FOUNDATIONS OF MATHEMATICS AND PRE-CALCULUS GRADE 10

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1 FOUNDATIONS OF MATHEMATICS AND PRE-CALCULUS GRADE 10 [C] Commuicatio Measuremet A1. Solve problems that ivolve liear measuremet, usig: SI ad imperial uits of measure estimatio strategies measuremet strategies. [ME, PS, V] A2. Apply proportioal reasoig to problems that ivolve coversios betwee SI ad imperial uits of measure. [C, ME, PS] Geeral Outcome: Develop spatial sese ad proportioal reasoig. 1.1 Provide referets for liear measuremets, icludig millimetre, cetimetre, metre, kilometre, ich, foot, yard ad mile, ad explai the choices. 1.2 Compare SI ad imperial uits, usig referets. 1.3 Estimate a liear measure, usig a referet, ad explai the process used. 1.4 Justify the choice of uits used for determiig a measuremet i a problem-solvig cotext. 1.5 Solve problems that ivolve liear measure, usig istrumets such as rulers, calipers or tape measures. 1.6 Describe ad explai a persoal strategy used to determie a liear measuremet; e.g., circumferece of a bottle, legth of a curve, perimeter of the base of a irregular 3-D object. 2.1 Explai how proportioal reasoig ca be used to covert a measuremet withi or betwee SI ad imperial systems. 2.2 Solve a problem that ivolves the coversio of uits withi or betwee SI ad imperial systems. 2.3 Verify, usig uit aalysis, a coversio withi or betwee SI ad imperial systems, ad explai the coversio. 2.4 Justify, usig metal mathematics, the reasoableess of a solutio to a coversio problem. WNCP Commo Curriculum Framework for Grades Mathematics Foudatios of Mathematics ad Pre-calculus (Grade 10) / 47

2 Measuremet (cotiued) A3. Solve problems, usig SI ad imperial uits, that ivolve the surface area ad volume of 3-D objects, icludig: right coes right cyliders right prisms right pyramids spheres. [CN, PS, R, V] A4. Develop ad apply the primary trigoometric ratios (sie, cosie, taget) to solve problems that ivolve right triagles. [C, CN, PS, R, T, V] Geeral Outcome: Develop spatial sese ad proportioal reasoig. 3.1 Sketch a diagram to represet a problem that ivolves surface area or volume. 3.2 Determie the surface area of a right coe, right cylider, right prism, right pyramid or sphere, usig a object or its labelled diagram. 3.3 Determie the volume of a right coe, right cylider, right prism, right pyramid or sphere, usig a object or its labelled diagram. 3.4 Determie a ukow dimesio of a right coe, right cylider, right prism, right pyramid or sphere, give the object s surface area or volume ad the remaiig dimesios. 3.5 Solve a problem that ivolves surface area or volume, give a diagram of a composite 3-D object. 3.6 Describe the relatioship betwee the volumes of: right coes ad right cyliders with the same base ad height right pyramids ad right prisms with the same base ad height. 4.1 Explai the relatioships betwee similar right triagles ad the defiitios of the primary trigoometric ratios. 4.2 Idetify the hypoteuse of a right triagle ad the opposite ad adjacet sides for a give acute agle i the triagle. 4.3 Solve right triagles, with or without techology. 4.4 Solve a problem that ivolves oe or more right triagles by applyig the primary trigoometric ratios or the Pythagorea theorem. 4.5 Solve a problem that ivolves idirect ad direct measuremet, usig the trigoometric ratios, the Pythagorea theorem ad measuremet istrumets such as a cliometer or metre stick. 48 / Foudatios of Mathematics ad Pre-calculus (Grade 10) WNCP Commo Curriculum Framework for Grades Mathematics

