Clgne Academy Mathematics Department Algebra 1B (Aligned Text: Prentice Hall/Pearsn Algebra 1) Cre Knwledge Curriculum 78% Aligned Adpted: 08/2014 Bard Apprved: 08/28/2014 Updated: 08/12/2017 Page 0
Table f Cntents Math Department Lessn Plan Essentials... 2 Units and Pacing Charts Unit 1 Overview: Algebra 1A Review (Accelerated Study)... 3 Essential Vcabulary... 9 Pacing Chart... 10 Unit 2 Overview: 1 st, 2 nd, and x-degree Functins... 13 Essential Vcabulary... 17 Pacing Chart... 18 Unit 3 Overview: Right Triangles, Radicals & Ratinals... 20 Essential Vcabulary... 23 Pacing Chart... 24 Unit 4 Overview: Data Analysis, Advanced Divisin & Cre Knwledge... 26 Essential Vcabulary... 29 Pacing Chart... 30 Highlighted items indicate verlap f MN State Standards and the Cre Knwledge Sequence. Bxed items indicate cntent t be intrduced pst-mcas. Page 1
Math Department Lessn Essentials Tpic: Title f lessn. *Objective: Academic gal fr students t achieve by end f lessn. *Standard: MN State Standard r Cre Knwledge Sequence reference. Agenda: Sequence f instructin and activities Clsure: Brief summary/verview f lessn. May include frmative assessment. Hmewrk: Cntinued practice f lessn. May be used as frmative assessment. *Indicates required cmpnents. Nte: The text has been as clsely aligned with MN State Standards but additinal resurces may be required t include all skills (including within the Cre Knwledge Sequence). Resurces may be lcated n the s:drive under Mathematics Resurces and by grade level r n the Clgne Academy intranet. Further research/explratin may be required t lcate additinal resurces. Page 2
Overview Strand(s): Number & Operatin, Algebra, Gemetry & Measurement Unit 1: Algebra 1A Review (Accelerated Study) Apprximate Duratin f Study: 8 Weeks Between Interims. MNSS Knwledge Skills Real Numbers 8.1.1.1 8.1.1.2 8.1.1.3 Expnents 8.1.1.4 A ratinal number can be expressed as a fractin where the denminatr is nt equal t 0. Ratinal numbers may belng t mre than ne subset. A number that is nt ratinal is irratinal. The square rt f irratinal numbers is irratinal. The square rt f a psitive integer can be an integer r irratinal. The prduct f a nn-zer ratinal and irratinal number is irratinal. Varius methds can be used t apprximate and verify slutins t prblems invlving real numbers. Prperties f negative, zer, psitive and ratinal expnents generate equivalent numerical expressins. Prperties f Expnents: Any cnstant is raised t a pwer f 1: 7 = 7 1 Negative: x m = 1 x m x 3 = 1 x 3 Zer: x 0 = 1 26 0 = 1 Prduct f Pwers: x m x n = x m+n x 3 x 4 = x 7 Qutient f Pwers: xm = x n xm n = x 2 x5 Pwer f Pwers: (x m ) n = x m n (7x 3 ) 2 = 49x 6 x 7 Classify real numbers as ratinal r irratinal. Classify numbers as integer, whle, natural, imaginary. Perfrm peratins with ratinal and irratinal numbers. Estimate the square rt f irratinal numbers t the nearest tenth. Create equivalent expressins by using prperties f integer expnents. Extend the rules f expnents t fractinal expnents. x m n n = x m Unit 1 Page 3
Scientific Ntatin 8.1.1.5 Represent & Slve Equatins 8.2.4.2 8.2.4.1 Scientific ntatin is a methd f apprximating very large and very small numbers. Different technlgies represent scientific ntatin in different frms. Prperties f expnents can be used t perfrm peratins with numbers expressed in scientific ntatin. With physical measurements, Significant Digits are each f the digits f a number that are used t express it t the required degree f accuracy, starting frm the first nnzer digit. All nn-zer digits are significant. All zeres between significant digits are significant. All zeres t the right f the decimal pint and t the right f significant digits after a decimal pint are significant (Zeres t the right f a decimal pint and the left f significant digits are nt significant). Zeres after a nn-zer digit withut a decimal place, are nt significant. An equatin is a number, a variable r a cmbinatin f bth that includes an equal sign. Prperties f Equality and Inverse Operatins can be used t islate a variable when slving an algebraic equatin. Reflexive: a = a Transitive: If a = b, and b = c, then a = c Symmetric: If a = b then b = a Additin: If a = b, then a + c = b + c Subtractin: If a = b, then a c = b - c Multiplicatin: If a = b, then ac = bc Divisin: If a = b, then a c = b c Additive Inverse: a + (-a) = 0 Multiplicative Inverse: a 1 = 1 a An equatin is linear if it creates a straight, nn-vertical line when pltted n a crdinate plane. Cnvert between standard and scientific ntatin f numbers. Cmpare and rder numbers written in scientific ntatin. Recgnize and interpret results when using technlgy t perate n number written in scientific ntatin. Perfrm peratins with numbers in scientific ntatin. Wrk with significant digits. Perfrm peratins n numbers written in scientific ntatin using the crrect number f significant digits when physical measurements are invlved. (4.2 x 10 4 ) x (8.25 x 10 3 ) = 3.465 x 10 8, but if these numbers represent physical measurements, the answer shuld be expressed as 3.5 x 10 8 because the first factr, 4.2 x 10 4, nly has tw significant digits. 1,204 has fur significant digits. 1,200 has tw significant digits. 0.95 has tw significant digits but 0.950 has three. Slve multi-step equatins in ne variable. Slve equatins, in ne variable, with variables n bth sides. Slve fr ne variable in a multi-variable equatin in terms f ther variables (Literal Equatins/Frmulas). Justify the steps by identifying Prperties f Equality used. Plt a set f rdered pairs and surmise a reasnable graph f which the pints are a part. Identify cnstant rate f change. Unit 1 Page 4
