Grade 10 Academic Course Outline - Revised Sept. 2014. Unit 1: Linear Systems ( 15 days )

EXPECTATIONS TOPICS METHODOLOGY TEXT INFORMATION

1 Communication Activity Activities in pairs Overhead diagrams Or Preparedness formative Quiz

Activity and Communication Journal

2 E1. Solve problems that arise from realistic situations described in words or represented by linear systems of two equations involving two variables, by choosing an appropriate algebraic or graphical method

Modelling Real Life Problems - Review of Linear Equations and Independent/Dependent Variables

Investigation Part #1 Answer questions #1-7 Mini-Lesson on Ind/dep

P.50 #1ac,2c,4abdf

3 E1 Review Graphing Linear Equations (This is not a ministry expectation. But it is important enough to review)

Review: Slope & y-intercept and then Investigation P.10-13.

P.5 #5ad,6ad,7ad,8cd

4 E2. Solve systems of two linear equations involving two variables, using the algebraic method of substitution or elimination

Solving Systems of Equations using Substitution

Socratic Lesson overheads: P.20 -23 P. 26 #1ab,2ab,3,4ab,5a,12,13

5 E2 Solving Systems of Equations using Elimination (simple form)

Socratic Lesson overheads: p. 34-35 P.40 #1a,2b,3a,4a,5ad,7b,10,19b

6 E2 Solving Systems of Equations using Elimination (advanced form)

Socratic Lesson overheads P. 36-39

P.40 #12ac,13,18,20

7 E1 Translating English to Math "Who Wants to be a Mathematician?" (game)

Booklet: P.1 P.17 #1-3

8 E1 and E2 Word Problems*- Investments+Money

Socratic Lesson overhead Investment Booklet: P.2 #7 (set up only), P.46 #4

*Solve problems that arise from realistic situations described in words or represented by linear systems of two equations involving two variables by choosing an appropriate algebraic or graphical method

Money Booklet: P.3 #13 (set up only), P.27 #9,10,16

9 E1 and E2 Word Problems*- Mixture Socratic Lesson overhead P.47 #9,10,13,14 Booklet: P.3 #11,12

10 E1 and E2 Word Problems*- Distance Socratic Lesson overhead Booklet: P.3 #13,10 (set up only), P.2 #8,9 (set up only) P.46 #7,8

11 E1 and E2 Word Problems*- Overview Complete Booklet

12 Review (day 1) Worksheets P.48 #2,3,4ab,6,7,9b,10ab,12d,13,14,16, 17

13 Summative Quiz

14 Review (day 2)

Game (rally math) P.50 #1,3,4ac,5,6ac,7bd,8,11,12,13,15, 16ac,17,18,19

15 Test Day

Unit 2: Analytic Geometry ( 13 days )

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1 E4. Develop the formula for the length of a line segment, and use this formula to solve problems

Distance Formula Performance Task/Assessment: Helicopter Assignment

P.77 #1ac,2ac,4,5,6,10,12,19,25*

2 E5. Develop the equation for a circle with centre (0, 0) and radius r, by applying the formula for the length of a line segment E6. Determine the radius of a circle with centre (0, 0), given its equation; write the equation of a circle with centre (0, 0), given the radius; and sketch the circle, given the equation in the form x2 + y2 = r 2

Develop the Equation for a Circle with the centre of (0,0) and radius r by applying the length of a line formula

Activity- Full Service Socratic Lesson:

x2+y2=r2

P.96 #1acd,2ab,3ac,4ac,6,7

3 E3. Develop the formula for the midpoint of a line segment, and use this formula to solve problems

Develop the formula for the midpoint of a line segment and use it to solve problems

Define: Median and Perpendicular (Right) Bisector (Use glossary page 570

P.66: 1ac, 2ab, 5, 6, 12, 13, 22, 28ad

4 E4 Develop the formula for the length of a line segment and use this formula to solve problems (Part 1)

Lesson P.55 #5-8

5 E4 Develop the formula for the length of a line segment and use this formula to solve problems (Part 2)

Worksheet Worksheet

6 E7. Solve problems involving the slope, length, and midpoint of a line segment

Properties of a Line Segment

Performance Assessment

P.67 #8,16,17,19

7 E8. Determine, through investigation (e.g., using dynamic geometry software, by paper folding), some characteristics and properties of geometric figures

