Rangely RE 4 Curriculum Development 5 th Grade Mathematics

Size: px
Start display at page:

Download "Rangely RE 4 Curriculum Development 5 th Grade Mathematics"

Transcription

1 Unit Title Dctr We Still Need t Operate... Length f Unit 12 weeks Fcusing Lens(es) Inquiry Questins (Engaging Debatable): Structure Systems Standards and Grade Level Expectatins Addressed in this Unit Hw are mathematical peratins related? (MA10 GR.5 S.1 GLE.2 IQ.1) Why is zer imprtant in ur place value system? (MA10 GR.5 S.1 GLE.1 IQ.4) MA10 GR.5 S.1 GLE.1, MA10 GR.5 S.1 GLE.2 Unit Strands Cncepts Number and Operatins in Base Ten, Operatins and Algebraic Thinking, Measurement and Data Measurements, equivalence, rati, cnversin, unit, measurement systems, multiplicatin, divisin, cnstant rate (factr), place value, decimal system, decimals, pwers f ten, digits, magnitude, standard algrithm, partial prducts, prperties f peratins, distributive prperty, relatinship, runding, additin, subtractin, denminatr, numeratr, prduct, dividend, divisr, qutient, fractins, rder f peratins, slutins, cmpare Generalizatins My students will Understand that Factual Guiding Questins Cnceptual A cnstant applicatin f multiplicatin by 10 t btain the next higher unit, r divisin by 10 t btain the next lwer unit, demnstrates 10 as the cnstant rate/factr f cmpsing and decmpsing place value units in ur decimal system (MA10 GR.5 S.1 GLE.1 EO.a.i, a.ii, b.i, b.ii) Multiplicatin r divisin by a pwer f 10 increases r decreases their place value t a magnitude equivalent t the pwer f 10 (MA10 GR.5 S.1 GLE.1 EO.a.i, a.ii) In the standard algrithm fr multiplicatin f whle numbers, the pwer f 10 represented by the place value f the digit multiplier determines the crrespnding amunt t shift the partial prducts t the left (MA10 GR.5 S.1 GLE.2 EO.a) What is the relatinship between 654 and 65.4? What wuld it mean if we did nt have a place value system? (MA10 GR.5 S.1 GLE.1 IQ.2) What is the purpse f the decimal pint? What is the purpse f ur place value system? (MA10 GR.5 S.1 GLE.1 IQ.3) What makes ne strategy r algrithm better than anther? (MA10 GR.5 S.1 GLE.2 IQ.2) Hw many place values des the partial prduct shift when multiplying by the digit in the hundreds place? Why is dividing by 10 the equivalent t multiplicatin by 1/10? Hw des understanding ur place value system help t read, write and cmpare decimals? Why is a place value system beneficial? (MA10 GR.5 S.1 GLE.1 IQ.1) Why d yu mve the decimal pint tw places t the right when multiply 100 and tw places t the left when dividing by 100? Why d yu shift partial prducts ver ne place value when multiplying by the digit in the tens place? December 13, 2013 Page 16 f 21

2 Place value, prperties f peratins and the relatinship between multiplicatin and divisin supprt the divisin f multi digit numbers. (MA10 GR.5 S.1 GLE.2 EO.b) As with the runding f whle numbers, the accurate runding f decimals depends upn place value cncepts and an attentin t cntext (MA10 GR.5 S.1 GLE.1 EO.c) The algrithm fr the additin and subtractin f decimals, a simple extensin f the algrithm fr whle numbers, requires precise attentin t place value such that digits with crrespnding place values are aligned prir t jining r separating (MA10 GR.5 S.1 GLE.2 EO.c) The algrithm fr multiplicatin f decimals relies n the equivalence f a decimal t a crrespnding fractin with a denminatr that is a pwer f ten (MA10 GR.5 S.1 GLE.2 EO.c) The algrithm fr the divisin f decimals dictates that the decimal pint in the dividend crrespnd t the lcatin f the decimal pint in the qutient and when a decimal appears in the divisr bth divisr and dividend bth must be multiplied by the same pwer f ten t eliminate it (MA10 GR.5 S.1 GLE.2 EO.c) Universal rder f peratin ensures unifrmity and accuracy f slutins. (MA10 GR.5 S.1 GLE.2 EO.d) Hw is multiplicatin used when dividing multi digit numbers? What is the rle f place value in the divisin algrithm? Hw d yu rund a decimal number t the nearest hundredth? Hw many tenths make ne whle? Hw d yu determine the lcatin f the decimal pint in the prduct f tw decimal numbers? When using the standard algrithm fr divisin, what strategy prvides a methd fr handling divisin f decimals? What is the rder f peratins? Hw des the relatinship between multiplicatin and divisin supprt divisin when using the standard algrithm? (MA10 GR.5 S.1 GLE.2 IQ.1) Hw is runding f decimal numbers similar and different frm runding whle numbers? Why is it imprtant that digits with the same place value are aligned when adding r subtracting using the standard algrithm? Hw des multiplicatin f fractins justify the standard algrithm fr multiplicatin f decimals? Why des the multiplicatin f the divisr and dividend by the same pwer f ten create an equivalent divisin prblem? (hint: a/b is the same as a divided by b) Why des rder f peratins matter? December 13, 2013 Page 17 f 21