Special Equatins 8.2.4.6 (Abslute Value Equatins) Inequalities 8.2.4.4 8.2.4.5 The abslute value is mathematical cncept which cannt be defined using nly ne cnditin. The abslute value f a linear expressin can be used t mdel relatinships in varius cntexts. A cylindrical machine part is manufactured with a radius f 2.1 cm. with a tlerance f 1 cm. The radius r 100 satisfies the inequality r 2.1 0.01. Abslute Value Equatins must be slved by explring 2 cases: the negative case and the psitive case. Fr x + 8 = 12, the value within the abslute value bars may have been psitive r negative therefre the psitive case: x + 8 = 12 and the negative case: -(x + 8) = 12 are slved t find x = 4 r x = -20 (als: x + 8 = 12 r x + 8 = -12). x = c, tw slutins; x = 0, ne slutin; x = -c, n slutin (the abslute value f any quantity cannt be a negative number cannt have a negative distance). Slutins t abslute value equatins in ne variable can be represented visually. Linear Inequalities can be used t represent situatins where there are infinitely many pssibilities fr the slutin. Prperties f Inequality can be used t islate a variable when slving an algebraic inequality. Additin: If x < y, then x + z < y + z, (similarly fr >) Subtractin: If x < y, then x z < y z, (similarly fr >) Multiplicatin and Divisin: If x < y, and z > 0, then xz < yz; if x < y, and z < 0, then xz > yz. If x > y, and z > 0, then xz > yz; if x > y, and z < 0, then xz < yz. Slutins t inequalities in ne variable can be represented visually n a number line. Slve and justify prcedures taken t slve prblems invlving abslute values. Slve 2x 3 + 3x = 4x 2 Graph the slutin set f abslute value equatins n a number line. Use linear inequalities t represent relatinships in varius cntexts. Slve and graph the slutin set f a linear inequalities. Unit 1 Page 5
Special Inequalities 8.2.4.6 (Abslute Value Inequalities) Intr t Functins 8.2.1.1 8.2.1.2 8.2.1.3 8.2.2.1 9.2.2.3 Abslute Value Inequalities are slved by identifying the tw cnditins t be satisfied and slving their assciated cmpund inequality. Less-than symbls indicate an AND statement; greater-than symbls indicate an OR statement. x < c -c < x < c x > c x > c, x < -c Special Cases x > -c, all real number slutins. x < -c, n slutin. Slutins t abslute value inequalities in ne variable can be represented visually n a number line. A functin is a relatinship between an independent variable and a dependent variable in which the value f the independent variable determines the value f the dependent variable. The graph f a functin is the set f rdered pairs where each value f the input is assciated with a unique value f the utput. A relatin is any set f rdered pairs. The dmain is the set f all pssible values fr the input (independent variable usually x) f a relatin r functin. The range is the set f all the pssible values fr the utput (dependent variable usually y) f a relatin r functin. Functin Ntatin: f(x), can be used t represent relatinships. f(x) = y f(x)= 2x + 1 is the same as y = 2x + 1 A Linear Functin has an assciated straight, nn-vertical graph. N greater than an expnent f 1 n any variable. Linear functins represent relatinships in which changing the input variable by sme amunt leads t a change in the utput variable that is a cnstant times that amunt. Uncle Jim gave Emily $50 n the day she was brn and $25 n each birthday after that. The functin f(x) = 50 + 25x represents the amunt f mney Jim has given after x years. The rate f change is $25 per year. Slve and graph the slutin set f abslute value inequalities. A fd manufacturer makes 32-z bxes f pasta. Nt every bx weights exactly 32 z. The allwable difference frm the idea weight is at mst 0.05 z. The weight w satisfies the inequality w 32 32. Determine if a set f rdered pairs, a table, r a graph represents a functin. Write and use functin ntatin t evaluate functins fr inputs in their dmains. Interpret statements that use functin ntatin in terms f a cntext. The relatinship between the area f a square and the side length can be expressed as f(x) = x 2. In this case, f(5)= 25, which represents the fact that a square f side length 5 units has an area f 25 units squared. Select the apprpriate dmain t represent a given situatin. Graph a functin within a given dmain and range. Create a reasnable table f rdered pairs frm a given functin rule, plt the pints, and surmise its graph. Distinguish between the graphs f linear, quadratic, cubic, abslute value, and expnential functins. Write a functin t represent a linear relatinship between tw quantities. Unit 1 Page 6
Slpes & Lines 8.2.4.3 8.3.2.1 8.3.2.2 8.3.2.3 8.2.2.2 8.2.2.3 Linear Functins can be represented with tables, verbal descriptins, symbls, equatins and graphs. The slpe is a cnstant rate f change that measures the steepness f a line. The greater the slpe, the steeper the line. slpe (m) = y x = rise run = y 2 y 1 x 2 x 1 The relatinship between tw r mre lines can be determined by cmparing their slpes and y-intercepts. Equatins f lines can be fund given: tw crdinate pairs, ne crdinate pair and the slpe r the graph itself. Linear Equatins can be expressed using the fllwing frms: Slpe-Intercept Frm: y = mx + b Pint-Slpe Frm: y y1 = m(x x1) Standard Frm: Ax + By = C The y-intercept is zer when the functin represents a prprtinal relatinship (direct variatin). A relatinship between tw variables, x and y, is prprtinal if it can be expressed in the frm y = kx r y x = k (als y = mx + b where m = k and b = 0). The graph f a prprtinal relatinship is a straight, nnvertical line passing thrugh the rigin n the Cartesian Plane. Changes t a graph can be related directly t the equatin that describes the graph. Parallel lines have the same slpe. Perpendicular lines have slpes that are ppsite reciprcals. A line with m = 2 3 is perpendicular t a line with m = - 3 2. Translate frm ne linear functin representatin t anther. Find the slpe f any line given tw crdinate pairs. Given sufficient infrmatin, find the equatin f a line. Determine an equatin f the line thrugh the pints (-1, 6) and ( 2 3, 3 4 ). Identify graphical prperties f lines (slpes and intercepts). Graph linear equatins by find the x- and y-intercepts. Cnvert between slpe-intercept frm and standard frm (als pint-slpe t ther frms) and vice-versa. Slve and graph direct variatin equatins. Use linear equatins t represent situatins invlving a cnstant rate f change, including prprtinal and nn-prprtinal relatinships. Fr the cylinder with a fixed radius f length 5, the surface area A = 2π(5)h + 2π(5) 2, is a linear functin f height h, but the surface area is nt prprtinal t the height. Give the graph f a line, determine if it represents a direct variatin. Describe hw changes in the slpe and y-intercept affect the graph f a linear equatin. Interpret the meaning f the y-intercept and slpe f a linear functin. Use graphing technlgy t examine transfrmatins f linear equatins and their assciated graphs. Identify parallel and perpendicular lines. Write and graph the equatin f the line that passes thrugh a given pint that is parallel r perpendicular t a given line. Unit 1 Page 7
