Math Foundations 20 Work Plan

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1 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 t self, family, r cmmunity which culd be described using a system f linear inequalities in tw variables. Develp, generalize, explain, and apply strategies fr graphing and slving systems f linear inequalities, including justificatin f the chice f slid r brken lines. Develp, generalize, explain, and apply strategies fr verifying slutins t systems f linear inequalities, including the use f test pints. Explain, using examples, the meaning f the shaded regin in the graphical slutin f a system f linear inequalities. Write a system f linear inequalities fr a given graph. Match ptimizatin questins and the graphs f sets f linear inequalities. Apply knwledge f graphing f systems f linear inequalities and linear prgramming t slve ptimizatin questins. Resurces / Pssible Assessments Begin with a review f graphing linear equatins y = mx + b y-intercept x-intercept Determining slpe Regular wrksheets n graphing and wrd prblems. Assigned wrk frm Nelsn: Fundatins f Mathematics Demnstrate an understanding f the characteristics f quadratic functins in the frm: y = a(x p) 2 + q Vertex Intercepts Dmain and Range Axis f symmetry January 6-10 Identify situatins and bjects relevant t self, family, r cmmunity which culd be described using a quadratic functin. Develp, generalize, explain, and apply strategies fr determining the intercepts f the graph f a quadratic functin, including factring, graphing (with r withut the use f technlgy), and use f the quadratic frmula. Cnjecture and verify a relatinship amng the rts f an equatin, the zers f the crrespnding functin, and the x- intercepts f the graph f the functin. Explain, using examples, why the graph f a quadratic functin may have zer, ne, r tw x-intercepts. Write a quadratic equatin in factred frm given the zers f a crrespnding quadratic functin r the x-intercepts f a crrespnding quadratic functin. Develp, generalize, explain, and apply strategies (with r withut the use f technlgy) t determine the crdinates f the vertex f the graph f a quadratic functin. Develp, generalize, explain, and apply a strategy fr determining the equatin f the axis f symmetry f the graph f a quadratic functin when given the x-intercepts f the graph. Develp, generalize, explain, and apply strategies fr determining the crdinates f the vertex f the graph f a quadratic functin MR. OOSTEROM Page 1

2 Math Fundatins 20 Wrk Plan and fr determining if the vertex is a maximum r a minimum. Generalize abut and explain the effects n the graph f a quadratic functin when the values fr a, p, and q are changed. Develp, generalize, explain, and apply strategies fr determining the dmain and range f a quadratic functin. Explain what the dmain and range f a quadratic functin tell abut the situatin that the quadratic functin mdels. Develp, generalize, explain, and apply strategies fr sketching the graph f a quadratic functin. Slve situatinal questins invlving the characteristics and graphs f quadratic functins. Critique the statement Any functin that can be written in the frm y = a(x p)² + q will have a parablic graph Demnstrate understanding f prperties f angles and triangles: Deriving prfs based n therems and pstulates abut cngruent triangles Slving prblems January 1 2 weeks Identify and describe situatins relevant t self, family, r cmmunity that invlve parallel lines cut by transversals. Develp, generalize, explain, apply, and prve relatinships between pairs f angles frmed by transversals and parallel lines, with and withut the use f technlgy. Prve and apply the relatinship relating the sum f the angles in a triangle. Generalize, using inductive reasning, a rule fr the relatinship between the sum f the interir angles and the number f sides (n) in a plygn, with r withut technlgy. Apply knwledge f angles frmed by parallel lines and transversals t identify and crrect errrs in a given prf. Explre and verify whether r nt the angles frmed by nnparallel lines and transversals create the same angle relatinships as thse created by parallel lines and transversals. Slve situatinal prblems that invlve: angles, parallel lines, and transversals angles, nn-parallel lines, and transversals angles in triangles angles in plygns. Develp, generalize, explain, and apply strategies fr cnstructing parallel lines. MR. OOSTEROM Page 2