3 Key Knwledge and Skills: My students will What students will knw and be able t d are s clsely linked in the cncept based discipline f mathematics. Therefre, in the mathematics samples what students shuld knw and d are cmbined. Recgnize that in a multi digit number, a digit in ne place represents 10 times as much as it represents in the place t its right and 1/10 f what it represents in the place t its left (MA10 GR.5 S.1 GLE.1 EO.a) (5.CC.NBT.1) Recgnize that in a multi digit number, a digit in ne place represents 10 times as much as it represents in the place t its right and 1/10 f what it represents in the place t its left. PARCC i) Tasks have thin cntext r n cntext. ii) Tasks invlve the decimal pint in a substantial way (e.g., by invlving a cmparisn f a tenths digit t a thusandths digit r a tenths digit t a tens digit). Explain patterns in the number f zers f the prduct when multiplying a number by pwers f 10, and explain patterns in the placement f the decimal pint when a decimal is multiplied r divided by a pwer f 10 (MA10 GR.5 S.1 GLE.1 EO.a.i, a.ii) (5.CC.NBT.2) Use whle number expnents t dente pwer f 10 (MA10 GR.5 S.1 GLE.1 EO.a.iii) (5.CC.NBT.2) Use whle number expnents t dente pwers f 10. PARCC i) The explanatin aspect f 5.NBT.2 is nt assessed here. Read and write decimals t thusandths using base ten numerals, number names, and expanded frm (MA10 GR.5 S.1 GLE.1 EO.b.i) (5.CC.NBT.3a) Read, write, and cmpare decimals t thusandths. a. Read and write decimals t thusandths using base ten numerals, number names, and expanded frm, e.g = 3 x x x x (1/10) + 9 x (1/100) + 2 x (1/1000). PARCC i) Tasks assess cnceptual understanding, e.g. by including a mixture (bth within and between items) f expanded frm, number names, and base ten numerals. ii) Tasks have thin cntext r n cntext. Cmpare tw decimal s t thusandths based n meanings f the digits in each place, using >, =, < symbls t recrd the cmparisns (MA10 GR.5 S.1 GLE.1 EO.b.ii) (5.CC.NBT.3b) Read, write and cmpare decimals t thusandths. b. Cmpare tw decimals t thusandths based n meanings f the digits in each place, using >, =, and < symbls t recrd the results f cmparisns. PARCC i) Tasks assess cnceptual understanding, e.g. by including a mixture (bth within and between items) f expanded frm, number names, and base ten numerals. ii) Tasks have thin cntext r n cntext. Use place value understanding t rund decimals t any place (MA10 GR.5 S.1 GLE.1 EO.c) (5.CC.NBT.4) Use place value understanding t rund decimals t any place. PARCC i) Tasks have thin cntext r n cntext. Demnstrate understanding f the place value system by cmbining r synthesizing knwledge and skills articulated in 5.NBT.A. Prmpts d nt prvide visual fractin mdels; students may at their discretin draw visual fractin mdels as a strategy. PARCC 5.NBT.A Int. 1. Fluently multiply multi digit whle numbers using the standard algrithm (MA10 GR.5 S.1 GLE.2 EO.a) (5.CC.NBT.5) December 13, 2013 Page 18 f 21

4 Fluently multiply multi digit whle numbers using the standard algrithm. PARCC i) Tasks assess fluency implicitly, simply in virtue f the fact that there are tw substantial cmputatins n the EOY. Tasks need nt be timed. ii) The given factrs are such as t require an efficient/standard algrithm (e.g ). Factrs in the task d nt suggest any bvius ad hc r mental strategy (as wuld be present fr example in a case such as ). iii) Tasks d nt have a cntext. iv) Fr purpses f assessment, the pssibilities are 3 digit 4 digit. Find whle number qutients f whle numbers with up t fur digit dividends and tw digit divisrs, using strategies based n place value, the prperties f peratins, and the relatinship between multiplicatin and divisin; illustrate and explain the calculatin by using equatins, rectangular arrays, and/r area mdels. (MA10 GR.5 S.1 GLE.2 EO.b.i, b.ii) (5.CC.NBT.6) Find whle number qutients f whle numbers with up t fur digit dividends and tw digit divisrs, using strategies based n place value, the prperties f peratins, and/r the relatinship between multiplicatin and divisin. Illustrate and explain the calculatin by using equatins, rectangular arrays, and/r area mdels. PARCC i) Tasks d nt require students t illustrate r explain. ii) Tasks invlve 3 r 4 digit dividends and ne r tw digit divisrs. Add, subtract, multiply, and divide decimals t hundredths, using cncrete mdels r drawings and strategies based n place value, prperties f peratins, and the relatinship between additin and subtractin; relate the strategy t a written methd and explain the reasning used (MA10 GR.5 S.1 GLE.2 EO.c.i, c.ii) (5.CC.NBT.7) Add tw decimals t hundredths, using cncrete mdels r drawings and strategies based n place value, prperties f peratins, and/r the relatinship between additin and subtractin; relate the strategy t a written methd and explain the reasning used. PARCC i) Tasks d nt have a cntext. ii) Only the sum is required; explanatins are nt assessed here. iii) Prmpts may include visual mdels, but prmpts must als present the addends as numbers, and the answer sught is a number, nt a picture. iv) Each addend is greater than r equal t 0.01 and less than r equal t v) 20% f cases invlve a whle number either the sum is a whle number, r else ne f the addends is a whle number presented withut a decimal pint. (The addends cannt bth be whle numbers.) Subtract tw decimals t hundredths, using cncrete mdels r drawings and strategies based n place value, prperties f peratins, and/r the relatinship between additin and subtractin; relate the strategy t a written methd and explain the reasning used. PARCC i) Tasks d nt have a cntext. ii) Only the difference is required; explanatins are nt assessed here. iii) Prmpts may include visual mdels, but prmpts must als present the subtrahend and minuend as numbers, and the answer sught is a number, nt a picture. iv) The subtrahend and minuend are each greater than r equal t 0.01 and less than r equal t Psitive differences nly. (Every included subtractin prblem is an unknwn addend prblem included in 5.NBT.7 1.) v) 20% f cases invlve a whle number either the difference is a whle number, r the subtrahend is a whle number presented withut a decimal pint, r the minuend is a whle number presented withut a decimal pint. (The subtrahend and minuend cannt bth be whle numbers.) Multiply tenths with tenths r tenths with hundredths, using cncrete mdels r drawings and strategies based n place value, prperties f peratins, and/r the relatinship between additin and subtractin; relate the strategy t a written methd and explain the reasning used. PARCC i) Tasks d nt have a cntext. ii) Only the prduct is required; explanatins are nt assessed here. iii) Prmpts may include visual mdels, but prmpts must als present the factrs as numbers, and the answer sught is a number, nt a picture. December 13, 2013 Page 19 f 21

