AOPS_CP Week 4

lilijia Posted in AOPS_Counting_Probability，
30 September 2019
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AOPS-CP Week 4: Chapter 3: Correcting for Overcounting

Lesson Review

1. Permutations with repeated elements:

https://www.ck12.org/probability/permutations-with-repetition/lesson/Permutations-with-Repetition-BSC-PST/

https://www.mathwarehouse.com/probability/permutations-repeated-items.php

2. Counting pairs of items (understand why we need to divide by 2)

Formula to find the sum of n numbers (understand how we derived it step by step).

1+2+3+…+(n-1) + n = n (n+1) /2

3. Counting with symmetries

a) rotational symmetry (round table seats) = n!/n = (n-1)!

b) reflective symmetry (flipping over, key chain) = n!/2n = (n-1)!/2

 

Homework:

Page 52: 3.2.1, 3.2.2., 3.2.3, 3.2.5

Page 57: 3.3.1, 3.3.3, *3.3.5 (it’s a bonus, but not difficult. Just try!)

Page 61: 3.4.1, 3.4.3

 

Final Tips:

Please do not try to remember the formulas by heart, instead, try to understand them, and learn how to derive them.

We value procedures. Please show all your steps/procedures in math problem solving: both in classwork and homework. You will benefit from it in the long run.

SAT Math Week 4

lilijia Posted in SAT math，
30 September 2019
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SAT Math Week 4

Chapter 3: Exponential/Linear Growth/Decay

Sorry that I got sick and was not able to speak loud today. Thanks to my great little TA — Michelle Zhang who did an excellent job in facilitating the class, and all the students: this is a great cohort that every single member works hard and contributes to the math problem-solving! (Sorry, not everyone is in this picture. Next time let’s make sure no one is missed :P)

20190929 students

Here is the lesson review:

20190929 lesson review

 

Sorry, there is a typo in today’s worksheet. Question 4 should be “f = a∙b^x”, instead of “f = ax^b”. Thank you, Michelle, for pointing it out!!

For the two absent students, I have sent the worksheet (homework) to the email address in the school system. Please print it out and finish it by next Sunday. —- Also I will appreciate it very much if you could let me know that you will not be able to come to the class:)

Extra resources:

https://www.albert.io/learn/sat-math/linear-and-exponential-growth/linear-and-exponential-growth-26?page=1

See you next week! We will move forward to Chapter 4: Proportion then!

Please feel free to let me know if you have any questions/suggestions/feedback! Thank you!

Lijia

SAT_3: Percent

lilijia Posted in SAT math，
23 September 2019
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It is such a pleasure to work with this group! Each of the 10 students did a fantastic job today in contribution to the class discussion and demonstration of your work on the whiteboard!

First of all, thanks to Kevin, Irene, Julia, Marina, Angus, Austin, and Danielle for bringing your corrections to the pretest! I will continue to check the corrections next week:)

Congratulations to Julia, Ellen for getting all 15 problems right on the homework, followed by Emma (14/15), Irene and Danielle (13/15)! Keep up the good work, everyone! Practice makes perfect 🙂

I also appreciate how Sarah and Ellen explained the examples in class (loud, and confident), and how Marina and Julia reached out for questions. I firmly believe that this class of students have a great potential to learn and I look forward to seeing all your progress week by week!

Lesson Review:

Simple Interest: A = P (1+r% * t)

Compound Interest: A = P (1+r%/n) ^nt

Percent of change = (new value – old value )/old value * 100%

*for problems such as “how many percents is A greater/less than B”, we always choose B (the one after the word “than”) as the benchmark (what you compare with), and put b into the denominator.

Homework:

1) Finish Pretest Corrections if you have not finished all of them (use different colors, show the steps/procedures)

2) Corrections to Chapter 1 Exercises (use different colors, show the steps/procedures)

2) Finish the rest part of Chapter 2 Exercises (Page 20-22)

* If you have an incoming SAT test, please feel free to let me know. I will give you extra support (some sample test papers, some tips to prepare the exams and so on).

Last but not least, many thanks to Michelle, my great TA, for checking all the homework and explain the problems!

See you next Sunday!

AOPS_CP2: Basic Counting Techniques

lilijia Posted in AOPS_Counting_Probability，
23 September 2019
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Lesson Review:

We introduced 4 basic counting techniques today:

1) Casework: to divide the problem into different subcases, count each, and add the counts altogether. It helps break a counting problem into manageable pieces, but requires you to be organized and careful (do not omit any outcomes).

2) Complementary Method: what we want = total = what we do not want. n(A) = n(U)-n(A’)

3) Constructive Method: count how many ways we can construct a particular item.

4) Counting with restrictions: it is generally best to deal with the most severe restrictions first.

 

Some tips:

1) independent choices: multiply the number of options at each step; exclusive options: add the number of options.