Triangle Properties Definitions: Types of Triangles: scalene, isosceles, equilateral,

Complete Investigation (Method #1 only) on page 80.

right angled, median, altitude, perpendicular bisector

P.89 #1-6,9,10,18,20,21

8 E8 Quadrilaterals Properties

Lesson P.124 #3,7,9 P.143 # 4, 7, 9, 12, 14

9 E9. Verify, using algebraic techniques and analytic geometry, some characteristics of geometric figures (e.g., verify that two lines are perpendicular, given the coordinates of two points on each line; verify, by determining side length, that a triangle is equilateral, given the coordinates of the vertices E10. Plan and implement a multi-step strategy that uses analytic geometry and algebraic techniques to verify a geometric property (e.g., given the coordinates of the vertices of a triangle, verify that the line segment joining the midpoints of two sides of the triangle is parallel to the third side and half its length, and check using dynamic geometry software; given the coordinates of the vertices of a rectangle, verify that the diagonals of the rectangle bisect each other

Verify Characteristics of Quadrilaterals, Triangles & Circle given Vertices

(Ex: Given coordinates of the vertices verify that the line segment joining the midpoints of two sides is parallel to the third side and what’s its length. Given coordinates of a rectangle, verify that the diagonals of the rectangle bisect each other)

P.126 #14ac P.152 #4,5,8 P.150 #5

10 Review P.100 #1- 5,6a,7af,8,9abc,10,11,12,13 (shortest distance is the perpendicular distance), 14,15ac,16,17,18 P.152 #1a,4,5,8,9a,10,11

11 Summative Quiz

12 Review P.104 #1-7,8abcd,9,10,11,12ab,14 P.154 #6,7a,8,12

13 Test Day

Unit 3A: Quadratics Factoring ( 9 days )

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1 E11. Expand and simplify second-degree polynomial expressions [e.g., (2x + 5)2, (2x – y)(x + 3y)], using a variety of tools (e.g., algebra tiles, diagrams, computer algebra systems, paper and pencil) and strategies (e.g., patterning)

Expand & Simplify second degree polynomial expressions

Algetiles P.217 #1, 2ab, 3ae, 4ab, 6adh, 7ab, 8bc, 10 P.225 #1a, 2ad, 3a, 6bd, 12

2 E12. Factor polynomial expressions involving common factors, trinomials, and differences of squares using a variety of tools and strategies

Common Factoring Socratic Lesson - Review

P.234 #1bf, 2a, 3afh, 4, 5ad, 7ad, 8, 10, 11, 14, 15a, 16

3 E12 Factor Simple Trinomials Algetiles P.240 #1a, 3ab, 4, 5, 7abef, 8a, 9ac, 11ab, 12, 15, 16ab

4 E12 Difference of Squares Perfect Square Trinomials

Socratic Lesson P.253 #1abcf, 2, 3abd, 4abd, 6ab, 8abd, 9ab, 10bc, 15, 20abc

5 E12 Complex Trinomials- Decomposition

Algetiles P.246 #2eoo, 3eoo, 4eoo, 6eoo, 7a, 11, 17a, 18a

6 Review Worksheets P.256 #1eoo,2eoo,3,7adf,8-12,13c,14- 16,18-22

7 Summative Quiz

8 Review Game P.258 #1-3, 5-16, 18

9 Unit 3A Test

Unit 3B: Zeros of Quadratics ( 10 days )

EXPECTATIONS TOPICS METHODOLOGY TEXT INFORMATION

1 Quadratic Relations Differences Between Linear and Non-Linear Graphing Linear and Non- Linear

2 E13. Determine, through investigation with and without the use of technology, that a quadratic relation of the form y = ax2 + bx + c (a ? 0) can be graphically represented as a parabola, and that the table of values yields a constant second difference.

Discovering First and Second Differences

Worksheet - Oil's Not Well

P.254 #2(ii) P.280 #1

3 E14. Determine, through investigation, and describe the connection between the factors of a quadratic expression and the x-intercepts of the graph of the corresponding quadratic relation, expressed in the form y = a(x – r)(x – s).

