COLONEL BY SECONDARY SCHOOL 2017-2018

MPM 1DE COURSE OUTLINE

Unit Number

Unit Name Number of Periods

0 Introduction; Diagnostic test; Review 61 Polynomials and Equations 92 Exponents and Radicals 103 2D/3D Geometry & Optimizing Measurements (ISU1) 44 Linear and Non-linear Relations 155 Linear Systems 76 Trigonometry (ISU2) 27 Euclidean Geometry 118 Analytic Geometry 7

Preparation for EQAO 4EQAO 2Exam Review 4

Total: 81Textbooks: Principles of Mathematics 9; McGraw-Hill Ryerson (STUDENTS WILL HAVE)

Mathpower 10; McGraw-Hill Ryerson (STUDENTS WILL NOT HAVE)Mathematics: Principles and Processes 10; Nelson (STUDENTS WILL NOT HAVE)

Mathematics 9; Nelson (STUDENTS WILL NOT HAVE)

The mark breakdown is as follows:Course Work – 70%EQAO – 10% Final Exam – 20%

Assessment and Evaluation:Students will be evaluated using levels in the following strands and on the following overall expectations:

A. Number Sense and Algebra (NSA)NSA1: Manipulate numerical and polynomial expression (gr. 9)NSA2: Solve first-degree equations (gr. 9)NSA3: Demonstrate an understanding of exponent rules & radicals and apply them to simplify expressions (gr. 9)

B. Linear Relations (LR)LR1: Apply data-management techniques to investigate relationships between two variables (gr. 9)LR2: Determine the relationship between the form of an equation and the shape of its graph with respect to the linearity and non-linearity (gr. 9)LR3: Determine, through investigation, the properties of the slope and y-intercept of a linear relation (gr. 9)LR4: Solve problems involving linear relations (gr. 9 & 10)

C. Analytic Geometry (AG)AG1: Model and solve problems involving the intersection of two straight lines (gr. 9 (by graphing) & 10(algebraic)AG2: Solve problems using analytic geometry involving properties of lines and line segments (gr. 10)AG3: Verify geometric properties of triangles and quadrilaterals, using analytic geometry (gr. 10)

D. Trigonometry (TG)TG1: Use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity (gr. 10)TG2: Solve problems involving right triangles, using primary trig ratios and Pythagorean theorem (gr. 10)

E. Measurement and Geometry (MG)MG1: Determine, through investigation, the optimal values of various measurements (gr. 9)MG2: Solve problems involving the measurements of two-dimensional shapes and the

surface areas and volumes of three-dimensional figures (gr. 9)MG3: Verify, through investigation facilitated by dynamic geometry software, geometricproperties and relationships involving two-dimensional shapes, and apply the results to solving problems (gr. 9)

Students will be assessed and evaluated in a balanced manner with respect to the following categories of knowledge and skills: Knowledge and Understanding, Application, Communication, and Thinking. “The four categories should be considered as interrelated, reflecting the wholeness and interconnectedness of learning.” - taken from the Ontario ministry curriculum documents for Mathematics grade 9 and 10

Missed Evaluation Policy

It is the responsibility of the student to let the teacher know in advance if he/she will be missing any major evaluation for any known reason (medical appointment, school trip,…) so that the teacher and student can arrange an alternate date for the evaluation to take place. Additionally, if a student misses a major evaluation unexpectedly (illness, …), it is the student’s responsibility to contact the teacher as soon as possible to arrange an alternate date for the evaluation.

The student will be given a second opportunity to be evaluated on a date to be determined by the teacher within two weeks of the missed evaluation.

If the student misses the second opportunity to be evaluated, he/she will receive a zero for that evaluation to represent lack of evidence of achievement in the expectations covered by that evaluation.

Homework Policy

Homework is assigned daily and in quantities that the teacher deems most effective in helping students prepare to meet the overall expectations of the course. While homework is not directly calculated as part of the mark, there is a strong positive correlation between completion of homework and success in the course. So do your homework and, of course, don’t forget to always check your answers with the back of the book.

Unit 0: Introduction and ReviewOverall

ExpectationLesson

NumberTopic and Homework

Introduction to the Course:Diagnostic Test, Student Profile

PrerequisiteSkills:

Review of Number Sense,

Numeracyand

Geometry

RV-1

Review Number Systems (N,W,Z, , , R), Decimals & IntegersHomework: Prerequisite Skills Package Decimals (p. 1 - 2) Integers (p. 3 - 4)

RV-2

Review Order of Operations - Substitution - Roll Up GameHomework: Prerequisite Skills Package Order of Operations (p. 5) Substitution (p. 6)

RV-3

Review Fractions, Rate, Ratio and ProportionHomework: Prerequisite Skills Package Fractions (p. 7 - 8) Rate, Ratio and Proportion (p. 9 – 10)

