Mochi does Maths!

Ms Carolina's Math class

Class updates

Office hours:

Also, I would like to give you an update on how we are going to work because things have changed super fast and we are moving fully online, and I will share with you my office hours with you, that you can take advantage in person if you are on campus. 

I will be in Asama 25 Mon-Fri from 10:30 to 12:00. I can also receive your inquiries via hangouts from 8:00 to 18:00 (Japan standard time). Please understand that replies may be delayed.

Video Lessons:

The structure of the lessons is still dependent on you reading by yourself. I will follow the slides to create the videos and will have additional examples or content that may not be in the textbook. However, if you can't watch the videos, you should not worry, you still have access to all the textbooks and tasks via our classroom and mochidoesmaths.com.

Every other lesson there will be a task for you to submit. The submission of your tasks will be used to call attendance and to check on your progress, therefore, the submission of these activities is mandatory.

Each week, you will have 240 minutes worth of lessons.

Math IA:

I have updated an assignment in the classroom where you can submit your topic for the Math IA. There is a form that I need you to complete, make your one copy and submit it on April 27th, 2020

The other submission dates are kept unchanged, so you know you have a deadline if it is in the classroom. 

Math IA progress due - Sept 4th, 2020
Math IA first draft due - Oct 9th, 2020
Math IA final ver. due - Dec 11th, 2020

I only had the chance to talk to about 6 of you regarding your ideas for your Math IA, so please feel free to contact me and schedule a hangouts session during my office hours to discuss your idea and support you in checking if the idea is good or if it needs improvement. Please make sure you think of very focused research questions. Avoid feeling satisfied with a general statement or a topic, you must have a clear idea of the research question in order for me to help you move forward.

Paper 3:

If it's not obvious right now, we did not get a chance to have our paper 3, due to the unforeseen events that rushed everyone's departure from campus. So what I am thinking is still work with the questions I made available to you in the study guides, and we will do testing on that when we return in August.

Mini IA: 

You are still expected to submit this task but I will change the date so it counts for your final grade. I've changed the submission date to anytime before April 24th. You have had plenty of time to work on it, so it shouldn't be a problem! And if you submit earlier, that helps me to give you more detailed feedback.

Grades:

I have a basic idea of your performance that I have already shared with you in your report cards, and that will be the base of your PG. I will let you know of your individual PG after April 30. I expect that in this month your final PG will differ at most +-1 unit, and that will be based on your engagement, performance in tasks and any other evidence that we manage to collect before the end of April.

Make sure you submit all tasks requested and I expect you to do the tasks keeping the principles of academic honesty at all times in your minds. For example, if a task requires you to submit a test, make sure you use the specified time and submit your own work.

Letters of recommendation:

If you requested me to write a letter of recommendation, please take this opportunity to demonstrate all of your engagement, leadership skills, your commitment, your interest in Math, etc, so I will have really awesome things to say about you!

Video Lessons

Topic 3: Geometry and Trigonometry (Vectors)

Lesson 1: Vector equation of the line

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

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

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

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.

5. Do: Task 1 (paper 2) and Task 2 (Paper 1).

6. Submit: Please submit your answers to 5. in here.

Lesson 5: Intersection of 3 planes

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).

4. Submit: Submit your answers/solutions to 3 here.


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.

3. Do: After some of your classmates have posted their own questions/comments, reply to at least two of their questions/comments.

4. Do: If you need help to move forward, make an appointment with me and I will try my best to aid you. If you know of someone who shares your same questions, feel free to team up for the appointment.

5. Do: Kahoot! (Note: This Kahoot will expire on April 24, 2020)

Bonus materials

1. Tips for problem solving with vectors

2. Revision village - Vectors Look at playlist to the top right

3. Equations of 3D lines that are parallel to an axis - video example.

Topic 2: Functions

This unit will focus on understanding and recognizing the behaviour of the different families of functions, their domain and range, and what changes when functions are combined. The Topic we will be discussing are:

1. Domain and Range

2. Linear functions

3. Quadratic functions

4. Rational functions

5. Radical functions

6. Partial fractions and other rational functions

7. Absolute value functions and equations

8. Piecewise functions

9. Classification of functions according to their mapping

10. Classification of functions according to their parity

11. Operations with functions 

12. Inverse of a function

13. Transformations of functions

14. Properties of exponents

15. Exponential functions and equations

16. Properties of Logarithms

17. Logarithmic functions and equations

18. Trigonometric functions

19. Applications and modelling

Lesson 8: Domain and Range

April 14th, 2020

Approx. time 80 minutes


In this lesson you will learn:

- the concepts of domain and range.

