Rhythm and Melody

(Ability to read music not necessary to do these exercises).

Listen to song below.  First, follow the rhythm.  How many beats are there in a measure?  Those who haven’t studied music, you can still figure out what a measure is and how many beats are in there.  Listen for patterns that are repeated throughout the song.  The song is neatly structured.  Think of a measure as containing one breathful of sounds and ideas.

Next, graph the melody.  Draw up and down based on the musical notes.  Like this:

Don’t think about it, let your body go with the flow, your instincts will guide you.  Do this exercise enough and you’ll become a better dancer, I promise.  And you’ll teach yourself how to visualize music and Math so you can understand both better.  We’ll go over this tomorrow and consider what makes a melody and rhythm pleasurable.

Euphemisms

A euphemism is “a mild or indirect word or expression substituted for one considered to be too harsh or blunt when referring to something unpleasant or embarrassing.”  In other words, a euphemism is a polite and dangerous lie.  English professor, social critic, and curmudgeon Paul Fussell on euphemisms:

The middles cleave to euphemisms not just because they’re an aid in avoiding facts. They like them also because they assist their social yearnings towards pomposity. This is possible because most euphemisms permit the speaker to multiply syllables, and the middle class confuses sheer numerousness with weight and value.

I’ve noticed the same.  The poorly educated wrongly imagine the well educated as dainty and discreet, so they end up parodying themselves when they try to act high tone.  For to be well educated is to be able to confront, rather than escape from, the harsh realities of life, whether that be stepping on dog shit or death during a pandemic.

Again, some of the principles of good writing:

• Less is more
• Be honest
• Be clear
• Focus on your audience.
• Be accountable

Euphemisms violate the “be honest” and “be clear” principles.  It often violates the “less is more” and “be accountable” principles.

Below are a list of euphemisms.  Find a simpler and more precise word for each.  Example:

Quantitative Easing (euphemism)
Printing money out of thin air.

Here’s the list:

• Passed away
• Ethnic cleansing
• Friendly fire
• Collateral damage
• Put to sleep
• Pregnancy termination
• Restroom
• Project coordinator
• Full figured
• Escort

Yesterday’s Questions

Let’s review, answers in italics:

1. What are the total number of possible outcomes with each roll of a six sided dice, each side uniquely numbered 1-6?
   There are six possible outcomes.
2. What are the chances of getting a “3” on a roll of this dice?
   Since “3” is on one of the six sides and there are six possible outcomes, then 1/6 is the answer.
3. What are the chances of getting a “3” and a “3” on two rolls of this dice?
   1/6 chance of getting a “3” on first roll.  1/6 chance of getting a “3” on second roll.  So 1.6 * 1/6 = 1/36.
4. What are the chances of getting a “4” and then a “6” and then a “2” on three rolls of this dice?
   1/6 chance of getting a “4”; 1/6 chance of getting a “6” on second roll; 1/6 chance of getting a “2” on third roll.  So 1/6 * 1/6 * 1/6 = 1/216
5. What are the chances of getting three Heads on three tosses of a coin?
   1/2 * 1/2 * 1/2 = 1/8.  Let’s write out all possibilities so you can visualize it:
   HHH  HHT  HTT  TTT  TTH  THH  HTH  THT

The main takeaway is that each flip of a coin, each roll of a dice…is independent of all other flips and rolls.  Coins and dices don’t have memories.  It’s possible to flip a coin a million times and get Heads on all of them.

In next lesson we explore math in music.

Eliminate wordiness exercise

Possible answers to previous lesson’s editing exercise in italics:

1. I want to utilize my skills to help grow your organization.
   I want to use my skills to grow your organization.  (“utilize” means to use something that’s not normally used so that’s not the appropriate word; “help” is redundant, no point in it being there). 
2. She opened the envelope, which contained a confidential document inside.
   She opened the envelope, which contained a confidential document.  (no shit it’s inside, already pointed out with word “contained”).

3. After reading it with close scrutiny, she discovered it was written in the exact same handwriting as the mysterious note she’d received before.
   After reading it with scrutiny, she discovered it was written in the same handwriting as the mysterious note she’d received.  (“close” is redundant as “scrutiny” already means “close examination.” “Exact” is redundant and unnecessary adverb to modify “same.”  “Before” is redundant, we already know that the “mysterious note” preceded the opening of this document before the “before.”

4. The reason she knew this was because of handwriting studies in her past history.
   She knew this because of past handwriting studies. (“The reason” is redundant, as is “history,” we already know it’s in the past).

5. There is currently a lively, ongoing controversy among many sociologists and other professionals who study human nature : theories are being spun and arguments are being conducted among them about what it means that so many young people—and older people, for that matter—who live in our society today are so very interested in stories about zombies.
   (This is written by a fucktarded narcissistic social science academic.  This shit is the norm nowadays).  The controversy among those who study human nature is why so many people are interested in zombie stories.  

I’ll let Paul Fussell comment on number 5:

The middles cleave to euphemisms not just because they’re an aid in avoiding facts. They like them also because they assist their social yearnings towards pomposity. This is possible because most euphemisms permit the speaker to multiply syllables, and the middle class confuses sheer numerousness with weight and value.

Below are the answers (italicized) to questions from previous lesson:

1. What are the total number of possible outcomes with each coin toss?
   Two, as there two sides to a coin
2. What are the chances of you, after your 25 outcomes, getting a Tail on next toss?
   The first 25 outcomes are irrelevant, each toss is independent of all other tosses.  Coins don’t have memory or a sense of what’s right and wrong.  Tails is 1 possible outcome/2 total number of outcomes = 1/2
3. What are the chances of you getting Heads on both the next two tosses?
   First ask what is probability of getting heads in the first toss.  It’s 1/2.  What is probability of getting heads in the second toss?  It’s 1/2.  So 1/2.  1/2*1/2=1/4 is the answer.  Another way to look at it is to ask what are the possible outcomes for the two tosses?  

   TT    HH    HT    TH  

   HH happens once out of four possible outcomes. 

4. What are the chances of you getting Tails and then a Head in the next two tosses?
   Chances of getting Tails in first toss is 1/2.  Chances of getting Heads in second toss is 1/2.  So 1/2*1/2=1/4.  Same approach as one used in question 3.  

Today’s Questions

1. What are the total number of possible outcomes with each roll of a six sided dice?
2. What are the chances of getting a “3” on a roll of this dice?
3. What are the chances of getting a “3” and a “3” on two rolls of this dice?
4. What are the chances of getting a “4” and then a “6” and then a “2” on three rolls of this dice?
5. What are the chances of getting three Heads on three tosses of a coin?

Editing Bad Writing Exercise — Adverbs

Yesterday’s exercise:

The following exercise will help you answer that question.  Improve the following sentences by removing an adverb:

1. Stacy has a really nice ass.
2. This book is rather boring.
3. Jim is quite handsome
4. This is simply unacceptable.
5. The cabin is somewhat far from here.
6. I can sorta do that.
7. It’s terribly cold in here.
8. I generally don’t go to the movies often.
9. This is absolutely terrible.
10. She’s a fairly good artist.

Compare what your revisions with the originals.  How are they different?   We’ll go over this next lesson.

Let’s compare, edited version in italics:

1. Stacy has a really nice ass.
   Stacy has a nice ass.
2. This book is rather boring.
   This book is boring.
3. Jim is quite handsome
   Jim is handsome
4. This is simply unacceptable.
   This is unacceptable.
5. You seriously must be joking.
   You must be joking.   
6. I can sorta do that.
   I struggle when doing that.
7. It’s terribly cold in here.
   It’s cold in here. 
8. I generally don’t go to the movies often.
   I don’t go to the movies often. 
9. This is absolutely terrible.
   This is terrible.
10. She’s a fairly good artist.
    She’s a decent artist.

Which version sounds more confident?  Which version sounds as if the writer is unsure of himself.  Which version sounds flaky?  Which version inspires trust and provides clarity?

Less is More Exercise

Let’s review “less is more” principle of good writing.

• Less is more

Be concise and succinct, use as few words and syllables as possible.  Write only what needs to be written.  It’s bad manners to waste people’s time.  We’ll practice brevity in next lesson.

Edit the following sentences:

1. I want to utilize my skills to help grow your organization.
2. She opened the envelope, which contained a confidential document inside.
3. After reading it with close scrutiny, she discovered it was written in the exact same handwriting as the mysterious note she’d received before.
4. The reason she knew this was becauseof handwriting studies in her past history.
5. There is currently a lively, ongoing controversy among many sociologists and other professionals who study human nature : theories are being spun and arguments are being conducted among them about what it means that so many young people—and older people, for that matter—who live in our society today are so very interested in stories about zombies.

Tip: look for redundancies and eliminate them.

