Mochi does Maths!

Ms Carolina's Math class

Topic 1 - Algebra

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:

1. Assigned reading.
2. Video
3. Video and classroom examples
4. Class work.

Videos may  contain 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.

In this section you will find all the video lessons regarding our first unit: Algebra. 


Essential understandings: 

Number and algebra allow us to represent patterns, show equivalencies and make generalizations which enable us to model real-world situations. Algebra is an abstraction of numerical concepts and employs variables which allow us to solve mathematical problems. 


Suggested concepts embedded in this topic: Generalization, representation, modelling, equivalence, patterns, quantity AHL: Validity, systems. 


Content-specific conceptual understandings: 

• Modelling real-life situations with the structure of arithmetic and geometric sequences and series allows for prediction, analysis and interpretation. 

• Different representations of numbers enable equivalent quantities to be compared and used in calculations with ease to an appropriate degree of accuracy. 

• Numbers and formulae can appear in different, but equivalent, forms, or representations, which can help us to establish identities. 

• Formulae are a generalization made on the basis of specific examples, which can then be extended to new examples. 

• Logarithm laws provide the means to find inverses of exponential functions which model real-life situations. 

• Patterns in numbers inform the development of algebraic tools that can be applied to find unknowns. 

• The binomial theorem is a generalization which provides an efficient method for expanding binomial expressions. 


AHL 

• Proof serves to validate mathematical formulae and the equivalence of identities. 

• Representing partial fractions and complex numbers in different forms allows us to easily carry out seemingly difficult calculations. 

• The solution for systems of equations can be carried out by a variety of equivalent algebraic and graphical methods.

                                                                                                              MAA HL Subject guide IBO 2019

Week 2: Sept 7th - 11th

Lesson 1 - Basics

TZ2:
September 8th, 2020
TZ1: 
September 9th

Approx. time 80 minutes


In this lesson you will learn or revise:

- the use of scientific notation.

- to operate numbers in scientific notation (+ - x /).

- To apply exponents to numbers written in scientific notation.


INSTRUCTIONS

Before you come to class

- Read: Kognity reading Assignment assignment (Lesson 1 - Algebra - Introduction) (10 minutes)

- Watch: Please watch this session's video lesson Lesson 1 - Algebra - Introduction. (25 minutes)

In class:

- Do: If there are any questions regarding the materials, please ask them at this time.

- Do: Kahoot! Let's all go to https://kahoot.it/ for a quick game!

- Submit: By the end of the lesson complete the Kognity task Lesson 1 - Algebra - Introduction Exercise Set and submit to Managebac the question assigned on the video about number sets.

- Homework: Watch next lesson's video and read the assigned sections in preparation for next class.

Lesson 2 - Arithmetic Sequences

TZ2:
September 10th, 2020

TZ1: 

September 14th

Approx. time 80 minutes


In this lesson you will learn:

- the concept of sequence.

- to identify an arithmetic sequence.

- to find a general formula for an arithmetic sequence.

- to find the number of terms in an arithmetic sequence.

- to predict the nth term of an arithmetic sequence. 


INSTRUCTIONS

Before Class:

- Read: Kognity reading Assignment assignment (Assignment 2020-09-01)

- Watch: Video lesson for this session Algebra - Lesson 2 - Algebraic sequences

During class:

- Do: If there are any questions regarding the materials, please ask them at this time.

- Pay close attention to Further examples.

- Do: Kognity. Lesson 2 - Arithmetic Sequences Set

- Homework: Watch next lesson's video and read the assigned sections in preparation for next class.

Week 3: Sept 14th - 18th

Lesson 3: Arithmetic Series and Sigma notation

TZ2:
September 14th, 2020

TZ1: 

September 15th

Approx. time 80 minutes


In this lesson you will learn:

- to identify a geometric sequence.

- to find a general formula for a geometric sequence.

- the concept of series.

- to read and write using appropriate notation (sigma notation).

- to identify an arithmetic series.

- to find a general formula for an arithmetic series.

- to find the number of terms in an arithmetic series.

- to find the partial sum of an arithmetic series. 


INSTRUCTIONS

Before Class:

- Read: Kognity reading Assignment assignment (Lesson 3: Arithmetic Series and Sigma notation)

- Watch: Video lessons for this day:

                Lesson 3 - Part I     Geometric Sequences; 

                Lesson 3 - Part II    Series and Sigma notation

                Lesson 3 - Part III   Arithmetic Series

Please make sure to take a 5 minute break between videos. Stretch your arms, legs and torso!