2) Sometimes when you get stuck at complicated problems, try to start with some simple cases, and find a pattern, or hint, to help you solve the “big problem”.

 

Homework:

Page 34: Ex2.2.1, 2.2.3, 2.2.5* (*bonus, highly recommended)
Page 38: Ex 2.3.1, 2.3.3
Page 41: Ex 2.4.1, 2.4.3
Page 44: Ex 2.5.1, 2.5.4

AOPS_CP Week 2 Homework

lilijia Posted in AOPS_Counting_Probability，
17 September 2019
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Thanks to Tiffany (William’s mom) for sharing the first two chapters of the E-book. Here are the screenshots of the problems. In case the textbook has not arrived by Sunday, students can use these to finish the homework.

17  2  34 5 6

 

Feel free to reach out if you have any question! See you on Sunday!

Wechat Group 快到碗里来^_^

lilijia Posted in AOPS_Counting_Probability, SAT math，
16 September 2019
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AOPS counting-probability Wechat Group

 

SAT math wechat group

AOPS CP_1. Counting is Arithmetic

lilijia Posted in AOPS_Counting_Probability，
15 September 2019
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Lesson Review:

1. The number of items in the list: a, a+1, …, b, b-1, where a≤b are integers, is b-a+1 (understand how it is derived).

2. Understand Venn Diagram

VDIntersections

3. Count multiple events: (the number of ways A can occur) times (the number of ways B can occur)

4. Permutation: selelct r items in order from a group of n items in P(n,r) ways:

P(n,r) = n x (n-1) x (n-2) x … (n-r+2) x (n-r+1) = n!/(n-r)!

5. Factoral: n! = n x (n-1) x (n-2) x … 3 x 2 x 1

Homework:

Page 5: Ex 1.2.1, 1.2.2, 1.2.6

Page 12: Ex 1.3.1, 1.3.3

Page 18: Ex 1.4.1, 1.4.3, 1.4.5

Page 21: Ex. 1.5.1 (a) (c), 1.5.2

 

SAT_2: Exponents and Radicals

lilijia Posted in SAT math，
15 September 2019
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09/15 Week 2: Exponents and Radicals

Agenda: 

  1. pre-test review and comments
  2. check: textbook, notebook, folder
  3. Chapter 1:  Exponents & Radicals

Lesson review:

Laws of exponents:

1. law of exponents

1. law of exponents & radicals

Homework:

  1. Make corrections to Pre-test 1 (bring it to school next week)
  2. Finish Chapter Exercise (Page 13-15): show the procedures of work

Extra online resource:

  1. https://www.albert.io/learn/sat-math/radical-and-rational-exponents
  2. https://www.varsitytutors.com/sat_math-help/exponents/algebra/squaring-square-roots-radicals

SAT Math Lesson 1

lilijia Posted in SAT math，
09 September 2019
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Lesson Review:

-Introduction

  • Course Description + Expectations to students
  • Teaching Schedule

-Pretest (2018 April SAT)

  • Session 3: 35 min, no calculator. 20 problems.
  • Session 4: 55 min, calculator allowed. 38 problems.

Please do not be scared by the Pretest.  (It is to help me get a better understanding of which content I should focus on for this year’s teaching). No score was given to any student. I record the percentage of correct answers for each problem:)

However, if you want to calculate/estimate how much you can get in this Pre-test, here is the raw score conversion table:

SAT score conversion table

A low score may be disappointing today, but shows a greater space for improvement 😛

I firmly believe that we will achieve a lot if we keep on working hard +working wisely 🙂

 

Homework:

– Scanvenger Hunt: Fill in the blanks of “Expectations to students”

– Prepare the textbookSAT math textbook https://www.amazon.com/gp/product/0989496422/ref=ox_sc_act_title_1?smid=ATVPDKIKX0DER&psc=1

 

– Join in Wechat Group SAT math wechat group

– Bring notebooks, pens, calculators, and yourself to the class next Sunday 🙂

 

Note that due to the increased enrollment size, we will move to a bigger classroom next week. Please stay tuned.

See you!

AOPS CP Lesson 1

lilijia Posted in AOPS_Counting_Probability，
09 September 2019
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Lesson Review:

– Introduction, Teaching Schedule

– Pretest

– Math is Fun activity: count how many squares of any size can be formed by connecting the dots in the 5X5 grid? (Refer to textbook Page 30-32)

Homework:

-Make corrections to Pretest A. (Pretest B is optional, don’t feel frustrated if you feel it difficult. If you can solve all the problems on Pretest B, you should skip this course :P)

-Buy the textbook online https://artofproblemsolving.com/store/item/intro-counting?gtmlist=Bookstore_Home, and bring it to school next Sunday.

-Join in the Wechat Group. AOPS counting-probability Wechat Group

-Preview Chapter 1: Counting is Arithmetic

 

*Note that our classroom has been changed to Rm 206. Look forward to seeing you next week!

 

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