We Had Fun With a Few Living Math Books

Posted by laughingstars - September 30th, 2009

“Living books” is an expression that I think was coined by educator Charlotte Mason. For more info. on Living Math books, check out this page at Living Math! (One of the best websites ever!) By the way, I just noticed there’s something on the page I just linked to about Chrysanthemum, one of the books we did. I’ll have to check that out! I always need fresh ideas.

After dinner, Trishy (age 5) and I read these books:

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Chrysanthemum by Kevin Henkes — This is a sweet picture book about a little mouse named Chrysanthemum. She is happy and confident and LOVES her wonderful name. Until she starts school. The other kids mock her long flower name, and it breaks her heart.

At one point, a classmate says “Her name is 13 letters! That’s half as many letters in the whole alphabet.”

I pulled out a Scrabble set, and Trishy and I laid out all the letters of the alphabet. Trishy seemed to be having fun with that, so we took our time, singing the alphabet song again and again as we put them in the right order. Then I spelled “Chrysanthemum” with Scrabble tiles. We counted the letters in “Chrysanthemum,” and we counted the letters in the alphabet. Then we divided the alphabet in half to show (in a very visual way) that each half contained 13 letters. (Pre-Reading Skills; Math: Computation: Counting; Math: Number Sense: Concept of Half)

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Then the Doorbell Rang by Pat Hutchins — This is a cute picture book, and it’s an old standby for exploring multiplication and division with the littles. Mom makes a dozen cookies for her two kids. Six apiece. Then two more children arrive, so each person only gets three. Then two more kids arrive. And so forth. I laid out 12 M&Ms (since we didn’t have chocolate chip cookies) and we divided them two ways, then four ways, and so forth as we progressed through the story. It was a fun way to introduce division to Trishy. Then we decided to eat the dozen M&Ms, but to share them with Sarah, so we worked out how to divide 12 M&Ms fairly 3 ways. Aha! I found another 8 M&Ms in my pocket! How can we divide them fairly between the two of us? (Math: Computation: Division & Number Sense)

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Annabelle Swift, Kindergartner by Amy Schwartz – Annabelle loves counting money and can count up to 100. She has trouble fitting in on her first day of Kindergarten; then she wows her teachers and classmates by counting all the pennies and nickels handed in for milk money ($1.08 total).

We got out some pennies and nickels and played with them a bit. I helped her count 100 pennies, and I explained what a nickel’s worth. Then she came up with the idea of playing a game where we took turns rolling two dice. Whatever number a player rolled, he earned that many cents. She quickly picked up on the idea of using combinations of nickels and pennies (for example, when she rolled 11, she selected 2 nickels and a penny). (Math: Counting; Computation: Addition Up to Sums of 12 (Adding Dice); Introduction to Counting by 5s; Math: Money Skills)

When I read this book with my son when he was six, I gave him $1.08 in pennies and nickels. I told him cartons of milk were 6 cents each and asked him how many kids must be in the class to accumulate $1.08. Even though he hadn’t been formally introduced to multiplication and division, he “got it” immediately.

Trishy’s My Father’s Dragon Lapbook

Posted by laughingstars - July 16th, 2009

This is 5-year-old Trishy’s first chapter book, and we are thoroughly enjoying it. I gave The My Father’s Dragon series to Sarah, now 15, and it has been passed down through all three kids.

This is adapted from Homeschool Share’s My Father’s Dragon Lapbook. Ami, who designed this terrific project, made a much more elaborate lapbook with her son.

This is our version:


This is my favorite part of Ami’s fabulous creation — Elmer Elevator’s knapsack with the things he took on the trip. Of course, each one (chewing gum, hair ribbons, etc.) is crucial to the plot. ;-)


We cut out images of some of the picture in the book — we found them here. We used them like sequencing cards. Trishy did a great job of putting the events in sequential order (narration, sequencing). Then we put them into a tiny book.


She decided to dictate a narration, referring to the pictures in the mini-book to put things in order. I noticed that she didn’t seem to really grasp the plot. She put events in order, but she didn’t remember how Elmer resolved each problem he encountered, nor did she seem to see the cause and effect involved. (I’m noting this because one reason for this blog is to document her unfolding developmental progress.) I suggested we re-read the book. I’m happy with where she’s at ;-) — but I don’t want her to miss “getting” this fun story, especially since she’s been having so much fun with it.