Arithmetic Sequence 8.2.1.4 8.2.2.4 Line f Best Fit 8.4.1.1 8.4.1.2 8.4.1.3 Technlgy can be used t examine the relatinships between slpes f parallel r perpendicular lines. Shapes, n a crdinate grid, can be identified by cmparing the slpes f the lines that cmpare the shapes. Visual and numerical patterns can be represented with a linear functin. Sme sequences have functin rules that can be used t find any term f the sequence. When the pattern in a sequence is identified, the sequence can be extended. An Arithmetic Sequence is a linear functin that can be expressed in the frm f(x)= mx + b, where x = 0, 1, 2, 3, The arithmetic sequence 3, 7, 11, 15 can be expressed as f(x)= 4x + 3. A recursive frmula is useful fr finding the next term in a sequence. The explicit frmula is mre cnvenient when finding the n th term. A scatter plt is a graph that relates tw different sets f data by displaying them as rdered pairs. Scatter plts can be used t find trends in data. The shape f the graph indicates the crrelatin between the data. Lines are widely used t mdel relatinships between tw quantitative variables. The clser each pint is t the Line f Best Fit, the better the fit. Graphing technlgy cmputes the equatin f the line f fit using a methd called Linear Regressin. Categrize plygns by finding the slpes f their sides. Analyze plygns n a crdinate system by determining the slpes f their sides. Given the crdinates f fur pints, determine whether the crrespnding quadrilateral is a parallelgram. Recgnize and extend an arithmetic sequence. Find a given term f an arithmetic sequence. Represent arithmetic sequences using equatins, tables, graphs and verbal descriptins. Slve prblems invlving arithmetic patterns. Find recursive and explicit frmulas. Cllect, display and interpret data using scatterplts. Use apprpriate titles, labels and units Use the shape f the scatterplt t infrmally estimate a line f best fit. Determine an equatin fr the line f best fit. Use graphing technlgy t display scatterplts and crrespnding lines f best fit. Unit 1 Page 8
The line f best fit can be used t estimate r predict values. Use a line f best fit t make statements abut apprximate rate f change. Make predictins abut values nt in the riginal data set. Given a scatterplt relating student heights t she sizes, predict the she size f a 5 4 student, even if the data des nt cntain infrmatin fr a student f that height. Asses the reasnableness f predictins using scatterplts by interpreting them in the riginal cntext. A set f data may shw that the number f wmen in the U.S. Senate is grwing at a certain rate each electin cycle. Is it reasnable t use this trend t predict the year in which the Senate will eventually include 1000 female Senatrs? Essential Vcabulary: Number Sets: Imaginary, R, Q, Z, W, N, Expnents, Equivalent, Scientific Ntatin, Significant Digits, Equatin, Expressin, Literal Equatin, Frmula, Prperties f Equality: Reflexive, Transitive, Additin, Subtractin, Multiplicatin, Divisin, Additive Inverse, Multiplicative Inverse; Linear, Cnstant Rate f Change, Abslute Value, Abslute Value Equatin, Abslute Value Inequality, Cases, Extraneus Slutin, Functin, Independent, Dependent, Dmain, Range, Input, Output, Relatin, Functin Ntatin: f(x); Linear Functin, Quadratic, Cubic, Expnential, Slpe, Cnstant, Rate f Change, Y-Intercept, Initial Value, Crdinate System, Crdinate Pair, Direct Variatin, Arithmetic Sequence, Cmmn Difference. INTERIM 1 Unit 1 Page 9
Pacing Chart Unit 1: Algebra 1A Review (Accelerated Study) Time Frame Tpic Suggested Activities/Assessments Resurces & Text Alignment Week 1 Week 1 Algebra 1A Review Real Numbers 8.1.1.1 8.1.1.2 8.1.1.3 PRE-TEST Cncept Byte: Always, Smetimes, r Never Cncept Byte: Clsure Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm 1-3: Real Numbers and the Number Line 1-5: Adding and Subtracting Real Numbers 1-6: Multiplying and Dividing Real Numbers 1-7 The Distributive Prperty Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. Week 2 Week 2 Algebra 1A Review Expnents 8.1.1.4 Algebra 1A Review Scientific Ntatin Cncept Byte: Pwers f Pwers and Pwers f Prducts Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm Cmmn Cre Editin: Skills Handbk pg. T807 Scientific Ntatin and Significant Digits Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm 7-1: Zer and Negative Expnents 7-3: Multiplying Pwers With the Same Base 7-4: Mre Multiplicatin Prperties f Expnents 7-5: Divisin Prperties f Expnents Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. 7-2: Scientific Ntatin Discuss Significant Digits (Significant Figures) Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. 8.1.1.5 Unit 1 Page 10
Week 3 Algebra 1A Review Represent & Slve Equatins 8.2.4.2 8.2.4.1 Special Equatins Cncept Byte: Mdeling One-Step Equatins Cncept Byte: Mdeling Equatins With Variables n Bth sides Cncept Byte: Finding Perimeter, Area, and Vlume Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm Cncept Bytes: Characteristics f Abslute Value Graphs 1-4: Prperties f Real Numbers 2-1: Slving One-Step Equatins 2-2: Slving Tw-Step Equatins 2-3: Slving Multi-Step Equatins 2-4: Slving Equatins With Variables n Bth Sides 2-5: Literal Equatins and Frmulas **Use Table f Values & Graphs t test fr linear equatins. Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. 3-7: Abslute Value Equatins and Inequalities 5-8: Graphing Abslute Value Functins Week 3 - Week 4 8.2.4.9 8.2.4.6 (Abslute Value Equatins) Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. Week 5 Week 6 Algebra 1A Review Inequalities 8.2.4.4 8.2.4.5 8.2.4.6 (Abslute Value Inequalities) Special Inequalities 8.2.4.6 (Abslute Value Inequalities) Cncept Byte: Mre Algebraic Prperties Cncept Byte: Mdeling Multi-step Inequalities Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm 3-1: Inequalities and Their Graphs 3-2: Slving Inequalities Using Additin r Subtractin 3-3: Slving Inequalities Using Multiplicatin r Divisin 3-4: Slving Multi-Step Inequalities 3-6: Cmpund Inequalities Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. 3-7: Abslute Value Equatins and Inequalities Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments Unit 1 Page 11
