Syllabus Plan 2014-15

Grade 9 Advanced Geometry Algebra 1

It is assumed that, when appropriate, graphing display calculators and other forms of technology will be used throughout this course.

In the Geometry section, a GSP5 activity from Exploring Geometry was studied almost every day; often being completed for homework.

Week 1: Introduction to School and course/Introduction to Geometry No Chapter in the book

1. Define Geometry

2. Understand the difference between a Theorem and a Postulate

3. Discuss Euclid and his contribution to Geometry

4. Discuss Euclid’s 5 Postulates

Weeks 2-4: Unit 1: Parallel and Perpendicular Lines Chapter 3

1. Define parallel and skew lines

2. Understand the parallel and perpendicular postulate

3. Identify a transversal

4. Identify corresponding, alternate exterior, alternate interior and consecutive interior angles

5. Use the properties of corresponding, alternate exterior, alternate interior and consecutive interior angles

6. Understand the properties of perpendicular lines

7. Understand the properties of parallel lines

8. Use the properties of parallel and perpendicular lines

9. Use the properties of parallel lines in the coordinate plane

10. Write equations of parallel and perpendicular lines Excludes 3.2 (proof and perpendicular lines)

Weeks 5-7: Unit 2: Triangles Mostly Chapter 4 and 5.1 (Perpendiuclars and Bisectors)

1. Classify a triangle based on its sides 2. Classify a triangle based on its angles

3. Identify interior and exterior parts of a triangle

4. Use the Triangle Sum Theorem

5. Use the Exterior Angle Theorem

6. Understand the concept of congruence in figures

7. Name congruent parts of congruent figures

8. Prove that two triangles are congruent using the Side, Side, Side Method

9. Prove that two triangles are congruent using the Side, Angle, Side Method

10. Prove that two triangles are congruent using the Angle, Side, Angle Method

11. Prove that two triangles are congruent using the Angle, Angle, Side Method

12. Solve problems using the properties of isosceles and equilateral and right triangles

13. Understand the concept of angle bisectors and perpendicular bisectors Excludes 4.7 (Triangles and Coordinate Proof)

Weeks 8-10: Unit 3: Quadrilaterals Chapter 6 (Completed sections 6.1 and 6.7 thoroughly. Sections 6.2, 6.3, 6.4, 6.5, 6.6 – done, but less questions practiced.)

1. Describe a polygon 2. Understand and identify a regular polygon 3. Know the sum of the interior angles of a quadrilateral 4. Know the properties of a parallelogram 5. Use the properties of a parallelogram to find angle measures and side lengths 6. Prove angle measures and side lengths using the properties of parallelograms 7. Prove that certain quadrilaterals are parallelograms 8. Understand and recognize that squares, rectangles and rhombuses are special parallelograms 9. Define a square, rhombus and rectangle 10. Use the diagonals of special parallelograms to solve problems 11. Define a trapezoid and kite 12. Understand the properties of an isosceles trapezoid 13. Know the mid-segment theorem of a trapezoid 14. Use the properties of kites to solve problems 15. Identify the special quadrilaterals 16. Find the areas of triangles 17. Find the areas of quadrilaterals

Weeks 11-14: Unit 4: Transformations Chapter 7

1. Understand the concept of a transformation, the image and pre-image

2. Identify isometries 3. Understand and apply a reflection

4. Find the mirror image and line of reflection

5. Find the distance and midpoint between a point and its image under a reflection

6. Understand and apply a rotation

7. Find the center and angle of rotation

8. Identify rotational symmetry

9. Understand and apply a translation

10. Translate points in the coordinate plane

11. Translate points using vectors

12. Identify the components of a vector

13. Understand and apply a glide reflection

14. Find the composition of transformations

15. Describe a composition of transformations

16. Describe a frieze pattern – left out because of time;

17. Identify a frieze pattern – left out because of time.

Weeks 15-17: Unit 5: Similarity Chapter 8

1. Compute the ratio of two units

2. Simplify ratios

3. Use ratios in problems

4. Find a proportion

5. Understand properties of proportions

6. Solve equations using proportions

7. Solve Geometric problems using proportions

8. Identify similar polygons

9. Compare ratios of perimeters of polygons to the ratios of the sides of polygons

10. Identify similar triangles

11. Prove that two triangles are similar

12. Use proportions in similar triangles 13. Identify dilations as either a reduction or an enlargement

Week 18: Geometry Project

Weeks 19-20: Exams

Weeks 21-23: Unit 6: Circles Chapter 10 (Completed Sections 10.1-10.3 completed thoroughly.)