- how to distinguish a functions from a relation using the vertical line test.

- to identify the graphs, end behaviour, domain and range of Linear and Quadratic functions.


INSTRUCTIONS

- Read: Mathematics Analysis and Approaches HL by Oxford, pages 72 - 85

- Watch: Video lessons part I, part II, additional video you may want to watch: part III (bonus - vertical line test)

- Do: work along part IV.

- Submit: Look at the picture on Investigation 5, on page 83. Use it as inspiration to create your own original character. Please use Geogebra or Desmos to create your own character, playing with quadratics, and lines. Submit your picture here.

Lesson 9: Rational functions and Radical functions

April 15th, 2020

Approx. time 80 minutes


In this lesson you will learn:

- to identify the graphs of rational and radical functions.

- determine the domain and range of rational and radical functions.

- the concept of asymptote.

- to find the vertical and horizontal asymptotes of rational functions.


INSTRUCTIONS

- Read: Mathematics Analysis and Approaches HL by Oxford, pages 86 - 90.

- Watch: Video lessons part I, part II, Examples (optional) part III.

- Do: Answer the question posted in the classroom stream corresponding to this lesson.

- Do: Mathematics Analysis and Approaches HL by Oxford, Exercise 2C (page 89) and Exercise 2D (page 90).

Lesson 10: Asymptotes and partial fractions

April 20th, 2020

Approx. time 80 minutes


In this lesson you will learn:
- To understand asymptotes as end behaviour for functions. (Part I)
- How to find asymptotes of rational functions. (Part I)
- How to find oblique asymptotes. (Bonus)
- How to express rational functions as partial fractions. (Part II)

INSTRUCTIONS
- Read: Mathematics Analysis and Approaches HL by Oxford, pages 90 - 93
- Watch: Video lessons part I, part II (two examples), Bonus
- Do: Mathematics Analysis and approaches by Oxford, Exercise 2E, questions 3 and 7.
- Do: Mathematics Analysis and approaches by Oxford, Exercise 2F, questions 3 and 7.
- Submit: Do and submit your answers to the questions included in this form.

Lesson 11: Absolute value functions

April 21st, 2020

Approx. time 80 minutes


In this lesson you will learn:
- The concept of absolute value. (part I)
- The graph, domain and range of the function f(x)=|x|. (part I)
- How absolute value changes graphs of other functions, |f(x)|. (part I)
- How to solve equations and inequalities involving absolute value. (part II and part III)

INSTRUCTIONS
- Read: Mathematics Analysis and approaches HL by Oxford, page 93 - 99.
- Watch: Video lessons part I (absolute value functions), part II (Equations), part III (inequalities)
- Do: Mathematics analysis and approaches HL by Oxford, Exercise 2H, questions e and g, page 98.
- Do: Mathematics analysis and approaches HL by Oxford, Exercise 2I, questions 1a, 1d, 1e, 2a, 2d. page 100.
Do: Comment on the lesson stream: how are you?

Lesson 12: Mini IA time

April 22nd, 2020

Approx. time 80 minutes


INSTRUCTIONS

- Do: Answer the corresponding question posted in google classroom.

- Work on your Mini IA, due to be submitted by Friday April, 24th to Google classroom.

Lesson 13: Piecewise functions and continuity

April 27th, 2020

Approx. time 80 minutes


In this lesson you will learn:
- the concept of piecewise functions (Part I)
- to graph piecewise functions (Part I)
- to identify the domain and range of piecewise functions (Part I)
- the concept of continuity (Part II)
- to determine whether a piecewise function is continuous or discontinuous. (Part II)

INSTRUCTIONS
Read: Mathematics analysis and approaches by Oxford page 100-101.
Watch: Video lessons Part I, Part II.
Do: Mathematics Analysis and approaches by oxford, exercise 2J, page 101, even questions.
Do: Create a graph for a continuous piecewise function, including clearly the domain and the range, and post (a link to) the picture in the answer to the question for lesson 13 in classroom.

Lesson 14: Classification of functions

April 28th, 2020

Approx. time 80 minutes


In this lesson you will learn:

- to classify functions according to their mapping. (Part I)

- to classify functions according to their parity. (Part II)


INSTRUCTIONS

- Read: Mathematics analysis and approaches by Oxford pages 102 - 108.