Solve Quadratics by Factoring (zeros)

Socratic Lesson P.279 #1adeg,2acfg,3abde,5abef, 6ac,7,9a,11,13,14,21bi*,ii

4 E15. Solve quadratic equations that have real roots, using a variety of methods (i.e., factoring, using the quadratic formula, graphing

Quadratic Formula Socratic Lesson P.300 #1bd, 2ac, 6, 9ade, 11, *21

5 E16. Interpret real and non-real roots of quadratic equations, through investigation using graphing technology, and relate the roots to the x-intercepts of the corresponding relations

Problem Solving

Discuss the Difference Between Real and Non-real Roots

Use Examples P.312 #1 and P.313 #2

P.312 #3,6,9,11,12,18

6 E17. Solve problems arising from a realistic situation represented by a graph or an equation of a quadratic relation, with and without the use of technology

Problem Solving Take-up Take up Full Solutions to the Homework Questions

P.313 #19,20,21,22,24,27a

7 Review Worksheets P.316 #4,5,6,10,11,13 P.318 #2,5,6,10,13,16b,17,18

8 Summative Quiz

9 Review P.320 #1,13,16,19,20 P.441 #34,35ac P.444 #56,57,59,60,62

10 Unit B Test (50 minutes) (includes expectations from unit 3A)

Unit 3C: Quadratics and Completing the Square ( 12/13 days * )

EXPECTATIONS TOPICS METHODOLOGY TEXT INFORMATION

1

E18. collect data that can be represented as a quadratic relation, from experiments using appropriate equipment and technology or from secondary sources; graph the data and draw a curve of best fit, if appropriate, with or without the use of technology

Quadratic Dental Model

2 E.19 Compare, through investigation using technology, the features of the graph of y = x2 and the graph of y = 2x, and determine the meaning of a negative exponent and of zero as an exponent E20. Identify, through investigation using technology, the effect on the graph of y = x2 of transformations

Transformations of a Quadratic: Part 1 Introduce/Review: vertex, equation of axis of symmetry, roots, directions of opening Discovery Worksheets

P.178 #1,3ab,4aceh,6,8,13

3 E21. Explain the roles of a, h, and k in y = a(x – h )2 + k, using the appropriate terminology to describe the transformations, and identify the vertex and the equation of the axis of symmetry.

Transformations of a Quadratic: Part 2 Discovery Worksheets P.178 #4adf,5d,7ab,12a

4 E22. Sketch by hand, the graph of y = a(x – h )2 + k by applying transformations to the graph of y = x2 E23. Determine the equation, in the form y = a(x – h)2

Graphing and Analyzing: y=a(x-h)2+k Socratic Lesson P.185 #1eoo, 3, 4, 6, 8, 10, 11

+ k, of a given graph of a parabola.

5 E24. Identify the key features of a graph of a parabola (i.e., the equation of the axis of symmetry, the coordinates of the vertex, the y-intercept, the zeros, and the maximum or minimum value), and use the appropriate terminology to describe them.

Maximum and Minimum Values of a Quadratic Relation

Sketch y=ax2+bx+c using a graphing calculator

Investigation - Graphing Calculators P.267-9 Do Practice 270:1-5ace (include sketch)

P.271 #9 (Include a sketch of the graphs and indicate the max and min points on each graph)

6 Using Zeros to Find the Vertex-Midvalue

Method & Sketch y=ax2+bx+c:

using x & y intercepts and

symmetry

Socratic Lesson Example #1 on P.284-5

P.289 #3,4,5ae,6b,7b P.288 #1,2 (Extra practice)

7 E25. Express y = ax2 + bx + c in the form y = a(x – h)2 + k by completing the square in situations involving no fractions, using a variety of tools

Completing the Square (no

fractions) (y=x2+bx+c): Part 1

Socratic Lesson P.270 #2adf, 3eoo,4bc,5,6

8 E26. sketch or graph a quadratic relation whose equation is given in the form y = ax2 + bx + c, using a variety of methods (e.g., sketching y = x2 – 2x – 8 using intercepts and symmetry; sketching y = 3x2 – 12x + 1 by completing the square and applying transformations; graphing h = –4.9t2 + 50t + 1.5 using technology) E27. Explore the algebraic development of the quadratic formula (e.g., given the algebraic development, connect the steps to a numerical example; follow a demonstration of the algebraic development

