Math Foundations 10 Work Plan

Transcription

1 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 December 1 week 6 Majr Learning Indicatrs Develp, generalize, explain, and apply strategies fr determining the greatest cmmn factrs r least cmmn multiples Explain the relatinship between factrs and multiples. Determine the prime factrs f a whle number and explain the strategies used. Analyze cncretely, pictrially, r numerically and explain whether a whle number is a perfect square r a perfect cube. Develp, generalize, explain, and apply strategies fr determining the square rt f a perfect square and the cube rt f a perfect cube. Investigate and reprt abut the numbers 0 and 1 with respect t factrs, multiples, square rts, and cube rts. Slve prblems that invlve prime factrs, greatest cmmn factrs, least cmmn multiples, square rts, r cube rts Resurces / Pssible Assessments 10.5 Understanding f Multiplicatin and factring f plynmial expressins: Multiplying mnmials, binmials, trinmials Cmmn factrs Trinmial factring Relating multiplicatin and factring f plynmials December 6-10 Develp, generalize, explain, and apply a strategy f symblic manipulatin t determine the prduct f tw binmials by analyzing cncrete and pictrial mdels. Explain the relatinship between the multiplicatin f tw binmial expressins and the area f a rectangular regin. Develp (cncretely, pictrially, r symblically), explain, and apply understanding f hw multiplicatin f binmials is related t the multiplicatin f tw-digit numbers (e.g., use algebra tiles and base ten blcks t cmpare and relate the prducts f (x+1)(3x+2) and (11)(32)). Develp, generalize, explain, and apply a strategy fr multiplying plynmials. Analyze the multiplicatin f tw plynmials fr errrs and explain the strategy used. Explain why evaluating at a value fr the variable in a prduct f plynmials in factred frm shuld give the same slutin as evaluating the expanded and simplified frm f the plynmial prduct at the same value (e.g., explain why x 2 +5x+6 shuld have the same value as (x+3)(x+2) when evaluated at x = -4). Explain, using cncrete r visual mdels, hw the prcesses f factring and multiplicatin are related. Develp (using cncrete materials, pictures, r visualizatin), generalize, explain, and apply strategies fr factring and verifying the factrs f binmials, including numerical binmial expressins (e.g., 32+20=4(8+5)). MR. OOSTEROM Page 1

2 Math Fundatins 10 Wrk Plan Srt a set f plynmials accrding t the type(s) f factring that culd be applied t them. Explain and apply strategies fr determining whether given factrs are thse f a given plynmial. Develp, generalize, explain, and apply strategies fr factring a trinmial. Critique the statement any trinmial can be factred int tw binmial factrs. Explain hw differences f squares can be factred using trinmial factring strategies. Explain why it is imprtant t lk fr cmmn factrs first when factring a trinmial 10.2 Demnstrate understanding f irratinal numbers in bth radical and expnential frm: Representing Simplifying Identifying Ordering Relating t ratinal numbers Applicatin f laws f expnents December January 1 2 weeks Srt, with justificatin, a set f numbers int ratinal and irratinal numbers. Create and explain a pattern that describes the decimal frm f an irratinal number (e.g., write the digits frm 0 t 9 in rder, then put tw f each digit fllwed by three f each digit and s n). Apprximate the value f a given irratinal number and explain the strategy used. Order a set f Real numbers, including ratinal and irratinal numbers, n a number line and explain the strategies used. Express a radical as a mixed radical in simplest frm (limited t numerical radicands). Express a mixed radical as an entire radical (limited t numerical radicands). Explain, using examples, hw changing the value f the index f a radical impacts the value f the radical. Represent, such as thrugh the use f a graphic rganizer, the relatinships amng the subsets f the Real numbers: natural, whle, integer, ratinal, and irratinal. Analyze patterns t generalize why Analyze patterns t generalize why and a > 0 Extend and apply the laws f expnents Analyze simplificatins f expressin invlving radicals and pwers Express pwers with ratinal expnents as radicals and vice versa Create a representatin that cnveys the relatinship between pwers, ratinal numbers and irratinal numbers MR. OOSTEROM Page 2

