# Mochi does Maths!

## Ms Carolina's Math class

### Office Hours

Office hours will happen on a rotation basis during a cycle.

Week A - Tuesday 7:00 - 8:00 PM JST
Week B - Wednesday 7:00 - 8:00 PM JST

### Video Lessons

The structure of the lessons is as follows:

2. Video
3. Video and classroom examples
4. Class work.
Suggested concepts embedded in this topic:
Generalization, space, relationships, equivalence, representation, AHL: Quantity, Modelling.

Content-specific conceptual understandings:
• The properties of shapes depend on the dimension they occupy in space.
• Volume and surface area of shapes are determined by formulae, or general mathematical relationships or rules expressed using symbols or variables.
• The relationships between the length of the sides and the size of the angles in a triangle can be used to solve many problems involving position, distance, angles and area.
• Equivalent measurement systems, such as degrees and radians, can be used for angles to facilitate ease of calculation.
• Different representations of the values of trigonometric relationships, such as exact or approximate, may not be equivalent to one another.
• The trigonometric functions of angles may be defined on the unit circle, which can visually and algebraically represent the periodic or symmetric nature of their values. AHL • Position and movement can be modelled in three-dimensional space using vectors.
• The relationships between algebraic, geometric and vector methods can help us to solve problems and quantify those positions and movements.                                                                                                                                                                                                     IBO MAA HL Subject guide 2019

### Trigonometry

In this unit you will learn:

- Angles and their measurements in degrees and radians.

- Unit circle: terminal points, supplementary and complementary angles.

- Right angled trigonometry

- Non-right angled trigonometry

- Trigonometric functions

- Trigonometric identities

### Vectors

In this unit you will learn:

- the concept of vector.

- How to operate vectors wit sum, difference scalar product and vector product.

- the concept of unit vector.

- the equation of a line in a 3D space.

- how to find intersections of lines in space.

- the equation of a plane in space

- how to find intersections between lines and planes, and planes and planes in space.

### Lesson 1: Vector equation of the line AHL 3.14

March 31st, 2020.

Approx. time: 80 minutes

In this lesson we will review the vector equation of the line.

INSTRUCTIONS:
1. Read: from the textbook Mathematics analysis and approaches HL by Oxford, pages 605 to 613.
2. Watch: the video lessons: https://youtu.be/UpU8fpsAhkU and https://youtu.be/hP5z69zV_yw
3. Do: exercise 9F, page 610, question 2 and 3. (Oxford)

### Lesson 2: Angles between two lines AA HL 3.15

April 1st, 2020

Approx. time: 60 minutes

In this lesson we will learn how to:

- calculate the angle between two lines

- identify if two lines are parallel, perpendicular or neither.

INSTRUCTIONS

1. Read: from the textbook Mathematics analysis and approaches HL by Oxford, pages 612 to 613.

2. Watch: video lessons part I and part II

3. Do: Exercise 9G, page 613-614, questions 2, 4, 5. (Oxford)

4. Do: questions 4, 5, and 6 in the attachment.
5. Submit: https://forms.gle/ZSzzoKSqdf8ZxkxXA

### Lesson 3: Equation of a plane AA HL 3.17

April 2nd, 2020

Approx. time 60 minutes

In this lesson we will learn how to:

- Find the equation of a plane using three points.

- Find the equation of a plane using one line and one point.

- Find the equation of a plane using a vector perpendicular to the plane and one point.

INSTRUCTIONS

1. Do: On google classroom's stream for lesson 3, write a post discussing what you think are the minimum requirements to define a plane.

2. Read: from the textbook Mathematics HL by Cambridge, pages 439-448.

3. Read: from the textbook Mathematics analysis and approaches HL by Oxford, page 621-622.

4. Watch: video lessons part Ipart II, and part III.

5. Do: Mathematics HL by Cambridge, page 447, Exercise 14D, one problem (a or b or c) from each numeral. (example: 1a, 2b, 3c, etc)

### Lesson 4: Planes, lines and intersections AA HL 3.18

April 6th, 2020

Approx. time 80 minutes

In this lesson we will learn how to find the intersections between

- find the intersections between lines and planes,

- find the intersections between planes with other planes,

- find the angle between a line and a plane.

INSTRUCTIONS

1. Read: from the textbook Mathematics analysis and approaches HL, pages 628-633.

2. Watch: video lessons part I and part II and part III.

3. Do: Exercise 9J (Oxford), page 630, question 2 and 3.

4. Do: Exercise 9K (Oxford), page 633, question 2, 3, and 4.

### Lesson 5: Intersection of 3 planes AA HL 3.18

April 7th, 2020

Approx. time 80 minutes

In this lesson we are going to learn how to:

- identify the different ways three planes can intersect and

- calculate those intersections.

INSTRUCTIONS

1. Do: Visit Geogebra applet and play with the three equations of planes in the bottom. Feel free to change the numbers and plotting different planes. Identify as many configurations for three planes as you can find and write a post with your observations on the classroom stream for this lesson.

2. Read: Mathematics Analysis and approaches HL by Oxford, page 625-628.

3. Watch: Video lessons part I and part II.

4. Do: Mathematics Analysis and approaches HL exercise 9I, page 628, question 4, 5, 6, 7.

### Lesson 6: Applications and further examples

April 8th, 2020

Approx. time 80 minutes

In this lesson you will learn about some applications of vectors.

INSTRUCTIONS

1. Watch: Choose two video lessons to watch: part I: Kinematics, part II: Newtonian Mechanics, part III: IB style question (27 mark question (~30 minutes)).

2. Do: Mathematics: Analysis and approaches HL, exercise 9L, question 1 and 3.

3. Do: Vectors study guide. This guide includes 3 IB past exam questions for which you will be asked to submit answers, and a few more exercises for you to practice for which submission is not required (practice at your own leisure).

### Lesson 7: Vectors Revision

April 13th, 2020.

Approx time 80 minutes

In this lesson you are asked to take some time to review your notes and assess your own learning. Although there is no new learning allocated to this lesson, I encourage you to reflect on those concepts that need reinforcement and ask for help should you need it. This lesson's activity is in the form of a Kahoot. Please play it to complete this lesson and this unit as soon as possible.

INSTRUCTIONS

1. Revise: Go through your notes, and check for any items that remain unclear or are still curious about regarding vectors and write questions about them.

2. Do: Share at least two questions/comments in the classroom stream for this lesson.