3 Math Fundatins 20 Wrk Plan 20.5 Demnstrate understanding f csine law and sine law (including the ambiguus case) January - Identify and describe situatins relevant t self, family, r cmmunity that invlve triangles withut a right angle. Develp, generalize, explain, and apply strategies fr determining angles r side lengths f triangles withut a right angle. Draw diagrams t represent situatins in which the csine law r sine law culd be used t slve a questin. Explain the steps in a given prf f the sine law r csine law. Illustrate and explain hw ne, tw, r n triangles culd be pssible fr a given set f measurements fr tw side lengths and the nn-included angle in a prpsed triangle. Develp, generalize, explain, and apply strategies fr determining the number f slutins pssible t a situatin invlving the ambiguus case. Slve situatinal questins invlving triangles withut a right angle. Midterm Exam expected t cver at least half f this unit. First week f in place f the Friday quiz 20.3 Expand and demnstrate understanding f prprtinal reasning related t: rates scale diagrams scale factr area surface area vlume January 6 10 Identify and describe situatins relevant t ne s self, family, r cmmunity that invlve prprtinal reasning. Create nn-symblic representatins fr rates, including pictures and graphs. Describe situatins in which a given rate might ccur. Explain the meaning f rates given in cntext, such as the arts, cmmerce, the envirnment, medicine, r recreatin. Slve situatinal questins that require the use f prprtinal reasning, including thse that invlve the islatin f a variable. Analyze situatins in which unit rates can be determined and suggest reasns why the rates wuld r wuld nt be used t make decisins in each situatin (i.e., are ther factrs in the situatin utweighing the imprtance f the mathematical calculatins?). Explain, using examples, the relatinship between the slpe f a graph and a rate. Identify and explain the effect f factrs within given situatins that culd influence a particular rate. Slve situatinal questins invlving rates, including unit rates. Identify and describe situatins relevant t ne s self, family, r cmmunity that invlve scale diagrams f 2-D shapes and 3-D bjects and determine the scale factr fr the situatins. Develp, generalize, explain, and apply strategies fr slving situatinal questins based upn scale diagrams f 2-D shapes and 3-D bjects, including the determining f scale factrs and unknwn dimensins. MR. OOSTEROM Page 3

4 Math Fundatins 20 Wrk Plan Draw, with r withut the use f technlgy, a scale diagram f a 2-D shape relevant t self, family, r cmmunity t a specified scale factr (enlargement r reductin). Slve situatinal prblems invlving scale diagrams f 2-D shapes and 3-D bjects. Determine relatinships between scale factr and area f 2-D shapes r surface area f 3-D bjects; and scale factr, surface area, and vlume f 3-D bjects. Develp, generalize, explain, and apply strategies fr determining scale factrs, areas, surface areas, r vlumes given the scale factr r the rati f areas, surface areas, r vlumes f 2-D shapes and 3-D bjects. Explain, with justificatin, the effect f a change in scale factr n the area f a 2-D shape r the surface area r vlume f a 3-D bject. Slve situatinal questins that invlve scale factrs, areas, surface areas, and vlumes, including nes that require the manipulatin f frmulas 20.1 Demnstrate understanding f mathematics invlved an histrical event r an area f interest Develp a rubric r ther scring schema fr the assessment f the research and presentatin. Cllect primary r secndary data (quantitative r qualitative) related t the tpic. Assess the accuracy, reliability, and relevance f the primary r secndary data (quantitative/qualitative) cllected by: identifying examples f bias and pints f view identifying and describing the data cllectin methds determining whether r nt the data are relevant determining whether r nt the data are cnsistent with infrmatin btained frm ther surces n the same tpic. Interpret data, using statistical methds if applicable. Identify cntrversial issues, if any, and present multiple sides f the issues with supprting data. Organize and create a presentatin (ral, written, multimedia, etc.) f the research findings and cnclusins. Prject Details t be determined Part f this prject will be cncurrent with ther tpics s that students can wrk n it at hme and in schl. MR. OOSTEROM Page 4