The game we started:

You’ll need a quarter and 50 pennies to play this game.  Twenty five of the pennies belong to the pupil.  Pupil plays the following game:

Tosses the quarter and guesses if it lands Heads of Tails.  When pupil wins, she gets a penny.  When he loses, he gives a penny.  Do this 25 times and write down the result of each toss.

Then you were asked:

Calculate the following:

• Winning and losing percentages

• Percentage of times coin lands on Heads and Tails

Here’s what I got:

Winning percentage: 10 out of 25 = 10/25 = 2/5 = .400 favorable outcomes.
Losing percentage: 1.000-.400=.600

Percentage of times landed on Heads: 14/25=56%
Percentage of times landed on Tails: 100-56=44%

What did you get?

Questions:

1. What are the total number of possible outcomes with each coin toss?
2. What are the chances of you, after your 25 outcomes, getting a Tail on next toss?
3. What are the chances of you getting Heads on both the next two tosses?
4. What are the chances of you getting Tails and then a Head in the next two tosses?

We’ll review those questions next time.

How to Recognize Bad Writing Exercises — too many adverbs

I’m not talking about bad grammar.  This is about style, and you need to be able to recognize bad writing in order to become a good writer because good writers edit their own work.

Here are a few principles of good writing:

• Less is more
• Be honest
• Be clear
• Focus on your audience.
• Be accountable

If you don’t agree with the above, then go back to sleep.  If you do, let’s review each:

• Less is more

Be concise and succinct, use as few words and syllables as possible.  Write only what needs to be written.  It’s bad manners to waste people’s time.  We’ll practice brevity in next lesson.

• Be honest.

Be transparent, avoid euphemisms.  When you’re not  honest, you’re not clear.

• Be clear

Be precise and concrete, avoid abstractions.

• Focus on your audience

Never show off, the point of writing is to communicate effectively, that’s it.

• Be accountable

Use the active voice instead of passive voice.

Today’s exercise involves adverbs.  An adverb is used to express the degree, the extent to which something is happening.  “It’s very hot,” with “very” as adverb describing how hot it is.  (There are other types of adverbs, let’s start with these).  In any case, too many adverbs is a sign of bad writing.  Why is that?

The following exercise will help you answer that question.  Improve the following sentences by removing an adverb:

1. Stacy has a really nice ass.
2. This book is rather boring.
3. Jim is quite handsome
4. This is simply unacceptable.
5. You must seriously be joking.
6. I can sorta do that.
7. It’s terribly cold in here.
8. I generally don’t go to the movies often.
9. This is absolutely terrible.
10. She’s a fairly good artist.

Compare what your revisions with the originals.  How are they different?   We’ll go over this next lesson.

You’ll need a quarter and 50 pennies to play this game.  Twenty five of the pennies belong to the pupil.  Pupil plays the following game:

Tosses the quarter and guesses if it lands Heads of Tails.  When pupil wins, she gets a penny.  When he loses, he gives a penny.  Do this 25 times and write down the result of each toss.  Example:

Let P = Prediction
Let A = Actual
Let H – Heads
Let T – Tails

P  A

1. H  H

2. H  T

3. H  T

4. T  T

5. H  H

6. H  T

7. T  H

8. And so on till 25.

Calculate the following:

• Winning and losing percentages
• Percentage of times coin lands on Heads and Tails.

That’s it for today.  We’ll go deeper tomorrow.

College Admissions Essay (Part IV)

Here’s the prompt again:

Joan of Arkansas. Queen Elizabeth Cady Stanton. Babe Ruth Bader Ginsburg. Mash up a historical figure with a new time period, environment, location, or occupation, and tell us their story.
—Inspired by Drew Donaldson, AB’16

Here’s what we have thus far:

Soong Ching Linguini, daughter of renown restaurateur Alfredo Linguini and his mistress Valentina Ching, loves Italian food.  She has two half sisters, the daughters of her father and his wife, Colette.  The elder half-sister, Amalea Linguini loves money, so she married the owner of Olive Garden.  The younger half-sister Maria Linguini loves power, so she married Italy’s most influential food critic.  Soong expressed her love of Italian food by apprenticing with and eventually marrying a chef known for his linguini alfredo.  After he died, she took over his restaurant and was determined to improve on his linguini alfredo recipe.  She searched for superior ingredients, innovated better ways to make linguini and the alfredo sauce, and experimented with more exotic uses and combinations of ingredients.