3 Algebra ad Number B1. Demostrate a uderstadig of factors of whole umbers by determiig the: prime factors greatest commo factor least commo multiple square root cube root. [CN, ME, R] B2. Demostrate a uderstadig of irratioal umbers by: represetig, idetifyig ad simplifyig irratioal umbers orderig irratioal umbers. [CN, ME, R, V] Geeral Outcome: Develop algebraic reasoig ad umber sese. 1.1 Determie the prime factors of a whole umber. 1.2 Explai why the umbers 0 ad 1 have o prime factors. 1.3 Determie, usig a variety of strategies, the greatest commo factor or least commo multiple of a set of whole umbers, ad explai the process. 1.4 Determie, cocretely, whether a give whole umber is a perfect square, a perfect cube or either. 1.5 Determie, usig a variety of strategies, the square root of a perfect square, ad explai the process. 1.6 Determie, usig a variety of strategies, the cube root of a perfect cube, ad explai the process. 1.7 Solve problems that ivolve prime factors, greatest commo factors, least commo multiples, square roots or cube roots. 2.1 Sort a set of umbers ito ratioal ad irratioal umbers. 2.2 Determie a approximate value of a give irratioal umber. 2.3 Approximate the locatios of irratioal umbers o a umber lie, usig a variety of strategies, ad explai the reasoig. 2.4 Order a set of irratioal umbers o a umber lie. 2.5 Express a radical as a mixed radical i simplest form (limited to umerical radicads). 2.6 Express a mixed radical as a etire radical (limited to umerical radicads). 2.7 Explai, usig examples, the meaig of the idex of a radical. 2.8 Represet, usig a graphic orgaizer, the relatioship amog the subsets of the real umbers (atural, whole, iteger, ratioal, irratioal). WNCP Commo Curriculum Framework for Grades Mathematics Foudatios of Mathematics ad Pre-calculus (Grade 10) / 49

4 Algebra ad Number (cotiued) B3. Demostrate a uderstadig of powers with itegral ad ratioal expoets. [C, CN, PS, R] Geeral Outcome: Develop algebraic reasoig ad umber sese. 1 a 3.1 Explai, usig patters, why a =, a Explai, usig patters, why a = a, > Apply the expoet laws: m m+ ( a )( a ) = a m m a a = a, a 0 m m ( ) a = a m ab = a b m m ( ) a b a b =, b 0 to expressios with ratioal ad variable bases ad itegral ad ratioal expoets, ad explai the reasoig. 3.4 Express powers with ratioal expoets as radicals ad vice versa. 3.5 Solve a problem that ivolves expoet laws or radicals. 3.6 Idetify ad correct errors i a simplificatio of a expressio that ivolves powers. 50 / Foudatios of Mathematics ad Pre-calculus (Grade 10) WNCP Commo Curriculum Framework for Grades Mathematics

5 Algebra ad Number (cotiued) Geeral Outcome: Develop algebraic reasoig ad umber sese. B4. Demostrate a uderstadig of the multiplicatio of polyomial expressios (limited to moomials, biomials ad triomials), cocretely, pictorially ad symbolically. [CN, R, V] B5. Demostrate a uderstadig of commo factors ad triomial factorig, cocretely, pictorially ad symbolically. [C, CN, R, V] (It is iteded that the emphasis of this outcome be o biomial by biomial multiplicatio, with extesio to polyomial by polyomial to establish a geeral patter for multiplicatio.) 4.1 Model the multiplicatio of two give biomials, cocretely or pictorially, ad record the process symbolically. 4.2 Relate the multiplicatio of two biomial expressios to a area model. 4.3 Explai, usig examples, the relatioship betwee the multiplicatio of biomials ad the multiplicatio of two-digit umbers. 4.4 Verify a polyomial product by substitutig umbers for the variables. 4.5 Multiply two polyomials symbolically, ad combie like terms i the product. 4.6 Geeralize ad explai a strategy for multiplicatio of polyomials. 4.7 Idetify ad explai errors i a solutio for a polyomial multiplicatio. 5.1 Determie the commo factors i the terms of a polyomial, ad express the polyomial i factored form. 5.2 Model the factorig of a triomial, cocretely or pictorially, ad record the process symbolically. 5.3 Factor a polyomial that is a differece of squares, ad explai why it is a special case of triomial factorig whereb = Idetify ad explai errors i a polyomial factorizatio. 5.5 Factor a polyomial, ad verify by multiplyig the factors. 5.6 Explai, usig examples, the relatioship betwee multiplicatio ad factorig of polyomials. 5.7 Geeralize ad explai strategies used to factor a triomial. 5.8 Express a polyomial as a product of its factors. WNCP Commo Curriculum Framework for Grades Mathematics Foudatios of Mathematics ad Pre-calculus (Grade 10) / 51