5 iv) Each factr is greater than r equal t 0.01 and less than r equal t v) The prduct must nt have any nn zer digits beynd the thusandths place. (Fr example, 1.67 x 0.34 = is excluded because the prduct has an 8 beynd the thusandths place; cf. 5.NBT.3 and see p. 17 f Prgressin fr Number and Operatins in Base Ten.) vi) Prblems are 2 digit 2 digit r 1 digit by 3 r 4 digit. (Fr example, 7.8 x 5.3 r 0.3 x 18.24) vii) 20% f cases invlve a whle number either the prduct is a whle number, r else ne factr is a whle number presented withut a decimal pint. (Bth factrs cannt bth be whle numbers.) Divide in prblems invlving tenths and/r hundredths, using cncrete mdels r drawings and strategies based n place value, prperties f peratins, and/r the relatinship between additin and subtractin; relate the strategy t a written methd and explain the reasning used. PARCC i) Tasks d nt have a cntext. ii) Only the qutient is required; explanatins are nt assessed here. iii) Prmpts may include visual mdels, but prmpts must als present the dividend and divisr as numbers, and the answer sught is a number, nt a picture. iv) Divisrs are f the frm XY, X0, X, X.Y, 0.XY, 0.X, r 0.0X (cf. 5.NBT.6) where X and Y represent nn zer digits. Dividends are f the frm XYZ.W, XY0.X, X00.Y, XY.Z, X0.Y, X.YZ, X.Y, X.0Y, 0.XY, r 0.0X, where X, Y, Z, and W represent nn zer digits. [(Als add XY, X0, and X.)] v) Qutients are either whle numbers r else decimals terminating at the tenths r hundredths place. (Every included divisin prblem is an unknwnfactr prblem included in 5.NBT.7 3.) vi) 20% f cases invlve a whle number either the qutient is a whle number, r the dividend is a whle number presented withut a decimal pint, r the divisr is a whle number presented withut a decimal pint. (If the qutient is a whle number, then neither the divisr nr the dividend can be a whle number. Perfrm exact r apprximate multiplicatins and/r divisins that are best dne mentally by applying cncepts f place value, rather than by applying multi digit algrithms r written strategies. PARCC 5.NBT.Int.1 i) Tasks have n cntext. ii) See ITN Appendix F, sectin A, Illustratins f Innvative Task Characteristics, subsectin 4, Integrative tasks with machine scring f respnses entered by cmputer interface, subsectin Illustratins at the dmain level. Slve ne step wrd prblems invlving multiplying multi digit whle numbers. PARCC Int.1 i) The given factrs are such as t require an efficient/standard algrithm (e.g., 726 x 4871). Factrs in the task d nt suggest any bvius ad hc r mental strategy (as wuld be present fr example in a case such as 7250 x 400). ii) Fr purpses f assessment, the pssibilities are 3 digit 4 digit. Slve wrd prblems invlving three tw digit numbers. PARCC 5.Int.2 i) The given factrs are such as t require an efficient/standard algrithm (e.g., 76 x 48 x 39). Factrs in the task d nt suggest any bvius ad hc r mental strategy (as wuld be present fr example in a case such as 50 x 20 x 15). Use parentheses, brackets, r braces in numerical expressins, and evaluate expressins with these symbls (MA10 GR.5 S.1 GLE.2 EO.d.i) (5.CC.OA.1) Use parentheses, brackets, r braces in numerical expressins, and evaluate expressins with these symbls. i) Expressins have depth n greater than tw, e.g., 3 x [5 + (8 2)] is acceptable but 3 x [5 + (8 (4 2)] is nt. Write simple expressins that recrd calculatins with numbers, and interpret numerical expressins withut evaluating them (MA10 GR.5 S.1 GLE.2 EO.d.ii) (5.CC.OA.2) December 13, 2013 Page 20 f 21

6 Cnvert amng different sized standard measurement units within a given measurement system and use these cnversins in slving multi step, real wrld prblems (MA10 GR.5 S.1 GLE.1 EO.d.i, d.ii) (5.CC.OA.1 & 2) Write simple expressins that recrd calculatins with numbers. Fr example, express the calculatin add 8 and 7, then multiply by 2 as 2 X (8 + 7). PARCC i) Nte that expressins elsewhere in CCSS are thught f as recrding calculatins with numbers (r letters standing fr numbers) as well; see fr example 6.EE.2a. See als the first paragraph f the Prgressin fr Expressins and Equatins. Interpret numerical expressins withut evaluating them. Fr example, recgnize that 3 x ( ) is three times as large as withut having t calculate the indicated sum r prduct. PARCC Critical Language: includes the Academic and Technical vcabulary, semantics, and discurse which are particular t and necessary fr accessing a given discipline. EXAMPLE: A student in Language Arts can demnstrate the ability t apply and cmprehend critical language thrugh the fllwing statement: Mark Twain expses the hypcrisy f slavery thrugh the use f satire. A student in can demnstrate the ability t apply and cmprehend critical language thrugh the fllwing statement(s): Academic Vcabulary: When cnverting a 42 centimeters t meters, I first need t remember there are 100 centimeters in 1 meter. This means I will need t divide 42 centimeters by 100 t find ut the equivalent number f meters, because I am dividing by a pwer f ten the digits will remain the same in my answer I simply mve the decimal pint tw places t the left because 100 is 102, thus the answer is 0.42 meters. Measurements, centimeter, meters, inches, feet, cnvert, cnversins, parenthesis, measurement systems, multiplicatin, divisin, relatinship, runding, additin, subtractin, fractins, explain, cmpare, fluently Technical Vcabulary: Dividend, divisr, qutient, tenths, hundredths, thusandths, metric, rder f peratins, expnents, equivalence, units, place value, decimals, pwers f ten, digits, standard algrithm, denminatr, numeratr, prduct, qutient, divisr, factr, qutient, partial prducts December 13, 2013 Page 21 f 21

5 th grade Common Core Standards

5 th grade Common Core Standards 5 th grade Cmmn Cre Standards In Grade 5, instructinal time shuld fcus n three critical areas: (1) develping fluency with additin and subtractin f fractins, and develping understanding f the multiplicatin

More information

The standards are taught in the following sequence.

The standards are taught in the following sequence. B L U E V A L L E Y D I S T R I C T C U R R I C U L U M MATHEMATICS Third Grade In grade 3, instructinal time shuld fcus n fur critical areas: (1) develping understanding f multiplicatin and divisin and

More information

5 th Grade Goal Sheet

5 th Grade Goal Sheet 5 th Grade Gal Sheet Week f Nvember 26 th, 2018 Frm Ms. Simmns: Upcming dates: 11/26 Thanksgiving Break Packets are due 12/4 Prgress Reprts fr 2 nd Quarter 12/5 12/7 Benchmark Testing 12/11- Parent Partnership

More information

5 th Grade Goal Sheet

5 th Grade Goal Sheet 5 th Grade Gal Sheet Week f Nvember 19 th, 2018 Upcming dates: 11/19 Franklin Institute Field Trip: Pack a Lunch 11/22 and 11/23 Schl Clsed fr the Thanksgiving Break. Frm Ms. Simmns: Dear 5 th Grade Students,

More information

YEAR 6 (PART A) Textbook 6A schema

YEAR 6 (PART A) Textbook 6A schema YEAR 6 (PART A) Textbk 6A schema Chapter 1 Numbers t 10 Millin Lessn 1 Reading and Writing Numbers t 10 Millin T create and identify numbers t 10 000 000; t write in numerals and wrds numbers t 10 000

More information

Curriculum Development Overview Unit Planning for 8 th Grade Mathematics MA10-GR.8-S.1-GLE.1 MA10-GR.8-S.4-GLE.2

Curriculum Development Overview Unit Planning for 8 th Grade Mathematics MA10-GR.8-S.1-GLE.1 MA10-GR.8-S.4-GLE.2 Unit Title It s All Greek t Me Length f Unit 5 weeks Fcusing Lens(es) Cnnectins Standards and Grade Level Expectatins Addressed in this Unit MA10-GR.8-S.1-GLE.1 MA10-GR.8-S.4-GLE.2 Inquiry Questins (Engaging-

More information

MODULE ONE. This module addresses the foundational concepts and skills that support all of the Elementary Algebra academic standards.

