Grade 10 Academic Math – Course Outline

 

 

Unit 1:  Linear Systems

Unit 2:  Analytic Geometry

 

Unit 3:  Algebra & Quadratic Functions

Unit 4:  Quadratic Functions & Equations

 

Unit 5:  Trigonometry

 

Teacher Note:  Any topic listed as review, is previous knowledge and should not be evaluated.

 

 

Unit 1

Topic

Work

1.1

Feb 5

Mon

1st Day of Classes

Introductions- Ice Breakers

 

Review:  Number Sets

Review:  Integers and order of operations

Review:  Rational Numbers

Course pack Link

Handout, “Order of Operations”, “Evaluating Expressions”, “Adding and Subtracting rational numbers”, “Multiplying Rational numbers”, “Dividing Rational numbers”

 

Do every other question (Left side)

1.2

Tue Feb 6

Review:  Algebraic Expressions

Review:  Solving Linear Equations

 

 

 

P22 #1—3 (all); 4—7 (odd)

Review Solving Equations (odd questions only)

 

 

1.3

Feb 7

Wed

Review:  Linear Relations

Review:  Slope; equation of a line

Review Slope and Linear Relations (CP)

Review Linear Relations (odd questions only)

1.4

Feb 8

Thu

Review:  Linear Relationships- Graphing using 3 methods

Review:  Scatter Plots

P26 #1odd, 2ac, 4odd, 5odd, 6

P30 #1

P28 #1,4

1.5

Feb 9

Fri

Review:  Solving Systems of equations by graphing

Determine Number of Solutions of a Linear System

Convergence of two lines: parallel, intersect and congruent(by graphing)

Determining Points of Intersection Graphically

P60 #4,5, 7, 9,18

1.6

Feb 12

Mon

Solving Systems of equations by substitution and comparison

Solving Systems by Substitution

 

1.7

Feb 13

Tue

Practice solving Systems of equations by comparison

 

P92 #1ac, 2ac, 4ac, 5, 7ace, 8ace

P93 #9—11, 21

1.8

Feb 14

Wed

Solving Systems of equations by elimination – Day 1

 

Introduction to Elimination(CP)

Solving Systems by Elimination

 

P102 #6

1.9

Feb 15

Thu

Solving Systems of equations by elimination – Day 2

(Quiz – solving linear systems by graphing, substitution and verifying)

P102   #7—10, 22, 24

Hardcore #25

1.10

Feb 16

Fri

Creating a System of Equations

P51 #7-13, 20 (Do not solve)

Treasure Hunt

1.11

Feb 20

Tue

Solving word problems I (Number, Geometry, Money and Age Problems)

Solving word problems 1

P51 #7, 8, 9, 11, 13, 20 (Solve)

P62 #15

P93 #13, 17

P103 #14, 18

1.12

Feb 21

Wed

Solving word problems II– speed and percentage

Solving word problems 2

 

P51 #12, 15, 18, 19, 21, 22, 24, 28

P93 #14, 25

P103  #15, 17

1.13

Feb 22

Thu

Quiz – Word Problems

Solving Word Problems – A Mixed Set

Solving Systems – Word Problems:  #1, 2, 9, 12, 13, 14, 17, 21, 22

1.14

Feb 23

Fri

Review for Test

Summary of Solving Systems

 

P51 #10, 14

P62 #14, 16

P71 #13

P83 #8, 12

P94 #18

1.15

Feb 26

Mon

More Review

P121 #3

P125 #13

P128 #16c, 17—20

P131 #21c, 22—25

MATHO

1.16 Feb 27

Tue

Test 1 – Linear Systems

 

 

 


 

 

 

 

Unit 2

Topic

Teacher Note:  We will limit triangle centres to drawing them, except Centroid, which we will find algebraically. 

Finding Centroid algebraically(given definition) would then be an appropriate Application question for the test.  Finding any other centre algebraically (given definition) would be an appropriate Problem Solving question for the test.