Week 6 Algebra 1A Review Intr t Functins 8.2.1.1 8.2.1.2 8.2.2.1 9.2.2.3 Cncept Byte: Graphing Functins and Slving Equatins Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm Unit 1 Desms - Plygraph 4-1: Using Graphs t Relate Tw Quantities 4-2: Patterns and Linear Functins 4-4: Graphing a Functin Rule 4-5: Writing a Functin Rule 4-6: Frmalizing Relatins and Functins Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. Week 7 Week 8 Week 9 Algebra 1A Review Slpes & Lines 8.2.4.3 8.3.2.1 8.3.2.2 8.2.2.2 8.2.2.3 Arithmetic Sequence 8.2.2.4 Cncept Byte: Investigating y = mx + b Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm 5-1: Rate f Change and Slpe 5-2: Direct Variatin 5-3: Slpe-Intercept Frm 5-4: Pint-Slpe Frm 5-5: Standard Frm 5-6: Parallel and Perpendicular Lines Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. 4-7: Sequences and Functins Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. Week 9 Review Week 10 Interim 1 Page 12 Unit 1
Overview Strand(s): Algebra, Gemetry & Measurement Unit 2: 1 st, 2 nd, and x-degree Functins. Apprximate Duratin f Study: 8 Weeks Between Instructin. MNSS Knwledge Skills Systems 8.2.4.7 8.2.4.8 A system is a set f tw r mre linear equatins cntaining tw r mre variables. A slutin t a system is the crdinate pair that satisfies all equatins f the system. Systems can be slved symblically, graphically and numerically. A system with 0 slutins prduces parallel lines. A system with 1 slutin prduces intersecting lines. A system with infinite slutins prduces cincident lines. A system can be slved by substitutin (algebraically), eliminatin r by graphing. The pints f intersectins f tw graphs are simultaneus slutins f the relatins that define them. The slutins f a system can be fund by: Identifying the pints f intersectin f tw functins graphically. Setting the expressins f bth functin equal t each ther and slving Represent relatinships in varius cntexts using systems f linear equatins. Determine the number f slutins that a system may have by inspectin r by analyzing the graph. Slve systems f linear equatins. Marty s cell phne cmpany charges $15 per mnth plus $0.04 per minute fr each call. Jeannine s cmpany charges $0.25 per minute. Use a system f equatins t determine the advantages f each plan based n the number f minutes used. Slve and list apprximate numerical slutins t systems. Slve a system f tw linear equatins in tw variables algebraically and interpret the answer graphically. Check whether a pair f numbers satisfies a system f tw linear equatins in tw unknwns by substituting the numbers int bth equatins. Unit 2 Page 13
Plynmials 9.2.3.2a 9.2.3.3 (Nt assessed via MCAs) A mnmial is a real number, a variable r a prduct f a real number and ne r mre variables with whle number expnents. A degree f a mnmial is the sum f the expnents f its variables. The degree f a nnzer cnstant is 0. Zer has n degree A plynmial is a mnmial r a sum f mnmials. Prperties f Algebra can be used t rearrange and cmbine like terms f plynmials. Varius methds can be used t multiply plynmials. Sme special cases, within plynmial multiplicatin, are easy t identify and have a pattern t their prducts. (a + b) 2 = a 2 + 2ab + b 2 (a b) 2 = a 2 2ab + b 2 (a + b)(a b) = a 2 b 2 Factring a plynmial reverses the multiplicatin prcess. Plynmials can be factred t yield expressins that are simpler t manipulate and make equatin slving easier. Write plynmials in standard frm. Classify plynmials. 2x 3 + 4x 5 + 3x 4 is a Quintic Trinmial. Add and subtract plynmials. Use Distributive Prperty, a table r stacking t multiply plynmials. Stacking: 3x 2 5x + 3 2x - 2-6x 2 + 10x - 6 + (6x 3-10x 2 + 6x) 6x 3 16x 2 + 16x - 6 Multiply special cases. Factr secnd- and higher-degree plynmials when standard techniques apply. Factr GCF, gruping, special binmial cases, difference f tw squares, perfect square trinmials. Factr trinmials using the Factr/Sum r Bx Methds. Page 14 Unit 2
Quadratics 9.2.1.5a (Standard Frm Only) 9.2.1.6 9.2.1.9 9.2.2.1 8.2.4.9 9.2.4.1 9.2.2.3 (Quadratics) (Nt assessed via MCAs) A quadratic plynmial can be used t define a quadratic functin. Written as y = ax 2 + bx + c in standard frm. Parent functin: y = ax 2, where a = 1. A quadratic functin is a nnlinear functin that mdels situatins where the rate f change is nt cnstant. The graph f a quadratic functin is a symmetric curve with a highest r lwest pint crrespnding t a maximum r minimum value. Fr y = ax 2 + bx + c if a > 0 (psitive), the functin has a minimum; if a < 0 (negative), the functin has a maximum. The zeres f a quadratic functin are the slutins t the functin. Squares and square rts are inverse peratins. Quadratic Frmula is used t find the zeres f a quadratic functin. x = b ± b2 4ac 2a The discriminant is used t determine the number f slutins a quadratic functin has. b 2 4ac > 0; the functin has 2 real slutins. b 2 4ac = 0; the functin has 1 real slutin. b 2 4ac < 0; the functin has n real slutins. Quadratics can be used t mdel prblems invlving bjects under the frce f gravity and slved using varius methds. Sketching the graph, guess-and-check, data tables, factring, quadratic frmula. The altitude f an bject under the frce f gravity: a = -16t 2 + vt + h where a is the altitude f the bject in feet, t is time in secnds, v is the initial upward velcity f the bject in feet per secnd and h is the initial height f the bject. An bject thrwn dwnward with an initial velcity f v feet per secnd travels a distance d = 16t 2 + vt, where t is time in secnds. Unit 2 Identify and graph a quadratic functin. Determine if a relatin is quadratic. Determine if a quadratic functin has a maximum r minimum. Determine the equatin f the axis f symmetry. Determine the crdinates f the vertex. x-crdinate f the vertex: x = b 2a Determine the dmain and range f a quadratic functin. Identify intervals f increase and decrease. Explain the effect that changing the values f a and c has n the graph f a quadratic functin. Slve quadratic functins in ne variable. By factring, graphing, using square rts, r cmpleting the square, r using the quadratic frmula. Use squaring t slve prblems that lead t quadratic equatins. 3x + 4 = x Clear fractins t slve equatins that lead t linear r quadratic equatins. Shw the prf f the quadratic frmula by cmpleting the square. Use the zer prduct prperty t reveal the zeres f a quadratic functin. Cmplete the square t write a quadratic expressin as the difference f tw squares. Slve physical wrd prblems. Mtin f an bject under the frce f gravity. Page 15