We also put in a library pocket for animal cards. I made nine cards showing the different species who cohabitated on wild island. We talked a bit about classification — reviewing characteristics of mammals, for instance, and talking about different types of mammals (e.g. “primates are mammals that have hands,” “ungulates usually have hooves…”)



Our map of Tangerina Island and Wild Island.



A little living math — thanks, Ami! She got a little confused figuring out how many mouths, how many eyes, and how many legs 7 tigers have. So I got out 7 little plastic animals and she counted. (introducing skip counting; multiplication)

Elmer Elevator and Elementary Math

Posted by laughingstars - July 3rd, 2009

Trishy has been very interested in numbers lately. She spends a lot of time writing numerals and asking about the numbers they represent. (“What is nine-zero?” … “Ninety … nine tens;” “Is three and four seven?” and so forth)

We just finished My Father’s Dragon, which is full of math. Julie at Living Math first made me aware of how many wonderful kids books are also living math books.

Trishy recently taught herself to add while playing Rat-a-Tat-Cat — she got tired of waiting for someone to add up her score and did it herself. My approach is usually not to teach her things (unless she asks) or even necessarily to introduce new ideas. Instead I’m kind of like an anthropologist, observing and taking notes.:-) Does this make sense?

I noticed she added by counting on (for example, 0 + 1 + 1 + 4 … “zero … one … two … three, four, five, six) I know this is one of the addition techniques they teach to early elementary school students. Many professional teaching methods mirror kids’ own intuitive learning processes. Another example was how my older daughter’s Kindergarten teacher made it a goal for the kids to write with “invented spelling.” This is a natural, intuitive part of the process of learning to write for many kids — natural learning guru John Holt has written about it. :-) It bothers me, though, when educators turn this kind of thing on its head. Instead of understanding that this is a common developmental milestone, and using this knowledge to help observe and celebrate the process, it’s pushed on kids. My older daughter was pushed to write with “invented spelling” long before she was ready. And some children just don’t learn this way.

As we were reading the adventures of Elmer Elevator, we got to the part where he ate 7 of the tangerines he’d put in his knapsack. Trishy stopped me. “How many did he have to start with?”

“I don’t know.”

“Why don’t you know? Go back and find out?”

We discovered that Elmer started out with 31 tangerines in his knapsack, because that was how much room he had.

“Let me figure out how many were left,” Trishy said. “I’ll count backwards. Thirty one … thirty … twenty-nine … twenty-eight … twenty-seven … twenty-six … twenty-five … twenty-four.”

Later Elmer picked 7 more tangerines, and Trishy worked out that this got him back to 31. (inverse functions)

I thought that was cool. Many other mathy moments came up in this book. Trishy studied the seven tigers in one picture, as they watched each other chewing gum. She paired them up. I pointed out that one was left over, and I mentioned the concept of odd numbers. We counted their 14 eyes by counting by twos. She also counted the 18 crocodiles in another picture. She still has a little trouble with that, because she tends to skip “17.”

She also had fun making a few predictions about how he would use the various items in his knapsack (which included chewing gum, lollipops, magnifying glasses, a comb, toothbrush, toothpaste, hair ribbons, and a jackknife) in his adventures. (“I wonder what he’ll use to get through the knot on that rope?” … “The knife!”)

Animal Farm

Posted by laughingstars - December 10th, 2008

Monday, we wrapped up our reading and discussion of George Orwell’s Animal Farm. (Click the link for a summary of the book and discussion of the characters.) Here is a video on the historical symbolism in Animal Farm. I watched it with the kids after our discussion, because I wanted them to draw their own conclusions rather than having them spoon fed to us.

For our discussion, I used the chapter on this novel in Deconstructing Penguins as a model. I took out the pictures and character summaries the kids had done for each major character in this book. Then we spread them out on the coffee table.

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I talked to them about Animal Farm being considered an allegory for the outcome of the Russian Revolution. In explaining the concept of allegory, I mentioned how Aslan represents Christ in The Lion, the Witch and the Wardrobe. They grasped that immediately.