MODULE ONE. This module addresses the foundational concepts and skills that support all of the Elementary Algebra academic standards. Mdule Fundatinal Tpics MODULE ONE This mdule addresses the fundatinal cncepts and skills that supprt all f the Elementary Algebra academic standards. SC Academic Elementary Algebra Indicatrs included in

More information

Domains: Operations and Algebraic Thinking Clusters: Clusters outlined in bold should drive the learning for this period of instruction.

Domains: Operations and Algebraic Thinking Clusters: Clusters outlined in bold should drive the learning for this period of instruction. Weeks 6-10 September/Octber/Nvember envisinmath2.0 Tpics 3-4 Critical Area(s): Multiplicatin and Divisin FOCUS fr Grade 3 Majr Wrk 70% f time Supprting Wrk 20% f time Additinal Wrk 10% f time 3.OA.A.1-2-3-4

More information

CHAPTER 2 Algebraic Expressions and Fundamental Operations

CHAPTER 2 Algebraic Expressions and Fundamental Operations CHAPTER Algebraic Expressins and Fundamental Operatins OBJECTIVES: 1. Algebraic Expressins. Terms. Degree. Gruping 5. Additin 6. Subtractin 7. Multiplicatin 8. Divisin Algebraic Expressin An algebraic

More information

Monroe Township School District Monroe Township, New Jersey

Monroe Township School District Monroe Township, New Jersey Mnre Twnship Schl District Mnre Twnship, New Jersey Preparing fr 6 th Grade Middle Schl *PREPARATION PACKET* Summer 2014 ***SOLVE THESE PROBLEMS WITHOUT THE USE OF A CALCULATOR AND SHOW ALL WORK*** Yu

More information

Math Foundations 10 Work Plan

Math Foundations 10 Work Plan Math Fundatins 10 Wrk Plan Units / Tpics 10.1 Demnstrate understanding f factrs f whle numbers by: Prime factrs Greatest Cmmn Factrs (GCF) Least Cmmn Multiple (LCM) Principal square rt Cube rt Time Frame

More information

1 of 11. Adding Signed Numbers. MAT001 Chapter 9 Signed Numbers. Section 9.1. The Number Line. Ordering Numbers. CQ9-01. Replace? with < or >.

1 of 11. Adding Signed Numbers. MAT001 Chapter 9 Signed Numbers. Section 9.1. The Number Line. Ordering Numbers. CQ9-01. Replace? with < or >. Sectin 9 Adding Signed Numbers The Number Line A number line is a line n which each pint is assciated with a number 0 Negative numbers Psitive numbers f The set f psitive numbers, negative numbers, and

More information

NUMBERS, MATHEMATICS AND EQUATIONS

NUMBERS, MATHEMATICS AND EQUATIONS AUSTRALIAN CURRICULUM PHYSICS GETTING STARTED WITH PHYSICS NUMBERS, MATHEMATICS AND EQUATIONS An integral part t the understanding f ur physical wrld is the use f mathematical mdels which can be used t

More information

Emphases in Common Core Standards for Mathematical Content Kindergarten High School

Emphases in Common Core Standards for Mathematical Content Kindergarten High School Emphases in Cmmn Cre Standards fr Mathematical Cntent Kindergarten High Schl Cntent Emphases by Cluster March 12, 2012 Describes cntent emphases in the standards at the cluster level fr each grade. These

More information

This section is primarily focused on tools to aid us in finding roots/zeros/ -intercepts of polynomials. Essentially, our focus turns to solving.

This section is primarily focused on tools to aid us in finding roots/zeros/ -intercepts of polynomials. Essentially, our focus turns to solving. Sectin 3.2: Many f yu WILL need t watch the crrespnding vides fr this sectin n MyOpenMath! This sectin is primarily fcused n tls t aid us in finding rts/zers/ -intercepts f plynmials. Essentially, ur fcus

More information

Name AP CHEM / / Chapter 1 Chemical Foundations

Name AP CHEM / / Chapter 1 Chemical Foundations Name AP CHEM / / Chapter 1 Chemical Fundatins Metric Cnversins All measurements in chemistry are made using the metric system. In using the metric system yu must be able t cnvert between ne value and anther.

More information

Give a personal point of view on a text. Re-explain a text with confidence.

Give a personal point of view on a text. Re-explain a text with confidence. Reading Nn-Negtiables (Minimum end f year expectatins) Y3 Y4 Y5 Y6 Decding/ Phnics Patterns and Rhymes Cmprehensin and Understanding Cmment n the way characters relate t ne anther. Knw which wrds are essential

More information

Unit 2 Expressions, Equations, and Inequalities Math 7

Unit 2 Expressions, Equations, and Inequalities Math 7 Unit 2 Expressins, Equatins, and Inequalities Math 7 Number f Days: 24 10/23/17 12/1/17 Unit Gals Stage 1 Unit Descriptin: Students cnslidate and expand previus wrk with generating equivalent expressins

More information

MATHEMATICS CURRICULUM Grade 4

MATHEMATICS CURRICULUM Grade 4 MIDDLETOWN PUBLIC SCHOOLS MATHEMATICS CURRICULUM Grade 4 Middle Schl REVISED June 2014 8/20/2014 1 T he Mathematics Curriculum fr grades K-12 was revised June 2014 by a K-12 team f teachers. The team,

More information

Year 5 End of Year Expectations Reading, Writing and Maths

Year 5 End of Year Expectations Reading, Writing and Maths Year 5 End f Year Expectatins Reading, Writing and Maths Year 5 Reading Wrd reading Apply their grwing knwledge f rt wrds, prefixes and suffixes (mrphlgy and etymlgy), as listed in Appendix 1 f the Natinal

More information

Function notation & composite functions Factoring Dividing polynomials Remainder theorem & factor property

Function notation & composite functions Factoring Dividing polynomials Remainder theorem & factor property Functin ntatin & cmpsite functins Factring Dividing plynmials Remainder therem & factr prperty Can d s by gruping r by: Always lk fr a cmmn factr first 2 numbers that ADD t give yu middle term and MULTIPLY

More information

Loudoun County Public Schools

Loudoun County Public Schools 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,

More information

Unit 1 Equations and Inequalities

Unit 1 Equations and Inequalities Unit 1 Equatins and Inequalities Number f Days: 29 9/5/17 10/13/17 Unit Gals Stage 1 Unit Descriptin: Students extend their understanding f slving linear equatins in ne variable t slving equatins with

More information

B. Definition of an exponential

B. Definition of an exponential Expnents and Lgarithms Chapter IV - Expnents and Lgarithms A. Intrductin Starting with additin and defining the ntatins fr subtractin, multiplicatin and divisin, we discvered negative numbers and fractins.

