文字接龍 Shiritori

Age: 4.75 & 7.75

Presentation: 文字接龍 Shiritori

The kids and I played a fun game today while eating our Chocolate Chip cookies at Fat Apples.  It’s something I’ve played with Thumper since she was about 4.5.  This game is a great way to gauge what words your kids know, to have them think outside of the box, to be aware of tones, and lastly, to learn vocabulary from you.

In Japanese, the game is called Shiritori.  Not sure what you would call it in English.  But you could totally do a similar version in English with ending syllables or ending letters.

The Rules

The way you play is simple.  One person starts with a word (i.e. 2+ Chinese characters), probably a noun.  The next person connects it by re-using the last character.  For example, 天空,空腹,腹部,部首,手腳,餃子.  You will note that it’s often a two character word used, even more often a noun.  But, the rules are wide open.  I’ve allowed the kids to use idioms (成語), phrases (大人->人都不在家), to allow the changing to tones between turns (天空->恐龍).

There are rules for what you cannot do as well.  I don’t usually allow the kids to use 子 as ending character, because it’s hard to connect.  Or, you cannot go in circles; 天空->空空 would be bad.

How We Play

This is a game we often play in the car.  Super great for that 15-20 minute drive to and from school.  Typically Thumper starts.  I try to think up of words that are NOT children’s daily words.  Otherwise you will keep using things like balloon, colors, food they eat, etc because it’s easy and things they know.    I make sure to introduce words that I know are new vocabulary, and explain them.  For example 空腹 is something Thumper doesn’t know.  For Astroboy, I have to be patient and wait more than 10 seconds before asking him leading questions.  For example, today he had to use “吃”, and I had to ask him in various ways “What do you like to eat?”  before he could make up a word.  It isn’t because he doesn’t understand the concept, but very young children have a tough time thinking up answers.  They would do much better if you gave them choices instead.

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十項式排列 Decanomial Layout

Age: 4.75 & 7.75


  • Tables Layout
  • Decanomial Layout: Finding Squares
  • Adjusted Decanomial: Commutative Law
  • Adjusted Decanomial: Tower of Jewels
  • Stacking the cubes

Even though I’ve shown Thumper presentations from squaring & cubing, and squares and cubes, we actually never finished some of the introductory exercises in squaring and cubing.  After reading a blog post about it from What Did We Do All Day, I finally found time to do it with the children on Sunday. What Did We Do All Day has a really great post about the exercises and also the variations within the different albums.  I don’t have the NAMC or Montessori R&D albums, though I do have another really detailed AMS album I used as reference when creating my math album this semester.  Ultimately, since my goal was just to show the children these exercises without accompanying written work, I went with  my album.  Partly because I feel I don’t have a strong grasp of how to implement followup work, but also partly because I just wanted Thumper to have the physical experience without all the written work, which often discourages her from working. IMG_6144

These presentations for me are just exercises that are fun and arouses the children’s interest in the squaring and cubing material, all the while giving them a sensorial experience of what it means to square and to cube.  I took all the related exercises together and we just flowed with it.  The whole thing took about 2-4 hours, with lots of breaks in between.  In the classroom, you would do this with at least two children.  I think 2 is a good number.  Anymore and the layouts get messed up way too easily.

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Audio: 說給兒童聽的中國故事 Learning Chinese history through Children-Can-Listen Chinese History

Age: 7.75 & 4.75
Grade: 1st+
chinese history

The children and I have been immersed in the world of Chinese history the last 2 weeks.  I finally managed to put it on my iPhone.  We’ve been listening to them off and on, on our trips to the Books and Me Library in Los Altos.  Thumper loves it, and Astroboy, though he cannot understand most of what he’s hearing, he’s picking up vocabulary and also loves singing the songs.

