a given set frm least t greatest and greatest t least. SUGGESTED ACTIVITIES (Internet, ActiveStudi Flipcharts, Wrksheets) Vcabulary and definitins (fr Spanish and nn Spanish speakers) Vcabulary matching activity Numeratr and Denminatr Representing Fractins Draw and Shade in the fllwing fractins Name and write the fractins in English Write the fractins fr clred parts Recall multiplicatin facts thrugh the twelves table, and the crrespnding divisin facts. Recgnize equivalent fractins a. Cmpare and rder fractins and mixed numbers; 4.2 b. Represent equivalent fractins; and, 4.2 c. Identify the divisin statement that represents a fractin. Reduce fractins t lwest terms. Twer f Bars Equivalency Chart Which shw furths? Explring Equivalent Fractins Lwest Terms Simplifying Fractins Instructins Simplest Frms Change fractins t higher terms. 18

19 Find cmmn denminatrs. Change unlike fractins t like fractins. Cmpare fractins using the symbls >, <, and =. 4.2 Cmparisn Symbls Cmparing Fractin Bars Cmparing Fractin Circles a. Identify and represent integers; 6.3 b. Order and cmpare integers; 6.3 c. Identify and describe the abslute value f integers Represent multiplicatin and divisin, using area, set, and number line mdels, and create and slve prblems that invlve multiplicatin f tw whle numbers, ne factr 99 r less and the secnd factr 5 r less. Order fractins frm least t greatest and frm greatest t least a. Identify and represent integers; 6.3 b. Order and cmpare integers; 6.3 c. Identify and describe the abslute value f integers. Identify prper and imprper fractins. Change fractins t mixed r whle numbers. Changing mixed numbers t fractins. Identify and cmplete patterns. Find missing numbers Fractins in Order Change fractins t mixed r whle numbers Cmparing Fractins 19

20 UNIT 8: MULTIPLYING AND DIVIDING FRACTIONS CONTENT OBJECTIVES / GRADE RELATED SUGGESTED ACTIVITIES (Internet, Activ Studi Flipcharts, Wrksheets) Identify key wrds and terms related t multiplying and dividing fractins: canceling, simplifying, invert, flip, reciprcal Multiply fractins. Simplify fractins a. Multiply and divide fractins and mixed numbers; and, 6.6 b. Estimate slutins and then slve single-step and multistep practical prblems invlving additin, subtractin, multiplicatin, and divisin f fractins. Vcabulary and definitins (fr Spanish and nn Spanish speakers) Multiply fractins using canceling a. Multiply and divide fractins and mixed numbers; and, 6.6 b. Estimate slutins and then slve single-step and multistep practical prblems invlving additin, subtractin, multiplicatin, and divisin f fractins. Cnvert a whle number t a fractin. Multiply fractins and whle numbers a. Multiply and divide fractins and mixed numbers; and, 6.6 b. Estimate slutins and then slve single-step and multistep practical prblems invlving additin, subtractin, multiplicatin, and divisin f fractins. Multiply mixed numbers a. Multiply and divide fractins and mixed numbers; and, 6.6 b. Estimate slutins and then slve single-step and multistep practical prblems invlving additin, subtractin, multiplicatin, and divisin f fractins. 20

21 Divide whle numbers and fractins by fractins. Identify reciprcal fractins a. Multiply and divide fractins and mixed numbers; and, 6.6 b. Estimate slutins and then slve single-step and multistep practical prblems invlving additin, subtractin, multiplicatin, and divisin f fractins. Dividing fractins by whle numbers a. Multiply and divide fractins and mixed numbers; and, 6.6 b. Estimate slutins and then slve single-step and multistep practical prblems invlving additin, subtractin, multiplicatin, and divisin f fractins. Divide fractins by mixed numbers. Divide mixed numbers by fractins a. Multiply and divide fractins and mixed numbers; and, 6.6 b. Estimate slutins and then slve single-step and multistep practical prblems invlving additin, subtractin, multiplicatin, and divisin f fractins. Divide mixed numbers by mixed numbers a. Multiply and divide fractins and mixed numbers; and, 6.6 b. Estimate slutins and then slve single-step and multistep practical prblems invlving additin, subtractin, multiplicatin, and divisin f fractins. Slve wrd prblems using fractins. 21