- Watch: Video lessons Part I, Part II.

- Do: Mathematics Analysis and approaches by oxford, exercise 2K, page 105.

- Do: Mathematics Analysis and approaches by oxford, exercise 2L, page 108.

- Submit: Consider the information that you have learnt up to this point about functions. Please submit the answers to the exercises included in the following form.


Lesson 15: Operations with functions

April 29th, 2020

Approx. time 80 minutes


In this lesson you will learn:

- how to add, subtract, multiply and divide functions. (Part I)

- to identify the domain and range of a resulting functions. (Part I)

- to do the composition of functions (Part II)

- to identify the domain and range of a composition. (Part II)


INSTRUCTIONS

- Read: Mathematics analysis and approaches by Oxford pages 108 - 111.

- Watch: Video lessons Part I, Part II, Part III (examples 1, 2), Part IV (Examples 3, 4, 5)

- Do: Mathematics Analysis and approaches by oxford, exercise 2M, page 111.

- Do: Write a comment in the stream for this lesson giving your own example of a function that is the composition of three functions, f(g(h(x))) and state the individual functions f, g, and h. (example: f(g(h(x)))=1-(x+1)^2, where f(x)=1-x, g(x)=x^2, and h(x)=x+1)


Lesson 16: Inverse functions

May 4th, 2020

Approx. time 80 minutes


In this lesson you will learn:

- The concept of identity function. (Part II)

- the concept of inverse function and how to find them. (Part I)

- the concept of self inverse. (Part II)

- how to find the domain and range of an inverse functions. (Part III)


INSTRUCTIONS

- Read: Mathematics analysis and approaches by Oxford pages 112 - 116.

- Watch: Video lessons Part I, Part II, Part III.

- Do: Mathematics Analysis and approaches by oxford, exercise 2N, page 116.

- Submit: Please submit the  answers to the exercises included in the following form.

Lesson 17: Transformations of functions I

May 5th, 2020

Approx. time 80 minutes


In this lesson you will learn:

- to transform functions using vertical and horizontal displacements. (Part I)

- to transform functions using magnifications. (Part II)

- to transform functions using reflections. (Part II)


INSTRUCTIONS

- Read: Mathematics analysis and approaches by Oxford pages 117 - 127.

- Watch: Video lessons Part I, Part II.

- Do: Mathematics Analysis and approaches by oxford, exercise 2O, page 118, questions 3, 5, and 6.

- Do: Mathematics Analysis and approaches by oxford, exercise 2P, page 120, question 2.

- Do: Mathematics Analysis and approaches by oxford, exercise 2Q, page 126, questions 1 and 3.

- Do: play this kahoot! (Link expires May 15th) Game PIN: 05886179


Lesson 18: Transformations of functions II (Further examples)

May 6th, 2020

Approx. time 80 minutes


This is a practice lesson. In this lesson you will continue to learn:

- How to graph functions with multiple transformations

- How to write a function's equation undergoing multiple transformations


INSTRUCTIONS

- Read: Mathematics analysis and approaches by Oxford pages 127 - 139.

- Watch: Video lessons Part I (Further Examples).

- Do: Mathematics Analysis and approaches by oxford, exercise 2R, page 134, question 2.

- Do: Mathematics Analysis and approaches by oxford, exercise 2S, page 139.

- Submit: Please submit the  answers to the exercises included in the following form.


Lesson 19: Properties of Exponents and Exponential equations

May 11th, 2020

Approx. time 80 minutes


For this lesson you need to review beforehand:

- Properties of exponents (Bonus video)

- Factorization


In this lesson you will learn:

- How to solve equations with exponentials algebraically. (Part I)

- How to solve equations with exponentials using technology. (Part II)

- Graphs of exponential functions. (Part I)


INSTRUCTIONS

- Read: Mathematics Analysis and approaches HL by Oxford, pages 460 - 464

- Read: Mathematics analysis and approaches HL by Oxford, pages 473 - 475 (476* Read only up to the yellow information box and recommend doing investigation 11 (to understand number e), you do not need to be concerned about the text that follows this box yet AND investigation 12 question 6.)