The set has 10 books and 30 CDs for a total of 60 stories on Chinese History.  The books are more like background info that you could read.  But the CDs are way more interesting.  I’ve been growing to really love the series and plan to eventually get their World History and Famous People series as well.  Let me count the ways of how I love them:

  • Every CD starts with an intro which defines what history is, and introduces the guides of the stories.  There is a little 8 year old girl, 姍姍, and a little boy, who is 5.  They talk to an old man, 魔鏡公公, who tells them the stories.  The two children bicker and talk before and after each story.  They ask questions that children may have after a story, and in a way, summarize what you’re hearing into colloquial language so it’s easier to understand.  The children and I also love it also because the characters are 3 years apart and they way they talk are sometimes just like how Astroboy and Thmper talk to each other.
  • Each story also starts or ends with two theme songs.  We’ve been singing them in the house.  One is 朝代歌.  The dynasties got turned into both a chant and a song.
    It’s neat hearing the kids chant the dynasty names. I never really learned it as a child. The other is just a theme song that talks about how bees love honey and monkeys love to climb trees and kids love listening to Chinese History stories.


    As usual, we change the lyrics up for fun, partly because I’m old and I cannot remember the lyrics. We keep thinking up other things that “like” other things, “xx 愛 放屁, yy 愛唱歌”, etc.

  • The stories are interesting!  History can often be presented as a bunch of dates and names to remember.  Hard to remember 5000 years worth of names and dates.  But really they are stories.  In an audio format, there are song effects, hard vocabulary are explained, and most importantly, they can listen to it again and again.  I remember watching Japanese historical drama as an adult and wanting to find out more about Japanese history because of it.  I hope these series do the same thing for the children.  Here is a sample from the publisher’s youtube channel.
  • An additional reason is because they’re listening to history, Thumper is picking up words that are traditionally use more in historical settings rather than modern speech; words like 爹,娘 (old way of calling your parents),敝上 (what a subject calls his emperor), etc.

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Improving our Chinese through audio resources – Elementary

As we start getting into the harder level Chinese, more subject vocabularies, and thinking about grammar, I keep coming back to the need to use our audio resources better.  Everytime I read to Thumper, and we encounter words I think she shouldn’t have been exposed to, she tells me she has because of the TV she’s watched or what she’s listened to.  Having that prep work done already made it easier to introduce reading and writing.  By prep work I mean, she knows how to speak the language and understands (listening) the language.  Since Chinese is not the dominant language in this country, it is a more time efficient way for us to learn the language through listening than studying it through a textbook.

With that in mind, I’ve finally started pulling out more of the audio resources I have saved in my Evernote.  Here are some of them:

  • The Children-Can-Listen Encyclopedia – Best Thing Ever.  For anything we’re learning, I try to have the kids listen to it in the car.   The encyclopedia is really just DK encyclopedia translated.  But they add a fun factor by having a 2 adults and 2 children interact and explain vocabulary as they go along.  I find that I myself remember the vocabulary more when I hear it used in speech than reading text.   We’ve learned about money, Australia, worms, Solar System, vaccines, poisonous animals, micros (Thumper’s fascination).  Speaking of micros, here is a prime example of something they’re obviously not going to study until they’re way older.  But just like how the children are exposed to this vocabulary in English now through our daily interactions with them, this encyclopedia provides the exposure I can’t provide day to day.
  • The Children-Can-Listen Chinese History – When I pulled this out for Thumper at age 5+, she was not interested, the vocabulary was too hard for her.  However, at 7, she loves the stories!  It’s still quite advanced in terms of vocabulary, but I guess she understands enough to be interested in the story itself.  As usual they add the 2 adults and 2 children to explain things as they go along.  Interestingly enough, though Astroboy loses interest eventually and probably can’t understand this at all, he doesn’t complain about it.  From what I’ve read, parents have kids listen to this in Taiwan in pre-school level even though they may not understand it.  They can move on to the book version (The Children-Can-Read Chinese History) when they get older.  There is also another history audio set called 吳姐姐說故事, but that is for upper elementary or junior high.
  • 聽廣播啦2 – Thumper had been listening to English pop songs when her father drives.  One day she said, “I like Tailor Swift!”  With her limited amount of exposure time to English pop, I realized I need to add the Chinese in ASAP!  I had been putting it off and putting it off till now.  This app has hundreds of radio stations in Taiwan, and actually all over the world as well.  I try to pull it out when we’re doing house chores and in the morning before we start school.  Taiwan’s radio scene is funky to me.  Often a station will just play a mix of English and Chinese songs.  I just usually browse around until I find something I like.  I’ve favorited a few: E-Classical 臺北愛樂, anything from 中廣 (ex.中廣流行網) as that’s kind of like BCC.  What I’m looking for, and haven’t found, is shows similar to Radio Lab or NRP’s Wait Wait Don’t Tell Me.   It’s cool listening to the commercials and daily news in the morning.  I think those provide the more useful Chinese.
  • 喜馬來亞 –
    I have not really used this though I have found SO MANY Chinese audiobooks this way. Apparently China has a much better developed podcast culture.  You can search a specific book title or just do things like 兒童 and you’ll get many people reading stories to their kids.  Many of those are quite professional sounding.  For example, you can get Magic Treehouse and Harry Potter (哈利波特), etc.  The reason I don’t use this is that it requires an Internet Connection, some more research, and the children can’t pull it up themselves.
  • Podcasts through iTunes – 
    I searched and found through iTunes a ton of podcasts as well.  We’ve listened to these.  The good thing about podcasts is that you can download and listen when you have time, especially when you drive.  You can search for “寫給孩子的世界歷史”, “品德生活列車”,“寵壞你的耳朵”,“寶寶總動員“.  Honestly the only thing we’ve listened to is “全家生活FUN!”, a podcast run by a Chinese minister who talks about his family’s life here in the U.S.  I liked the show because they’re talking about things the kids would know, like going to Disneyland or Las Vegas.  But it can be boring sometimes because it isn’t a story.  The others I’ve downloaded and never listened to.  I really dislike moral stories and many podcasts are full of these.  秋木叔叔講故事 seems to be promising.

And then there are all the CDs that come with our books.  So many now a days come with bilingual CD. I especially like “I like Martine” series and the sets from 信誼 (寶寶閱讀列車,幼幼閱讀列車), and lastly, we can’t forget Ciao Hu 巧虎.  That is the best out of the bunch at all levels.  They have stories, songs, subject matter studies, all at the right appropriate level for the children.

I’ve got a ton more, but as I stated in info overload, I don’t use most of my collected material.  So I’m trying to just focus on one or two at a time and not be so greedy.  Otherwise sometimes I’m not sure how to fit it all in.

Characters #501-#510

蛇It is indeed a lot of work to try to write sentences with just 500 characters under your belt and making sure that you reuse characters you just learned, while also making sure you introduce new vocabulary that uses the same character later on. Plus, it has to follow your theme. I came up with the first 3 characters on Monday, then changed the order completely on Tuesday when I had to add new words.  As of now, I’m heavy on first grade characters, and low on verbs and adjectives.  Often, I come up with a sentence, only to realize I need to introduce this OTHER character first, and then 3 characters later, I see it’s all nouns. All this to say, it took me a few hours……and I have 10.  I’m having lot of fun though. Sadly, it took Thumper all of 3 minutes to go through the 3 characters on Monday.  She said she knew them.   I wonder just how many characters she actually knows. On my word doc, I color-coded the characters to highlight current character and review character.  I also made a list of words introduced.   Too lazy to do color-code here.  So here they are.

#601 蛇
平常沒太陽時, 蛇在暖的燈下。

#602 錢

#603 借
我沒有十塊錢, 想跟媽媽借。

#604 但

#605 食
老鼠,蛋,小鳥 是蛇的食物,

#606 第

#607 龜

#608 躲
如果你要抓它,他會躲進水裡 。


#610 洋

Analyzation of Sagebook Character Choices

I have finally come up with how I’m going to choose my next characters.  That took me two blurry eye days and back to drinking coffee.  I know I don’t really need to do things this way.  It would save me so much time to just use a textbook.  For some reason I enjoy the process of analyzing and inputting data.   I also want to be able to keep track of characters learned.  There is obviously another way to do this, when the child practices writing characters, log it in your logbook.  Voila.