3 Math Fundatins 10 Wrk Plan 10.3 Demnstrate understanding f SI and imperial units f measurement. Linear measurement Surface area f spheres, cnes, cylinders, prisms, and pyramids Vlumes Relatinships with measurements systems January Prvide persnal referents fr linear measurements, including millimetre, centimetre, metre, kilmetre, inch, ft, yard, and mile and explain the chices. Justify the chice f units and r referents fr determining r estimating linear, surface area, r vlume measurements in different cntexts Explain the selectin f measuring tls and the strategies used t determine linear measurements Critique the statement: The length f a wall is greater in yards than in metres Cmpare imperial and SI units Strategies and /r frmulas fr cnverting with SI and imperial units (linear, surface area, and vlume) Verify with explanatin, a cnversin f units Analyze 3D bjects, their nets land labelled diagrams fr determining surface area and vlume Prblem slving using situatinal questins related t surface area and vlume f spheres, cnes, etc Apply frmulas fr determining surface area and vlume Explain the relatinship between vlumes f right cnes and right prisms and right pyramids and right prisms 10.4 Develp and apply the primary trignmetric ratis, SIN, COS, TAN t slve prblems invlving right triangles. January 6 10 Develp, generalize, explain, and apply relatinships between the ratis f side lengths and angle sizes in similar right triangles. Demnstrate hw t identify the hyptenuse f a right triangle and the adjacent and ppsite sides t an acute angle in that right triangle. Slve prblems, with r withut the use f technlgy, invlving ne r mre right triangles by applying primary trignmetric ratis and/r the Pythagrean Therem. Create and slve prblems that invlve indirect and direct linear measurements by using the primary trignmetric ratis, the Pythagrean Therem, and measurement instruments such as a clinmeter r metre stick Midterm Exam expected t cver at least half f this unit. First week f in place f the Friday quiz 10.6 Expand and apply understanding f relatins and functins: Relating data graphs and situatins Analyzing and interpreting Prvide and discuss examples f different types f relatins relevant t ne s life, family, r cmmunity (e.g., persn A is the mther f persn B, r persn A is a brther f persn B.). Explain, by prviding situatinal and graphical examples, the relatinship between the categries f relatins and functins. Critique the statement Relatins and functins are the same thing. This and the remaining units will be tied tgether fr the remaining weeks f the term MR. OOSTEROM Page 3

4 Math Fundatins 10 Wrk Plan Distinguish between relatins and functins Graph, with r withut technlgy, a set f data, and determine the restrictins n the dmain and range. Explain why data pints shuld r shuld nt be cnnected n the graph fr a situatin. Prvide and explain examples f situatins that culd be represented by a given graph. Sketch a graph t represent a situatin presented rally r in writing. Determine, and express in a variety f ways, the dmain and range f a graph, a set f rdered pairs, r a table f values. Generalize, explain, and apply strategies fr determining whether a set f rdered pairs r a graph represents a functin Demnstrate understanding f slpe alng with: Lines and segments Rate f change Parallel lines Perpendicular lines Prvide examples, relevant t self, family, r cmmunity, t explain the imprtance f slpe. Illustrate and explain, using examples relevant t self, family, r cmmunity, hw slpe is rate f change. Determine the slpe f a line segment by using the measurement r calculatin f the rise and run. Classify lines in a given set as having psitive r negative slpes, and explain hw the sign f the slpe affects the interpretatin r meaning f the slpe. Explain the meaning f zer r slpes with n Real value. Explain why the slpe f a straight line can be determined by using any tw distinct pints n that line. Draw a line given its slpe and a pint n the line. Determine anther pint n a line, given the slpe and a pint n the line. Generalize, explain, and apply strategies fr determining whether tw lines are parallel r perpendicular. Apply knwledge and skills related t slpe t slve situatinal questins relevant t self, family, and cmmunity (e.g., determine the slpes f the ples in a tepee and the impact f changing the slpes n the dimensins and strength f the tepee) Demnstrate understanding f linear functins using: Wrds, rdered pairs, tables f values, functin ntatin and equatins March Critique the statement any straight line is the graph f a linear functin. Explain, using examples, the impact f the dmain f a linear functin n the graph f the functin (e.g., if the dmain is nt all Real numbers, then the graph will nt shw a slid line). Analyze situatins t identify, with justificatin, the independent MR. OOSTEROM Page 4