More information

MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b

MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b . REVIEW OF SOME BASIC ALGEBRA MODULE () Slving Equatins Yu shuld be able t slve fr x: a + b = c a d + e x + c and get x = e(ba +) b(c a) d(ba +) c Cmmn mistakes and strategies:. a b + c a b + a c, but

More information

Stage 6 PROMPT sheet. 2 > -2 We say 2 is bigger than -2-2 < 2 We say -2 is less than 2. 6/2 Negative numbers. l l l l l l l

Stage 6 PROMPT sheet. 2 > -2 We say 2 is bigger than -2-2 < 2 We say -2 is less than 2. 6/2 Negative numbers. l l l l l l l Stage 6 PROMPT sheet 6/ Place value in numbers t 0millin The psitin f the digit gives its size Ten millins Millins Hundred thusands Ten thusands thusands hundreds tens units 4 5 6 7 8 Example The value

More information

Building to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems.

Building to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems. Building t Transfrmatins n Crdinate Axis Grade 5: Gemetry Graph pints n the crdinate plane t slve real-wrld and mathematical prblems. 5.G.1. Use a pair f perpendicular number lines, called axes, t define

More information

/ / Chemistry. Chapter 1 Chemical Foundations

/ / Chemistry. Chapter 1 Chemical Foundations Name Chapter 1 Chemical Fundatins Advanced Chemistry / / Metric Cnversins All measurements in chemistry are made using the metric system. In using the metric system yu must be able t cnvert between ne

More information

MATHEMATICS CURRICULUM Grade 3

MATHEMATICS CURRICULUM Grade 3 MIDDLETOWN PUBLIC SCHOOLS MATHEMATICS CURRICULUM Grade 3 Elementary Schl Curriculum Writers: Mary Alice Chrabascz, Mary Claneri, Danielle Laurie, Laurie Oliveira, Cathy Palkvic, Kim Pearce, Jen Pesare,

More information

7 TH GRADE MATH STANDARDS

7 TH GRADE MATH STANDARDS ALGEBRA STANDARDS Gal 1: Students will use the language f algebra t explre, describe, represent, and analyze number expressins and relatins 7 TH GRADE MATH STANDARDS 7.M.1.1: (Cmprehensin) Select, use,

More information

GRADE 5 QUARTER 4 SUGGESTED PACING

GRADE 5 QUARTER 4 SUGGESTED PACING SUGGESTED PACING STRAND: PHYSICAL SCIENCE (PS) Tpic: Light, Sund and Mtin This tpic fcuses n the frces that affect mtin. This includes the relatinship between the change in speed f an bject, the amunt

More information

Instructional Plan. Representational/Drawing Level

Instructional Plan. Representational/Drawing Level Instructinal Plan Representatinal/Drawing Level Name f Math Skill/Cncept: Divisin Prcess and Divisin with Remainders Prerequisite Skills Needed: 1.) Mastery f dividing cncrete bjects int equal grups. 2.)

More information

Lifting a Lion: Using Proportions

Lifting a Lion: Using Proportions Overview Students will wrk in cperative grups t slve a real-wrd prblem by using the bk Hw D yu Lift a Lin? Using a ty lin and a lever, students will discver hw much wrk is needed t raise the ty lin. They

More information

District Adopted Materials: Pre-Calculus; Graphing and Data Analysis (Prentice Hall) 1998

District Adopted Materials: Pre-Calculus; Graphing and Data Analysis (Prentice Hall) 1998 Grade: High chl Curse: Trignmetry and Pre-Calculus District Adpted Materials: Pre-Calculus; Graphing and Data (Prentice Hall) 1998 tandard 1: Number and Cmputatin The student uses numerical and cmputatinal

More information

Differentiation Applications 1: Related Rates

Differentiation Applications 1: Related Rates Differentiatin Applicatins 1: Related Rates 151 Differentiatin Applicatins 1: Related Rates Mdel 1: Sliding Ladder 10 ladder y 10 ladder 10 ladder A 10 ft ladder is leaning against a wall when the bttm

More information

Functions. EXPLORE \g the Inverse of ao Exponential Function

Functions. EXPLORE \g the Inverse of ao Exponential Function ifeg Seepe3 Functins Essential questin: What are the characteristics f lgarithmic functins? Recall that if/(x) is a ne-t-ne functin, then the graphs f/(x) and its inverse,/'~\x}, are reflectins f each

More information

Millburn ASG Numeracy Developmental Milestones

Millburn ASG Numeracy Developmental Milestones Millburn ASG Numeracy Develpmental Milestnes Acknwledgement The Millburn Assciated Schls Grup (ASG) Numeracy Develpmental Milestnes have been develped using the Highland Numeracy Prgressin and wrk by Educatin

More information

Weathering. Title: Chemical and Mechanical Weathering. Grade Level: Subject/Content: Earth and Space Science

Weathering. Title: Chemical and Mechanical Weathering. Grade Level: Subject/Content: Earth and Space Science Weathering Title: Chemical and Mechanical Weathering Grade Level: 9-12 Subject/Cntent: Earth and Space Science Summary f Lessn: Students will test hw chemical and mechanical weathering can affect a rck

More information

Basics. Primary School learning about place value is often forgotten and can be reinforced at home.

Basics. Primary School learning about place value is often forgotten and can be reinforced at home. Basics When pupils cme t secndary schl they start a lt f different subjects and have a lt f new interests but it is still imprtant that they practise their basic number wrk which may nt be reinfrced as

More information

Unit 1 Functions Overview: Power, Polynomial, Rational, Exponential, and Logarithmic

Unit 1 Functions Overview: Power, Polynomial, Rational, Exponential, and Logarithmic Number f : 39 9/6/16 10/28/16 Unit Gals Stage 1 Unit Descriptin: In this unit, students extend their knwledge f functins and mdels. Students analyze functins and their prperties including dmain and range,

More information

MATHEMATICS CURRICULUM Grade 4

MATHEMATICS CURRICULUM Grade 4 MIDDLETOWN PUBLIC SCHOOLS MATHEMATICS CURRICULUM Grade 4 Middle Schl Curriculum Writers: Erica Bulk, Hlly Cusens, Meghan Frd, Jennifer Hlubesk, Deb O Bryan, and Deanne Reilly January 2012 2/20/2012 Middletwn

More information

Math Foundations 20 Work Plan

Math Foundations 20 Work Plan Math Fundatins 20 Wrk Plan Units / Tpics 20.8 Demnstrate understanding f systems f linear inequalities in tw variables. Time Frame December 1-3 weeks 6-10 Majr Learning Indicatrs Identify situatins relevant

More information

Competency Statements for Wm. E. Hay Mathematics for grades 7 through 12:

Competency Statements for Wm. E. Hay Mathematics for grades 7 through 12: Cmpetency Statements fr Wm. E. Hay Mathematics fr grades 7 thrugh 12: Upn cmpletin f grade 12 a student will have develped a cmbinatin f sme/all f the fllwing cmpetencies depending upn the stream f math

More information

A Correlation of. to the. South Carolina Academic Standards for Mathematics Precalculus

A Correlation of. to the. South Carolina Academic Standards for Mathematics Precalculus A Crrelatin f Suth Carlina Academic Standards fr Mathematics Precalculus INTRODUCTION This dcument demnstrates hw Precalculus (Blitzer), 4 th Editin 010, meets the indicatrs f the. Crrelatin page references

More information

Y10 Foundation SOW Term 1

Y10 Foundation SOW Term 1 Y10 Fundatin SOW Term 1 Algebra Fcus Students shuld be cmpletely familiar with all the rules f algebra Plt straight line graphs f functins by setting up a table f x and y pints as crdinate pairs (by use

More information

COMMON CORE STATE STANDARDS THIRD GRADE

COMMON CORE STATE STANDARDS THIRD GRADE COMMON CORE STATE STANDARDS THIRD GRADE ENGLISH LANGUAGE ARTS STANDARDS» READING: LITERATURE KEY IDEAS AND DETAILS RL.3.1. Ask and answer questins t demnstrate understanding f a text, referring explicitly

More information

MATHEMATICS SYLLABUS SECONDARY 5th YEAR

MATHEMATICS SYLLABUS SECONDARY 5th YEAR Eurpean Schls Office f the Secretary-General Pedaggical Develpment Unit Ref. : 011-01-D-8-en- Orig. : EN MATHEMATICS SYLLABUS SECONDARY 5th YEAR 6 perid/week curse APPROVED BY THE JOINT TEACHING COMMITTEE

More information

Chemistry/ Biotechnology Reference Sheets

Chemistry/ Biotechnology Reference Sheets Cmmn Metric Prefixes: Giga (G) = 1,000,000,000 = Kil (k) = 1,000 = Deci (d) =.1 = Milli (m) =.001 = Nan (n) =.000000001 = 9 6 1 10 Mega (M) = 1,000,000 = 1 10 0 1 10 Basic unit = meter, gram, liter, secnd

More information

Area of Learning: Mathematics Foundations of Mathematics and Pre-calculus 10

Area of Learning: Mathematics Foundations of Mathematics and Pre-calculus 10 Area f Learning: Mathematics Fundatins f Mathematics and Pre-calculus 10 Big Ideas Elabratins Algebra allws us t generalize relatinships thrugh abstract thinking. generalize: The meanings f, and cnnectins

More information

Biochemistry Summer Packet

Biochemistry Summer Packet Bichemistry Summer Packet Science Basics Metric Cnversins All measurements in chemistry are made using the metric system. In using the metric system yu must be able t cnvert between ne value and anther.

More information

[COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t o m a k e s u r e y o u a r e r e a d y )

[COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t o m a k e s u r e y o u a r e r e a d y ) (Abut the final) [COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t m a k e s u r e y u a r e r e a d y ) The department writes the final exam s I dn't really knw what's n it and I can't very well

More information

Revision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax

Revision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax .7.4: Direct frequency dmain circuit analysis Revisin: August 9, 00 5 E Main Suite D Pullman, WA 9963 (509) 334 6306 ice and Fax Overview n chapter.7., we determined the steadystate respnse f electrical

More information

ENG2410 Digital Design Arithmetic Circuits

ENG2410 Digital Design Arithmetic Circuits ENG24 Digital Design Arithmetic Circuits Fall 27 S. Areibi Schl f Engineering University f Guelph Recall: Arithmetic -- additin Binary additin is similar t decimal arithmetic N carries + + Remember: +

More information

1 PreCalculus AP Unit G Rotational Trig (MCR) Name:

1 PreCalculus AP Unit G Rotational Trig (MCR) Name: 1 PreCalculus AP Unit G Rtatinal Trig (MCR) Name: Big idea In this unit yu will extend yur knwledge f SOH CAH TOA t wrk with btuse and reflex angles. This extensin will invlve the unit circle which will

More information

MODULE FOUR. This module addresses functions. SC Academic Elementary Algebra Standards:

MODULE FOUR. This module addresses functions. SC Academic Elementary Algebra Standards: MODULE FOUR This mdule addresses functins SC Academic Standards: EA-3.1 Classify a relatinship as being either a functin r nt a functin when given data as a table, set f rdered pairs, r graph. EA-3.2 Use

More information

Department: MATHEMATICS

Department: MATHEMATICS Cde: MATH 022 Title: ALGEBRA SKILLS Institute: STEM Department: MATHEMATICS Curse Descriptin: This curse prvides students wh have cmpleted MATH 021 with the necessary skills and cncepts t cntinue the study

More information

Area of Learning: Mathematics Pre-calculus 12

Area of Learning: Mathematics Pre-calculus 12 Area f Learning: Mathematics Pre-calculus 12 Big Ideas Elabratins Using inverses is the fundatin f slving equatins and can be extended t relatinships between functins. Understanding the characteristics

More information

Section 5.8 Notes Page Exponential Growth and Decay Models; Newton s Law

Section 5.8 Notes Page Exponential Growth and Decay Models; Newton s Law Sectin 5.8 Ntes Page 1 5.8 Expnential Grwth and Decay Mdels; Newtn s Law There are many applicatins t expnential functins that we will fcus n in this sectin. First let s lk at the expnential mdel. Expnential

More information

Chapter One. Matter and Energy - Chemistry the study of matter and its changes the "central science" Natural Laws

Chapter One. Matter and Energy - Chemistry the study of matter and its changes the central science Natural Laws Chapter One Matter and Measurement http://www.chemistry.armstrng.edu/ nivens/curse_list.htm OWL HOMEWORK REQUIRED!!! Matter and Energy - Chemistry the study f matter and its changes the "central science"

More information

Preparation work for A2 Mathematics [2018]

Preparation work for A2 Mathematics [2018] Preparatin wrk fr A Mathematics [018] The wrk studied in Y1 will frm the fundatins n which will build upn in Year 13. It will nly be reviewed during Year 13, it will nt be retaught. This is t allw time

More information

Colorado 21 st Century Skills Mathematical Practices:

Colorado 21 st Century Skills Mathematical Practices: Curriculum Development Course at a Glance Planning for 8 th Grade Mathematics Content Area Mathematics Grade Level 8 th Grade Course Name/Course Code Standard Grade Level Expectations (GLE) GLE Code 1.

More information

We can see from the graph above that the intersection is, i.e., [ ).