Completing the Square (y=ax2+bx+c); Part 2 Develop Quadratic Formula with students using completing the square (students are not responsible to prove the Quad. Formula)

Sketch y=ax2+bx+c using the method of completing the square

*Read "Did you know?" bottom of page 273

P.270#7,10,11eoo,17ab*,19ab*

9 E28. Determine the zeros and the maximum or Max/Min problems-Solve problems represented by a graph or a quadratic

P.271 #14,23,24, P.311 #2a,17abcd

minimum value of a quadratic relation from its graph (i.e., using graphing calculators or graphing software) or from its defining equation (i.e., by applying algebraic techniques) E29. Solve problems arising from a realistic situation represented by a graph or an equation of a quadratic relation, with and without the use of technology

equation with and without the use of technology

10 Review Worksheet P.316 #2ac,3a,7acdf,8,9,14

11 Summative Quiz

12 Review Game P.318 #1b,3,4ab,8,9,12,16

13 12 Test Day (includes expectations from units 3A & 3B)

Unit 4: Trigonometry ( 13 days )

EXPECTATIONS TOPICS METHODOLOGY TEXT INFORMATION

1 E30. Determine, through investigation, the relationship between the ratio of two sides in a right triangle and the ratio of the two corresponding sides in a similar right triangle, and define the sine, cosine, and tangent ratios.

Review:

1. Rates, Ratios & Proportion 2. 2. Angle Theorems 3. 3. Congruent/Similarity

Socratic Lesson P.326 #1, 3, 5 P.328 #9

2 E31. Verify, through investigation (e.g., using dynamic geometry software, concrete materials), the properties of similar triangles (e.g., given similar triangles, verify the equality of corresponding angles and the proportionality of corresponding sides); E32. Describe and compare the concepts of similarity and congruence

Comparing congruent & similar triangles Investigation P.336 (ruler and protractor required)

P.333 #1,2,4-8,13,16 Journal: Page 333 (top of page) C1a,b

3 E33. Solve problems involving similar triangles in realistic situations (e.g., shadows, reflections, scale models, surveying

Modeling Similar Triangles Socratic Lesson P.347 #1, 3, 5, 6,a,b,e, 9, 11, 14, *20

4 E34. Determine the measures of the sides and angles in right triangles, using the primary trigonometric ratios and the Pythagorean theorem

Trigonometric Ratios ( SOH CAH TOA) Socratic Lesson P.362 #1eoo, 3eoo P.372 #1eoo, 2eoo, 3ab, 4ab

5 E35. Solve problems involving the measures of sides and angles in right triangles in real life applications, using the primary trigonometric ratios and the Pythagorean theorem.

Solving Right Angled Triangles Using Trig ratios (SOH CAH TOA): Part 1

Socratic Lesson P.362 #4abc, 5ab, 6ab, 8, 10, 12, 15 P.372 #6ac, 7ac, 8a, 9a, 10a,f, 15, 16, 21, *29, *33

6 E35 Solving Right Angled Triangles Using Trig ratios (SOH CAH TOA): Part 2

Socratic Lesson P.374 #12 P.380 #5, 6, 11, 15

7 E30 and E35 Clinometer Performance Assessment

8 E36. Explore the development of the sine law within acute triangles (e.g., use dynamic geometry software to determine that the ratio of the side lengths equals the ratio of the sines of the opposite angles; follow the algebraic development of the sine law and identify the application of solving systems of equations E.38 determine the measures of sides and angles in acute triangles, using the sine law and the cosine law.

Sine Law Socratic Lesson P.402 #1a, 2a, 3a, 4a, 5a, 7a, 10, 11, 12, 20

9 E37. explore the development of the cosine law within acute triangles (e.g., use dynamic geometry software to verify the cosine law; follow the algebraic development of the cosine law and identify its relationship to the Pythagorean theorem and the cosine ratio

Cosine Law Socratic Lesson P.409 #1a, 2a, 3a, 4, 5a, 7, 8, 15, 16 P.418 #1a, 2a, 3a

10 E38. Solve problems involving the measures of sides and angles in acute triangles

Review P434 - 435 Socratic Lesson P.386 #1ab,2,3,5,6,8,9,10,11,14,15ac,16 ad,17,19,21ac,27,28,29 P.430 #1-12

11 Summative Quiz

12 Review

13 Test Day