Unit 1 – Rational Expressions and Operations (P&P 11)



COLONEL BY SECONDARY SCHOOL 2017-2018

MPM 1DE COURSE OUTLINE

|Unit Number |Unit Name |Number of Periods |

|0 |Introduction; Diagnostic test; Review |6 |

|1 |Polynomials and Equations |9 |

|2 |Exponents and Radicals |10 |

|3 |2D/3D Geometry & Optimizing Measurements (ISU1) |4 |

|4 |Linear and Non-linear Relations |15 |

|5 |Linear Systems |7 |

|6 |Trigonometry (ISU2) |2 |

|7 |Euclidean Geometry |11 |

|8 |Analytic Geometry |7 |

| |Preparation for EQAO |4 |

| |EQAO |2 |

| |Exam Review |4 |

Total: 81

Textbooks:

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, geometric

properties 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 Review

|Overall Expectation |Lesson Number |Topic and Homework |

| | |Introduction to the Course: |

| | |Diagnostic Test, Student Profile |

|Prerequisite |RV-1 |Review |

|Skills: Review of | |Number Systems (N,W,Z,[pic], [pic], R), Decimals & Integers |

|Number Sense, | |Homework: Prerequisite Skills Package |

|Numeracy | |Decimals (p. 1 - 2) Integers (p. 3 - 4) |

|and Geometry | | |

| |RV-2 |Review |

| | |Order of Operations - Substitution - Roll Up Game |

| | |Homework: Prerequisite Skills Package |

| | |Order of Operations (p. 5) Substitution (p. 6) |

| |RV-3 |Review |

| | |Fractions, Rate, Ratio and Proportion |

| | |Homework: 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 Equations

|Overall Expectation |Lesson Number |Topic and Homework |

| | |Textbook Distribution |

|NSA1 |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 [pic] monomial (involving same variable) (gr. 9) |

| | |polynomial [pic] monomial (involving different variables) , binomial [pic] binomial (gr. 10) |

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

| | | |

| | |HOMEWORK: |

| | |Multiplication: |

| | |Text: p. 166 # 7ac, 8ac, 9ac, 13ab, 16ac, 18, 19, 20 |

| | |Homework 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 [pic] 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 |Part 1 due: in two weeks |

| | |Hand out formula sheets and booklets | |

| | |Explain independent |Part 2 due: two weeks after part 1 was due |

| | |Discuss FORM | |

| | |(gr. 9) |Part 3 due: two weeks after part 2 was due |

| | | | |

| | |ASSIGNMENT: | |

| | |Complete the independent study booklet | |

|MG1 |2 |Independent Study – Optimizing Measurements |All due: in one or two weeks |

| | |Place students in groups and have them complete the | |

| | |investigations |** use a 2 day in-class investigation for optimization |

| | |Summarize all the conclusions with students |to allow for all investigations to be carried out by |

| | | |all students** |

| | |ASSIGNMENT: | |

| | |p. 488 # 3, 5, 8 p. 495 # 4, 5, 7 | |

| | |p. 502 # 2a, 5, 7 p. 508 # 3, 4, 6 | |

| | |p. 513 # 4, 5, 6 | |

| |1 | | |

| | |Evaluation 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 points |

| | |HOMEWORK: |

| | |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, 6 |

| | |Homework 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 #6abc |

| | |p. 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 Systems

|Overall Expectation |Lesson Number |Topic 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 |Word Problems |

| |LS-5 |Numbers (age), quantity, money (coin), percentage, distance |

| | |(gr. 10) |

| | | |

| | |HOMEWORK: |

| | |Homework Sheet LS-4/5 Application Problems |

| | |Review |

| | | |

| | |Evaluation on AG1 |

Unit 6: Trigonometry (Independent Study)

|Overall Expectation |Number of |Topic and Homework |Due dates |

| |Periods | | |

|TG1&TG2 |1 |Independent Study – Trigonometry (gr. 10) |Part 1 due: in two weeks |

| | |Hand out the booklets |Parts 2 & 3 due: two weeks after part 1 |

| | |Explain the independent study (make own notes, do the homework, due dates,|was due |

| | |will be marked, etc.) |Part 4 due: one week after parts 2 & 3 |

| | |Start writing the note for part 1 as a class |were due |

| | | | |

| | |HOMEWORK: | |

| | |Complete the independent study booklet | |

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

Unit 7: Euclidean Geometry

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

|Overall Expectations |Lesson Number |Topic and Homework |

|MG3 |EG-0 |Geogabra – in the Computer Lab (or students may bring in their laptops) |

| | |Students will have 2 periods to work in class to: |

| |(2 periods) |Learn about GEOGEBRA by working through the labs |

| | |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 – 4 |

| | |Homework 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 Geometry

|Overall Expectations |Lesson Number |Topic 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 |

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