RV-4

Review Measurement and Geometry - Area, Parallel Line Transversal Theorem, Opposite Angles, Complementary Angles, Supplementary Angles Homework: Prerequisite Skills Package Area (p. 11) Geometry (p. 12)Review Quiz

Unit 1: Polynomials and EquationsOverall

ExpectationLesson Number

Topic and Homework

Textbook DistributionNSA1 P&E-1 Terminology; Add and Subtract Like Terms and Polynomials

**add and subtract with up to two variables (gr. 9)****add and subtract with more than two variables (gr. 10)** HOMEWORK:Text: p. 134 # 1,3,5,6 p. 152 # 8, 9, 11 p. 157 # 5, 6ab, 9

NSA1 P&E-2 Multiplying Polynomials- distributive property, polynomial monomial (involving same variable)

(gr. 9)- polynomial monomial (involving different variables) , binomial

binomial (gr. 10)- expand and simplify polynomial expressions (gr. 9 & gr. 10)

HOMEWORK:Multiplication:Text: p. 166 # 7ac, 8ac, 9ac, 13ab, 16ac, 18, 19, 20Homework Sheet P&E-2 Multiplying Polynomials

NSA1 P&E-3 Division by a Monomial- division by a monomial (gr. 10)

HOMEWORK:Division:Homework Sheet P&E-3 Dividing Polynomials

Evaluation on NSA1

NSA2 P&E-4 Solving Equations - solve simple equations- solve multi-step equations (include solving with variables on both sides,

solving with brackets)- Checks- (all gr. 9)

HOMEWORK:Text: p. 193 # 3, 5, 9, 16 p. 200 # 1,4 – 7

NSA2 P&E-5 Solving Equations (with fractions)

HOMEWORK:Text: p. 208 # 1, 3, 4, 5, 6, 9, 10c, 11

NSA2 P&E-6 Solving Inequalities- solve in real numbers and in integers (gr. 10)

HOMEWORK:Homework Sheet P&6 Solving Inequalities

NSA2 P&E-7 Formulas: Isolating Variables**(gr. 9)**** more difficult questions are gr. 10**

HOMEWORK:Text: p. 215 # 2, 3(Solving word problem questions: pg. 227 # 6, 7, 9, 10, 13a)Homework Sheet P&7 Isolating Variables in Formulas

Evaluation on NSA2

***Start Measurement Independent Study soon!!!***

Unit 2: Exponents and Radicals

Overall Expectation

Lesson Number

Topic and Homework

NSA3 E&R-1 Powers of Ten and Scientific Notation- Definitions (base, power, exponent, expanded form)- Powers of ten (positive exponents: gr. 9, negative exponents: gr. 10)- Scientific notation (gr. 9)

HOMEWORK:Homework Sheet E&R-1 Powers of Ten and Scientific Notation

NSA3 E&R-2 Zero and Negative Exponents**(gr. 10)**

HOMEWORK:Homework Sheet E&R-2 Zero and Negative Exponents

NSA3 E&R-3 Multiplication and Division of Powers**involving one and two variables with positive exponents ( gr. 9)****involving more than two variables and negative exponents (gr. 10)**

HOMEWORK:Text: p. 127 # 2, 4, 7ab, 8abcegh, 9ad, 15

NSA3 E&R-4 Power of a Power

HOMEWORK:Homework Sheet E&R-4 Power or a Power

NSA3 E&R-5 Applications of Powers- Exponential growth, decay, half-life (old gr. 9)

HOMEWORK:Homework Sheet E&R-5 Application of Powers

NSA3 E&R-6 Radicals- Square roots as an exponent ½- Cubic root, etc.- All gr. 10

HOMEWORK:Homework Sheet E&R-6 Radicals

NSA3 E&R-7 Mixed and Entire Radicals- Entire radicals mixed radicals (gr. 10)- Pythagorean theorem (gr. 9)

HOMEWORK:Homework Sheet E&R-7 Mixed and Entire Radicals

Overall Expectation

Lesson Number

Topic and Homework

NSA3 E&R-8 Simplifying Radical Expressions- Add, subtract, multiply and divide radical expressions

HOMEWORK:Homework Sheet E&R-8 Radical Expressions Review

Evaluation NSA3

***This ISU unit should be done before Christmas break***

Unit 3: 2D & 3D Measurement & Optimizing Measurements(Independent Study)

Overall Expectations

Number of Periods

Topic and TENTATIVE Homework/Assignment

TENTATIVE due dates

MG2 1 Independent Study – 2D & 3D Measurement

- Hand out formula sheets and booklets

- Explain independent - Discuss FORM - (gr. 9)