To that I add:

For instance, Soong invented a new type of mill that produces flour made from wheat and rice to make a linguini that’s less sticky and a touch lighter to bite.  She infused her alfredo sauce with sesame oil and cumin, which went well with the Peking duck linguini alfredo.  Soong even served a peanut butter and jelly linguini alfredo, to which she adds peanut butter to the alfredo sauce and sprinkles the dish with strawberries.  Such bold dishes elevated Soong’s reputation to one of the greatest Italian chefs ever, and she was invited to compete on Iron Chef America, where she defeated Mario Batali and wowed the judges with pineapple linguini popsicles as dessert.

Her sister Amalea’s husband, the owner and CEO of Olive Gardens, offered Soong an opportunity to create a line of supermarket products.  Soong turned him down, telling him that she wants to focus on evolving and elevating Italian cuisine, not on making products for mass consumption.  Last year, the Italian government declared her a national treasure, becoming the second chef in the world given that honor, the first being master sushi chef Jiro Ono of Japan.  Soong continues to work at her restaurant six days a week, thinking of new ways to make and serve linguini alfredo.

The end.  Let us know if you need help with your college admissions essays.

Ask about Alive Juice Bar’s tutoring services.  Free or pay what you can.  Our tutors have degrees from US News top 10 universities.  We cover most subjects, from AP Physics to SAT prep to college admissions essays.

—————————————————————————————-

Let’s move on to final three questions of the LSAT logic set.  The conditions and questions:

An athlete has six trophies to place on an empty three-shelf display case. The six trophies are bowling trophies F, G, and H and tennis trophies J, K, and L. The three shelves of the display case are labelled 1 to 3 from top to bottom. Any of the shelves can remain empty. The athlete’s placement of trophies must conform to the following conditions:

• J and L cannot be on the same shelf
• F must be on the shelf immediately above the shelf that L is on.
• No single shelf can hold all three bowling trophies
• K cannot be on Shelf 2

QUESTION 3

(Conditions are italicized) Again, write out what each letter stands for, like this:

Bowling: F, G, H
Tennis: J, K, L

1. ?
2. J
3. ?

Since L and J can’t be on the same shelf and L can’t be on the first shelf because F must be on the shelf immediately above the shelf that L is on.  So now we have:

1. ?
2. J F
3.   L

The answer is 3. F

Logic problems are easy once you have everything organized.

QUESTION 4

QUESTION 5

or

1. ? ? ?
2. F ? ?
3. L G

Now let’s at each condition:

1. If H is on Shelf 3, then J is on Shelf 2. (This must be true because if H is on Shelf 3, then Shelf 1 must be empty.  And since J and L can’t be on the same shelf, J must be on Shelf 2)
2. K and L are on the same shelf. (If L is on shelf 2 and the Shelf 3 is empty, then K and L can’t be on same shelf)
3. If H is on Shelf 2, then J is on Shelf 3. (You can still have F H J on Shelf 2 if Shelf 1 is empty)
4. F and K are on the same shelf. (If Shelf 1 is empty, then F and K can’t be on same Shelf because K can’t be on Shelf 2)
5. If J is on Shelf 2, then H is on Shelf 1.  (If J is on Shelf 2, H can be either on Shelf 1 or 3)

Draw it out and it’s not that difficult.

College Admissions Essay, University of Chicago prompt, Part III

Here’s the prompt again:

Joan of Arkansas. Queen Elizabeth Cady Stanton. Babe Ruth Bader Ginsburg. Mash up a historical figure with a new time period, environment, location, or occupation, and tell us their story.
—Inspired by Drew Donaldson, AB’16

Here’s what we have thus far:

The Soong sisters grew up in early 20th century Shanghai.  The eldest, Soong Ai-ling, is known for her love of money, married the wealthiest man in China.  The youngest, Soong Mei-ling, is known for her love of power, married the leader of the KMT, the man who would become president of the Republic of China.  The middle sister, Soong Ching-ling, is remembered for her love of her country and she married revolutionary leader Sun Yat-Sen, the founder of modern China, against her family’s wishes.  Soong Ching-ling eventually broke with her family and joined the Communist Party, remaining in mainland China as her family fled to Taiwan to set up provisional government, aka Republic of China, at the conclusion of the civil war.  She died as one of the most revered political figures in the history of China.

So I’ve taken Soong out of China and into the animated world of Ratatouille, where she is Soong Ching Linguini, daughter of Alfredo Linguini and his mistress Valentina Ching (not from movie, I made her up), daughter of an Italian seamstress and a Chinese textile manufacturer.

