Applying the Concepts 10 - McGraw-Hill Ryerson

FOUNDATIONS OF MATHEMATICS, GRADE 10, APPLIED(MFM2P)Correlation to Mathematics: Applying the Concepts 10Proportional ReasoningCodeSpecific ExpectationsAchievement ChartCategoriesUsing Proportional Reasoning to Solve Problems from ApplicationsPR1.01PR1.02PR1.03solve problems involving percent, ratio,rate, and proportion (e.g. in topics suchas interest calculation, currencyconversion, similar triangles,trigonometry, direct and partialvariation related to linear functions) bya variety of methods and models (e.g.diagrams, concrete materials, fractions,tables, patterns, graphs, equations);draw and interpret scale diagramsrelated to applications (e.g. technicaldrawings);distinguish between consistent andinconsistent represenations ofproportionality in a variety of contexts(e.g. explain the distortion of figuresresulting from irregular scales; identifymisleading features in graphs; identifymisleading conclusions based oninvalid proportional reasoning).Solving Problems Involving Similar TrianglesPR2.01PR2.02PR2.03determine some properties of similartriangles (e.g. the correspondence andequality of angles, the ratio ofcorresponding sides) throughinvestigation, using dynamic software;solve problems involving similartriangles in realistic situations (e.g.problems involving shadows,reflections, surveying);define the formulas for the sine, thecosine, and the tangent of angles, usingthe ratios of sides in right triangles.knowledge/understandingthinking/inquiry/problemsolvingapplicationMathematics:Applying theConcepts 10, Sectionsand Page Referencessections 1.1, 1.2, 1.3,1.4pages 4−23application sections 1.5, 1.6pages 24−33knowledge/understandingcommunicationsection 1.7pages 34−38knowledge/understanding section 6.1pages 206−214thinking/inquiry/problemsolvingapplicationknowledge/understandingcommunicationSolving Problems Involving the Trigonometry of Right TrianglesPR3.01PR3.02calculate the length of a side of a righttriangle, using the Pythagoreantheorem;determine the measures of the sides andangles in right triangles, using theprimary trigonometric ratios;sections 6.2, [6.4]pages 215−223,231−236sections 7.1, 7.2, 7.3pages 250−273knowledge/understanding sections 6.3, 6.4pages 224−236knowledge/understandingthinking/inquiry/problemsolvingsections 7.1, 7.2, 7.3pages 250−273Correlation MFM2P to Mathematics: Applying the Concepts 10 1

PR3.03PR3.04PR3.05solve problems involving the measuresof sides and angles in right triangles(e.g. in surveying, navigation);determine the height of an inaccessibleobject in the environment around theschool, using the trigonometry of righttriangles;describe applications of trigonometry invarious occupations.thinking/inquiry/problemsolvingapplicationthinking/inquiry/problemsolvingapplicationcommunicationapplicationsections 7.1, 7.2, 7.3,7.4pages 250−278sections 7.1, 7.4pages 250−258,274−280sections 7.1, 7.2, 7.3,7.4pages 250−280Linear FunctionsCodeSpecific ExpectationsApplying Piecewise Linear FunctionsLF1.01LF1.02LF1.03explain the characteristics of situationsinvolving piecewise linear functions(e.g. pay scale variations, gasconsumption costs, water consumptioncosts, differentiated pricing, motion);construct tables of values and sketchgraphs to represent given descriptionsof realistic situations involvingpiecewise linear functions, with andwithout the use of graphing calculatorsor graphing software;answer questions about piecewiselinear functions by interpolation andextrapolation, and by consideringvariations on given conditions.Interpreting Systems of Linear EquationsLF2.01LF2.02LF2.03LF2.04determine the point of intersection oftwo linear relations arising from arealistic situation, using graphingcalculators or graphing software;interpret the point of intersection of twolinear relations within the context of arealistic situation;solve systems of two linear equations intwo variables by the algebraic methodsof substitution and elimination;solve problems represented by linearsystems of two equations in twovariables arising from realisticsituations, by using an algebraicmethod and by interpreting graphs.Manipulating Algebraic ExpressionsLF3.01write linear equations by generalizingfrom tables of values and by translatingwritten descriptions;Achievement ChartCategoriescommunicationapplicationknowledge/understandingapplicationknowledge/understandingthinking/inquiry/problemsolvingknowledge/understandingapplicationcommunicationapplicationMathematics:Applying theConcepts 10, Sectionsand Page Referencessection 4.1pages 132−138sections 4.2, 4.3pages 139−152section 4.4pages 153−159section 5.1pages 168−174section 5.2pages 175−181knowledge/understanding sections 5.3, 5.4pages 182−196thinking/inquiry/problemsolvingapplicationsections 5.1, 5.2, .5.3,5.4pages 168−196knowledge/understanding sections 3.5, 3.6pages 104−113Correlation MFM2P to Mathematics: Applying the Concepts 10 2

