Tag Archives: K-12

Degrees and angles | 角度

Today in the fourth grade weekend lesson we learned about angles📐 and degrees. We explained what degrees was first🥇 because angles are classified using degrees📏. Degrees were discovered by Egyptians. They invented the degree symbol ° and also came up with the 360° circle⚪.  There is an interesting history of how they connect the movement of the Sun with time.   They first divided a year into 360 days, noting that the Sun moved in a circle. Around 1500 BC Egyptians divided 24 hours⏳, though the hours varied with the seasons originally. Then the Greek astronomers made the hours equal. About 300 to 100 BC the Babylonians subdivided the hour into base-60 factions: 60 minutes an hour and 60 seconds in a minute.

We use degrees to measure angles. An angle is a figure formed by two rays🛴 called sides of the angle. In geometry there are three types of angles: an acute angle between 0 and 90 degrees, right angle a 90 degree angle, and an obtuse angle between 90 and 180 degrees. In 1936 a clay tablet was found buried at Shush (Khuzestan region of Iran🌏) some 350km from the ancient city of Babylon on which was inscribed a script that was only translated as late as 1950. The text provided confirmation that the Babylonians measured angles using the figure of 360 to form a circle. The Babylonians knew that the perimeter of a hexagon was exactly equal to six times the radius of a circumscribed circle. This is why they chose to divide a circle in 360 parts⚪. If we did not discover degrees or angles we would not be able to build anything properly🧱. So if we tried building a house without degrees or angles the house would collapse🏚.

We will talk about triangles next time.

Welcome to our New Google Classroom!!😃

Hello everybody!😃 Welcome back to Magic Math Mandarin.  Since we are staying home because of covid-19, we brought our classes to google classroom so our students can keep on learning even during this pandemic👩‍🏫. Now we can all communicate with each other online💻. In this classroom we will be learning Chinese🈷, math➗, and programming👩‍💻. Our teachers will put new assignments everyday about each topic.  If you would also like to join our wonderful classrooms then here is the class code mtxl6j4

Remember to stay home and don’t get sick!😷 Please join our classroom today!👍💖

 

How to Assign A Shortcut Key to a Style in MS Word

Hello everybody!😃 Today in class we learned how to assign a shortcut key 💻 to a style in Word. What we learned today will be very useful if you are changing all the fonts in a Word document and if you must finish very quickly. In class we assigned a shortcut ourselves. The shortcut is Ctrl Shift E. We made this shortcut to be able to change whatever words we highlight to the font called Normal style in Word.

To do this in Word you have to be on the Home page. Then look in the box called styles and click the thing on the bottom right corner.

After you press that pick a style then click the arrow 🔽 on the style you want.

Then click modify and click Format on the bottom left corner. When you press that there will appear some option click Shortcut Key.

Pick a shortcut you want to give to your style and then press assign.

Yay!! You have now learned how to assign a shortcut key to whatever style you want in MS Word 👨‍🎓👩‍🎓! We will learn much more things in the future😃. Anything is possible.

The White Lion🦁 | 白狮子

Today in class we talked about the story called “The White Lion”. The young👩 minds remember and tell that story so well.

The story is about a little white lion🦁.

The story began in a dark night where the white lion and his big brother were waiting for their mother to come back with dinner.  They were small cubs. The brother of the white lion went to see if their mother was close by.

But a snake bit his brother and ate him.  The little white lion ran as fast as he could from the snake.  He got lost so he just climbed a tree to rest in for the night.  Meanwhile in a village close by villagers were running out of food. The villagers sent a boy👦🏾 to go to the woods to look for food.
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秋天好 | Autumn is good

Today in class we talked about autumn (qiū)(tiān) in this weekend’s Chinese lesson.

(qiū)(tiān)(dào)(qiū)(tiān)(hǎo)
(lán)(lán)(tiān)(kōng)白(bái)(yún)飘(piāo)
(bǎo)(bǎo)(tái)(tóu)(hā)(hā)(xiào)
magic math mandarin

Fall is here.  Fall is good.
Blue sky and white clouds.
The baby looks up and laughs.

Besides 中文, we are also working with other organizations to help children with computer programming 编程.

极客星晨少儿编程

zero, one and two | 零,一,二

It is not easy for a young child to comprehend multiplication by 1, as how they are taught in school is often the robotic multiplication table.   She or he can very quickly answer mutiplications by 2, or 3.    Because of this, questions like “what is the product of 1,2, 3, 4” (i.e. 4 factorial) can get a wide range of answers because the number “1” confuses the young mind.

Pychologist says that an infant learns the number 2 before the number 1.   And we can see why: with 2, there is something to compare against, like two fingers.  If there is only one finger, there is no variation, it is confusing.