22 UNIT 9. ADDING and SUBTRACTING FRACTIONS CONTENT OBJECTIVES / GRADE RELATED SUGGESTED ACTIVITIES (Internet, ActiveStudi Flipcharts, Wrksheets) Identify key wrds and terms related t adding and subtracting fractins: like fractins, unlike fractins Add and subtract fractins with the same denminatr a. Multiply and divide fractins and mixed numbers; and, 6.6 b. Estimate slutins and then slve single-step and multistep practical prblems invlving additin, subtractin, multiplicatin, and divisin f fractins. Vcabulary and definitins (fr Spanish and nn Spanish speakers) Evaluate whle number numerical expressins, using the rder f peratins limited t parentheses, additin, subtractin, multiplicatin, and divisin Add and subtract prper fractins having like denminatrs f 12 r less. Add fractins with like mixed numbers a. Multiply and divide fractins and mixed numbers; and, 6.6 b. Estimate slutins and then slve single-step and multistep practical prblems invlving additin, subtractin, multiplicatin, and divisin f fractins Evaluate whle number numerical expressins, using the rder f peratins limited t parentheses, additin, subtractin, multiplicatin, and divisin. Subtract fractins with like mixed numbers a. Multiply and divide fractins and mixed numbers; and, 6.6 b. Estimate slutins and then slve single-step and multistep practical prblems invlving additin, subtractin, multiplicatin, and divisin f fractins. 22

23 Evaluate whle number numerical expressins, using the rder f peratins limited t parentheses, additin, subtractin, multiplicatin, and divisin. Subtract frm whle numbers a. Multiply and divide fractins and mixed numbers; and, 6.6 b. Estimate slutins and then slve single-step and multistep practical prblems invlving additin, subtractin, multiplicatin, and divisin f fractins Evaluate whle number numerical expressins, using the rder f peratins limited t parentheses, additin, subtractin, multiplicatin, and divisin. Add unlike fractins a. Multiply and divide fractins and mixed numbers; and, 6.6 b. Estimate slutins and then slve single-step and multistep practical prblems invlving additin, subtractin, multiplicatin, and divisin f fractins. Additin Wrksheet Examples Evaluate whle number numerical expressins, using the rder f peratins limited t parentheses, additin, subtractin, multiplicatin, and divisin. Subtract unlike fractins a. Multiply and divide fractins and mixed numbers; and, 6.6 b. Estimate slutins and then slve single-step and multistep practical prblems invlving additin, subtractin, multiplicatin, and divisin f fractins Evaluate whle number numerical expressins, using the rder f peratins limited t parentheses, additin, subtractin, multiplicatin, and divisin. Add unlike mixed numbers 23

24 a. Multiply and divide fractins and mixed numbers; and, 6.6 b. Estimate slutins and then slve single-step and multistep practical prblems invlving additin, subtractin, multiplicatin, and divisin f fractins Evaluate whle number numerical expressins, using the rder f peratins limited t parentheses, additin, subtractin, multiplicatin, and divisin. Subtract unlike mixed numbers a. Multiply and divide fractins and mixed numbers; and, 6.6 b. Estimate slutins and then slve single-step and multistep practical prblems invlving additin, subtractin, multiplicatin, and divisin f fractins Evaluate whle number numerical expressins, using the rder f peratins limited t parentheses, additin, subtractin, multiplicatin, and divisin. Slve multi-part wrd prblems Evaluate whle number numerical expressins, using the rder f peratins. 24