6 Relatios ad Fuctios Geeral Outcome: Develop algebraic ad graphical reasoig through the study of relatios. C1. Iterpret ad explai the relatioships amog data, graphs ad situatios. [C, CN, R, T, V] C2. Demostrate a uderstadig of relatios ad fuctios. [C, R, V] C3. Demostrate a uderstadig of slope with respect to: rise ad ru lie segmets ad lies rate of chage parallel lies perpedicular lies. [PS, R, V] 1.1 Graph, with or without techology, a set of data, ad determie the restrictios o the domai ad rage. 1.2 Explai why data poits should or should ot be coected o the graph for a situatio. 1.3 Describe a possible situatio for a give graph. 1.4 Sketch a possible graph for a give situatio. 1.5 Determie, ad express i a variety of ways, the domai ad rage of a graph, a set of ordered pairs or a table of values. 2.1 Explai, usig examples, why some relatios are ot fuctios but all fuctios are relatios. 2.2 Determie if a set of ordered pairs represets a fuctio. 2.3 Sort a set of graphs as fuctios or o-fuctios. 2.4 Geeralize ad explai rules for determiig whether graphs ad sets of ordered pairs represet fuctios. 3.1 Determie the slope of a lie segmet by measurig or calculatig the rise ad ru. 3.2 Classify lies i a give set as havig positive or egative slopes. 3.3 Explai the meaig of the slope of a horizotal or vertical lie. 3.4 Explai why the slope of a lie ca be determied by usig ay two poits o that lie. 3.5 Explai, usig examples, slope as a rate of chage. 3.6 Draw a lie, give its slope ad a poit o the lie. 3.7 Determie aother poit o a lie, give the slope ad a poit o the lie. 3.8 Geeralize ad apply a rule for determiig whether two lies are parallel or perpedicular. 3.9 Solve a cotextual problem ivolvig slope. 52 / Foudatios of Mathematics ad Pre-calculus (Grade 10) WNCP Commo Curriculum Framework for Grades Mathematics

7 Relatios ad Fuctios (cotiued) Geeral Outcome: Develop algebraic ad graphical reasoig through the study of relatios. C4. Describe ad represet liear relatios, usig: words ordered pairs tables of values graphs equatios. [C, CN, R, V] C5. Determie the characteristics of the graphs of liear relatios, icludig the: itercepts slope domai rage. [CN, PS, R, V] 4.1 Idetify idepedet ad depedet variables i a give cotext. 4.2 Determie whether a situatio represets a liear relatio, ad explai why or why ot. 4.3 Determie whether a graph represets a liear relatio, ad explai why or why ot. 4.4 Determie whether a table of values or a set of ordered pairs represets a liear relatio, ad explai why or why ot. 4.5 Draw a graph from a set of ordered pairs withi a give situatio, ad determie whether the relatioship betwee the variables is liear. 4.6 Determie whether a equatio represets a liear relatio, ad explai why or why ot. 4.7 Match correspodig represetatios of liear relatios. 5.1 Determie the itercepts of the graph of a liear relatio, ad state the itercepts as values or ordered pairs. 5.2 Determie the slope of the graph of a liear relatio. 5.3 Determie the domai ad rage of the graph of a liear relatio. 5.4 Sketch a liear relatio that has oe itercept, two itercepts or a ifiite umber of itercepts. 5.5 Idetify the graph that correspods to a give slope ad y-itercept. 5.6 Idetify the slope ad y-itercept that correspod to a give graph. 5.7 Solve a cotextual problem that ivolves itercepts, slope, domai or rage of a liear relatio. WNCP Commo Curriculum Framework for Grades Mathematics Foudatios of Mathematics ad Pre-calculus (Grade 10) / 53

