FOUNDATIONS OF MATHEMATICS GRADE …

1 Markville Secondary School FOUNDATIONS OF MATHEMATICS - GRADE 10 APPLIED MFM2P1-01 Course Rationale: This course enables students to consolidate their understanding of linear relations and extend their problem-solving and algebraic skills through investigation, the effective use of technology, and hands-on activities. Students will develop and graph equations in analytic geometry; solve and apply linear systems, using real-life examples; and explore and interpret graphs of quadratic relations. Students will investigate similar triangles, the trigonometry of right triangles, and the measurement of three-dimensional figures. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.

2 Units of Study: The following comprise the units of study for this course: unit 1: Linear Relations unit 2: Linear Equations unit 3: Linear Systems unit 4: Quadratic Relations unit 5: Quadratic Expressions unit 6: Volume and Surface Area unit 7: 2D s and Trigonometry Assessment and Evaluation: Assessment is the ongoing process of collecting information about student achievement. A variety of assessment tools will be used. Assessment may be diagnostic, formative or summative. Diagnostic and formative assessments do not carry a mark weight. Summative assessments count towards the final mark. Seventy percent of the GRADE will be based on evaluations conducted throughout the course; thirty percent will be based on a final evaluation administered at the end of the course.

3 Course Evaluation: Term Work 70% unit Tests 32% Quizzes 13% Journals 10% Performance Assessments 15% Final Evaluation 30% Summative 10% Exam 20% Textbook FOUNDATIONS of MATHEMATICS 10: Pearson COST $70 MARKVILLE SECONDARY SCHOOL GRADE 10 APPLIED MATHEMATICS unit 1 B LINEAR RELATIONS Days Expectations Methodology Suggested Homework 1 ( ) Connect the rate of change of a linear relation to the slope of the line, and define the slope as the ratio m = rise run Graphing Calculator Investigation Text Messaging Page 100 # 1, 2, 4, 5, 6 Pg 106 # 1ad, 2ac, 4, 7, 8, 10, 15 1 ( ) Identify, through investigation with technology, the geometric significance of m and b in the equation y = mx + b Graphing Calculator Investigation Slope and y-intercept Pg 111 Investigation A and B Pg 115 # 1ab, 2ac, 4, 6ab, 7, 8ab, 9, 11 1 ( )

4 Identify, through investigation, y = mx + b as a common form for the equation of a straight line, and identify the special cases x =a ,y =b Identify, through investigation, properties of the slopes of lines and line segments, using graphing technology to facilitate investigation, where appropriate / \ 0 zero undef pos neg Graphing Calculator Investigation Pg 121 # 1 - 5 Pg 124 # 1, 2abcd, 3, 4ac, 7ac, 9 Pg 145 # 11 1 ( ) Determine the equation of a line, given its graph, the slope and y B intercept, or the slope and a point on the line Investigate the equation of a line Pg 128, 129 method #1 Pg 133 # 1ab, 2, 5acdeg, 6ab, 4 1 ( ) Determine the equation of a line given two points on the line Pg 135 # 7, 9, 14 1 ( ) Graph lines by hand, using a variety of techniques.

5 Y B intercept and slope x and y B intercepts table of values Pg 143 # 1ace, 3ac, 5, 9, Graph using x and y-intercepts 1) - x + y = 5 2) 2x + 4y = 8 1 (Review) Summarize all sections Pg 146 # 1, 2, 4, 5 (graph by hand), 6, 9acd, 10abcd, 11abc 1 (Quiz) - Summative Quiz 1 (Review) - Game Game Pg 148 # 1, 2, 3, 4, 6, 7 1 (Test) - unit 1 Test unit 2 B LINEAR EQUATIONS unit 3 B LINEAR SYSTEMS Days Expectations Methodology Suggested Homework 1 ( ) Solve and verify, one step, first degree, equations involving one variable Pg. 159 #1 - 4 1 ( ) Solve and verify, two step, first degree, equations involving one variable Pg. 160 # 5, 6, 8, 9 1 ( ) Solve and verify equations with more than one variable term including equations with fractional coefficients Pg.