ASSIGNMENT:Complete the independent study booklet

Part 1 due: in two weeks

Part 2 due: two weeks after part 1 was due

Part 3 due: two weeks after part 2 was due

MG1 2 Independent Study – Optimizing Measurements

- Place students in groups and have them complete the investigations

- Summarize all the conclusions with students

ASSIGNMENT:p. 488 # 3, 5, 8 p. 495 # 4, 5, 7p. 502 # 2a, 5, 7 p. 508 # 3, 4, 6p. 513 # 4, 5, 6

All due: in one or two weeks

** use a 2 day in-class investigation for optimization to allow for all investigations to be carried out by all students**

1Evaluation on MG1 & MG2

Unit 4: Linear and Non-linear Relations

Overall Expectation

Lesson Number

Topic and Homework

LR1 LR-1

Distance vs Time Graphs- CBR activity- Interpretation of graphs (gr. 9)

HOMEWORK:Text: p. 91 #C1, 1, 3, 4, 5, 7

LR3 LR-2

Slope- Vocabulary (rise, run, steepness)- Formula (gr. 9)- Positive, negative, zero, undefined slope (gr. 9)- Find k (gr. 10)

HOMEWORK:Text: p. 259 #5, 9, 12a, 13

LR2 LR-3

Graphing Lines using a Table of Values- Gr. 9

HOMEWORK: Homework Sheet LR-3 Graphing Using a Table of Values

LR2 LR 4

Linear Equations Investigation- Investigation to graph lines using DESMOS with sliders for m and b

HOMEWORK:Summarize Investigation

LR2 LR-5

Graphing Lines using Slope and y-intercept & x-y-intercepts- Gr. 9

HOMEWORK:Text: p. 320 #3-6, 9, 11

LR2 LR-6

Graphing Lines with Restrictions using Technology- Domain and range- Graph lines with restrictions by hand and using DESMOS or graphing

calculator

HOMEWORK: Homework Sheet LR-6 Graphing Lines With Restrictions Optional: Linear Relations Art

Evaluation on LR1 and LR2

LR3 LR-7

Equation of Line in Slope y-intercept form- Include vertical and horizontal lines

HOMEWORK:Text: p. 303 #C1

p. 304 #1-4, 7, 10

LR3 LR-8

Parallel and Perpendicular Lines- Investigation Gr. 9

HOMEWORK:Text: p. 328 #3-7, 9

LR3 LR-9

Finding the Equation of a Line I- Find the equation given slope and a point, parallel to/perpendicular to

and a point, two pointsHOMEWORK:Text: p. 335 #1, 2 p. 342 #1-4

LR3 LR-10

Finding the Equation of a Line II- Find the equation of a line using slope y = mx + b (gr. 9); using point

slope form y – y1 = m(x – x1) (gr. 10)- Writing final answers in standard form Ax + By + C = 0 (gr. 10)

HOMEWORK:Text: p. 336 #5, 6Homework Sheet LR-10 Finding the Equation of a Line

LR4 LR-11

Graphing Applications I- Use words, table of values, graphs, equations

HOMEWORK:Text: p. 64 #1 p. 85 #6abcp. 73 #2-4 (for each determine if relationship is linear/nonlinear, draw the line or curve of best fit, state if you interpolated or extrapolated to predict, and determine if data is discrete or continuous)

LR4 LR-12

Graphing Applications II- Identify independent/dependent variable- Scatter plot, lines/curves of best fit- Discrete or continuous data- Describe trend/relationship, interpret slope, y-intercept- Find values by interpolating/extrapolating, using equation or table- Direct/partial variation

HOMEWORK:Text: p. 242 #C1, 1, 2, 5 p. 250 #C1, 1, 3, 5, 6

LR2 LR-13

Nonlinear Relations and Finite Differences- Exponential, radical, cubic using a table of values- State domain and range (gr. 10)- First differences (gr. 9) and second differences (gr. 10)

HOMEWORK:Text: p. 275 #1, 2 (also determine if its quadratic), 4, 5

Evaluation on LR3 and LR4

***Start Trigonometry Independent Study soon!!!***

Unit 5: Linear SystemsOverall

ExpectationLesson

NumberTopic and Homework

AG1 LS-1 Solving Linear System by Graphing- Review graphing (table of values, m & b, intercepts, calculator)- Checks- (gr. 9)

USE OF GRAPHING CALCULATORS

HOMEWORK:Text: p. 348 # 1, 2, 7, 9 Homework Sheet LS-1 Solve Linear System by Graphing

AG1 LS-2 Solving Systems: Method of Substitution- include brackets, fractions, decimals- (gr. 10)

HOMEWORK:Homework Sheet LS-2 Solve Linear Systems – Substitution Method

AG1 LS-3 Solving Systems: Method of Elimination- include brackets, fractions, decimals- (gr. 10)

HOMEWORK:Homework Sheet LS-3 Solve Linear Systems – Elimination Method

AG1 LS-4 LS-5

Word Problems- Numbers (age), quantity, money (coin), percentage, distance- (gr. 10)

HOMEWORK:Homework Sheet LS-4/5 Application ProblemsReview

Evaluation on AG1

Unit 6: Trigonometry (Independent Study)

Overall Expectation

Number of Periods

Topic and Homework Due dates

TG1&TG2 1 Independent Study – Trigonometry (gr. 10)- Hand out the booklets- Explain the independent study (make own

notes, do the homework, due dates, will be marked, etc.)