Expnential Functins 9.2.2.2 9.2.2.3 (Expnential Only) Gemetric Sequence 8.2.1.5 8.2.2.5 An expnential functin mdels a situatin where an initial value has been repeatedly multiplied by the same psitive number. f(x)= b g x where b is the initial value, g is the grwth factr and x is a real number. In an expnential functin, the expnent is the independent variable. In general, the graph f an expnential functin never crsses the x-axis (always greater than 0). An expnential functin can mdel grwth r decay f an initial amunt. Cmpund Interest mdels expnential grwth r decay. Cmpund Interest Frmula: A = P(1 + r n )nt Visual and numerical patterns can be represented with nnlinear functins. A Gemetric Sequence has an initial value and a subsequent sequence f values based n a cmmn rati. A gemetric sequence can be mdeled with an expnential functin. A gemetric sequence is a nn-linear, expnential functin that can be expressed in the frm f(x)= ab x, where a is the initial value, b is the grwth factr and x = 0, 1, 2, 3, The gemetric sequence 6, 12, 24, 48,, can be expressed in the frm f(x)= 6(2 x ) A recursive frmula (a n = a n 1 r) is useful fr finding the next term in a sequence. The explicit frmula (a n = a 1 r n 1 ) is mre cnvenient when finding the n th term. Identify an expnential functin. Evaluate and graph expnential functins. Represent and slve prblems using expnential functins. Investment Grwth/Decay If a girl invests $100 at 10% annual interest, she will have 100(1.1) x dllars after x years. Depreciatin/Appreciatin Ppulatin Grwth/Decay Recgnize and extend a gemetric sequence. Find the nth term f a gemetric sequence. Represent gemetric sequences using equatins, tables, graphs and verbal descriptins. Slve prblems invlving gemetric patterns. Extensin: Use recursive and explicit frmulas. Essential Vcabulary: System, Slutin, Simultaneus Slutins, Cincident Lines, Systems: Incnsistent, Cnsistent, Dependent, Independent; Bundary Line, System f Linear Inequalities, Expnential Functin, Expnential Grwth, Expnential Decay, Grwth Factr, Decay Factr, Cmpund Interest, Depreciatin, Appreciatin, Gemetric Sequence, Cmmn Rati, Recursive, Explicit, Sequence, Term, N th Term, Pythagrean Therem, Cnverse, Right Triangle, Hyptenuse, Leg, Perimeter, Distance Frmula, Plygn, Quadratic Functin, Parent Functin, Maxima, Minima, Zeres, Discriminant, Axis f Symmetry, Vertex, Dmain, Range, Interval f Increase/Decrease, Cmpleting the Square, Zer Prduct Prperty, Mnmial, Degree, Plynmial, Quartic, Quintic, Stacking (t multiply plynmials), Special Cases,. INTERIM 2 Unit 2 Page 16
Pacing Chart Unit 2: 1 st, 2 nd and x-degree Functins Time Frame Tpic Suggested Activities/Assessments Resurces & Text Alignment Week 11 Week 12 Week 13 Week 14 Week 16 Systems 8.2.4.7 8.2.4.8 Plynmials 9.2.3.2a 9.2.3.3 (Nt assessed via MCAs) Quadratics 9.2.1.5a (Standard Frm Only) 9.2.1.6 9.2.1.9 9.2.2.1 8.2.4.9 9.2.4.1 9.2.2.3 (Quadratics) (Nt assessed via MCAs) : Cncept Byte: Slving Systems Using Tables and Graphs Cncept Byte: Slving Systems Using Algebra Tiles Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm Cncept Byte: Using Mdels t Multiply Cncept Byte: Using Mdels t Factr Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm Cncept Byte: Cllecting Quadratic Data Cncept Byte: Finding Rts Cncept Byte: Perfrming Regressins Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm 6-1: Slving Systems by graphing 6-2: Slving systems Using substitutin 6-3: Slving Systems Using Eliminatin 6-4: Applicatins f Linear Systems Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. 8-1: Adding and Subtracting Plynmials 8-2: Multiplying and Factring 8-3: Multiplying Binmials 8-4: Multiplying Special Cases 8-5: Factring x 2 + bx + c 8-6: Factring ax 2 + bx + c 8-7: Factring Special Cases 8-8: Factring by Gruping Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. 9-1: Quadratic Graphs and Their Prperties 9-2: Quadratic Functins 9-3: Slving Quadratic Equatins 9-4: Factring t Slve Quadratic Equatins 9-5: Cmpleting the Square **Cmplete the Square t Derive Quadratic Frmula** 9-6: The Quadratic Frmula and the Discriminant 9-7: Linear, Quadratic and Expnential Mdels (Optinal) Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. Unit 2 Page 17
Week 17 Week 17 Expnential Functins 9.2.2.2 9.2.2.3 (Expnential Only) Gemetric Sequence 8.2.1.5 8.2.2.5 Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm Cncept Byte: Gemetric Sequences Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm ; Review Week 18 Week 19 Interim 2 7-6: Expnential Functins 7-7: Expnential Grwth and Decay Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. 7-8 (Cmmn Cre Editin): Gemetric Sequences Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. Unit 2 Page 18
Overview Strand(s): Algebra Unit 3: Right Triangles, Radicals & Ratinals Apprximate Duratin f Study: 9 Weeks Between Instructin. MNSS Knwledge Skills Pythagrean Therem 8.3.1.1 8.3.1.2 8.3.1.3 Pythagrean Therem: a 2 + b 2 = c 2, where a and b are legs and c is the hyptenuse. The sum f the squares f the lengths f the legs is equal t the square f the length f the hyptenuse. Cnverse f the Pythagrean Therem: If the sum f the squares f the tw shrter sides f a triangle is equal t the square f its lngest side, then it is a right triangle. The Pythagrean Therem can be used t find the distance between any tw pints in a crdinate plane. Distance Frmula: d = (x 1 x 2 ) 2 + (y 2 y 1 ) 2 Use Pythagrean Therem t slve prblems invlving right triangles. Determine the perimeter f a right triangle, given the lengths f tw f its sides. Shw that a triangle with side lengths 4, 5 and 6 is nt a right triangle. Slve prblems invlving the cnverse f the Pythagrean Therem. Use irratinal numbers t represent lengths. Find the distance between tw pints n a hrizntal, vertical r diagnal line in a crdinate system. Trignmetric Ratis 9.3.4.1b 9.3.4.3 The Pythagrean Therem can be infrmally justified by using measurements, diagrams and cmputer sftware. In a right triangle the csine f an angle is the rati f the adjacent side t the hyptenuse. In a right triangle the sine is the rati f the ppsite side t the hyptenuse. In a right triangle the tangent is the ratin f the ppsite side t the adjacent side. Sine, csine and tangent ratis can be used t find the measurements f sides r angles f right triangles. Inverses (sin -1, cs -1 and tan -1 ) are used t find angle measures given the trignmetric rati. Prve and explain a simple prf f the Pythagrean Therem. Prfs: Bhaskara, Garfield, Chinese Square. Find and use trignmetric ratis. Use a scientific calculatr t determine the apprximate value f any acute angle. Use a scientific calculatr t determine the apprximate value f an acute angle f a given sine, csine, r tangent. Unit 3 Page 19
Radicals 9.2.3 9.2.3.6 Prerequisite t: 9.2.4.7 Radical Operatins Prerequisite t: 9.2.4.7 A radical includes the radical symbl: ; the expressin underneath the symbl is the radicand, the index which indicates the degree f the radical. 3 Fr 27, 3 is the index; find the third rt f the radicand 27. Radical expressins can be simplified using the multiplicatin and divisin prperties f square rts. Ratinalizing the denminatr f a radical expressin remves the radical frm the denminatr f the expressin. Multiplicatin and Divisin Prperties f Square Rts are extensins f the Prperties f Expnents. Prperties f ratinal expnents generate equivalent numerical expressins. Ratinal Expnents: (x) m n n = ( x) m (7x) 2 3 = ( 7x) 2 Prperties f real numbers can be used t perfrm peratins with radical expressins. Denminatrs f sme radical expressins can be ratinalized by multiplying by cnjugates. Additin and subtractin cannt be perfrmed n unlike radicals. 3 Simplify radicals invlving prducts and qutients. Ratinalize the denminatr f a simple radical expressin. Raise a psitive number t a fractinal pwer and simplify apprpriately. Add and subtract radical expressins. Radical Equatins 9.2.4.7 8.2.4.9 A radical equatin is an equatin that has a variable as the radicand. Sme radical equatins can be slved by squaring bth sides and testing the slutins. Extraneus slutins may arise when slving radical equatins. When extraneus slutins are tested, they d nt slve the riginal equatin. Extraneus slutins are nt the same as n slutins. Slve equatins that cntain radical expressins. Identify extraneus slutins. Explain why extraneus slutins are nt slutins at all. Slve an equatin with radical expressins n bth sides f the equal sign. Identify radical equatins with n slutin. Unit 3 Page 20
Graphing Square Rts 9.2.2.6 Ratinal Simplificatin 9.2.3.2 9.2.3.3 Ratinal Operatins (Expressins) 9.2.3.2 9.2.3.3 The parent functin fr the family f square rt functins is f(x) = x. Square rts functins are radical functins. The value f the radicand cannt be negative. Square rt functins can be graphed by pltting pints r using translatins f the parent square rt functin. Vertical translatins are indicated by the cnstant utside f the radicand. f(x) = x + k If k > 0, translate up. If k < 0, translate dwn. Hrizntal translatins are indicated by the cnstant in the radicand. f(x) = x + h If h < 0, translate t the right. If h > 0, translate t the left. A ratinal expressin is an expressin with a plynmial in its denminatr and numeratr: plynmial. plynmial A ratinal expressin has been cmpletely simplified when the numeratr and denminatr have n cmmn factr ther than 1. Ratinal expressins are simplified by dividing ut cmmn factrs fund in the numeratr and denminatr. An excluded value is the value f x fr which a ratinal expressin f(x) is undefined. Excluded values indicate the lcatin f hles in the graph in the riginal functin, called vertical/hrizntal asympttes. A cmplex fractin cntains ne r mre fractins in the numeratr, denminatr r bth. Unit 3 Cmplex fractins can be rewritten using divisin symbls. Multiplicatin and divisin f ratinal expressins is perfrmed using the same methd as multiplicatin and divisin f fractins. Plynmial factring is used t simplify ratinal expressins befre r after peratins have been perfrmed. Factring a plynmial, in the numeratr r denminatr may reveal identical expressins. Identical expressins, in cmplex fractins, can be divided ut. Unit 3 Graph square rt functins manually r using graphing technlgy. Translate graphs f square rt functins manually r using graphing technlgy. Determine the apprpriate dmain f a square rt functin. Simplify ratinal expressins. Identify excluded values. Identify value f vertical and/r hrizntal asympttes. (Graphing at end f unit.) Multiply and divide ratinal expressins. Express ratinal peratin slutins in simplest frm. Simplify cmplex fractins. Page 21
Ratinal Equatins 9.2.2 Additin and subtractin f ratinal expressins is perfrmed using the same methd as additin and subtractin f fractins. Additin and subtractin f ratinal expressin can nly be cmpleted if the fractins have like denminatrs. A ratinal equatin can be slved by first multiplying each side f the equatin by the LCD. Crss Prducts Prperty can be used t slve equatins where each side is a single ratinal expressin. While slving a ratinal equatin a quadratic expressin may be prduced n ne side f the equal sign, use factring t slve. Slving ratinal equatins may prduce extraneus slutins. Slutins must be checked t verify whether they are extraneus slutins r nt. Cmbined rate (Wrk) wrd prblems are simplified by determining a unit rate r least cmmn multiple unit f time. If persn A cmpletes a jb in 5 hurs and persn B cmpletes the same jb in 6 hurs then persn A cmpletes 1 f the jb in an hur and persn B cmpletes 5 1 f the jb in an hur. Alternatively, persn A cmpletes 6 6 jbs in 30 hurs and persn B cmpletes 5 jbs in 30 hurs; cmbine and find the unit rate. A relatinship between tw variables, x and y, is inversely prprtinal if it can be expressed in the frm k = y r xy = k. x If the prduct f tw variables is a nnzer cnstant, then the variables frm an inverse variatin. Graphs f inverse variatin will nt intersect the x- r y-axis. Add and subtract ratinal expressins. Slve ratinal equatins and prprtins. Slve cmbined rate prblems. Identify extraneus slutins. Slve cmbined rate (wrk) wrd prblems that invlve linear equatins. Write and graph equatins fr inverse variatins. Cmpare direct and inverse variatin. Determine if data represents inverse r direct variatin. Identify direct r inverse variatin given a situatin. Unit 3 Page 22