I outlined what I knew about the Russian Revolution, which didn’t take long. ;-) I mentioned the condition of the serfs under the old feudal system, Karl Marx’s ideas, the overthrow of the tsar, the failed Menshevek Revolution, the Bolshevik Revolution, Lenin, Trotsky, and Stalin. We talked about Stalin’s reign of terror and the way people lived in the Soviet Union during my lifetime. People lived in terror of the government, and party leaders owned cars and private homes while workers lived in over-crowded apartments and stood in line for bread and toilet paper.

I had a friend in college whose grandmother was from Poland. She spent her life waiting in line for meager food rations. After she immigrated to the U.S., she walked into a grocery store. Seeing the unimaginable abundance — shelves loaded with food of all kinds — she burst into tears. Whenever I am tempted to complain about, well, ANYTHING, I remember her.

James and Sarah didn’t have any difficulty connecting some of the characters in Animal Farm to the historical figures I mentioned. For example, Farmer Jones is the tsar, Snowball is Trotsky, and Napoleon is Stalin. They had no trouble seeing that Moses, the silly raven who sat on Farmer Jones’ shoulder with his stories of eternal life on Sugarcandy mountain, represented the church, and they understood what that implied about Orwell’s view of religion. We talked a bit about the church’s role in history.

I think it’s important to distinguish between the historical role of organized religion in helping maintain an unjust social hierarchy, including the divine right of kings and all that, and the spiritual truth that churches can offer. It’s also worthwhile to look at how the role of organized religion has changed. I did an interesting research project in college on the Catholic church’s role in Latin America — it went from holding down the “lower” classes to being a champion of the poor.

We also talked a little but about Orwell’s atheism and socialism and his view of humanity and of history. Sarah thought Orwell’s view of human history was bleak — it was inevitable that tyranny was going to win out. Borrowing a page from Deconstructing Penguins, I guided them to think about whether any basically good characters could have triumphed over Napoleon and established a truly fair and equal society. After all, Orwell was a socialist himself; would he write a book saying that a socialist revolution was wholly hopeless?

“Was there any animal — besides the pigs — who could read? Was anyone else as intelligent as the pigs?” They realized that Benjamin the donkey was. However, he refused to involve himself in animal politics, just saying cryptically that “donkeys live a long time.” He didn’t take a stand until it was too late. The kids realized that Benjamin represented “the smart people” — the intellectuals. Orwell saw them putting themselves above politics and refusing to use their education, and their ability to think critically and write persuasively, to improve the world.

Sarah said hesitantly, “Benjamin is Daddy.” She was referring to the fact that Matt, who is a very intelligent, good man, chooses not to vote. In a nutshell he doesn’t see any politicians as being worth it, and he doesn’t foresee any real change in our system. He and I debate about that a lot.

Of course, Benjamin could have been killed, in a second, by the pigs’ “secret police” — the dogs Napoleon had trained to do his bidding. Again, I took a page from Deconstructing Penguins. I asked, “Is there anyone the dogs were afraid of?” James immediately said, “Boxer.” He referred to the part of the story where the powerful workhorse, Boxer, accidentally stepped on a dog and sent them all running with their tails between their legs. Boxer didn’t understand what was happening on Animal Farm, but Benjamin did. The two of them together could have been an unbeatable team.

That’s why I love this book and couldn’t wait to share it with my kids. It’s not for it’s dark view of human nature, though there’s a grain of truth there. It’s for the underlying message of hope and of the responsibility we all have to be educated as best we can, be thoughtful citizens, and have the courage to take a stand.

In talking about this responsibility, we also returned to the subject of Stalin’s dictatorship and segued into Nazi Germany. I mentioned this poem:

When the Nazis came for the communists,
I remained silent;
I was not a communist.
When they locked up the social democrats,
I remained silent;
I was not a social democrat.
When they came for the trade unionists,
I did not speak out;
I was not a trade unionist.
When they came for the Jews,
I did not speak out;
I was not a Jew.
When they came for me, there was no one left to speak out.

by Friedrich Gustav Martin Niemöller

Deconstructing Luna

Posted by laughingstars - September 11th, 2008

Sarah and I are reading a lot of young adult literature together. We did a simple literature study on Luna by Julie Anne Peters using some of the methods described in Deconstructing Penguins by Nancy & Lawrence Goldstone. This novel deals with issues that are sensitive to some, including a teenaged boy who is transgendered.

