Download Unit 1 - Geometry and Trigonometry

Geometry and Trigonometry
What was tricky in this unit?
Chapter 1: Measurement and Geometry
Chapter 2: Trigonometry
MAP4C Unit 1 Plans Plans:
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In the top right corner of each day’s lesson are the coded curriculum expectations and the
associated textbook sections.
UNDERLINE AND BOLD indicates due date or summative (count for marks) evaluations.
Anything bolded should be completed for homework.
C1.1, C1.2
Text 1.1
Unit 1 Day 1: 2D Area
1. Seating plan.
2. General introductions: Website, Course Overview, Calendar, Mark tracking, Textbooks.
3. Unit conversions – by hand and by app.
4. Areas – basic formulas, composite shapes by net or components.
5. Discuss Key Concepts.
6. Text p. 11 # 4, 6, 8, 12 (a-d), 14.
7. Get first day sheet signed and bring it to class tomorrow.
C1.3
Text 1.2
Unit 1 Day 2: Volume
1. Volume – basic formulas, composite figures by net or components.
2. Discuss Key Concepts.
3. Text p. 23 # 5, 6, 7, 9, 12
C1.2
Text 1.3
Unit 1 Day 3: 3D Surface Area
1. Different from Day 1 because we’re dealing with 3D shapes.
2. Gizmos: Surface Areas of Prisms, Cylinders, Pyramids, and Cones.
3. Shape nets & using sum of individual shape areas.
4. Discuss Key Concepts.
5. Text p. 32 # 3, 5, 6, 9, 11
C2.1, C2.2
Text 1.4
Unit 1 Day 4: Optimize Perimeter and Area
1. Define optimization and examples of constraints.
2. 36 cubes activity: arrange in different rectangular or square shapes & determine perimeter
and area. What is the smallest perimeter?
3. D2L U5A4 Optimal Area Simulation Demo.
4. Derive generic formula for perimeter as a function of length – graph to show optimal result.
Repeat for different area.
5. Discuss Practice A # 1 – 4.
6. Text p. 43 # 6, 11, 12, 14, 16
C2.1, C2.3
Text 1.5
Unit 1 Day 5: Investigate Optimum Volume and Surface Area
Computer Lab
1. Gizmos logins.
2. Work on the Optimization Investigation.
3. Work on the Optimization Investigation.
C2.1, C2.3
Text 1.5
Unit 1 Day 6: Investigate Optimum Volume and Surface Area
Computer Lab
1. Work on the Optimization Investigation.
2. Work on the Optimization Investigation (due next class).
C2.1, C2.3
Text 1.6
Unit 1 Day 7: Analyse Optimum Volume and Surface Area
1. Optimization Investigation Due.
2. Demonstrate derivation of two variable formulas for surface area and volume of a square
based pyramid, triangular based pyramid, and cylinder.
3. Demonstrate how to develop a table of values for the formulas in Excel.
4. Graph the formulas in Excel and discuss results.
5. Discuss Key Concepts
6. Text p. 61 # 5, 6, 8, 9, 13
Unit 1 Day 8: Chapter 1 Review
1. General Review and Test Information
2. Text p. 64 # 1 – 7, 9, 11, 12, 14, 15
3. Prepare binders for homework and organization evaluation.
Unit 1 Day 9: Geometry Test
1. Full period test. Arrive with binder ready for evaluation.
C3.1, C3.2, C3.3
Text 2.1 & 2.2
Unit 1 Day 10: Trigonometric Ratios
Computer Lab
1. Trigonometric Functions Investigation.
2. Work on Trigonometric Functions Investigation.
C3.1, C3.2, C3.3
Text 2.1 & 2.2
Unit 1 Day 11: Trigonometric Ratios Continued
Computer Lab
1. Trigonometric Functions Investigation.
2. Finish Trigonometric Functions Investigation (due next class).
C3.1, C3.2, C3.3
Text 2.1 & 2.2
Unit 1 Day 12: Inclined Planes & Pulley Problems
1. Trigonometric Functions Investigation Due
2. Summary lesson on trigonometric functions for acute and obtuse angles including sketch of
quadrants and signs of trig functions in each quadrant.
3. Discuss Key Concepts for 2.1 & 2.2.
4. Text p. 80 # 6, 9, 11, 13.
5. Text p. 93 # 4, 10, 13.
C3.1
Text 2.3
Unit 1 Day 13: Sine Law
1. Sine Law formula, uses, and examples.
2. Discuss Key Concepts.
3. Text p. 101 # 4, 7, 9, 11, 14.
C3.1
Text 2.4
Unit 1 Day 14: Cosine Law
1. Cosine Law formula, uses, and examples.
2. Discuss Key Concepts.
3. Text p. 110 # 4, 7, 9, 11, 13.
C3.4, C3.5
Text 2.5
Unit 1 Day 15: Applications of Trigonometry
1. Use Example 2 to show different ways of solving the same problem.
2. Discuss Key Concepts
3. Introduce Research Assignment
4. Provide an example of a triangle and ask students in groups to find as many different ways as
possible to solve it – discuss results.
5. Text p. 126 # 3, 6, 7, 9, 11.
Unit 1 Day 16: Research Assignment
Computer Lab
1. Class period to work on the Research Assignment
2. Work on the Research Assignment
Unit 1 Day 17: Research Assignment
Computer Lab
1. Class period to work on the Research Assignment
2. Work on the Research Assignment – DUE AT THE END OF CLASS!
Unit 1 Day 18: Chapter 2 Review
4. General Review and Test Information
5. Text p. 130 # 1 – 3, 6, 7, 9, 12, 14, 15.
6. Prepare binders for homework and organization evaluation.
Unit 1 Day 19: Trigonometry Test
2. Full period test. Arrive with binder ready for evaluation.
SOHCAHTOA
Trigonometry
-use for right triangles only
START
Does the triangle have a
90° angle?
-use when given an acute angle and one side
and need a second side.
yes
-use when given two sides and need an
angle.
Hypotenuse
Adjacent
no
Opposite
𝑯𝒚𝒑𝟐 = 𝒂𝒓𝒎𝟐 + 𝒂𝒓𝒎𝟐
Are you given two angles?
yes
-use when given two sides
and need a third side.
no
Find the third angle using
the angle sum theorem
(all angles sum to 180°).
-use for right triangles only.
Hypotenuse
Arm
Do you have a set of opposites?
Arm
(An angle and its opposite side)
no
yes
Cosine Law
𝑎2 = 𝑏 2 + 𝑐 2 − (2𝑏𝑐 cos 𝐴)
Sine Law
Use when finding a side.
𝑎
sin 𝐴
2
cos 𝐴 =
2
2
(𝑏 + 𝑐 − 𝑎 )
(2𝑏𝑐)
Use when finding an angle.
=
𝑏
sin 𝐵
=
𝑐
sin 𝐴
sin 𝐶
𝑎
Use when finding a side.
=
sin 𝐵
𝑏
=
sin 𝐶
𝑐
Use when finding an angle.