During class:

- Do: If there are any questions regarding the materials, please ask them at this time.

- Do: Visit Joinmyquiz.com and join the Quiz using the pin:47171360. Make sure to use your real name. You have 15 questions and will have 15 minutes to complete this test. This will be a formative assessment.

- Do: Kognity. Lesson 3 - Arithmetic Series and Sigma notation Set

- Homework: Watch next lesson's video and read the assigned sections in preparation for next class. Complete the Exercise sets by the end of each week (Sunday).


Lesson 4: Geometric Series and Convergence

TZ2:
September 16th, 2020

TZ1: 

September 21st

Approx. time 80 minutes


In this lesson you will learn:

- to find the number of terms in a geometric sequence.

- to predict the nth term of a geometric sequence. 

- to identify a geometric series.

- to find a general formula for a geometric series.

- to find the number of terms in a geometric series.

- to find the partial sum of a geometric series.

- applications of geometric sequences and series.


INSTRUCTIONS

Before Class:

- Read: Kognity reading Assignment assignment Lesson 4 - Geometric series and Convergence

- Watch: Video lessons for this day:

              Lesson 4 - Part I         Geometric Series

              Lesson 4 - Part II        Infinite Geometric Series and convergence.

During class:

- Please ask any questions you may have at this time.

- Worked examples.

- Quiz (25 minutes)

- Do: Kognity. Lesson 4: Geometric Series and convergence Practice Set


Lesson 5: Applications

TZ2:
September 17th, 2020

TZ1: 

September 23rd

Approx. time 80 minutes


In this lesson you will learn:

- Applications of sequences and series to real life situations.


INSTRUCTIONS

Before Class:

- Read: Kognity reading Assignment assignment Lesson 5 - Applications

During class:

- If you have any questions please address them at this time.

- Further examples on Applications: compound interest, appreciation, depreciation, etc.

- Do: Kognity. Lesson 5: Applications Set


Week 4: Sept 21 - Sep 25th

Lesson Mini IA I

TZ2:
September 22nd, 2020

TZ1: 

September 21st - 25th

Approx. time 80 minutes


In this lesson you will reinforce your knowledge of sequences and series.


INSTRUCTIONS

Before Class:

- Look at the exploration (Essay) Examples and get an idea of what an essay in Mathematics looks like.

- Check out the MAA HL subject guide and read the exploration section. Make special note of the assessment criteria.

- Note down any questions you have at this time.


During class:

- Download the document Mini IA and attempt to complete the task within the 80 minutes of this lesson.

- Make sure you write your work in an organized manner since you will need it to write it in the form of an essay.

- Work the time of the lesson in writing your essay.


Lesson Mini IA II

In this lesson you will reinforce your knowledge of sequences and series.


INSTRUCTIONS

Before Class:

Make sure you have your notes where you solved the task in the previous lesson and bring them to class. You will need to bring your computer, your calculator and any other materials you have identified as a need for you to write the essay. 


During class:

- Use the time of this lesson to start writing your essay.

- Make sure you write your work in an organized manner since you will need it to write it in the form of an essay.


Homework: One more lesson will be given for you to write the essay. Make sure you make some progress at home so that you are ready to submit your essay by the end of the next lesson.

Week 5: Sept. 28th - Oct. 2nd

Lesson Mini IA III

September 29th


In this lesson you will reinforce your knowledge of sequences and series.


INSTRUCTIONS

Before Class:

Make sure you have your notes where you solved the task in the previous lesson and bring them to class. You will need to bring your computer, your calculator and any other materials you have identified as a need for you to write the essay. 


During class:

- Use the time of this lesson to start writing your essay.

- Make sure you write your work in an organized manner since you will need it to write it in the form of an essay.


Homework: 

- This is the final lesson given to you for working on your essay. Please go through the samples of assessed student work and the subject guide to get a better understanding of the expectations of the essay ad the assessment criteria. You are asked to finished writing your essay at home  (Submission date December 4th on Google Classroom)

- Read and watch the videos for lesson 6.

Lesson 6 - Proof I

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Week 6: Oct 5th - Oct. 9th

Lesson 7 - Proof II

 

Lesson 8: Proof by Mathematical induction I

 

Lesson 9: Proof by Mathematical Induction II

 

Review and Practice

 

Week 7: