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

Transcription

1 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 cncepts and prcedures in a variety f situatins. Benchmark 1: Number ense The student demnstrates number sense fr real numbers and algebraic expressins. Benchmark 2: Number ystems and Their Prperties The student demnstrates an understanding f the real number system; recgnizes, applies, and explains their prperties, and extends these prperties t algebraic expressins. Benchmark 3: Estimatin The student uses cmputatinal estimatin with real numbers in a variety f situatins. Benchmark 4: Cmputatin The student mdels, perfrms, and explains cmputatin with real numbers and plynmials in a variety f situatins. tandard 2: Algebra The student uses algebraic cncepts and prcedures in a variety f situatins. Benchmark 1: Patterns The student recgnizes, describes, extends, develps, and explains the general rule f a pattern in a variety f situatins. Benchmark 2: Variables, Equatins, and Inequalities The student uses variables, symbls, real numbers, and algebraic expressins t slve equatins and inequalities in variety f situatins. Benchmark 3: Functins The student analyzes functins in a variety f situatins. Benchmark 4: Mdels The student develps and uses mathematical mdels t represent and justify mathematical relatinships fund in a variety f situatins invlving tenth grade knwledge and skills. tandard 3: Gemetry The student uses gemetric cncepts and prcedures in a variety f situatins. Benchmark 1: Gemetric Figures and Their Prperties The student recgnizes gemetric figures and cmpares and justifies their prperties f gemetric figures in a variety f situatins. Benchmark 2: Measurement and Estimatin The student estimates, measures and uses gemetric frmulas in a variety f situatins. Benchmark 3: Transfrmatinal Gemetry The student recgnizes and applies transfrmatins n tw- and three-dimensinal figures in a variety f situatins. Benchmark 4: Gemetry Frm An Algebraic Perspective The student uses an algebraic perspective t analyze the gemetry f tw- and three-dimensinal figures in a variety f situatins.

2 Indicatrs The student Blm s trand equence knws, explains, and uses equivalent representatins fr real numbers and algebraic expressins including integers, fractins, decimals, percents, ratis; ratinal number bases with integer expnents; ratinal numbers written in scientific ntatin; abslute value; time; and mney (2.4.K1a) ($), e.g., 4/2 = ( 2); a (-2) b (3) = b 3 /a 2 knws and explains what happens t the prduct r qutient when a real number is multiplied r divided by (2.4.K1a): a ratinal number greater than zer and less than ne, a ratinal number greater than zer and less than ne, a ratinal number greater than ne, a ratinal number less than zer identifies all the subsets f the real number system [natural (cunting) numbers, whle numbers, integers, ratinal numbers, irratinal numbers] t which a given number belngs (2.4.K1m) names, uses, and describes these prperties with the real number system and demnstrates their meaning including the use f cncrete bjects (2.4.K1a) ($): cmmutative (a + b = b + a and ab = ba), assciative [a + (b + c) = (a + b) + c and a(bc) = (ab)c], distributive [a (b + c) = ab + ac], and substitutin prperties (if a = 2, then 3a = 3 x 2 = 6); identity prperties fr additin and multiplicatin and inverse prperties f additin and multiplicatin (additive identity: a + 0 = a, multiplicative identity: a 1 = a, additive inverse: = 0, multiplicative inverse: 8 x 1/8 = 1); symmetric prperty f equality (if a = b, then b = a); additin and multiplicatin prperties f equality (if a = b, then a + c = b + c and if a = b, then ac = bc) and inequalities (if a > b, then a + c > b + c and if a > b, and c > 0 then ac > bc); zer prduct prperty (if ab = 0, then a = 0 and/r b = 0) uses and describes these prperties with the real number system (2.3.K1a) ($): transitive prperty (if a = b and b = c, then a = c), reflexive prperty (a = a). A n a l y s i s Applicatin Applicatin Functins Functins Plar Crdinates Teaching Time Onging 10 Onging Applicatin

3 estimates real number quantities using varius cmputatinal methds including mental math, paper and pencil, cncrete bjects, Applicatin and/r apprpriate technlgy (2.4.K1a) ($) knws and explains why a decimal representatin f an irratinal number is an apprximate value(2.4.k1a). Applicatin Onging cmputes with efficiency and accuracy using varius cmputatinal methds including mental math, paper and pencil, cncrete bjects, and apprpriate technlgy (2.4.K1a) ($) perfrms and explains these cmputatinal prcedures (2.4.K1a): N additin, subtractin, multiplicatin, and divisin using the rder f peratins multiplicatin r divisin t find ($): a percent f a number, e.g., what is 0.5% f 10? percent f increase and decrease, e.g., a cllege raises its tuitin frm $1,320 per year t $1,425 per year. What percent is the change in tuitin? percent ne number is f anther number, e.g., 89 is what percent f 82? a number when a percent f the number is given, e.g., 80 is 32% f what number? manipulatin f variable quantities within an equatin r inequality (2.4.K1d), e.g., 5x 3y = 20 culd be written as 5x 20 = 3y r 5x(2x + 3) = 8 culd be written as 8/(5x) = 2x + 3; simplificatin f radical expressins (withut ratinalizing denminatrs) including square rts f perfect square mnmials and cube rts f perfect cubic mnmials; simplificatin r evaluatin f real numbers and algebraic mnmial expressins raised t a whle number pwer and algebraic binmial expressins squared r cubed; simplificatin f prducts and qutients f real number and algebraic mnmial expressins using the prperties f expnents; matrix additin ($), e.g., when cmputing (with ne peratin) a building s expenses (data) mnthly, a Applicatin Onging Onging

4 matrix is created t include each f the different expenses; then at the end f the year, each type f expense fr the building is ttaled; scalar-matrix multiplicatin ($), e.g., if a matrix is created with everyne s salary in it, and everyne gets a 10% raise in pay; t find the new salary, the matrix wuld be multiplied by 1.1. finds prime factrs, greatest cmmn factr, multiples, and the least cmmn multiple f algebraic expressins (2.4.K1b) identifies, states, and cntinues the fllwing patterns using varius frmats including numeric (list r table), algebraic (symblic ntatin), visual (picture, table, r graph), verbal (ral descriptin), kinesthetic (actin), and written arithmetic and gemetric sequences using real numbers and/r expnents (2.4.K1a); e.g., radiactive half-lives; patterns using gemetric figures (2.4.K1h); algebraic patterns including cnsecutive number patterns r equatins f functins, e.g., n, n + 1, n + 2,... r f(n) = 2n 1 (2.4.K1c,e); ynthesis Trig Functins 10 Applicatin special patterns (2.4.K1a), e.g., Pascal s triangle and the Fibnacci sequence knws and explains the use f variables as parameters fr a specific variable situatin (2.4.K1f), e.g., the m and b in y = mx + ynthesis Cnic ectins 10 b r the h, k, and r in (x h) 2 + (y k) 2 = r 2 manipulates variable quantities within an equatin r inequality (2.4.K1e), e.g., 5x 3y = 20 culd be written as 5x 20 = 3y r 5x(2x + 3) = 8 culd be written as 8/(5x) = 2x + 3 slves (2.4.K1d) ($): N linear equatins and inequalities bth analytically and graphically; quadratic equatins with integer slutins (may be slved by trial and errr, graphing, quadratic frmula, r factring); N systems f linear equatins with tw unknwns using integer cefficients and cnstants; radical equatins with n mre than ne inverse peratin arund the radical expressin; equatins where the slutin t a ratinal equatin can be simplified as a linear equatin with a nnzer denminatr, e.g., 3 = 5. Applicatin Onging

5 (x + 2) (x 3) equatins and inequalities with abslute value quantities cntaining ne variable with a special emphasis n using a number line and the cncept f abslute value. expnential equatins with the same base withut the aid f a calculatr r cmputer, e.g., 3 x + 2 = 3 5 evaluates and analyzes functins using varius methds including mental math, paper and pencil, cncrete bjects, and graphing utilities r ther apprpriate technlgy (2.4.K1a,d-f) matches equatins and graphs f cnstant and linear functins and quadratic functins limited t y = ax 2 + c (2.4.K1d,f) determines whether a graph, list f rdered pairs, table f values, r rule represents a functin (2.4.K1e-f) determines x- and y-intercepts and maximum and minimum values f the prtin f the graph that is shwn n a crdinate plane (2.4.K1f) identifies dmain and range f: relatinships given the graph r table (2.4.K1e-f) linear, cnstant, and quadratic functins given the equatin(s) (2.4.K1d) uses functin ntatin evaluates functin(s) given a specific dmain ($) knws, explains, and uses mathematical mdels t represent and explain mathematical cncepts, prcedures, and relatinships. Mathematical mdels include: prcess mdels (cncrete bjects, pictures, diagrams, number lines, hundred charts, measurement tls, multiplicatin arrays, divisin sets, r crdinate grids) t mdel cmputatinal prcedures, algebraic relatinships, and mathematical relatinships and t slve equatins ((1.1.K1-3, 1.2.K1, 1.2.K3-4, 1.3.K1-4, 1.4.K1, 1.4.K2a-b, 2.1.K1a, 2.1.K1d, 2.1.K2, 2.2.K4, 2.3.K1, 3.2.K1-3, 3.2.K6, 3.3.K1-4, 4.2.K3-4) ($); factr trees t mdel least cmmn multiple, greatest cmmn factr, and prime factrizatin (1.4.K3) algebraic expressins t mdel relatinships between tw successive numbers in a sequence r ther numerical patterns (2.1.K1c) ynthesis Functins, Trig Functins, Applicatin Cnic ectins 10 Applicatin Applicatin Applicatin Applicatin ynthesis Cmprehensin, Functins Cmprehensin, Functins Functins, Trig Functins, Graphs Onging

6 equatins and inequalities t mdel numerical and gemetric relatinships (1.4.K2c, 2.2.K3, 2.3.K1-2, 3.2.K7) ($) functin tables t mdel numerical and algebraic relatinships (2.1.K1c, 2.2.K2, 2.3.K1, 2.3.K3, 2.3.K5) ($) crdinate planes t mdel relatinships between rdered pairs and equatins and inequalities and linear and quadratic functins (2.2.K1, 2.3.K1-6, 3.4.K1-8) ($) cnstructins t mdel gemetric therems and prperties (3.1.K2, 3.1.K6) tw- and three-dimensinal gemetric mdels (gebards, dt paper, crdinate plane, nets, r slids) and real-wrld bjects t mdel perimeter, area, vlume, and surface area, prperties f twand three-dimensinal figures, and ismetric views f three-dimensinal figures (2.1.K1b, 3.1.K1-8, 3.2.K1, 3.2.K4-5, 3.3.K1-4) scale drawings t mdel large and small real-wrld bjects Pascal s Triangle t mdel binmial expansin and prbability gemetric mdels (spinners, targets, r number cubes), prcess mdels (cncrete bjects, pictures, diagrams, r cins), and tree diagrams t mdel prbability (4.1.K1-3) frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, charts, tables, single and duble stem-and-leaf plts, scatter plts, bx-andwhisker plts, histgrams, and matrices t rganize and display data (4.2.K1, 4.2.K5-6) ($) Venn diagrams t srt data and shw relatinships (1.2.K2) recgnizes and cmpares prperties f tw-and threedimensinal figures using cncrete bjects, cnstructins, drawings, apprpriate terminlgy, and apprpriate technlgy (2.4.K1h) uses the Pythagrean Therem t (2.4.K1h): determine if a triangle is a right triangle find a missing side f a right triangle Applicatin Onging

7 recgnizes and describes (2.4.K1g-h): cngruence t triangles using: ide-ide-ide (), Angle-ide-Angle (AA), ide-angle-ide (A), and Angle-Angle-ide (AA); the ratis f the sides in special right triangles: and recgnizes and identifies parts f a circle: arcs, chrds, sectrs f circles, secant and tangent lines, central and inscribed angles (2.4.K1h) determines and uses number apprximatins (estimatins) fr length, width, vlume, temperature, time, distance, perimeter, area, surface area, and angle measurement using standard and nnstandard units f measure (2.4.K1a) ($) selects and uses measurement tls, units f measure, and level f precisin apprpriate fr a given situatin t find accurate real number representatins fr length, weight, vlume, temperature, time, distance, area, surface area, mass, midpint, and angle measurements (2.4.K1a) ($) states, recgnizes, and applies frmulas fr (2.4.K1h) ($) perimeter and area f squares, rectangle, and triangles circumference and area f circles; vlume f rectangular slids knws, explains, and uses ratis and prprtins t describe rates f change (2.4.K1d) ($), e.g., miles per galln, meters per secnd, calries per unce, r rise ver run describes and perfrms single and multiple transfrmatins [refectin, rtatin, translatin, reductin (cntractin/shrinking), enlargement (magnificatin/grwing)] n tw- and threedimensinal figures (2.4.K1a). recgnizes and examines tw- and three-dimensinal figures and their attributes including the graphs f functins n a crdinate plane using varius methds including mental math, paper and pencil, cncrete bjects, and graphing utilities r ther apprpriate technlgy (2.4.K1f) Applicatin Applicatin Applicatin Applicatin Trig Functins, Graphs Trig Functins, Triangles, Cnic ectins Angles Graphs Angles, Graphs, Cnic ectins uses the Pythagrean Therem t find distance (may use the distance frmula) (2.4.K1f). Applicatin recgnizes the equatin y = ax 2 + c as a parabla; represents and identifies characteristics f the parabla including pens upward r pens dwnward, steepness (wide/narrw), the Cnic ectins

8 vertex, maximum and minimum values, and line f symmetry; and sketches the graph f the parabla (2.4.K1f).