Anyways, to come up with the list, first I had to analyze the books and how the characters show up.  It’s really fascinating and took me down different paths.  I learned a few things on how the characters are introduced.

  • Progression of character difficulty:  As the series progressed, more and more characters from second “grade” and beyond showed up.  I say “grade” because they’re saying 3000 characters by 6th grade.  The first “grade” has 508 characters.  It’s really 510 because they added but never introduced 一 and 完.  Second grade was 716!  By series 5, about 50% was from second grade.  Often, the higher the grade level, the more strokes and more abstract meaning.  Obviously this is how most people teach characters.  But what I like about Sage is that they do introduce characters from higher grade level early on.  Many of them are used in children’s books.  Oh! and I also realized, going through all 3000 characters, that if you can get to about 3rd grade, which is 1866 characters, you’re pretty set.  Those seemed to have characters I would deem important to know the meaning of.
  • Division by grammar functions: There is an even division of grammar characters.  For example, they will introduce nouns, verbs, and the other “stuff”; adjective, adverbs, conjunction, interjection, preposition, particles, in a pretty even distribution.  I learned that really, you cannot look at a Chinese character and say it is a verb, a noun, or an adjective.  They combine with other characters to form a word and those words then have grammar functions.  But, I tried anyway because I did not want to look up how each word was introduced in Sage and then define them.  I don’t think I’m too far off though.
  • Words:  Related to grammar functions, I think I will need to introduce different words based on same character as the books in the series progresses.
  • Division by Theme: Characters in a series are grouped by theme.  For example, the Blue series introduces pronouns, direction, numbers, verbs, and helping verbs.  Red series, the last one, introduces school, family life, community life, social life, science, social studies, personal relationships.  Within each book in the series, characters from each theme are introduced.  Looking at the themes, you can see it kind of goes from people outward to community and school life.
  • Character Review:  Because a few characters from each theme is introduced in each book, the child reviews previous characters from the previous book when they introduce new characters in the same theme.  This is in addition to reviewing characters from the chapters you just learned.  I imagine this is the hardest part I’m going to have when I come up with sentences.
  • Other:  Since each character could have multiple meaning depending on words it’s used in, the series makes sure to introduce these words.  As the series progresses, the number of characters per sentence gets longer.   They also introduce other grammar points like questions.  In the beginning most of the sentences are based in reality.  They introduce children’s stories in the pink series (the monkey and pig).

Anyways, I calculated stats on grade level and grammar and decided that my characters will be chosen by themes as well.  Given that subject vocabulary is introduced early on in Montessori curriculum, I decided that I would focus on subjects such as geography, zoology, botany, and solar system.  But once I started choosing the characters, I realized it was really hard to choose!  I had to make sure there is a good distribution of grade level as there are still 200+ characters from 1st “grade” after 500 characters.  Then each series only really gives you about 50 nouns.   Then I have to make sure there is a good distribution of grammar functions, which means I have to look up the common words used for that character, knowing that I would need to introduce different words in the series based on each character.   I also wanted to introduce Chinese counters, conjunctions, colors, math concepts like 個十百千.  So many concepts still not introduced after 500 characters!

i had to narrow my theme for the 6th set given all these constraints.  On the other hand, it does provide me with themes for the 7th series.  Once I picked my 100, the problem comes with order of introduction.  I made a first pass, then as I started writing sentences, kept running into the problem of characters not being introduced yet.  Yikes!  Like the ubiquitous 它.  I guess they got around that problem by using 他.

What did I pick?