Graphing Ratinal Functins 9.2.1.7 9.2.2.6 Ratinal Functins are written in the frm f(x) = plynmial plynmial The characteristics f ratinal functins and their representatins are useful in slving real-wrld prblems. Ratinal functins have hles in their graphs called vertical and hrizntal asympttes. T graph a functin, f(x), it is necessary t understand the graph s behavir near values f x where the functin is undefined. In the graph f a ratinal functin f the frm y = a + c: x b The vertical asymptte ccurs at x = m when the value f f(m) is undefined. The hrizntal asymptte ccurs at y = c. Graph ratinal functins. Identify excluded values f ratinal functins. Graph the vertical asymptte. Graph the hrizntal asymptte. Essential Vcabulary: Sine, Csine, Tangent, Adjacent,, Trignmetric Rati, Undefined. Radical Expressins, Radical, Radical Equatin, Radicand, Ratinalize the Denminatr, Multiplicatin and Divisin Prperty f Square Rts, Perfect Square Factrs, Cnjugate, Unlike Radicals, Extraneus Slutin, Ratinal Expressin, Excluded Value, Vertical/Hrizntal Asymptte, Cmplex Fractin, Ratinal Equatin, Cmbined Rate (Wrk),s LCD, Crss Prducts Prperty, Inverse Variatin, Ratinal Functin, Asymptte, Vertical Asymptte, Hrizntal Asymptte. Interim 3 Unit 3 Page 23
Pacing Chart Unit 3: Right Triangles, Radicals & Ratinals Time Frame Tpic Suggested Activities/Assessments Resurces & Text Alignment Week 20 Pythagrean Therem 8.3.1.1 8.3.1.2 8.3.1.3 : Cncept Byte: Distance and Midpint Frmulas Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm 10-1: The Pythagrean Therem **Prf f Pythagrean Therem** Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. Trignmetric Ratis : Cncept Byte: Right Triangle Ratis 10-6: Trignmetric Ratis Week 20 Week 21 9.3.4.1b 9.3.4.3 Radicals 9.2.3 9.2.3.6 Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. 10-2: Simplifying Radicals Fractinal Expnents 7-5 (Cmmn Cre Ed.): Ratinal Expnents and Radicals Week 22 Week 23 Week 24 Prerequisite t: 9.2.4.7 Radical Operatins Prerequisite t: 9.2.4.7 Radical Equatins 9.2.4.7 8.2.4.9 Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. 10-3: Operatins With Radical Expressins Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. 10-4: Slving Radical Equatins Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. Unit 3 Page 24
Week 25 Week 26 Graphing Square Rts 9.2.2.6 Ratinal Simplificatin 9.2.3.2 9.2.3.3 Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm 10-5: Graphing Square Rt Functins Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. 11-1: Simplifying Ratinal Expressins Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. Week 27 Week 28 Ratinal Operatins (Expressins) 9.2.3.2 9.2.3.3 Ratinal Equatins 9.2.2 Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm 11-2: Multiplying and Dividing Ratinal Expressins 11-4: Adding and Subtracting Ratinal Expressins Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. 11-5: Slving Ratinal Equatins 11-6: Inverse Variatin Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. Week 28 Graphing Ratinal Functins 9.2.1.7 9.2.2.6 : Cncept Byte: Graphing Ratinal Functins Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm Week 29 Interim 3 11-7: Graphing Ratinal Functins Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. Unit 3 Page 25
Overview Strand(s): Algebra, Data Analysis & Prbability Unit 4: Data Analysis, Advanced Divisin & Cre Knwledge Apprximate Duratin f Study: 6 Weeks Between Interims. MNSS Knwledge Skills A frequency table grups a set f data values int intervals and tallies the number f time each element ccurs in each interval. The intervals d nt verlap, d nt have gaps, and are equal in size. Create and interpret a frequency table. Data Displays 9.4.1.1 Measures and Plts 9.4.1.1 9.4.1.2 A histgram, a special bar graph, rganizes numerical data int intervals. A histgram is used t display data frm a frequency table. Histgrams are useful fr displaying large data sets. Individual data elements are nt visible in a histgram. Each bar is f equal width and there are n gaps between bars. A cumulative frequency table displays the number f data values that are less than r equal t the upper limit f each interval. Special values can be used t describe a set f numerical data. The Measures f Central Tendency are: Mean, Median and Mde. The Measure f Dispersin, range, describes hw spread ut the values in a data set are. Outliers may affect any f the measures f central tendency r dispersin. Create and interpret histgrams. Describe a histgram in terms f its shape. Create and interpret a cumulative frequency table. Calculate mean, median, mde and range given a data set. Find a missing piece f data given the mean f the data. Make predictins/decisins given a measure f central tendency. Calculate measures f central tendency and dispersin given a data display. Unit 4 Page 26