Work

2.1

Feb 28

Properties of Triangles

Properties of Quadrilaterals

P34#1-4

P37 #1-4,7

P39#4,6gh

2.2

Mar 1

Distance on the plane I (distance to the origin) 

Distance on the plane II (distance between two points)

 

 

P151 #2, 3, 6—11, 14

P162     #2(a-f), 3, 4, 5, 8, 11

2.3

Mar 2

Midpoint of a Line Segment

P173 #2acegh, 4, 5, 8, 12, 13

2.4

Mar 5

The Equation of a Circle,

Note:  Only circles centred at the origin

 

Addtional Topic:  Circles centred at (h,k)

                         

 

P155 #1, 2, 4, 5, 9, 11, 12, 15

Applications of the Equation of a Circle

2.5

Mar 6

The Equation of a Circle

Handout Equations of circles

2.6

Mar 7

Quiz

Introducing:

- interior angles and exterior angles

- medians vs altitudes

- perpendicular bisectors vs angle bisectors

 - centroid, orthocentre, circumcentre, incentre

optional P31 #1, 2, 4, 5

 

Triangle Centres

 

P34 #1—8

2.7

Mar 8

 

Medians and Centroid

Extra practice #1a-d

2.8

Mar 9

Perpendicular Bisectors and Circumcentre

Extra practice #1a-d

 

March Break

 

 

2.9

Mar 19

Altitudes and Orthocentre

Extra practice #1a-d

2.10

Mar 20

Work Period

Cartesian Triangles a Summary

P174 #14,15,19

P194 #1,3,4,6,8,10,12-14,16-18

2.11

Mar 21

 Quiz- Terminology and Medians, Perpendicular Bisectors and Altitudes.

P196 #20, 22

2.12

Mar 22

Classifying Shapes on the Plane

P182 #3—10

2.13

Mar 23

Classifying Shapes on the Plane II

(one must get a lot of work done in class!)

P183 #17a, 18

 

Properties of Geometric Figures

2.14

Mar 26

Verifying Geometric Properties  

P203 #3—7, 10, 11

2.15

Mar 27

Review for Test 2

 

Chapter 2 review

(no answers for Part 1; check with your neighbour in class)

 

Optional review:

P209 #7—23

2.16

Mar 28

Test 2 – Analytic Geometry

Click here for learning goals checklist

 


 

 

 

 

 

Unit 3

Topic

Work

Mar 29

Review:  Exponent Laws

 

 

Exponent Laws

Exponent Laws 1  (odd letters)

Exponent Laws 2  (odd letters)

3.1

Apr 3

More Exponent Laws

-      Use patterning to discuss zero and negative exponents

 

 

Appendix:  More Exponent Laws (Hardcore!!)

Exponent Laws 3  (odd letters)

 

P228 #6—9

 

3.2

Apr 4

Using Zeros

Review expanding polynomials (grade 9 review)

Binomial Products (in one step!)

 

Appendix: Binomial Products

Expand and collect (odd #s)

Multiplying Binomials

 

P280 #1—5, 7odd

 

3.3

Apr 5

Common factoring and Factoring by Grouping

Common Factors

Factor by Grouping

3.4

Apr 6

Factoring simple trinomials,

Factoring Simple Trinomials

3.5 Apr 9

Factoring difficult trinomials,

Factoring Difficult Trinomials

 

Apr 10

Literacy Test- No classes

 

3.6  Apr 11

Factoring a difference of squares and perfect squares

Two Factoring Patterns (CP)

 

Factoring everything mixed together

(common factoring; simple trinomials; difficult trinomials; mixed; not factorable!)

Difference of Perfect Squares #1—4 (odd letters)

Factoring

3.7

Apr 12

Summarize ALL Factoring!