I have always felt that literature study should be done with a light hand. I took AP English in high school (overall, an excellent course), and I served time as a university English major. :-) With Sarah, I am not interested in delving deeply into things like symbolism and literary Christ figures, though we will want to touch on these things at some point. I have vivid memories of classes where we were supposed to come up with a new and different answer to the question “What does the fire in The Lord of the Flies symbolize? With all the English majors and professors out there writing papers — unless you come up with an idea that is particularly inspired or wildly bizarre — I trust it’s already been done.

This is part of the reason I found Deconstructing Luna helpful, even though it’s geared toward younger children. It reminded me to keep things simple, and it offered concrete strategies to help me get started.

So onto Luna. I think it is a good book for adolescent readers, especially those who — like Sarah — are interested in sexuality and gender identity issues. It does deal with mature themes, and it uses strong language.

The story is told from the point of view of an adolescent girl, Regan O’Neill. Her older brother, Liam,
is a transgendered teen, and Regan is the only one who knows his secret. At night he becomes Luna,
his female persona, his “true self.” He uses Regan’s room at night to dress in women’s clothes. During the day, he dresses in “boy role” and goes through his “normal” life. Feeling disconnected from himself and trapped in the wrong body, Liam becomes increasingly depressed.

Together, Liam and Regan keep Luna a secret from their parents. This is complicated by the fact that their dad has very traditional ideas about gender roles. He does not like his wife working outside the home, even though the family desperately needs the money. And he is anxious for Liam to be a typical “guy” and pushes him to play sports.

Meanwhile their mom, who has fought to carve out an identity for herself apart from her role as wife and mother, works as a wedding planner. At the same time, she has become increasingly angry and self-absorbed. One of the things I admire about this book is that it isn’t a trite story about a mom trying to liberate herself from obnoxious, chauvinistic husband. The characters are more complex than that. Even though I didn’t like some of the dad’s attitudes toward his wife and kids, and toward gender roles, I found myself identifying with him. I saw him trying to hold the family together as his wife, who also has a substance abuse problem, drifts away.

Meanwhile, Regan finds the task of protecting her brother/sister’s secret a heavy burden. When she is in about sixth grade, Regan’s peers start noticing something “weird” about Liam. She pulls away from them, living with few friends and struggling to begin dating a boy she really likes. She laments that she has become invisible — living through Liam — without a life of her own.

At breakfast, Sarah and I talked about protagonist/antagonist, conflict and themes. Our first task was to identify the protagonist and antagonist.

Contrary to popular belief, the protagonist is not necessarily the hero. We talked about this a bit. The protagonist is basically the person whose striving or struggles — the thing he is trying to accomplish — form the central conflict of the story. The antagonist tries to hold him back in what he’s trying to do.

After I presented this Sarah, Marie used The Lord of the Rings as an example. Frodo, the protagonist tries to destroy the Ring of Power, and Sauron (antagonist) tries to stop him. Of course, LOTR is a lot more complicated than that, but if you boil it down to its most basic elements — that’s the story.

Who are the protagonist and antagonist in Luna? There is no epic quest and no clear good and evil. It’s about real life, which is messy.

Sarah considered the following theories and we made a simple chart.

Liam is protagonist?What does Liam want to accomplish? Transitioning from male to female (a process that will culminate in sexual reassignment surgery)What qualities does he have?

  • brave
  • fashion conscious :-)
  • phenomenally smart
  • sensitive
  • effeminate
  • clever
  • independent
  • does things his own way
  • knows what he wants and will do anything to achieve it
  • sometimes seems self-obsessed, more concerned about his struggles and his male-to-female transition than in how his actions affect Regan.
So who is antagonist? Who is trying to hold Liam back from achieving his goal (transitioning)?