When we teach multiplication, don’t forget to show that math is an integral part of the real world around us.   It is invented to simplify addition.  Multiply by 1 means just the thing itself.  Multiply by 2 means adding two of this thing together.  Multiply by 3 means adding three of the thing together.  The thing can be a bag of candies or the footage of a home.

Finally, we should show children how to use computers (not calculators) to do computations.   While a question like “give me the sum from 1 to 199” can be solved within seconds with math tricks, a slightly different question “give me the product from 1 to 199” won’t work with the same trick.  But if you know how to make the computer do the job, you can still answer it within seconds.

 

Logarithm | 对数

As we had explored in previous classes, division is subtraction again and again and again, multiplication is adding again and again.  Exponentiation is multiply again and again and again— They are all inventions to simplify repeated computation.

So is the invention of logarithm: taking log is division again and again and again.   They were invented by John Napier who was a Scottish mathematician, physicist, and astronomer  in 1614 as a means to simplify calculations.

🙂 Today’s  Python numpy class summary:

Log10 means how many times divide by 10 will return you to 1. log10(100) will give you 2 because 100 divide by 10 twice returns us to one.
>>> np.log10(100)
One trillion divide by 10 twelve times returns it to 1.
>>> np.log10(1000000000000)

>>> np.linspace(0.0, 3.0, num=4)
Out: array([0., 1., 2., 3.])

>>> np.logspace(0.0, 3.0, num=4)
Out: array([   1.,   10.,  100., 1000.])

>>> np.linspace(0.0, 12.0, num=13)
Out: array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10., 11., 12.])
>>> np.logspace(0.0, 12.0, num=13)
Out: array([1.e+00, 1.e+01, 1.e+02, 1.e+03, 1.e+04, 1.e+05, 1.e+06, 1.e+07, 1.e+08, 1.e+09, 1.e+10, 1.e+11, 1.e+12])

Bonus:  Did you know that Engineers and scientists used to use a tool called “slide rule” (计算尺) to do logarithmic computations until 1970s when electronic computer and calculators came into use.  You should go and check it out if any of your grandparents have one of these.

Find if something is also somewhere else (contd) | 找一找那里是不是也有

Today’s class we continued the game of finding matches.  We expanded from numbers to names.

Let’s pretend that there is a room out there that has the following famous people:

room1 = pd.Series([‘Grace Hopper’, ‘Albert Einstein’,’Michael Faraday’,’Emmy Noether’,’Ada Lovelace’])

And another room with these famous people:

room2 = pd.Series([‘Isaac Newton’, ‘Thomas Edison’,’Mary Somerville’,’Matilda’,’Ada Lovelace’])

These two rooms are in building:

building = pd.concat([room1, room2], axis=1)

building.columns= [‘room1′,’room2’]

             room1            room2
0     Grace Hopper     Isaac Newton
1  Albert Einstein    Thomas Edison
2  Michael Faraday  Mary Somerville
3     Emmy Noether          Matilda
4     Ada Lovelace     Ada Lovelace

Now we want to find a list of people “who” in the building and the rooms.

who = np.array([‘Albert Einstein’,’Michael Faraday’,’Ada Lovelace’])

Are they in room 1?

np.isin(who, room1)
Out: array([ True,  True,  True])

Are they in room2?

np.isin(who, room2)

Out: array([False, False,  True])

Are they in the building?

np.isin(who, building)
Out: array([ True,  True,  True])

We are constantly comparing things.  How to compare is a very tricky and interesting subject.  You should look up the source code of the function in1d and see how it does it.

Count non-zeros using numpy.count_nonzero | 数非零数

Today our class practiced making the computer count number of non-zero numbers using the numpy library from Python.  This can be useful if you have a ton of numbers.

import numpy as np; import pandas as pd

some_array = np.array([[0,1,7,0,0],[3,0,0,2,19]])

array([[ 0,  1,  7,  0,  0],
[ 3,  0,  0,  2, 19]])

np.count_nonzero(some_array)

5

np.count_nonzero(some_array,  axis=0)  Count across the rows, i.e. count along the column

array([1, 1, 1, 1, 1], dtype=int64)

np.count_nonzero(some_array,  axis=1)  Count across the columns, i.e. count along the row

array([2, 3], dtype=int64)

We talked about this example:

d = {'Basket1': [3, 0], 'Basket2': [3, 4]}
df = pd.DataFrame(data=d, index=['Apple','Chips'])

# Count the number of non-zeros across the rows
pd.Series(np.count_nonzero(df, axis=0), index=df.columns.tolist())

This was the result we got.

Basket1    1
Basket2    2
dtype: int64

That was a very tiny data. If we have a dataset with a million rows and columns, we should definitely do this!

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