Then I wrote what I know about Alfredo Linguini and Valentina Ching:

Alfredo Linguini is a bumbling and sometimes kindhearted cook who, with the help of his rat friend named Remy, rises to become owner and chef of a prominent restaurant.  Alfredo’s real superpower is his ability to skate so in the end, he becomes a waiter on skates at the restaurant he and his wife Colette own, while his wife and pet rat, Remy, are the chefs. It was at his restaurant that he met the captivating Valentina Ching, a fashion designer and daughter of an Italian seamstress and a Chinese textile manufacturer.  Alfredo meets Valentina at her boutique and there they begin an affair that produces Soong Ching Linguini, a celebrated chef renown for her linguini alfredo.

I’m ready to write the essay.  Here it goes:

Soong Ching Linguini, daughter of renown restaurateur Alfredo Linguini and his mistress Valentina Ching, loves Italian food.  Unlike her half sisters, the elder Amalea Linguini who loves money so she married the owner of Olive Garden, and the younger Maria Linguini who loves power so she married the owner of Buca Di Beppo, Soong apprenticed with and married a chef known for his linguini alfredo.  After he died, she took over his restaurant and was determined to improve on his linguini alfredo recipe.  She searched for better ingredients, better ways to make linguini and the alfredo sauce.

 

 

 

I’ll finish this tomorrow.

QUESTION 1

Write it out like this:

Bowling: F, G, H
Tennis: J, K, L

2. G H

(Conditions are italicized) Since G and H are bowling trophies, and no single shelf can hold all three bowling trophies, then F, a bowling trophy, can’t be on shelf 2.  Which means tennis trophy F must be on shelf 1 because it can’t be on shelf 3 if it’s to satisfy condition that F must be on the shelf immediately above the shelf that L is on.  Which means L, a tennis trophy, is on second shelf.  The answer is 2, tennis trophy L is on shelf 2.

QUESTION 2

Another way to improve Math skills is to practice solving logic problems.  Here’s a set of LSAT (Law School Admissions Test) problems made up by Kaplan, a leading test prep center:

Question 1

Question 2

Question 3

Question 4

Question 5

We’ll review some of the questions tomorrow.  Tip: use a pencil and a notebook to sketch the question.  It’ll help you visualize the problem.

Advanced Essay Writing

Here’s a playful college admissions essay prompt, from The University of Chicago:

Joan of Arkansas. Queen Elizabeth Cady Stanton. Babe Ruth Bader Ginsburg. Mash up a historical figure with a new time period, environment, location, or occupation, and tell us their story.
—Inspired by Drew Donaldson, AB’16

What’s the first step?  For me, I list historical figures who intrigue me.  Here’s my list, I limited it to nine:

• Lee Kuan Yew
• Malcolm X
• Peter Abelard
• Soren Kierkegaard
• Joan of Ark
• Bathsheba
• Soong Ching-ling
• Ching Shih
• Franz Fanon

The one I really want to write about is Soong Ching-ling.  Next I write down what she’s known for.

The Soong sisters grew up in early 20th century Shanghai.  The eldest, Soong Ai-ling, is known for her love of money, so she married the wealthiest man in China.  The youngest, Soong Mei-ling, is known for her love of power, so she married the leader of the KMT, the man who would become president of the Republic of China.  The middle sister, Soong Ching-ling, is remembered for her love of her country and she married revolutionary leader Sun Yat-Sen, the founder of modern China, against her family’s wishes.  Soong Ching-ling eventually broke with her family and joined the Communist Party, remaining in mainland China as her family fled to Taiwan to set up provisional government, aka Republic of China, at the conclusion of the civil war.

The point is to keep it simple and write write write. Don’t think too much, and less is more.

Now we have to fuse her with something or another.  I’m open to anything, time, location, another person, I don’t mind.  I’m going to use the search engine for ideas.  I search for: “words that begin with ling.” That takes me to a site that lists many words that begin with “ling.”  Here are a few that intrigue me:

• lingerie
• lingua franca
• linguini
• linguistics

Next I search: “cities that begin with ling.”  I go to site with list but don’t find anything interesting, only a few small cities, all but one in China.  I’m going to pick “linguini” then and make this a foodie story.  I check to see if there’s anyone named Linguini and sure enough, the fictional Alfredo Linguini, the deuteragonist of the animated foodie film, Ratatouille.  So, I introduce:

Soong Ching Linguini, the daughter of Alfredo Linguini and his mistress Valentina Ching.