8 Relatios ad Fuctios (cotiued) Geeral Outcome: Develop algebraic ad graphical reasoig through the study of relatios. C6. Relate liear relatios expressed i: slope itercept form (y = mx + b) geeral form (Ax + By + C = 0) slope poit form (y y 1 = m(x x 1 )) to their graphs. [CN, R, T, V] C7. Determie the equatio of a liear relatio, give: a graph a poit ad the slope two poits a poit ad the equatio of a parallel or perpedicular lie to solve problems. [CN, PS, R, V] 6.1 Express a liear relatio i differet forms, ad compare the graphs. 6.2 Rewrite a liear relatio i either slope itercept or geeral form. 6.3 Geeralize ad explai strategies for graphig a liear relatio i slope itercept, geeral or slope poit form. 6.4 Graph, with ad without techology, a liear relatio give i slope itercept, geeral or slope poit form, ad explai the strategy used to create the graph. 6.5 Idetify equivalet liear relatios from a set of liear relatios. 6.6 Match a set of liear relatios to their graphs. 7.1 Determie the slope ad y-itercept of a give liear relatio from its graph, ad write the equatio i the form y = mx + b. 7.2 Write the equatio of a liear relatio, give its slope ad the coordiates of a poit o the lie, ad explai the reasoig. 7.3 Write the equatio of a liear relatio, give the coordiates of two poits o the lie, ad explai the reasoig. 7.4 Write the equatio of a liear relatio, give the coordiates of a poit o the lie ad the equatio of a parallel or perpedicular lie, ad explai the reasoig. 7.5 Graph liear data geerated from a cotext, ad write the equatio of the resultig lie. 7.6 Solve a problem, usig the equatio of a liear relatio. 54 / Foudatios of Mathematics ad Pre-calculus (Grade 10) WNCP Commo Curriculum Framework for Grades Mathematics

9 Relatios ad Fuctios (cotiued) Geeral Outcome: Develop algebraic ad graphical reasoig through the study of relatios. C8. Represet a liear fuctio, usig fuctio otatio. [CN, ME, V] C9. Solve problems that ivolve systems of liear equatios i two variables, graphically ad algebraically. [CN, PS, R, T, V] 8.1 Express the equatio of a liear fuctio i two variables, usig fuctio otatio. 8.2 Express a equatio give i fuctio otatio as a liear fuctio i two variables. 8.3 Determie the related rage value, give a domai value for a liear fuctio; e.g., if f(x) = 3x 2, determie f( 1). 8.4 Determie the related domai value, give a rage value for a liear fuctio; e.g., if g(t) = 7 + t, determie t so that g(t) = Sketch the graph of a liear fuctio expressed i fuctio otatio. 9.1 Model a situatio, usig a system of liear equatios. 9.2 Relate a system of liear equatios to the cotext of a problem. 9.3 Determie ad verify the solutio of a system of liear equatios graphically, with ad without techology. 9.4 Explai the meaig of the poit of itersectio of a system of liear equatios. 9.5 Determie ad verify the solutio of a system of liear equatios algebraically. 9.6 Explai, usig examples, why a system of equatios may have o solutio, oe solutio or a ifiite umber of solutios. 9.7 Explai a strategy to solve a system of liear equatios. 9.8 Solve a problem that ivolves a system of liear equatios. WNCP Commo Curriculum Framework for Grades Mathematics Foudatios of Mathematics ad Pre-calculus (Grade 10) / 55

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