We can see from the graph above that the intersection is, i.e., [ ). MTH 111 Cllege Algebra Lecture Ntes July 2, 2014 Functin Arithmetic: With nt t much difficulty, we ntice that inputs f functins are numbers, and utputs f functins are numbers. S whatever we can d with

More information

ECE 2100 Circuit Analysis

ECE 2100 Circuit Analysis ECE 2100 Circuit Analysis Lessn 25 Chapter 9 & App B: Passive circuit elements in the phasr representatin Daniel M. Litynski, Ph.D. http://hmepages.wmich.edu/~dlitynsk/ ECE 2100 Circuit Analysis Lessn

More information

CLASS. Fractions and Angles. Teacher Report. No. of test takers: 25. School Name: EI School. City: Ahmedabad CLASS 6 B 8709

CLASS. Fractions and Angles. Teacher Report. No. of test takers: 25. School Name: EI School. City: Ahmedabad CLASS 6 B 8709 SEPTEMBER 07 Math Fractins and Angles CLASS 6 Teacher Reprt Test Taken 4 5 6 7 8 Schl Name: EI Schl City: Ahmedabad CLASS SECTION EXAM CODE 6 B 8709 N. f test takers: 5 6.5 Average.5 9.0 Range (Scres are

More information

making triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y=

making triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y= Intrductin t Vectrs I 21 Intrductin t Vectrs I 22 I. Determine the hrizntal and vertical cmpnents f the resultant vectr by cunting n the grid. X= y= J. Draw a mangle with hrizntal and vertical cmpnents

More information

CS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007

CS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007 CS 477/677 Analysis f Algrithms Fall 2007 Dr. Gerge Bebis Curse Prject Due Date: 11/29/2007 Part1: Cmparisn f Srting Algrithms (70% f the prject grade) The bjective f the first part f the assignment is

More information

AP Statistics Notes Unit Two: The Normal Distributions

AP Statistics Notes Unit Two: The Normal Distributions AP Statistics Ntes Unit Tw: The Nrmal Distributins Syllabus Objectives: 1.5 The student will summarize distributins f data measuring the psitin using quartiles, percentiles, and standardized scres (z-scres).

More information

Fall 2013 Physics 172 Recitation 3 Momentum and Springs

Fall 2013 Physics 172 Recitation 3 Momentum and Springs Fall 03 Physics 7 Recitatin 3 Mmentum and Springs Purpse: The purpse f this recitatin is t give yu experience wrking with mmentum and the mmentum update frmula. Readings: Chapter.3-.5 Learning Objectives:.3.

More information

Area of Learning: Mathematics Pre-calculus 11. Algebra allows us to generalize relationships through abstract thinking.

Area of Learning: Mathematics Pre-calculus 11. Algebra allows us to generalize relationships through abstract thinking. Area f Learning: Mathematics Pre-calculus 11 Big Ideas Elabratins Algebra allws us t generalize relatinships thrugh abstract thinking. generalize: The meanings f, and cnnectins between, peratins extend

More information

How do scientists measure trees? What is DBH?

How do scientists measure trees? What is DBH? Hw d scientists measure trees? What is DBH? Purpse Students develp an understanding f tree size and hw scientists measure trees. Students bserve and measure tree ckies and explre the relatinship between

More information

8 th Grade Math: Pre-Algebra

8 th Grade Math: Pre-Algebra Hardin Cunty Middle Schl (2013-2014) 1 8 th Grade Math: Pre-Algebra Curse Descriptin The purpse f this curse is t enhance student understanding, participatin, and real-life applicatin f middle-schl mathematics

More information

EOG REVIEW NOTES Number Systems

EOG REVIEW NOTES Number Systems EOG REVIEW NOTES Number Systems Adding Fractins ) Find a cmmn denminatr. (LCM) 2) Cnvert the fractins. (Equivalent Denminatrs) ) Add the numeratrs and keep the denminatr. ) Simplify. Eamples f Adding Fractins

More information

Algebra2/Trig: Trig Unit 2 Packet

Algebra2/Trig: Trig Unit 2 Packet Algebra2/Trig: Trig Unit 2 Packet In this unit, students will be able t: Learn and apply c-functin relatinships between trig functins Learn and apply the sum and difference identities Learn and apply the

More information

Admissibility Conditions and Asymptotic Behavior of Strongly Regular Graphs

Admissibility Conditions and Asymptotic Behavior of Strongly Regular Graphs Admissibility Cnditins and Asympttic Behavir f Strngly Regular Graphs VASCO MOÇO MANO Department f Mathematics University f Prt Oprt PORTUGAL vascmcman@gmailcm LUÍS ANTÓNIO DE ALMEIDA VIEIRA Department

More information

Corrections for the textbook answers: Sec 6.1 #8h)covert angle to a positive by adding period #9b) # rad/sec

Corrections for the textbook answers: Sec 6.1 #8h)covert angle to a positive by adding period #9b) # rad/sec U n i t 6 AdvF Date: Name: Trignmetric Functins Unit 6 Tentative TEST date Big idea/learning Gals In this unit yu will study trignmetric functins frm grade, hwever everything will be dne in radian measure.

More information

ACADEMIC STANDARDS AND BENCHMARKS MATHEMATICS

ACADEMIC STANDARDS AND BENCHMARKS MATHEMATICS Table f Cntents Mathematics... 4 By the end f Grade 3... 4 By the end f Grade 5...7 By the end f Grade 8... 10 By the end f Grade 12... 14 Cmmunicatin... 16 Grade 1... 16 Grade 2... 17 Grade 3... 17 Grade

More information

Accelerated Chemistry POGIL: Half-life

Accelerated Chemistry POGIL: Half-life Name: Date: Perid: Accelerated Chemistry POGIL: Half-life Why? Every radiistpe has a characteristic rate f decay measured by its half-life. Half-lives can be as shrt as a fractin f a secnd r as lng as

More information

Mathematics Instructional Cycle Guide

Mathematics Instructional Cycle Guide Mathematics Instructinal Cycle Guide Cncept (7.RP.2) Rsemary Burdick, 2014 Cnnecticut Dream Team teacher 0 CT CORE STANDARDS This Instructinal Cycle Guide relates t the fllwing Standards fr Mathematical

More information

Credits: 4 Lecture Hours: 4 Lab/Studio Hours: 0

Credits: 4 Lecture Hours: 4 Lab/Studio Hours: 0 Cde: MATH 025 Title: ELEMENTARY ALGEBRA Divisin: MATHEMATICS Department: MATHEMATICS Curse Descriptin: This curse is a review f elementary algebra and requires previus experience in algebra. The curse

More information

Sample questions to support inquiry with students:

Sample questions to support inquiry with students: Area f Learning: Mathematics Calculus 12 Big Ideas Elabratins The cncept f a limit is fundatinal t calculus. cncept f a limit: Differentiatin and integratin are defined using limits. Sample questins t

