FOUNDATIONS OF MATHEMATICS GRADE … · Markville Secondary School FOUNDATIONS OF MATHEMATICS - GRADE 10 APPLIED MFM2P1-01 Course Rationale: This course enables students to consolidate

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.

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.

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 (1.1) 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

(1.2) 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

(1.3) 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

(1.4) 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

(1.5) Determine the equation of a line given two points on the line

Pg 135 # 7, 9, 14

1

(1.6) Graph lines by hand, using a variety of techniques:

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 (2.1) Solve and verify, one step, first degree, equations involving one variable

Pg. 159 #1 - 4

1

(2.2) Solve and verify, two step, first degree, equations involving one variable

Pg. 160 # 5, 6, 8, 9

1

(2.3) Solve and verify equations with more than one variable term including equations with fractional coefficients

Pg. 169 # 1abf, 3ad, 4, 5acefj, 6

1

(2.4) Solve and verify formulas with more than one variable

Pg. 180 # 1, 2, 4, 6, 10, 12 (need graphing calculator)

1 (2.5) 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


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


Days


Suggested Homework

1

(3.1) 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

(3.2) 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

(3.3) 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

(3.4) 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

(3.5) (Review) Review methods of solving a linear system of equations

Worksheet

1

(3.6) 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 1.6 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


1


Pg 226 # 1, 2ad, 3a, 4ab, 7ab, 9, 10bd

1 (Review) - Game

Game


UNIT 4 B QUADRATIC RELATIONS

Days


Suggested Homework

1 (4.1) 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

(4.2) 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

(4.3) 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 (4.4) Compare through investigation using technology, the graphical representations of a quadratic relation in the form y = ax

2 + 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)

Investigation Pg 329 # 1, 2a, 3, 4ac, 5, 6, 7

Pg 333 # 2ab, 4

1

(4.5) 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 (Review) - Game

Game


UNIT 5 B QUADRATIC EXPRESSIONS

UNIT 6 B VOLUME & SURFACE AREA (Imperial Measurement)

Days


Suggested Homework

1 (5.1) Expand and simplify second degree polynomial expressions involving one variable that consist of the product of two binomials OR the square of a binomial

Pg 286 # 1abe, 2ad, 3ae, 4ad, 5, 10, 12

1

(5.2) Factor binomials and trinomials involving one variable up to degree two, by determining a common factor using a variety of tools and strategies (e.g., algebra tiles)

Pg 294

# 2, 3, 4, 6, 7, 12, 13, 14, 17

1

(5.3) Factor simple trinomials of the form x

2 + bx + c

using a variety of tools and strategies

Pg 309 # 2, 3ad, 4, 5, 6, 7, 9, 10, 13

1 (5.4) Factor the difference of squares of the form x

2 -

a2

Pg 302 # 1, 4a – h, 7, 10, 11, 12, 13ab

1

Review B Factoring (Work Period)

Worksheet

1

Work Period – Review Expanding and factoring

Pg 312 # 1 – 4, 7, 8, 10, 12ab, 15, 16 Pg 314 # 1, 3, 4

1


1 (Review) - Game

Game


Days


Suggested Homework

1 (6.1) Use the imperial system when solving measurement problems

Pg 10 # 3ac, 4ac, 5b, 6b, 7, 9, 10, 11, 13

1

(6.2) Perform everyday conversions between the imperial system and the metric system

Pg 16 # 2, 3, 4, 5, 9, 10, 12, 13, 14

1

(6.3) Solve problems involving the volumes of prisms and pyramids

Pg 367 # 1ab, 2b,3df, 4ab, 5b, 6b, 9, 11

1

(6.4) Determine, through investigation, the relationship for calculating the surface area of a pyramid Solve problems involving the surface area of Prisms and pyramids

Pg 376 # 1af, 2ab, 3ab, 4a, 5, 6, 12

1

(6.5) Solve problems involving the surface areas and volumes of cylinders

Pg 386 # 1ad, 2ab, 3cd, 6, 9, 10, 12 (watch units in #2 and #3)

1

(6.6) Solve problems involving volume of cones and spheres

Pg 394 #1af, 2ab, 3, 4,5b, 6, 7, 9ab, 10

1

(6.7) Solve problems involving the surface areas and volumes of combined objects

Pg 402 # 1, 4, 6, 8 Journal-pg 402 #7

UNIT 7 B 2D’s & TRIGONOMETRY

1 (Review) Summarize all sections Pg 406 # 1 - 10 1


Pg 38 # 1a, 3, 4, 6, 7, 8, 9

1 (Quiz) Summative Quiz

1 (Review) Game

Pg 408 #1 - 7

1 (Test) Unit 6 Test

Days


Suggested Homework

1 (7.1) Review: Ratios, exponents, square roots, proportions, angle theorems, and Pythagorean theorem

Pg 4 # 3, 4, 5 Pg 44 #1bcgj, 2bcf, 3bdf, 4, 5, 7ab Pg 50 # 2ab, 3ac, 5, 6a, 7

1

(7.2)

Investigate properties of similar triangles using dynamic geometry software

Verify through investigation, properties of similar triangles

Geo sketchpad Investigation

1

(7.3) Determine the lengths of sides of similar triangles, using proportional reasoning

Socratic lesson

Pg 25 # 1a, 2ab, 4, 8, 9

1

(7.4) Solve problems involving similar triangles in realistic situations

Pg 33 # 4, 5, 6, 9, 10, 12, 14, 15

1

(7.5) Determine through investigation, the relationship between the ratio of two sides in a right triangle and the ratio of two corresponding sides in a similar right triangle, and define the sine, cosine, and tangent ratios

Primary Trigonometric Ratios Investigation using Geo Sketchpad

1

(7.6) Determine the measures of the sides in right triangles, using the primary trigonometric ratios and the Pythagorean theorem

Pg 59 # 1acd Pg 71 #1ac, 3a, 4, 5, 9, 14 Pg 79 # 1a, 3, 4, 7

1

(7.7) Determine the measure of the angles in right triangles, using primary trigonometric ratios and the Pythagorean theorem

Pg 71 # 2ab, 6, 8, 15 Pg 79 # 2ab, 8, 12

1

(7.8) Solve problems involving the measurements of sides and angles in right triangles in real life applications

Pg 86 # 4, 6, 8, 9, 11

1

(7.9) Describe, through participation in an activity, the application of trigonometry in an occupation

Clinometer Activity

Complete Clinometer activity

1

(Review) - Similar Triangle

Pg 38 # 1c, 10, 11, 12, 13, 15 Pg 40 # 8, 9, 11, 12

1 (Review) – Trigonometry Work Period

Pg 88 # 1 - 16


1 (Review) - Game

Pg 90 # 1 – 9 Pg 94 # 4, 5, 9, 11, 12


SUMMATIVE/ EXAM REVIEW

Days Expectations Methodology Suggested Homework

3 Summative – Pg 410 – creating a game

2 Play the games and have students (formatively) evaluate other groups

2+ Exam Review Pg 412 # 1 – 15, 17 – 28 (#24, 25 require graphing calculators)

Documents

FOUNDATIONS OF MATHEMATICS GRADE … · Markville Secondary School FOUNDATIONS OF MATHEMATICS - GRADE 10 APPLIED MFM2P1-01 Course Rationale: This course enables students to consolidate