LF3.02LF3.03LF3.04rearrange equations from the formy = mx + b to the form Ax + By + C = 0,and vice versa;solve first-degree equations in onevariable, including those with fractionalcoefficients, using an algebraic method;isolate a variable in formulas involvingfirst-degree terms.knowledge/understanding section 3.7pages 114−118knowledge/understanding sections 2.1, 2.2, 2.3,2.4pages 48−71knowledge/understanding sections 2.1, 2.2, 2.3,2.4pages 48−71Quadratic FunctionsCodeSpecific ExpectationsManipulating Algebraic ExpressionsAchievement ChartCategoriesMathematics:Applying theConcepts 10, Sectionsand Page ReferencesQF1.01 multiply two binomials and square abinomial;knowledge/understanding sections 9.1, 9.2pages 326−333QF1.02 expand and simplify polynomialexpressions involving the multiplyingknowledge/understanding section 9.3pages 334−337and squaring of binomials;QF1.03 describe intervals on quadraticfunctions using appropriate vocabulary(e.g. greater than, less than, between,from…to, less than 3 or greater than 7);communication throughout chapter 8and chapter 10Pages 288−317,364−388QF1.04 factor polynomials by determining acommon factor;knowledge/understanding section 9.4pages 338−341QF1.05 factor trinomials of the formx 2 + bx + c;knowledge/understanding section 9.6pages 345−348QF1.06 factor the difference of squares; knowledge/understanding section 9.5pages 342−344QF1.07 solve quadratic equations by factoring. knowledge/understanding section 9.7pages 349−353Investigating the Connection Between the Graphs and the Equations of QuadraticFunctionsQF2.01QF2.02QF2.03construct tables of values, sketchgraphs, and write equationsof the formy = ax 2 + b to represent quadraticfunctions derived from descriptions ofrealistic situations (e.g. vary the sidelength of a cube and observe the effecton the surface area of the cube);identify the effect of simpletransformations (i.e. translations,reflections, vertical stretch factors) onthe graph and the equation of y = x 2 ,using graphing calculators or graphingsoftware;explain the role of a, h, and k in thegraph of y = a(x − h) 2 + k;knowledge/understandingapplicationknowledge/understandingcommunicationknowledge/understandingcommunicationsections 8.1, 8.2, 8.3pages 288−304sections 8.2, 8.3, 8.4pages 293−311section 8.5pages 312−317Correlation MFM2P to Mathematics: Applying the Concepts 10 3

QF2.04expand and simplify an equation of theform y = a(x − h) 2 + k to obtain theform y = ax 2 + bx + c.Solving Problems Involving Quadratic FunctionsQF3.01QF3.02obtain the graphs of quadratic functionswhose equations are given in the formy = a(x − h) 2 + k or the formy = ax 2 + bx + c, using graphingcalculators or graphing software;determine the zeros and the maximumor minimum value of a quadraticfunction from its graph, using graphingcalculators or graphing software;knowledge/understanding section 10.2pages 369−374knowledge/understanding section 10.2pages 369−374knowledge/understandingthinking/inquiry/problemsolvingsections 10.1, 10.3,10.4pages 364−368,375−388LF3.03solve problems involving a givenquadratic function by interpreting itsgraph (e.g. given a formularepresenting the height of a ball overelapsed time, graph the function, usinga graphing calculator or graphingsoftware, and answer questions such asthe following: What is the maximumheight of the ball? After what length oftime will the ball touch the ground?Over what interval is the height of theball greater than 3 m?thinking/inquiry/problemsolvingapplicationsection10.4pages 381−388[also throughoutchapter 8 and chapter10]Correlation MFM2P to Mathematics: Applying the Concepts 10 4