More information

Eisenhower Middle School. Mathematics Summer Packet. Entering 7th Grade Algebra. Name:

Eisenhower Middle School. Mathematics Summer Packet. Entering 7th Grade Algebra. Name: Name: Eisenhwer Middle Schl Mathematics Summer Packet Entering 7th Grade Algebra The fllwing is a review f imprtant tpics in 6tr grade that will be needed fr 7th grade Algebra. D nt use a calculatr. It

More information

Putting Scientific Notation to Work

Putting Scientific Notation to Work 10 Putting Scientific Ntatin t Wrk Physics deals with sme very large and very small numbers. T wrk with such numbers, yu use scientific ntatin. Scientific ntatin is expressed as a number multiplied by

More information

, which yields. where z1. and z2

, which yields. where z1. and z2 The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin

More information

Cambridge Assessment International Education Cambridge Ordinary Level. Published

Cambridge Assessment International Education Cambridge Ordinary Level. Published Cambridge Assessment Internatinal Educatin Cambridge Ordinary Level ADDITIONAL MATHEMATICS 4037/1 Paper 1 Octber/Nvember 017 MARK SCHEME Maximum Mark: 80 Published This mark scheme is published as an aid

More information

District Adopted Materials: Algebra I (Glencoe/McGraw-Hill)

District Adopted Materials: Algebra I (Glencoe/McGraw-Hill) Grade: High Schl Curse: Algebra District Adpted aterials: Algebra (Glence/cGraw-Hill) Stard : Number Cmputatin The student uses numerical cmputatinal cncepts prcedures in a variety f situatins. Benchmark

More information

Calculus Placement Review. x x. =. Find each of the following. 9 = 4 ( )

Calculus Placement Review. x x. =. Find each of the following. 9 = 4 ( ) Calculus Placement Review I. Finding dmain, intercepts, and asympttes f ratinal functins 9 Eample Cnsider the functin f ( ). Find each f the fllwing. (a) What is the dmain f f ( )? Write yur answer in

More information

How topics involving numbers are taught within Budehaven Community School

How topics involving numbers are taught within Budehaven Community School Numeracy Acrss The Curriculum Hw tpics invlving numbers are taught within Budehaven Cmmunity Schl Cmpiled by James Grill - 1 - Cntents Tpic Page Intrductin 3 Basics 4 Estimating 5 Runding 6 Subtractin

More information

Public Key Cryptography. Tim van der Horst & Kent Seamons

Public Key Cryptography. Tim van der Horst & Kent Seamons Public Key Cryptgraphy Tim van der Hrst & Kent Seamns Last Updated: Oct 5, 2017 Asymmetric Encryptin Why Public Key Crypt is Cl Has a linear slutin t the key distributin prblem Symmetric crypt has an expnential

More information

Appendix A: Mathematics Unit

Appendix A: Mathematics Unit Appendix A: Mathematics Unit 16 Delaware Mdel Unit Gallery Template This unit has been created as an exemplary mdel fr teachers in (re)design f curse curricula. An exemplary mdel unit has undergne a rigrus

More information

Grade 6 EOY. PARCC Mathematics evidence statement tables are in draft form due to the iterative nature of the item development process.

Grade 6 EOY. PARCC Mathematics evidence statement tables are in draft form due to the iterative nature of the item development process. Statement Text Clarifications MP Calculator 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, The ratio of wings to beaks

More information

Trigonometric Ratios Unit 5 Tentative TEST date

Trigonometric Ratios Unit 5 Tentative TEST date 1 U n i t 5 11U Date: Name: Trignmetric Ratis Unit 5 Tentative TEST date Big idea/learning Gals In this unit yu will extend yur knwledge f SOH CAH TOA t wrk with btuse and reflex angles. This extensin

More information

Year 3 End of Year Expectations Reading, Writing and Maths

Year 3 End of Year Expectations Reading, Writing and Maths Year 3 End f Year Expectatins Reading, Writing and Maths Year 3 Reading Wrd reading Apply their grwing knwledge f rt wrds, prefixes and suffixes (etymlgy and mrphlgy) as listed in Appendix 1 f the Natinal

More information

Unit 2 Trigonometric Functions, Identities, and Equations

Unit 2 Trigonometric Functions, Identities, and Equations Number f : 43 10/30/17 1/19/18 Unit Gals Stage 1 Unit Descriptin: In this unit, students extend their knwledge f angles t rtatinal angles in the plane and radian measure. The six trignmetric functins are

More information

Physics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018

Physics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018 Michael Faraday lived in the Lndn area frm 1791 t 1867. He was 29 years ld when Hand Oersted, in 1820, accidentally discvered that electric current creates magnetic field. Thrugh empirical bservatin and

More information

Chapters 29 and 35 Thermochemistry and Chemical Thermodynamics

Chapters 29 and 35 Thermochemistry and Chemical Thermodynamics Chapters 9 and 35 Thermchemistry and Chemical Thermdynamics 1 Cpyright (c) 011 by Michael A. Janusa, PhD. All rights reserved. Thermchemistry Thermchemistry is the study f the energy effects that accmpany

More information

Lead/Lag Compensator Frequency Domain Properties and Design Methods

Lead/Lag Compensator Frequency Domain Properties and Design Methods Lectures 6 and 7 Lead/Lag Cmpensatr Frequency Dmain Prperties and Design Methds Definitin Cnsider the cmpensatr (ie cntrller Fr, it is called a lag cmpensatr s K Fr s, it is called a lead cmpensatr Ntatin

More information

Chem 115 POGIL Worksheet - Week 8 Thermochemistry (Continued), Electromagnetic Radiation, and Line Spectra

Chem 115 POGIL Worksheet - Week 8 Thermochemistry (Continued), Electromagnetic Radiation, and Line Spectra Chem 115 POGIL Wrksheet - Week 8 Thermchemistry (Cntinued), Electrmagnetic Radiatin, and Line Spectra Why? As we saw last week, enthalpy and internal energy are state functins, which means that the sum

More information

WRITING THE REPORT. Organizing the report. Title Page. Table of Contents

WRITING THE REPORT. Organizing the report. Title Page. Table of Contents WRITING THE REPORT Organizing the reprt Mst reprts shuld be rganized in the fllwing manner. Smetime there is a valid reasn t include extra chapters in within the bdy f the reprt. 1. Title page 2. Executive

More information

Part a: Writing the nodal equations and solving for v o gives the magnitude and phase response: tan ( 0.25 )

Part a: Writing the nodal equations and solving for v o gives the magnitude and phase response: tan ( 0.25 ) + - Hmewrk 0 Slutin ) In the circuit belw: a. Find the magnitude and phase respnse. b. What kind f filter is it? c. At what frequency is the respnse 0.707 if the generatr has a ltage f? d. What is the

More information