We’ll add to this story tomorrow.  Where are you at in your story?

Link to fraction drills: https://www.math-drills.com/fractions.php

Do each within 80 seconds, timed.  Do all five, then grade all five.  Repeat until mastery, 100 percent correct.

Visualize fractions verbal drill

Most people finish the problems by following a process, never stopping to think about what, for instance, 1/2 * 5/8 means.  Or what 3/4 + 3/4 means, most just want to get the answer right.  That’s when Math becomes boring, when it’s just a bunch of processes to memorize.

To fix that bad habit, you’re going to pick two questions from each worksheet and write about what’s happening in each question.  Example, for 1/2*5/4=5/8,  it means

My apple pie plus another quarter of an apple pie was divided in half and given to Jimmy.

Another example, 4/3+1/2=1 5/6 means

I have one apple pie plus 1/3 of an apple pie.  Amy gives me half of her apple pie so now I have almost two whole apple pies, one is missing one slice if the pie is cut into six slices.

This drill will help you visualize numbers when you do arithmetic so you can better understand what’s going on when you manipulate numbers.

The Privileged Poor, once the blog site of a now defunct clothing store, is now the site of the Alive Juice Bar tutoring service.   We’ll be posting daily lesson plans to help students get through indefinite school closures.

Answers and Explanations to Fill in Missing Numbers Exercise

Questions

• 1, 2, 4, x, 16, 32, 64
• 30, 23, x, 9
• 84, x, 66, 57
• 63, 61, 59, x
• 32, 40, 24, 16, 24, x, 8
• 1, 2, 6, 24, x
• x, 12, 18, 10, 6, 14, 5, 0, 10 (this one is very difficult, break it into three parts to find pattern)
• 8, 25, 52, 89, x

Answers

• 1, 2, 4, 8, 16, 32, 64  (pattern is next number is double of previous number)
• 30, 23, 16, 9 (difference of 7 between each number)
• 84, 75, 66, 57 (difference of 9 between each number)
• 63, 61, 59, 57 (difference of 2 between each number)
• 32, 40, 24, 16, 24, 8, 8

Group A:  32, 40, 24, 16

Group B:  16, 24, x, 8

What are the similarities in pattern?  I see that 32 is double of 16 in Group A.  And 16 is double of 8 in Group B.  40 is 8 more than 32 in Group A.  24 is 8 more than 32 in group B.  So if 40 is 16 more than 24 in Group A, then 24 must be 16 more than x in Group B.  24-16 = 8.

• 1, 2, 6, 24, 120 (pattern is 1×2 = second number, 2×3=third number, 6×4=fourth number, 24×5=fifth number, 120)
• x, 12, 18, 10, 6, 14, 5, 0, 10 (this one is very difficult, break it into three parts to find pattern)

Again, break sequence into parts.  Which group doesn’t make sense?  For me, it’s 5,0,10 sequence that’s odd.  Now figure out the relationship between numbers in this sequence.  I see 5-5=second number and 5+5=third number.  Let’s see if this works with other groups.  So,

10, 6, 14.  Hmmm, 10-10 doesn’t work.  Let’s still try to get to six using subtraction, 10-4=6, the second number.  And 10+4=14, the third number!  New theory, the first group will be subtracting and adding by 3.  Let’s try:

15, 12, 18

15-3=12. And 15+3=18!

• 8, 25, 52, 89, 136

Difference between 8 and 25 is 17.

Difference between 25 and 52 is 27

Difference between 52 and 89 is 37

Difference between 89 and 136 is 47.

Key takeaways:

1. Break difficult math problems into parts and then play with it.
2. To develop your intuition for patterns, practice basic arithmetic drills we provide in the first few lessons.

Make your own missing number problems. 

Notice we often ask students to make their own questions?  This not only trains them to be responsible for their own educations, it forces them to think about education from a teacher’s point of view.  It’s training them to see the world from different perspectives.

Make 10 of your own problems.  Example:

• 2, 100, 5, 103, x, 106

(answer is 8, pattern is difference of 3 between every other number).

Scrabble Anagram Drill

• P, N, O, I, A, S, Y

Make 5 words with the above seven letters.  Words must contain at least 3 letters.  Those of you with advanced verbal skills, bump it up to at least 4 letters.

Example: soapy