- Start writing the note for part 1 as a class

HOMEWORK:Complete the independent study booklet

Part 1 due: in two weeksParts 2 & 3 due: two weeks after part 1 was duePart 4 due: one week after parts 2 & 3 were due

1 Evaluation on TG1 & TG2 One week after part 4 due

Unit 7: Euclidean Geometry

*** All homework assigned from: “Euclidean Geometry Homework Package” ***Overall

ExpectationsLesson

NumberTopic and Homework

MG3 EG-0

(2 periods)

Geogabra – in the Computer Lab (or students may bring in their laptops) Students will have 2 periods to work in class to:

i) Learn about GEOGEBRA by working through the labsii) Investigate properties:

Angle Properties (OAT/CA/SA/CAT/SAT) Triangles: (Altitude, Angle Properties [SATT, ETT, ITT, EAT], Median, Perpendicular Bisectors, Angle Bisectors) Angle Properties of Quadrilaterals, Polygons Parallel Lines (PLT- F, C, Z) Angles of a Circle Cyclic Quadrilaterals * Consider collecting part of the labs for completion *

MG3 EG-1 Angle Properties- Definitions- OAT, CA, SA, CAT, SAT- (gr. 9)

HOMEWORK:Homework Sheet EG-1 Angle Properties

MG3 EG-2 Parallel Lines- PLT-Z, PLT-F, PLT-C- (gr. 8)

HOMEWORK:Homework Sheet EG-2 Parallel Lines

MG3 EG-3 Angle Relationships in Triangles- SATT, EAT, ETT, ITT- (gr. 9)

HOMEWORK:Homework Sheet EG-3 Angles, Parallel Lines and Triangles

AG5 EG-4 Triangle Centres- Altitude (orthocentre), median (centroid), perpendicular

bisector (circumcentre), angle bisector (incentre)- Midpoints and medians (gr. 9); everything else (gr. 10)

HOMEWORK:Homework Sheet EG-4 Triangle Centres

Overall Expectations

Lesson Number

Topic and Homework

MG3 EG-5 Angles in Quadrilaterals and Polygons- Angle relationships (interior and exterior) in all

quadrilaterals - Interior angle relationships in parallelograms - Polygon angle properties: Sum of exterior angles, sum of

interior angles with n sides - (gr. 9)

HOMEWORK:Text: p. 381 # 1 – 3, 5, 7, 13 p. 391 # 1 – 3 Homework Sheet EG-5 Angles in Quadrilaterals and Polygons

MG3 EG-6 Polygon Properties- Midsegments: Quadrilateral, triangle - Diagonals: Parallelogram, square, rhombus, rectangle, kite - (gr. 9)

HOMEWORK:Text: p. 398 # 1, 4 p. 405 # 1 – 4Homework Sheet EG-6 Polygon Properties

MG3 EG-7 Angles of Circles and Cyclic Quadrilaterals **(gr. 10)**

HOMEWORK:Homework Sheet EG-7 Angles of Circles and Cyclic Quadrilaterals Review

Evaluation on MG3

Unit 8: Analytic GeometryOverall

ExpectationsLesson

NumberTopic and Homework

AG2 AG-1 Length of a Line Segment and Midpoint- Derive length of a line segment formula from Pythagorean

Theorem (gr. 10)- Midpoint formula; include word problems (gr. 10)

HOMEWORK:Homework Sheet AG-1 Length of a Line Segment Midpoint Formula t

AG2 AG-2 Equation of a Circle with Centre (0,0)- Deduce equation of a circle formula from length of a line

segment (gr. 10)

HOMEWORK:Homework Sheet AG-2 Equations of Circles

AG2 AG-3 Properties of Triangles and Quadrilaterals - Find equations of medians, right bisectors, altitude (gr. 10)

HOMEWORK:Homework Sheet AG-3 Properties of Triangles and Quadrilaterals

Evaluation on AG2

AG2 AG-4 Finding the Circumcentre and Centroid

HOMEWORK:Homework Sheet AG-4 Finding the Circumcentre and Centroid

AG3 AG-5 Distance from a Point to a Line

HOMEWORK:Homework Sheet AG-5 Distance from a Point to a Line

Evaluation on AG3