25 UNIT 10. DECIMALS CONTENT OBJECTIVES / GRADE RELATED Identify key wrds and terms related t decimals: decimals, decimal pint, decimal places, mixed decimals Identify decimals and their parts. Read and write decimals Add and subtract prper fractins having like denminatrs f 12 r less. SUGGESTED ACTIVITIES (Internet, ActiveStudi Flipcharts, Wrksheets) Vcabulary and definitins (fr Spanish and nn Spanish speakers) Decimal Squares Decimal Place Value a. Estimate sums, differences, prducts, and qutients f whle numbers; 4.4 b. Add, subtract, and multiply whle numbers. 4.4 c. Divide whle numbers, finding qutients with and withut remainders. 4.4 d. Slve single-step and multistep additin, subtractin, and multiplicatin prblems with whle numbers. Cmpare tw decimals. 4.4 Cmpare and Order Decimals a. Read, write, represent, and identify decimals expressed thrugh thusandths; 4.3 b. Rund decimals t the nearest whle number, tenth, and hundredth; 4.3 c. Cmpare and rder decimals; and, 4.3 d. Given a mdel, write the decimal and fractin equivalents a. Identify and represent integers; 6.3 b. Order and cmpare integers; 6.3 c. Identify and describe the abslute value f integers. 25

26 Order decimals a. Recgnize and name fractins in their equivalent decimal frm and vice versa; and, 5.2 b. Cmpare and rder fractins and decimals in a given set frm least t greatest and greatest t least a. Read, write, represent, and identify decimals expressed thrugh thusandths; 4.3 b. Rund decimals t the nearest whle number, tenth, and hundredth; 4.3 c. Cmpare and rder decimals; and, 4.3 d. Given a mdel, write the decimal and fractin equivalents a. Identify and represent integers; 6.3 b. Order and cmpare integers; 6.3 c. Identify and describe the abslute value f integers. Identify equivalent decimals a. Read, write, represent, and identify decimals expressed thrugh thusandths; 4.3 b. Rund decimals t the nearest whle number, tenth, and hundredth; 4.3 c. Cmpare and rder decimals; and, 4.3 d. Given a mdel, write the decimal and fractin equivalents. Add and subtract decimals a. Read, write, represent, and identify decimals expressed thrugh thusandths; 4.3 b. Rund decimals t the nearest whle number, tenth, and hundredth; 4.3 c. Cmpare and rder decimals; and, 4.3 d. Given a mdel, write the decimal and fractin equivalents. 26

27 Create and slve single-step and multistep practical prblems invlving additin, subtractin, multiplicatin, and divisin with r withut remainders f whle numbers. Multiply decimals. 5.4 Multiply decimals by 10, 100, Divide decimals by whle numbers and by decimals. 5.6 Divide decimals by 10, 100, and Slve multi-part decimal prblems. 4.9 Terminating and Repeating Decimals Slve single-step and multistep practical prblems invlving additin, subtractin, multiplicatin, and divisin f decimals. Rename decimals as fractins in lwest terms a. Investigate and describe the cncept f negative expnents fr the pwers f ten; 7.1 b. Determine scientific ntatin fr numbers greater than zer; 7.1 c. Cmpare and rder f fractins, decimals, percents, and numbers written in scientific ntatin; 7.1 d. Determine square rts Rename fractins as decimals. 27 Fractin Decimal Jigsaw Puzzle Fractins and Decimals

28 a. Investigate and describe the cncept f negative expnents fr the pwers f ten; 7.1 b. Determine scientific ntatin fr numbers greater than zer; 7.1 c. Cmpare and rder f fractins, decimals, percents, and numbers written in scientific ntatin; 7.1 d. Determine square rts a. Investigate and describe fractins, decimals, and percents as ratis; 6.2 b. Identify a given fractin, decimal, r percent frm a representatin; 6.2 c. Demnstrate equivalent relatinships amng fractins, decimals, and percents; and, 6.2 d. Cmpare and rder fractins, decimals, and percents. Rund decimals. Mney. Recgnize and use US currency Read temperature t the nearest degree frm a Celsius thermmeter and a Fahrenheit thermmeter. Real thermmeters and physical mdels f thermmeters will be used a. Cunt and cmpare a cllectin f pennies, nickels, dimes, and quarters whse ttal value is $2.00 r less; and, 2.10 b. Crrectly use the cent symbl ( ), dllar symbl ($), and decimal pint (.). 28