5 Math Fundatins 20 Wrk Plan 20.2 Demnstrate understanding f inductive and deductive reasning including: Analyzing cnjectures Analyzing special puzzles and games Prviding cnjectures Slving prblems March Nte: It is intended that: prfs NOT be limited t the tw clumn prf style analysis and cnjectures related t spatial puzzles and games be incrprated thrughut the curse. Make cnjectures by bserving patterns and identifying prperties, and justify the reasning. Prvide examples f hw inductive reasning might lead t false cnclusins. Critique the fllwing statement Decisins can be made and actins taken based upn inductive reasning. Identify situatins relevant t self, family, r cmmunity invlving inductive and/r deductive reasning. Prve algebraic number relatinships, such as divisibility rules, number prperties, mental mathematics strategies, r algebraic number tricks using deductive reasning. Prve cnjectures using deductive reasning. Analyze an argument fr its validity. Identify errrs in prfs that lead t incrrect cnclusins (e.g., a prf that ends with 2 = 1). Slve situatinal questins that invlve inductive r deductive reasning. Determine, explain, and verify strategies fr slving puzzles r winning games, such as: guess and check analyze a pattern make a systematic list create a drawing r mdel eliminate pssibilities slve simpler prblems wrk backward. Create a variatin f a puzzle r a game, and describe a strategy fr slving the puzzle r winning the game Demnstrate understanding f nrmal distributin, including standard deviatin and z-scres March Identify situatins relevant t self, family, r cmmunity in which standard deviatin and the nrmal distributin are used and explain the meaning and relevance f each. Explain the meaning and purpse f the prperties f a nrmal curve, including mean, median, mde, standard deviatin, symmetry, and area under the curve. Calculate, using technlgy, the ppulatin standard deviatin f a data set. MR. OOSTEROM Page 5

6 Math Fundatins 20 Wrk Plan Critique the statement Every set f data will crrespnd t a nrmal distributin. Analyze a data set t determine if it apprximates a nrmal distributin. Cmpare the prperties f tw r mre nrmally distributed data sets and explain what the cmparisn tells yu abut the situatins that the sets represent. Explain, using examples that represent multiple perspectives, the applicatin f standard deviatin fr making decisins in situatins such as warranties, insurance, r pinin plls. Slve situatinal questins that invlve the interpretatin f standard deviatins t make decisins. Determine, with r withut technlgy, and explain the meaning f the z-scre fr a given value in a nrmally distributed data set. Pse and slve situatinal questins relevant t self, family, r cmmunity that invlve nrmal distributins and z-scres Demnstrate understanding f the interpretatin f statistical data, including: Cnfidence intervals Cnfidence levels Margin f errr March Nte: It is intended that the fcus f this utcme be n interpretatin f data rather than n statistical calculatins. Identify and explain the significance f the cnfidence interval, margin f errr, r cnfidence level stated with respect t statistical data relevant t self, family, r cmmunity. Explain hw cnfidence levels, margins f errr, and cnfidence intervals can be impacted by the size f the randm sample used. Make inferences and decisins with justificatin abut a ppulatin frm sample data using cnfidence intervals. Prvide and critique examples frm print r electrnic media in which cnfidence intervals and cnfidence levels are used t supprt a particular psitin. Supprt a psitin r decisin relevant t self, family, r cmmunity by analyzing statistical data, as well as cnsidering ther factrs. Final Exam with fcus n units cvered since. 85% Feb. Mar. 15% Nv.- Jan Marking Scheme Assignments 25% Will be cver several tpics, limited class time will be given t cmplete these Class wrk 10% Onging during each class shuld be cmpleted and submitted at the end f the week Friday Quiz 15% Last 20 minutes f class every Friday Midterm 25% First week f Final Exam 25% Last week f March MR. OOSTEROM Page 6

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