  1. Hoyt Doucet? (a bully who called Liam a “fag” and a “pervert,” even before Liam outed himself as a transgendered individual) What qualities does Hoyt have? Sarah described him as an “asshole” and “really mean to Liam.” That about sums it up. Hoyt is basically a one-dimensional character who is not really integral to the story.
    We crossed him off the list of suspects.
  2. Liam’s mom? Sarah described her this way:
    • self centered,
    • screechy
    • neurotic
    • whiny
    • detached
    • does nothing but talk to “Handy Andy”
      (her business partner)
    • Leaves Liam at the mercy of his dad’s “butch beating”

    Is Mom holding Liam back from transitioning and finding acceptance for who he really is? Regan eventually realizes that Mom has always known his “secret” on some level, and she has held fast to her denial. In this way, according to Sarah, she “left Liam in the Atlantic without a life boat” when he really needed her support.

  3. Liam’s Dad? Sarah described him as “macho mucho,” having stereotypical views of gender. He can be seen as holding Liam back from transitioning through his gender role expectations. He definitely wants Liam to be “all boy.” And while any parent might have difficulty with such a revelation, this makes it particularly difficult to approach him with the truth.
  4. Regan? Is she holding Liam back, even as she is trying to love and support him, by being terribly afraid of what people will think when he transitions? Even though she sees how depressed he is in “boy role,” empathizes with and supports him, and feels burdened by the secret, she urges him NOT to tell others. According to Sarah, “Sometimes she is really mean. The idea of his having a sex change really freaks her out, and she worries a lot about how it will affect her.”
Is Regan the protagonist?
What does she want to accomplish? To live her own life.

What qualities does she have?

  • giving, always does what others want her to do
  • has trouble setting limits for herself
  • smart “in a different way” from Liam
  • musical
  • shy
  • not as brave as Liam
  • doesn’t know what she really wants
  • sometimes seems self-obsessed because she is more worried about how Liam’s transitioning affects her rather than about his struggles.
If Regan is protagonist, is Liam the antagonist? He holds Regan back from being free to live her own life, though not intentionally, by “having her keep a huge secret and having her help him transition.”

So maybe Liam is the protagonist and ironically, his closest supporter — and the only person who knows Luna, Liam’s real self — is the antagonist. It seems equally possible that Regan, struggling for her own identity and her own life, is the protagonist and Liam, whose needs seem to be holding her hostage, is the antagonist. This is highlighted by the fact that
brother and sister can be seen as having opposite qualities. For example, Regan seems, unlike Liam, not to know what she wants, and she can be seen as less courageous and more conventional. They love each other, and readers can easily
empathize with both of them; this highlights the fact that the antagonist and protagonist are not necessarily “bad guy” and “good guy,” nor are they necessarily enemies.

Sarah and I suspect that both these scenarios are true. Can Liam really transition as long is he is close to his sister? And can Regan ever find her own identity, and live her own life, as long as she is close to Liam? I guess the ending of the book is really inevitable.

We also still think Liam vs. Mom & Dad are viable contenders for the antagonist & protagonist/central conflict slot. We agreed that a book does not necessarily have ONE antagonist & protagonist and conflict. In this case, these literary elements are multi-dimensional.

When I was in school, we were sometimes given worksheets on literature with blans to fill in things like “plot,” “conflict” and “theme.” We assumed we’d be graded on whether we worked out the”right” answers. I see these things less as questions to be answered as a process of discussion about the book. I don’t really care whether we figure out the “right” answer or whether we come to a conclusion at all. The act of exploring these questions — that’s the thing.

Finally we talked about theme. What is the theme of Luna?

1. Gender Identity — This theme is made explicit in many ways. Sarah pointed out — and I think this is an apt observation — that these things are often less subtle in YA literature. Mom struggles with her husband’s role expectations for her, as wife. Liam struggles with gender expectations on several levels. Regan ponders the role of gender expectations in our lives and how they limit us.

2. The Individual vs. Family & Society — Liam struggles to establish his (her) identity in the face of family and societal expectations. Regan struggles with this on many levels. In addition to the burden of being her brother’s entire support system, she deals with the fact that teachers have certain expectations because of her ultra-brilliant older brother. She
and Liam even share the same best friend. Mom struggles to establish an identity separate from her family.

I told Sarah I thought a book’s theme was a bit like light shining on a piece of quartz. If you see the same ideas, or the same struggles, reflected in the story in many different ways, chances are it’s a central theme.