29 UNIT 11. PERCENT CONTENT OBJECTIVES / GRADE RELATED Identify key wrds and terms related t percent: percent, sales tax, discunt, sale price, cmmissin, base salary, grss salary, percent increase, percent decrease Write percents. Change percents t decimals a. Investigate and describe the cncept f negative expnents fr the pwers f ten; 7.1 b. Determine scientific ntatin fr numbers greater than zer; 7.1 c. Cmpare and rder f fractins, decimals, percents, and numbers written in scientific ntatin; 7.1 d. Determine square rts Find a percent f a number. 7.4 Find sales tax. 7.4 Find the amunt f discunt. 7.4 Change decimals t percents. 6.1 SUGGESTED ACTIVITIES (Internet, ActiveStudi Flipcharts, Wrksheets) Vcabulary and definitins (fr Spanish and nn Spanish speakers) Decimals and Percents Wrking with Discunts Decimals and Percents a. Investigate and describe the cncept f negative expnents fr the pwers f ten; 7.1 b. Determine scientific ntatin fr numbers greater than zer; 7.1 c. Cmpare and rder f fractins, decimals, percents, and numbers written in scientific ntatin; 7.1 d. Determine square rts 29

30 Change fractins t percents a. Investigate and describe fractins, decimals, and percents as ratis; 6.2 b. Identify a given fractin, decimal, r percent frm a representatin; 6.2 c. Demnstrate equivalent relatinships amng fractins, decimals, and percents; and, 6.2 d. Cmpare and rder fractins, decimals, and percents. Fractin-Percent Instructins Fractin, Decimal, Percent Fractins t Percents Three Numbers a. Investigate and describe the cncept f negative expnents fr the pwers f ten; 7.1 b. Determine scientific ntatin fr numbers greater than zer; 7.1 c. Cmpare and rder f fractins, decimals, percents, and numbers written in scientific ntatin; 7.1 d. Determine square rts Find the percent given the whle and the part Slve single-step and multistep prblems, using prprtinal reasning. Find the percent increase/decrease Slve single-step and multistep prblems, using prprtinal reasning. Find the whle given the percent and the part Slve single-step and multistep prblems, using prprtinal reasning. Finding the riginal price given the percent and the new price Slve single-step and multistep prblems, using prprtinal reasning. Slve wrd prblems invlving percent Slve single-step and multistep prblems, using prprtinal reasning. 30

31 UNIT 12. RATIOS AND PROPORTIONS CONTENT OBJECTIVES / GRADE RELATED SUGGESTED ACTIVITIES (Internet, ActiveStudi Flipcharts, Wrksheets) Identify key wrds and terms related t ratis and prprtins: rati, prprtin, crss prducts, rate, multiple unit pricing, scale drawing, scale Write a rati t cmpare tw quantities a. Identify and represent integers; 6.3 b. Order and cmpare integers; 6.3 c. Identify and describe the abslute value f integers. Vcabulary and definitins (fr Spanish and nn Spanish speakers) Ratis Definitin Intrductin t Ratis Rati Identificatin Muntains Identify prprtins a. Slve practical prblems invlving ratinal numbers, percents, ratis, and prprtins; and, 8.3 b. Determine the percent increase r decrease fr a given situatin. Slve prprtins a. Slve practical prblems invlving ratinal numbers, percents, ratis, and prprtins; and, 8.3 b. Determine the percent increase r decrease fr a given situatin. Use prprtins t find the price f any number f the same items given the multiple unit price. Use prprtins t find the number f items that can be bught fr a certain amunt f mney given the multiple unit pricing. 7.6 Interpret a scale drawing. Find an actual length f an bject frm a scale drawing. 7.6 Use prprtins t slve wrd prblems. Using Prprtins Practice Sheets 31