More mixed factoring (not factorable)

 

(Quiz – Factoring)

Some Mixed Factoring

Mixed Factoring

 

P307 #2—7(odd)

 

Optional: Factor Like a Pro (odd #s)

3.9

Apr 13

Solving Quadratic Equations By Factoring

Solving Quadratic Equations

Solving Quadratics by Factoring

 

P309 #17

P315 #1—3 (odd), 5—7

3.10

Apr 16

Finite Differences – Day 1

(to determine linear, quadratic, including y=2x)

 

Finite Differences Investigation (CP)

 

P254 #2, 4, 13, 14

Finite differences

3.11

Apr 17

Introduction to Quadratic Relationships

(sketching from table of values)

vocab: vertex, zeros and axis of symmetry

Introduction to Quadratic Relationships – Page 1 and 2 only

Introduction to Quadratic Relationships – Page 3 and 4

P257 #6, 12, 16

3.12


Apr 18

Quadratic equations and functions

(Check your graphs using software.)

Explain that the equation y=x2 is a quadratic

Quadratic Relations and Equations

 

P308 #8

Graphing Quadratics by Factoring

3.13

Apr 19

Factored Form for a Quadratic Equation

- Graph and write the equation in factored form

- including fractions

- Sub a point to find the a-value

 

Factored Form (CP)

Pg 266 #1, 3-5, 7,9

3.14

Apr 20

Problems involving Quadratics – Day 1

(height; area; $; others)

 

Quiz

Height Problems

Quadratic Problems Examples

Quadratic Word Problems 

 

3.15

Apr 23

Problems involving Quadratics – Day 2

P308 #9, 11—13

P316 #4, 10, 12ab, 13a, 18 (#18 is not factorable)

3.16 Apr 24

Writing the equation given graph and word problems

P282 #6, 8—13, 22

3.17

Apr 25

Review for Test 3

Review Algebra

P326 #4odd, 5-7, 9odd, 10a)

3.18

Apr 26

Review for test 3

P326  11odd, 13, 14odd, 15—17, 19, 20

P228 #4,5

3.19  Apr 27

Test 3 – Quadratic Equations

 


 

 

 

 

 

 

Unit 4

Topic

Work

Expectations

4.2

Apr 30

The Quadratic Function – Day 1

(Using Desmos or Graphing calculator?)

 

The Quadratic Function 

1 B(i)

1 B(ii)

4.3

May 1

The Quadratic Function – Day 2

 (Using Desmos or Graphing calculator?)

The Quadratic Function II

Graphing - graph by hand; no computer

Transformations of

1 B(i)

1 B(ii)

1 B(iii)

1 B(iv)

4.4

May 2

Completing The Square

Key Ideas P360

Perfect Square Trinomials

Completing the Square I

 

P390 #1, 2, 4, 5, 6

1 C(v)

4.5

May 3

Completing The Square II

 

 

Completing The Square II #5

Completing the Square III

 

P391 #8, 9

1 C(v)

4.6

May 7

Converting Quadratic Forms (CP)

Practice completing the square

CP131 Converting Quadratic Forms

P351 #1, 2, 5—10

1 C(v)

4.7

May 8

The Quadratic Function III

 

(Quiz – vertex form & completing the square)

Graphing Quadratics (odd #s)

P352 #11, 12, 14, 20

 

 

1 C(vi)

4.8

May 9

Solving quadratics by completing the square and factoring

Solving Quadratics by Factoring

Solving Quadratics by Completing the Square

1 C(viii)

4.9

May 10

The Quadratic Formula

Development of the Quadratic Formula (CP)

 

The Quadratic Formula

Solving Quadratics using the Quadratic Formula

 

P403 #4, 6, 12

1 C(vii)

1 C(viii)

4.10

May 11

The Quadratic Formula II

-      Using the Discriminant

Intercepts and roots (CP)

P403  #3, 5, 8, 9, 11, 14, 17, 20, 24

-      Discuss question 11 with class

 

1 C(iv)

4.11

May 14

Solving Quadratic Problems

Use Text P282 #6 as an intro

Quadratic Functions & Equations

 

P404 #13, 15, 16, 18, 19, 21, 22, 25

1 C(viii)

1 D(ii)

4.12

May 15

Optimization problems – Day 1

Max/Max Statements

Steps for Solving Min/Max Problems

Optimization Problems #1—3

 

P355 #21

P391 #11—14

1 D(i)

1 D(ii)

4.13

May 16

Optimization problems II – Day 2

 

 

Appendix:  Maximize Revenue and Profit (odds)