- Watch: Video lessons part I, Part II, Bonus (optional - watch first)

- Do: Mathematics Analysis and approaches HL by Oxford, exercise 7C questions 2, 6, 8, page 464.
-Do: Mathematics Analysis and Approaches HL by Oxford, exercise 7E questions 3, 4, 5, page 481-482.

- Do: Answer the question in the classroom for the corresponding lesson 19.

Lesson 20: Properties of logarithms and logarithmic equations I

May 12th, 2020

Approx. time 80 minutes


For this lesson you need to review beforehand:

- The concept of logarithm (Bonus video by Vi Hart)

- Factorization


In this lesson you will learn:

- The definition of logarithm (Part I)

- The properties of logarithms (Part I)

- The graph of logarithmic functions (Part I)

- The connection between logarithms and exponential functions (Part I)


INSTRUCTIONS

- Read: Mathematics Analysis and approaches by Oxford, pages 465 - 472

- Read: Mathematics Analysis and approaches by Oxford, pages 477** - 482 (477 from Investigation 13)

- Watch: Video Lessons part I, Bonus (Bi Vi Hart - Optional)

- Do: Mathematics Analysis and Approaches HL by Oxford, Exercise 7E questions 6, 7, 8, 10

- Submit: Form

Lesson 21: Properties of logarithms and logarithmic equations II

May 13th, 2020

Approx. time 80 minutes


For this lesson you need to review beforehand:

- The concept of logarithm (Bonus video by Vi Hart)

- Factorization


In this lesson you will learn:

- To solve equations with Logarithms (Part I)

- The laws of logarithms (Part I and III)


INSTRUCTIONS

- Read: Mathematics Analysis and approaches by Oxford, pages 465 - 472

- Read: Mathematics Analysis and approaches by Oxford, pages 477** - 482 (477 from Investigation 13)

- Watch: Video Lessons part I, part III, and part II (examples), Bonus (Bi Vi Hart - Optional)

- Do: Mathematics Analysis and approaches by Oxford, exercise 7D, odd questions, page 472.

- Do: Answer in classroom the question corresponding to Lesson 21


Lesson 22: Trigonometric functions Part I

May 18th, 2020

Approx. time 80 minutes


For this lesson you need to review beforehand:

- Trigonometric ratios

- Trigonometric identities


In this lesson you will learn:

- The graphs of Sine, Cosine and Tangent as functions of x (Investigation and Part I)

- How to graphs Sine and cosine (Part II and III)

- How to transform the graphs of sine and cosine (Part III)


INSTRUCTIONS

- Do and Submit: Trigonometric functions activity. You will need: blank paper, ruler, protractor, thread, compass (or any circular object of about 6 cm in diameter). Submit your work in the corresponding classroom assignment for lesson 22.

- Read: Mathematics Analysis and approaches by Oxford, pages 410 - 417

- Watch: Video Lessons part I, part II, and part III.

- Do: Mathematics Analysis and approaches by Oxford, exercise 6N, questions 1, 2, and 4. 

- Do: Mathematics Analysis and approaches by Oxford, exercise 6O, questions 1 and 4 (a, b, c, d).


Lesson 23: Trigonometric functions part II

May 19th, 2020

Approx. time 80 minutes


For this lesson you need to review beforehand:

- Trigonometric ratios

- Trigonometric identities


In this lesson you will learn:

- To model data using trigonometric functions (Part I)

- To solve word problems involving trigonometric functions (Part II)


INSTRUCTIONS

- Read: Mathematics Analysis and approaches by Oxford, pages 410 - 417

- Watch: video lessons Part I and Part II

- Do: Mathematics Analysis and approaches by Oxford, exercise 6O, questions 2 and 3.

- Do: In the stream for this lesson mention 3 things, places, etc you have seen in your culture/city/etc that can be modelled through a sine or cosine curve.


Lesson 24: Trigonometric functions Part III

May 20th, 2020

Approx. time 80 minutes


For this lesson you need to review beforehand:

- Trigonometric ratios

- Trigonometric identities


In this lesson you will learn:

- To graph calculate inverse trigonometric functions (Part I)

- To solve trigonometric equations by hand and using technology (Part II)


INSTRUCTIONS

- Read: Mathematics Analysis and approaches by Oxford, pages 418 - 421

- Watch: video lessons Part I, Part II.

- Do: Mathematics analysis and approaches HL by Oxford, exercise 6P, questions 2, 4, 5.

- Submit: Assignment sent via Kognity: Functions review.