32 Unit 13. GRAPHICS AND STATISTICS CONTENT OBJECTIVES / GRADE RELATED Identify key wrds and terms related t graphics and statistics: data, graph, pictgraph, mean, median, mde, histgram, key, symbls, labels, title, represent, prbability, statistics, impssible, pssible, certain, utcme, event, less likely, mre likely, chance Read and make pictgraphs, bar graphs, and line graphs. Use a bar graph t display data in either hrizntal r vertical frm. Use a duble graph t cmpare tw different sets f data abut the same thing. 1.18, 1.19, 2.23, 3.21, 3.22, 4.20, a. Cllect and rganize data, using bservatins, measurements, surveys, r experiments; 3.17 b. Cnstruct a line plt, a picture graph, r a bar graph t represent the data; and, 3.17 c. Read and interpret data represented in line plts, bar graphs, and picture graphs and write a sentence analyzing data. SUGGESTED ACTIVITIES (Internet, ActiveStudi Flipcharts, Wrksheets) Vcabulary and definitins (fr Spanish and nn Spanish speakers) Hurs spent watching televisin Hw d we get t schl Cnstruct pictgraph instructins Fish Sales Students Favrite Sprts Bar Graph Mdels Sales by Dming Family Pizza Favrite Sprts 2 pages Ging t the Mvies Recgnize and describe a variety f patterns frmed using numbers, tables, and pictures, and extend the patterns, using the same r different frms Given a prblem situatin, cllect, rganize, and interpret data in a variety f frms, using stemand-leaf plts and line graphs a. Make cmparisns, predictins, and inferences, using infrmatin displayed in graphs; and, 8.13 b. Cnstruct and analyze scatterplts Make cnnectins between any tw representatins (tables, graphs, wrds, and rules) f a given relatinship. Use single and duble line graphs t shw change ver time and t cmpare sets f related data. Mrs. Clark s Readers Line Graph & Questins Jaguars and Panthers Duble Line Graph & Questins Lunch Time Answer Questins and Make a line Graph 32

33 Prblem slving: chsing a scale Read circle graphs and histgrams. Use a circle graph t shw hw a ttal amunt f smething is divided int parts. Use a histgram t shw hw many items ccur between tw numbers Circle/Pie Graphs Rita s Jb _ Graphs and Questins Tutti-Frutti Make a Circle Graph Hurs in a Day Circle Graph TSW, given a prblem situatin, a. Cnstruct circle graphs; b. Draw cnclusins and make predictins, using circle graphs; and, c. Cmpare and cntrast graphs that present infrmatin frm the same data set a. TSW, given data fr a practical situatin, cnstruct and analyze histgrams; and, 7.11 b. TSW, given data fr a practical situatin, cmpare and cntrast histgrams with ther types f graphs presenting infrmatin frm the same data set Represent relatinships with tables, graphs, rules, and wrds Determine the prbability f independent and dependent events with and withut replacement. Find the mean, median, mde, and range f a set f data a. Investigate and recgnize the identity prperties fr additin and multiplicatin; 33 Marbles, Marbles Finding the Mean (Average) Finding the Median Which wuld yu chse? Mean, Median, Mde, and Range Finding the Mean, Median, Mde, and Range