1. Define a circle and its various parts including a radius, diameter, chord, secant and tangent 2. Use the properties of tangents in circles 3. Define a major and minor arc of a circle 4. Find the measure of an arc of a circle 5. Use the properties of chords in circles 6. Find the measure of an inscribed angle 7. Use the theorems of inscribed polygons in a circle 8. Find the measure of angles of tangents and chords in a circle – did not do, time. 9. Find the lengths of segments in a circle – did not do, time. Excludes 10.6 and 10.7 (equations of circle and locus)

Weeks 24-25: Unit 7: Right Triangles and Trigonometry Chapter 9 (Sections 9.2, 9.3, 9.5 & 9.6 done thoroughly).

1. Solve problems using the Pythagorean Theorem

2. Find the area of a triangle using the Pythagorean Theorem

3. Determine if a triangle is right, obtuse or acute

4. Find the six different Trigonometric ratios

5. Find the length of a side using a calculator and Trigonometry

6. Find the measure of an angle using a calculator and Trigonometry

7. Use Trigonometric ratios in word problems Excludes 9.1 (Similar Right Triangles), 9.4 (Special Right Triangles), 9.7 (Vectors) The British text, Rayner, is wonderfully useful pp. 118-127.

Week 26: Discovery Week

Check-out Algebra book, begin Algebra class, though students keep Geometry book

Weeks 27-28: Unit 8: Linear Inequalities Chapter 6.1-6.3 (Sections 6.1, 6.2, 6.3 and 6.5 done thoroughly) 1. Solve one-step inequalities in one variable

2. Graph inequalities on a number line

3. Find and graph the solution to Multi-Step inequalities in one variable

4. Find and graph the solution to conjunction compound inequalities

5. Find and graph the solution to disjunction compound inequalities

6. Graph linear inequalities in two variables Excludes: 6.4 - 6.7 (statistics)

Weeks 29-31: Unit 9: Linear Systems of Equations and Inequalities Chapter 7 (Sections 7.1-7.6 done thoroughly)

1. Solve systems of linear equations by graphing

2. Solve systems of linear equations by graphing on GDC

3. Solve systems of linear equations by substitution

4. Solve systems of linear equations by elimination

5. Graph systems of linear inequalities

Weeks 32-33: Unit 10: Functions From Chapters 1, 4 and 8

1. What is a function (1.7)

2. Mapping diagrams (1.7)

3. Vertical Line Test (4.8)

4. Function Notation (4.8)

5. Linear Functions

6. Scatterplots and performing linear regressions on a set of data using a GDC and a spreadsheet program (sections 5.4 and 5.7 helpful). Also, H&H SL and Math Studies books good for correlation questions.

Weeks 34-35: Unit 11: Quadratic Equations and Functions Chapter 9 (Sections 9.1, 9.2, 9.3 and 9.4 completed thoroughly).

1. Solve quadratic equations by finding square roots (9.1)

2. Simplify radicals (square roots only) (9.2)

3. Graph quadratics given in standard form (using -b/2a and symmetry) (9.3)

4. Solve quadratics by graphing (9.4) 5. Solve quadratics using the quadratic formula – left for grade 10 after ‘completing the square’.

6. Graph quadratic inequalities (9.7) – not done, time.

7. A great amount of time was spent on factoring quadratics, by: common factors, grouping, difference of two squares and . Then quadratic equations with these skills were taught; including word problems. A British book, Rayner, pp. 39-45 was used extensively.

Week 36: Unit 12: Probability Unfortunately never got there.

1. Understand basic probability rules

2. Solve basic probability problems

3. Understand basic probability problems using “And” and “Or”

Weeks 37-38: Exams

Topics to be covered in MS: Introduce and cover basic concepts of: Parallel and Perpendicular Lines, Triangles, Quadrilaterals, Circles Teach: Perimeter, Area, and Volume of Triangles, Quadrilaterals, Circles Surface Area and Volume of three dimensional shapes

Algebra Assumptions: Students should be able to:  Perform operations on integers, fractions and decimals (+, -, x, ÷, compare) follow order of operations, apply the distributive property, use and manipulate variables  Check that a value is a solution to a linear equation or inequality  Solve linear equations  Solve linear inequalities  Rearrange the subject of an equation  Graph Linear Equations both by hand and using technology  Find and use the slope of a line  Determine direct variation and inverse variation equations  Write Linear Equations in point-slope form, slope intercept form amd standard form  Students are NOT assumed to be able to do statistics, have an introduction to functions or perform regressions  Students can apply product of powers, power of powers, and division of powers and use the properties of exponents  Factorize algebraic expressions and basic quadratic expressions  Solve basic quadratic equations  Work with simple probability and simple statistics  Understand the concept of a Venn Diagram