All this to say, for the next set I aim to have about 50% second grad characters, followed by first grade, and third grade.  My current breakdown is:

  • Adjective 13
  • Conjunction 4
  • Noun 47
  • Preposition 1
  • Verb 29

My theme will be Math Counters, Geography, and Zoology.   I know it will change as I progress because I will find characters I need that’s not on my list.  But it gives me a starting point.  Another problem I’m having is, how hard to I make the sentences?  Do I write for a 5 year old or 7 year old?

Lastly, as usual, one project leads to another and another.  I kept thinking as I went through the characters that I really need to introduce radicals and counters.  So for sure radicals is next.  I feel like the characters are going to start getting confusing because of their similarities and it’s time to introduce radicals to help with meaning.

Introduction to Squares and Square Root – 平方與平方根

Age: 7.5

Presentation: Transformation of a Square, Passing from One Square to Another, Concept and Notation of Square Roots, Extracting a square root for numbers less than 225.

After our introduction presentation about a month ago to squaring and cubing, I gave some more to Thumper on Monday, as part of my studying for my oral exam.  Maybe a terrible reason to give presentations, but, I’m discovering, we’re actually at exactly the right age for learning how to make squares.  She really loved the material and learning.  There were many, “aha!  I know why” moments.  I wish everyone could learn their squares this early!


Finding the 2 squares in the big square

Transformation of a Square is the first presentation.  Here is where you hold up a 10 square, and using rubber hands, divide it up so that it has 2 perfect squares and 2 rectangles.  For our example, we divided it into (4+6)2.  Then you talk about what you just did.  This 10 got split up into a 4 and a 6 and 2(4×6) rectangles.  All this gives you: 10 = 4 + 2(4×6) + 6.


Had to give a bored Astroboy a task to do.

Thumper tried it herself with other squares.  She has not quite figure out that the equation uses only 2 numbers.  So you can predict what the equation is even without looking at the concrete square.  But I was so good, I did not tell her.  Of course, being an elementary child, she wanted to try this “division on a 1-square and 2-square, which doesn’t play as nicely.  After playing with the squares, we wrote down the equation on our whiteboard and made some mental math calculations to verify that it all adds up.  The next exercise in the presentation had her drawing her own squares.  She drew a 17×17 square.  But was unable to write out the equation correctly.


Passing from 5-square to 6-square

We then moved on to Passing from One Square to Another, which she immediately wanted to do when she was playing with the squares during the first presentation.  Because the first thing she did when trying to see what squares fit into the big 10 was to try to use the other bead squares to reconstruct.  In this presentation, you first try to go from a 4 to a 5, write the equation out.  Then you go from 4 to a 9.  Because she had learned how to transform a square, she knew how to write the equation out.  9 = 4 + 2(4+5) + 52.


Passing from 5 square to 9 square

Technically I really shouldn’t have continued on with square root.  But I wanted to practice.  So I just gave her a short intro with the Concept and Notation of Square Roots and Extracting a square root for numbers less than 225, since those just use her knowledge of what a square is.

In these two presentations, you basically learn what a square root is, and then you try to figure out the square root of a number by using pegs.  See how many perfect squares you can build before you run out of pegs.  For example, we started with trying to find the square root of 14.  You do it by first building 1 square, then building it into a 2 square, then 3 square.  You have to stop after 3 square, with 5 as a remainder.

I stopped after that because she needs more practice, especially with her not being too familiar with multiplication yet.  And the next steps starts getting into algebraic expressions, using and instead of numbers.  I think that’s a bit too early for her.

But isn’t the material and concept fun and easy to learn?  I never thought about squares and square roots this way, but it makes so much sense when you are playing with concrete materials.

I find the children get math in Chinese because of the way we count.  BUT, they get confused by the place values because it’s not the same as in English.  So we will continue to teach math in Chinese, with English thrown in when I introduce nomenclature.

Chinese Nomenclature

Here are some words you will need to know to teach squaring and cubing in Chinese.

  • square – 平方
  • cube – 立方
  • square root –  平方根
  • cube root – 立方根
  • radical – 根號
  • radicand – 開方數