34 6.19 b. the multiplicative prperty f zer; and, 6.19 c. the inverse prperty fr multiplicatin a. Describe mean as a balancing pint; and, 6.15 b. Decide which measure f center is apprpriate fr a given purpse a. Describe mean, median, and mde as measures f center; 5.16 b. Describe mean as fair share; 5.16 c. Find the mean, median, mde, and range f a set f data; and, 5.16 d. Describe the range f a set f data as a measure f variatin. Find simple prbability: calculate and express numerically the chance that smething will happen Graph inequalities n a number line. Impssible? What is the prbability? Prbability Prbability Practice Chance it! Vcabulary Review Answer Key Describe the relatinship fund in a number pattern and express the relatinship Make predictins and determine the prbability f an utcme by cnstructing a sample space a. Cmpare and cntrast dependent and independent events; and, 6.16 b. Determine prbabilities fr dependent and independent events Investigate and describe the difference between experimental prbability and theretical prbability f an event Determine the prbability f cmpund events, using the Fundamental (Basic) Cunting Principle. 34

35 Unit 14. CUSTOMARY MEASUREMENT CONTENT OBJECTIVES / GRADE RELATED Identify key wrds and terms related t custmary measurements: measuring, length, custmary system f measurement, weight, scale, capacity, elapsed time, degrees ( ), cnvert, pint, quart, galln Change units f length, weight, and capacity. 6.9 Change units f time. Find elapsed time SUGGESTED ACTIVITIES (Internet, ActiveStudi Flipcharts, Wrksheets) Vcabulary and definitins (fr Spanish and nn Spanish speakers) An Inch Measuring in Inches Selecting Custmary Units fr Length Table f Measurements fr Length Cnverting Custmary Units f Length Cnverting Custmary Units f Length Practice Weight Scales Estimate and Weight Let s Weight with Beans Weighing with Punds Weighing with Ounces Tables f Measurements fr Weight Estimating Weight in Ounces, Punds, and Tns What d we use t measure (unces, punds, r tns)? Cnverting Weight in the Custmary System Practice Cnverting in the Custmary System What Wuld Yu Chse? (cup, pint, quart, r galln)? Equivalency Chart Cnversin Chart Tables f Measurements fr Capacity Capacity Challenge Cnverting Units f Time Hw Much Time has Passed? What will the Time be? Passing Time Regruping Time 35

36 6.9 USA Time Znes Time, please! Acrss the Miles Find changes in temperature. Slve prblems using custmary measurements Unit 15. METRIC MEASUREMENT Pacemaker Basic Mathematics Chapter 15 CONTENT OBJECTIVES / GRADE RELATED Identify key wrds and terms related t metric measurements: metric system, meter, gram, liter, unit price, measuring, cnvert Identify prefixes used in the metric system. SUGGESTED ACTIVITIES (Internet, ActiveStudi Flipcharts, Wrksheets) Vcabulary and definitins (fr Spanish and nn Spanish speakers) Prefixes used in the metric system Change metric units f length, mass, and liquid capacity Let s Measure With Metric System Hw Lng? What Wuld Yu Use? Measuring Review Sheets Can Yu Find? Selecting Metric Units Table f Measurements fr Length Cnverting Metric Units Cnverting Metric Units Practice Units f Length Custmary and Metric Mre Abut Length Table f Measurements fr Weight Estimating Weight in Grams and Kilgrams Mre Practice with Metric Measurements Language Practice Writing Abut Weight What d we Use t Measure (grams r kilgrams)?

37 Cnverting Weight in the Metric System Mre Practice with Weight in the Metric System Review f Weight What Wuld Yu Use, Milliliter r liter? Capacity Metric Units Practice The Language f Capacity Cmpare metric and custmary units f measurements. 6.9 Slve prblems using metric measurements Cmparing Custmary and Metric Units f Length Which is it? Ounces, Punds, Tns, r Kilgrams? Prblem Slving with Weight Prblem Slving Capacity Unit 16. GEOMETRY CONTENT OBJECTIVES / GRADE RELATED Identify key wrds and terms related t gemetry: pint, line, line segment, ray, straight, curved, angle, prtractr, right angle, acute angle, btuse angle, plygns, perimeter, area, parallelgram, circumference, radius, space figure, vlume Recgnize pints and lines a. identify and describe representatins f pints, lines, line segments, rays, and angles, including endpints and vertices; and 37 SUGGESTED ACTIVITIES (Internet, ActiveStudi Flipcharts, Wrksheets) Vcabulary and definitins (fr Spanish and nn Spanish speakers) Vcabulary Wall Chart Lines Parallel, Perpendicular, Intersecting Lines Quiz