A bx-and-whisker plt is used t display quantitative data and is pltted n a number line. Bx-and-Whisker plts are split int fur quartiles, each representing 25% f the data. Five data pints are displayed n a bx-and-whisker plt. Minimum, First Quartile, Secnd Quartile (Median), Third Quartile, Maximum. The Interquartile Range is nt affected by the minimum, maximum, r any utliers. It nly represents the middle f the data set. Percentiles separate data int 100 equal parts. When cllecting data, it is imprtant fr the results t accurately represent the situatin; methds f cllecting data must be fair and unbiased. Surveys can use randm, systematic, r stratified sampling methds. A bivariate set f data includes tw distinct variables; univariate uses nly ne variable. Results gained frm a sample can be used t draw cnclusins abut the ppulatin frm which the sample was drawn. Cnstruct and interpret a bx-and-whisker plt. Calculate the interquartile range f a set f data displayed in a bxand-whisker plt. Find a percentile rank. Use percentile rank t find a data value in a set rdered frm least t greatest. T find the k th percentile, multiply k% by the ttal number f values n (the prduct is called the index). If necessary, rund the value up t the nearest whle number. Cunt the values in the set until reaching the index. Classify data as quantitative r qualitative. Analyze samples and surveys t determine bias. Design and cnduct a survey. Samples and Surveys Unit 4 Page 27
Cunting Methds 9.4.3.1 Prbability 9.4.3.2 A sample space f an experiment is a display f the set f all pssible utcmes f that experiment. Cunting methds can be used t find the number f pssible ways t chse bjects with and withut regard t rder. If the arrangement f bjects in a sequence is imprtant, a permutatin can be used t find the sample space f arrangements. The Factrial functin: multiply a series f descending natural numbers. 5! = 5 4 3 2 1 = 120 Permutatins can be calculated with and withut repetitin f bjects. With repetitin: n r, where n is the number f bjects and r is the number f chices allwable - chse a 4 digit number using digits 0 9: 10 4. Withut repetitin, the number f bjects must be reduced after each chice is made. Chse a 4 digit number using digits 0 9; bjects wuld reduce by ne each time. 10 9 8 7 r 10!(stp here; nly 4 digits are needed.) Cancel ut the remaining factrs by dividing by n! 6!: npr = (n r)!. If the arrangement f bjects in a sequence is nt imprtant, a cmbinatin can be used t find the sample space f arrangements. n! ncr = r!(n r)! The prbability f an event is the chance that an event will ccur; represented by a percent, decimal r fractin with a value that falls between 0 and 1. The clser t ne, the mre likely the event will ccur; the clser t 0, the less likely the event will ccur. Number desired events Prbability = Ttal number f pssible utcmes Prbability can be used t make predictins abut future events. Theretical Prbability is based n what shuld r is expected t happen. Experimental Prbability is based n data cllected frm repeated trials. Find sample spaces by calculating permutatins and cmbinatins. Sample space fr tw dice. Determine theretical and experimental prbabilities frm given r cllected data. Perfrm experiments t cnfirm r refute prbabilities. Calculate dds in favr r against an event. In favr fr:against Against against:fr Design an experiment that illustrates Law f Large Numbers. Unit 4 Page 28
Dividing Plynmials 9.2.3.2 9.2.3.3 Mixture, Digit, Age Cre Knwledge The Law f Large Numbers states that the experimental prbability will apprach the theretical prbability as the number f trials increases. A simple event has a single utcme. A cmpund event is an event that is made up f tw r mre simple events. Synthetic divisin is a methd f dividing plynmials. Divisin f plynmials is perfrmed using similar methds as when dividing real numbers. Expnent prperties can be used when dividing by a mnmial. When dividing plynmials by using the lng divisin algrithm, the dividend must be in standard frm and missing terms must be included using cefficients f 0. Linear equatins r systems f linear equatins can be used t slve wrd prblems invlving mixtures, digits, age, r cmbined rate. Cnstructing a three clumn chart may be a helpful t rganize the infrmatin needed t write an equatin (the number f rws may vary) fr a mixture prblem. Understanding f place value is used t slve digit wrd prblems. Divide plynmials using synthetic divisin r prperties f expnents. Slve mixture wrd prblems that invlve linear equatins. Slve digit wrd prblems that invlve linear equatins. An age wrd prblem invlving ne persn can be translated int Slve age wrd prblems that invlve linear equatins. an integer prblem. 2 years ag, Sansa s age was half the age she will be in 3 years: x 2 = 1 (x + 3). 2 A table is helpful in slving age prblems invlving tw r mre peple. Essential Vcabulary: Frequency Table, Interval, Histgram, Outlier, Cumulative Frequency Table, Skewed, Unifrm, Symmetric, Measures f Central Tendency, Measure f Dispersin, Mean, Median, Mde, Range, Outlier, Bx-and-Whisker Plt, Quartile, Maximum, Minimum, Interquartile Range, First Quartile, Secnd Quartile, Third Quartile, Percentile, Percentile Rank, Index, Survey, Randm, Systematic, Stratified, Univariate, Bivariate, Sample, Ppulatin, Bias, Quantitative, Qualitative, Permutatin, Cmbinatin, Factrial, Multiplicatin Cunting Principal, Sample Space, Prbability, Simple Event, Outcme, Cmpund Event, Theretical Prbability, Experimental Prbability, Cmplement f an Event, Odds, Trials, Law f Large Numbers, Synthetic Divisin, Wrd Prblems: Mixture, Age, Digit, Cmbined Rate, Mtin f Object Under Frce f Gravity, Altitude, Velcity. Interim 4 Unit 4 Page 29
Pacing Chart Unit 4: Data Analysis, Advanced Divisin & Cre Knwledge Time Frame Tpic Suggested Activities/Assessments Resurces & Text Alignment Week 31 Week 32 Grade 8 Grade Level Review Mathematics MCA Week 33 Data Displays 9.4.1.1 : Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm 12-2: Frequency and Histgrams Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. Week 33 Measures and Plts 9.4.1.1 9.4.1.2 : Cncept Byte: Standard Deviatin Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm 12-3: Measures f Central Tendency and Dispersin 12-4: Bx-and-Whisker Plts Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. : Cncept Byte: Designing Yur Own Survey 12-5: Samples and Surveys Week 33 Samples and Surveys Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. Week 34 Cunting Methds 9.4.3.1 : Putting It All Tgether: Perfrmance Tasks PwerAlgebra.cm 12-6: Permutatins and Cmbinatins Resurces include: Math Vides, Online Assessment, Algebra 1 Cmpanin, Interventins and Enrichments. Unit 4 Page 30