6 169 # 1abf, 3ad, 4, 5acefj, 6 1 ( ) Solve and verify formulas with more than one variable Pg. 180 # 1, 2, 4, 6, 10, 12 (need graphing calculator) 1 ( ) Express the equation of a line in the form y = mx + b given the form Ax + By + C = 0 Pg. 188 # 2, 4ab, 6, 8, 10, 12a 1 (Review) Summarize all sections Pg. 190 # 2 10, 12, 13, 14 1 (Review) Continue review Complete yesterday s work Pg. 192 # 1, 2ade, 4, 5, 7ace, 8ab 1 (Quiz) - Summative Quiz 1 (Review) - Game Game 1 (Test) - unit 2 Test Days Expectations Methodology Suggested Homework 1 ( ) Determine graphically the point of intersection of two linear relations (graphing lines by hand) Solve problems that arise from realistic situations described in words or presented by given linear systems of two equations involving two variables, by choosing an appropriate algebraic or graphical method Pg 201 # 1ad, 2a, 3b, 4b, 10, 11, 13a, 15 1 ( )

7 Solve systems of two linear equations involving two variables with integral coefficients, using the method of substitution Solve problems that arise from realistic situations described in words or presented by given linear systems of two equations involving two variables, by choosing an appropriate algebraic or graphical method Pg 209 #1abde 1 ( ) Substitution: Part II Solve systems of two linear equations involving two variables with integral coefficients, using the method of substitution Solve problems that arise from realistic situations described in words or presented by given linear systems of two equations involving two variables, by choosing an appropriate algebraic or graphical method Pg 209 # 3abc, 5, 16, 17 1 ( )

8 Solve systems of two linear equations involving two variables with integral coefficients, using the method of elimination Solve problems that arise from realistic situations described in words or presented by given linear systems of two equations involving two variables, by choosing an appropriate algebraic or graphical method Pg 216 # 1abf, 3, 9 1 ( ) (Review) Review methods of solving a linear system of equations Worksheet 1 ( ) Solve systems of two linear equations using TI-83 Plus graphing calculator Investigation- Finding the Point Of Intersection (Green Handout. found in the filing cabinet under phone) From Handout Practice a, b, c, f - draw graphs in notes 1 Performance Assessment Solve problems that arise from realistic situations described in words or presented by given linear systems of two equations involving two variables, by choosing an appropriate algebraic or graphical method Worksheet OR Pg 228 #1a, 2a, 3b, 6, 7 1 (Quiz) - Summative Quiz 1 (Review) Summarize all sections Pg 226 # 1, 2ad, 3a, 4ab, 7ab, 9, 10bd 1 (Review) - Game Game 1 (Test) - unit 3 Test unit 4 B QUADRATIC RELATIONS Days Expectations Methodology Suggested Homework 1 ( )

9 Collect data that can be represented as a quadratic relation, from experiments using appropriate equipment and technology Investigation Pg 245 (need TI83+ and CBR s) Pg 249 # 1, 2ab, 6acd 1 ( ) Determine through investigation using technology, that a quadratic relation of the form y = ax2 + bx + c (a 0) can be graphically represented as a parabola, and determine that the table of values yields a constant second difference Investigation Pg 264 266 Part A & B Pg 269 # 2ac, 1ab, 5, and worksheet on Finite Differences 1 ( ) Identify the key features of a graph of a parabola, using a given graph or a graph generated with technology from its equation and use the appropriate terminology to describe these features Investigation A & B on Pg 254 - 256 Pg 260 #1, 3, 4, 6 (#3 requires a graphing calculator) Pg 262 #5 Performance assessment - 2 pictures 1 ( ) Compare through investigation using technology, the graphical representations of a quadratic relation in the form y = ax2 + bx + c and the same relation in the factored form y = (x - r)(x - s), and describe the connections between each algebraic representation and the graph (students do NOT have to find x-intercepts without graphing)

10 Investigation Pg 329 # 1, 2a, 3, 4ac, 5, 6, 7 Pg 333 # 2ab, 4 1 ( ) Solve problems involving a quadratic relation by interpreting a given graph or a graph generated with technology from its equation Solve problem by interpreting the significance of the key features of graphs obtained by collecting experimental data involving quadratic relations Use graphing calculators to calculate: *maximum height *length of time *Graphing calculators Pg 347 # 1, 2, 3, 6 1 Finish last day=s work (Review) Finish last day=s work Pg 352 # 1, 6, 8, 9 1 (Review) Summarize all sections Pg 272 # 1, 4, 7 Pg 274 #1 (do not graph), 2, 5 Pg 354 # 3, 6 1 (Quiz) - Summative Quiz 1 (Review) - Game Game 1 (Test) - unit 4 Test unit 5 B QUADRATIC EXPRESSIONS unit 6 B VOLUME & SURFACE AREA (Imperial Measurement) Days Expectations Methodology Suggested Homework 1 ( )