38 4.10 b. identify representatins f lines that illustrate intersectin, parallelism, and perpendicularity. Use a prtractr t measure and draw angles a. verify by measuring and describe the relatinships amng vertical angles, adjacent angles, supplementary angles, and cmplementary angles; and 8.6 b. measure angles f less than The student will classify 5.12 a. angles as right, acute, btuse, r straight; and 5.12 b. triangles as right, acute, btuse, equilateral, scalene, r issceles The student, using plane figures (square, rectangle, triangle, parallelgram, rhmbus, and trapezid), will develp definitins f these plane figures; and investigate and describe the results f cmbining and subdividing plane figures. Measure Each Angle Types f Angles Practice Quiz Identify plygns a. define plygn; and 4.12 b. identify plygns with 10 r fewer sides a. find perimeter, area, and vlume in standard units f measure; 5.8 b. differentiate amng perimeter, area, and vlume and identify whether the applicatin f the cncept f perimeter, area, r vlume is apprpriate fr a given situatin; 5.8 c. identify equivalent measurements within the metric system; 5.8 d. estimate and then measure t slve prblems, using U.S. Custmary and metric units; and 5.8. e. chse an apprpriate unit f measure fr a given situatin invlving measurement using U.S. Custmary and metric units. 5.9 The student will identify and describe the diameter, radius, chrd, and circumference f a circle The student will determine an amunt f elapsed time in hurs and minutes within a 24-hur perid The student will measure right, acute, btuse, and straight angles. 38 Acute, Right, and Obtuse Triangles Angles in a Triangle Triangles Warm-up Explring the Sum f the Interir Angles f a Triangle Interir Angles f Triangles Regular Plygns Drawing Regular and Irregular Plygns Hexagn Practice with Plygns Quadrilaterals Learning abut Quadrilaterals Quadrilateral Review Plygn Vcabulary Practice Vcabulary Challenge (analgies)

39 The student will determine cngruence f segments, angles, and plygns. The student will describe and identify prperties f quadrilaterals. The student will cmpare and cntrast the fllwing quadrilaterals based n prperties: parallelgram, rectangle, square, rhmbus, and trapezid. The student, given a plygn in the crdinate plane, will represent transfrmatins (reflectins, dilatins, rtatins, and translatins) by graphing in the crdinate plane. Find perimeter, circumference, area, and vlume a. investigate and slve practical prblems invlving vlume and surface area f prisms, cylinders, cnes, and pyramids; and 8.7 b. describe hw changing ne measured attribute f a figure affects the vlume and surface area. Slve area wrd prblems. 6.9 The student will make ballpark cmparisns between measurements in the U.S. Custmary System f measurement and measurements in the metric system a. define π (pi) as the rati f the circumference f a circle t its diameter; 6.10 b. slve practical prblems invlving circumference and area f a circle, given the diameter r radius; 6.10 c. slve practical prblems invlving area and perimeter; and 6.10 d. describe and determine the vlume and surface area f a rectangular prism. Perimeter Definitin Perimeter f a Rectangle Perimeter and Area f Parallelgrams Perimeter and Area f Triangles Find the Perimeter Finding Area Frmulas Area f Plygns Vcabulary Practice - Perimeter and Area Vcabulary Review Gemetry Definitins Pythagrean Therem Explring the Pythagrean Therem Using Yur Calculatr with the Pythagrean Therem Right Triangles and the Pythagrean Therem Using the Pythagrean Therem Prblem Slving with the Pythagrean Therem Vcabulary Practice with the Pythagrean Therem Parts f a Circle Circular Activity Sheet All Abut Circles 39