Optimization Problems #4—7

 

P355 #22

P391 #15 – 18, 20, 23

1 D(i)

1 D(ii)

4.14

May 17

Review Quadratic Functions – Day 1

Review Quadratic Functions

 

P404 #12, 23, 26

 

4.15

May 18

Review Quadratic Functions II – Day 2

Practice Test P429 

Optional review section P418—428

 

May 22

Test 4 – Quadratic Functions

Review and Preview

 


 

 

 

 

 

 

Unit 5

Topic

Work

Expectations

5.2

May 23

Investigating and Comparing triangles

Similar Triangles (CP)

P461 #4ab, 5cd, 6 – 10

3 A(i)

3 A(ii)

5.3

May 24

Investigating & Comparing Triangles

Congruent and Similar Triangles (CP)

 

Appendix:  Unique Triangles

Similar Triangles Practise

 

P475 #6 – 13, 15

3 A(iii)

5.4

May 25

Introduction to Trigonometry (in class)

Investigation – Developing Primary Trig Ratios (CP)

Trig Ratios and Right Triangles 

 

P496 #6, 8a – d, 10

3 B(i)

3 B(ii)

5.5

May 28

Using Trigonometry (SOH – CAH – TOA)

 

Appendix:  Trigonometry Ratios

Using Trig Ratios

 

P496 #3—5, 9 – 11, 17

3 B(ii)

5.6

May 29

Solving Right Triangles

Solving Right Triangles 

 

P500 #26

3 B(ii)

5.7

May 30

Applications of Trigonometry

Teach angles of elevation and depression

(Quiz)

Appendix:  Applications of Trigonometry

P498 #14, 15, 20, 23

P500 #27, 28, 30

3 B(iii)

5.8

May 31

Angles of Elevation & Angles of depression

Angles of elevation and depression

A Few More Trig Problems

3 B(iii)

5.9 June 1

Review

Right Angle Trig Review

 

P516 #2ab

P518 #3 – 5

P526 #4, 6, 7

 

5.10

June 4

OPTIONAL RIGHT ANGLE TRIG TEST

Carnival Day

 

5.11

June 5

The Sine Law – Day 1

 

Trig and Non-Right Triangles (CP)

Proving Sine Law (CP)

The Law of Sines  #1, 2  

 

P549 #1—4, 6—8

3 C(i)

5.12

June 6

The Sine Law – Day 2

Just for Fun…(Cayley questions)

The Law of Sines  #3—5

 

P550 #10, 15

P555 #1, 5, 9, 12

3 C(iii)

3 C(iv)

5.13

June 7

Introduction to the Law of Cosines

 

Proving Cosine Law (CP)

The Cosine Law #1ab, 2ab, 3

 

P566 #2, 4, 5

3 C(ii)

3 C(iii)

5.14

June 8

The Law of Cosines – Day 2

 

(Quiz – basic trig)

P567 #3, 6 – 10, 14

3 C(iii)

3 C(iv)

5.15

June 11

Solving Any Triangles – Day 1

Focus on efficiency & accuracy

Solving Triangles Inventory

 

P568 #13, 25 (clocks) 

P568 #15, 16, 19, 27 (bearings) 

P568 #26

3 C(iii)

3 C(iv)

5.16

June 12

Solving Any Triangles – Day 2

Just for Fun:  Triangle Inequality

Clocks & Bearing word problems

(P568 #25’s answer is WRONG and in the worst way.)

 

Appendix:  Triangle Inequality

* the homework is light because you are to revisit the difficult homework from yesterday

 

Problems Involving the Laws of Sines and Cosines

Trig Word Problems #1, 5, 8, 11

3 C(iv)

Review 1

June 13

Review of Trigonometry

P586 Practice Test

 

Review 2

June 14

Exam review I & II, Trigonometry

P587—588 Cumulative Review

Optional CP169—170 Trigonometry Review

 

Review 3

June 15

Exam review III & IV, Analytic Geometry

Final Exam Review (8 pages)

 

June 18

Exam review V & VI, Quadratics

 

 

June 19

Exam review