5 Math Fundatins 10 Wrk Plan and a dependent variable. Analyze situatins, graphs, tables f values, equatins, r sets f rdered pairs t determine if the relatinship described is linear. Match crrespnding types f representatins f linear relatins (e.g., situatins, graphs, tables f values, equatins, and sets f rdered pairs). Develp, generalize, explain, and apply strategies fr determining the intercepts (as values and rdered pairs) f a linear relatin frm its graph. Determine the slpe, dmain, and range f the graph f a linear relatin. Sketch examples f linear relatins t demnstrate the number f x r y intercepts pssible fr any line. Match, with explanatin, slpes and y-intercepts t graphs f linear relatins. Slve a situatinal questin that invlves the intercepts, slpe, dmain, r range f a linear relatin. Express the equatin f a linear relatin in different frms (including the slpe-intercept r general frm) and cmpare the graphs f the linear relatins. Generalize, explain, and apply strategies fr drawing r sketching the graph f a linear relatin in slpe-intercept, general, r slpepint frm, r functin ntatin. Graph, with and withut technlgy, a linear relatin given in slpeintercept, general, r slpe-pint frm, and explain the strategy used t create the graph. Analyze a set f linear relatins fr equivalent linear relatins (e.g., 2x +3y = 6 is equivalent t 4x + 6y = 12) and explain the reasning. Explain the relatinship between linear functins written in functin ntatin and written as equatins with tw variables, and hw t change between the tw frms. Apply knwledge and skills related t functin ntatin t slve situatinal questins. Determine the related range value, given a dmain value fr a linear functin (e.g., if f(x) = 3x 2, determine f( 1)) and explain what the resulting value tells abut the linear functin. Determine the related dmain value, given a range value fr a linear functin (e.g., if g(t) = 7 + t, determine t s that g(t) = 15) and explain what the resulting value tells abut the linear functin. Explain why a linear functin wuld never have a term f x 2 when in simplified frm. MR. OOSTEROM Page 5

6 Math Fundatins 10 Wrk Plan 10.9 Demnstrate understanding f writing and applicatin f equatins f linear relatins Graphing Pint that satisfies relatin and slpe Tw distinct pints that satisfy relatin Equatin f parallel and perpendicular lines t relatin March Develp, generalize, explain, and apply strategies fr writing an equatin fr a linear relatin using data btained frm a graph. Develp, generalize, explain, and apply strategies fr writing an equatin fr a linear relatin when given: a pint that satisfies the relatin and the slpe f the relatin tw pints that satisfy the relatin the crdinates f a pint that satisfy the relatin and the equatin f a line parallel r perpendicular t the line. Cmpare and critique the structure and purpses f different frms f linear relatins, including y=mx+b, Ax+By=C, and y-y1=m(x-x1) (e.g., there is n way t write a vertical linear relatin in the frm y = mx+b). Graph and write equatins fr linear data generated within an experiment r cllected frm a situatin. Apply knwledge and skills f linear relatins and their equatins t slve situatinal questins Slving Systems f linear equatins in tw variables algebraically and graphically March Match, with justificatin, situatins and systems f linear equatins. Sketch, describe, prvide and explain situatinal examples f the different ways that the graphs f tw linear equatins (tw variables) can intersect and explain the meaning f the pints f intersectin. Develp, generalize, explain, and apply strategies fr slving systems f equatins graphically, with and withut the use f technlgy and verify the slutins. Develp, generalize, explain, and apply strategies, including verificatin f slutins, fr slving systems f equatins algebraically. Critique the statement tw lines always intersect at exactly ne pint. Apply knwledge and skills with systems f linear equatins t slve situatinal questins. 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