40 a. describe vlume and surface area f cylinders; 7.5 b. slve practical prblems invlving the vlume and surface area f rectangular prisms and cylinders; and 7.5 c. describe hw changing ne measured attribute f a rectangular prism affects its vlume and surface area. The student will determine whether plane figures quadrilaterals and triangles are similar and write prprtins t express the relatinships between crrespnding sides f similar figures. 8.8 a. apply transfrmatins t plane figures; and 8.8 b. identify applicatins f transfrmatins. The student will cnstruct a three-dimensinal mdel, given the tp r bttm, side, and frnt views. Circumference f Circles Are f a circle Finding a Frmula fr the Area f a Circle Area f Circles Vcabulary Practice Circles Prisms verify the Pythagrean Therem; and apply the Pythagrean Therem. The student will slve practical area and perimeter prblems invlving cmpsite plane figures. Unit 17. Integers CONTENT OBJECTIVES / GRADE RELATED Identify key wrds and terms related t integers: integers, psitive integers, negative integers, ppsites. Identify and write integers SUGGESTED ACTIVITIES (Internet, ActiveStudi Flipcharts, Wrksheets) Vcabulary and definitins (fr Spanish and nn Spanish speakers) Psitive and Negative Numbers Oppsites Integers

41 7.3 a. mdel additin, subtractin, multiplicatin, and divisin f integers; and 7.3 b. add, subtract, multiply, and divide integers. Integer Number Line Cmpare and Order Integers Add integers with like signs. Add integers with unlike signs. Subtract integers. Multiply integers. Divide integers. Slve prblems using integers. Unit 18. Algebra CONTENT OBJECTIVES / GRADE RELATED Identify key wrds and terms related t algebra: equatin, cnstant, variable, number expressin, slutin, simplify, parentheses ( ), rder f peratins Represent and write variables and expressins. Identify slutins t equatins a. recgnize and demnstrate the meaning f equality in an equatin; and b. investigate and describe the assciative prperty fr additin and multiplicatin. The student will describe the relatinship fund in a number pattern and express the relatinship. 41 SUGGESTED ACTIVITIES (Internet, ActiveStudi Flipcharts, Wrksheets) Vcabulary and definitins (fr Spanish and nn Spanish speakers)cnstants, Variables, and Expressins Mre Cnstants, Variables, and Expressins Cnstants, Variables, and Expressins all arund us Vcabulary Practice Cnstants and Variables in my life Representing Multiplicatin Representing Divisin Wrds Assciated with Operatins Changing Wrds t Expressins Matching Expressins and Phrases Writing Expressins Review f Expressins Mre Vcabulary Practice Vcabulary Review Equatins and Expressins

42 a. investigate and describe the cncept f variable; 5.18 b. write an pen sentence t represent a given mathematical relatinship, using a variable; 5.18 c. mdel ne-step linear equatins in ne variable, using additin and subtractin; and 5.18 d. create a prblem situatin based n a given pen sentence, using a single variable. Simplify expressins with parentheses using the rder f peratins The student will investigate and recgnize the distributive prperty f multiplicatin ver additin. Slve equatins with ne peratin. Answer Key See chapter 6 activities Slving Equatins Using Inverse Operatin 6.18 The student will slve ne-step linear equatins in ne variable invlving whle number cefficients and psitive ratinal slutins. Slve equatins with mre than ne peratin The student will make cnnectins between any tw representatins (tables, graphs, wrds, and rules) f a given relatinship. slve multistep linear equatins in ne variable with the variable n ne and tw sides f the equatin; slve tw-step linear inequalities and graph the results n a number line; and identify prperties f peratins used t slve an equatin. The student will graph a linear equatin in tw variables. The student will identify the dmain, range, independent variable, r dependent variable in a given situatin. Slving Equatins Slving Tw-Step Equatins Slve prblems using ne-step and tw-step equatins. 42 Tran s CD Stre