Math: Problem Solvers!

Can you see the patterns emerging?

As mentioned a couple of weeks ago, Singapore Math is the backbone of our Math program. However, we also do whole-group inquiry and instruction in our Math group. One frequent group activity is using story problems to develop and practice new problem-solving strategies. 

One such strategy: Making an organized list.

Here's a recent problem we tackled together, starting out as a group, and finishing individually:

This type of problem gets kids thinking about a couple of different things. First of all, it quickly drives home the importance of devising some sort of methodical system for keeping track of your work. You can attempt to do this sort of problem in your head, but you will quickly find that you are either repeatedly coming up with duplicate combinations (actually, they're permutations, but we'll get to that in another lesson), or that you're missing some entirely. 

Instead, it becomes necessary to document your work, and to attempt to do so in an organized manner. In this case, we started by making a chart listing the fish costs, then methodically working from largest numbers to smallest: 

Using the Glass Fish as our basis, we can see a pattern emerging with the remaining numbers in each permutation. Can you see it? (Within each set of numbers for the Glass Fish, the Gouramis go down by one. Once you've populated your chart to a certain point, you can begin to notice patterns, which can inform the choices that you try. 

We did this problem largely together as a whole group. Kids have since had opportunities to try similar problems on their own. Here's another that suggests that you should employ the same strategy ("make an organized list"). 

Kids almost always buy in when there are goofy drawings involved. 

Here, we see the Weebles, the Wobbles, and the Widgets, all working together to rescue poor Wally Widget. (An aside: Before passing this out, I stressed that I want them to become confident problem-solvers in real world math situations. Then I gave them this problem, which is patently absurd. They laughed.)

And here they all are working together. 

Here's how we all got started, 

...and here are some final results: 

The more we've practiced, the more consistently kids have been able to spot patterns early in a problem, then use them to solve them. 

Time for School

Shugufa in 2009

Our Global Village experience has continued to inform our studies. This week, we watched the documentary Time for School. It's a fascinating project that chronicles the journeys of seven children from around the world as they begin their formal educations. The kids come from radically different cultures and backgrounds, and we've been talking about how different factors can help or hinder an education. For example, Ken from Japan lives in one of the wealthiest countries in the world. We watch as he begins school at six years old. He has already learned to read by his first day of class. He has tremendous cultural and family support, as well as a backpack stuffed full of new supplies. 

Neeraj in 2003.

Compare Ken's experience to those of Neeraj. On her first day of schook, she's about 9 or 10 years old (she's not sure), and living in rural India. Her mother takes an extremely dim view of education, arguing that she doesn't have an education, so why would her daughter need one? She also complains that the educated males in their village are unable to find work, and asks why should she bother educating her daughter as well? Neeraj is allowed to go to school only after a full day of hard labor. She attends a night school huddled around a small lantern with other girls from a similar situation. She walks home by herself each night, and arrives in her home after the rest of the household has gone to sleep.

We also meet children from Kenya, Romania, Brazil, and Benin. The first installment aired in 2003, and the filmmakers have followed up with each student twice since. The intention is to check in with each student multiple times over the course a twelve year period. (It's a similar idea to the more famous "Up" series, with a much more diverse set of subjects.)

You can view the original installment here: Time for School (2003). It's about an hour long, and it chronicles all seven children on their first day of school. It's fascinating in its own right. (But we didn't actually watch this in class.) 

Ken in 2003.

The second installment follows up on the kids three years later. It's about an hour and a half long. You can watch it online here: Back to School (2006) (We didn't watch this one in class either, but it's well worth your time.) 

Time for School 3 is available in two parts, and each is about an hour long. They show the students in 2009, and many of them are at crucial points in their educations. It also gives a recap of what we learned about each student and country in the previous installments. We watched these together in class, and you may have noticed your kids revisiting them at home to take notes on each respective student. 

Watch online: 
Time for School 3 (Part 1, featuring Shugufa, Jefferson, Neeraj, and Ken)
Time for School 3 (Part 2, featuring Nanavi, Raluca, and Joab)


There are plans for Time for School 2015, but it has yet to air. We've had discussions in class about where we think each child is by now, and why. 

In the weeks ahead, we'll also be exploring the nonprofits and NGOs that are doing work in these countries and communities to help students succeed. 

Math: A Singapore Math primer

Math groups at Summers-Knoll are taught four times a week at 8:55 AM. Almost the entire school (the 7/8s have Math later in the day) has Math at the same time so that kids at different points in math can join math groups that are at an appropriate level. These levels are determined by where each individual student is in their Singapore Math books. 

As I'm sure many of you know, Singapore Math is the backbone of our Math program. You can read a good primer about the program here. It is an article well worth your time, as there are aspects of the program that are unfamiliar to many parents and families. 

For example, the Singapore Bar Model! I've had a number of parents come up to me over the last few years saying, "I tried to help my kid do this problem last night, but I realized that I'd have to teach them algebra to do it." These parents have benefited from learning about the Singapore Bar Model, a useful way of thinking about and taking apart problems. 

Check out this slideshow to see how the Bar Model is taught and used throughout the program. Read through the whole thing. It seems simple at first (because it is!), but it can quickly become confusing if you skip ahead before understanding the earlier steps. 

This is true of the Singapore system in general: As a general rule, racing through the books is ill-advised. Singapore Math strives to teach students why things work in math, rather than just teaching an algorithm to use. It cultivates a deeper sense of understanding, which makes learning higher math concepts more natural later in their education. 

One way that Singapore does this is adding an additional pictorial step, such as the bar models. 

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Here are a few other things to keep in mind when working with your child in Singapore Math: 

The 4B Textbook and Workbook. They differ in important ways!

There are two books at each level: A Textbook and a Workbook. They differ in an important way: 

- The Textbook introduces topics, teaches strategies to approach problems, and exercises to practice. 

- The Workbook only provides additional practice problems. There is no instruction in the workbook. 

This means that, on balance, the Textbook is far more important than the Workbook! 

I drew a helpful cartoon to reinforce this in class the other day: 

Here's how the Textbook and the Workbook interact. A child starts out working in the textbook, which introduces a new concept. Here's an example from book 4B, introducing the concept of symmetry:

Most students will work through these two pages on their own (though I will also do direct instruction, depending on student needs and the complexity of the concept). Then, they'll get to a little arrow at the bottom of the page. Here's a close-up: 

This means that the student can turn to Exercise 42 in the Workbook to find more problems of this type for additional practice. 

Here's Exercise 42 in the Workbook: 

Your child's math assignment is very individualized to the work I've seen them do in the classroom. For some topics, I might assign the Textbook lesson, as well as the corresponding Workbook exercises. However, in other cases, I may opt to have a student skip the Workbook exercise if they've clearly demonstrated repeated mastery of the concept in class. (This becomes a useful contract with students: "I won't make you do busywork just because the book suggests it. But that means that when I do think you need to do the extra practice, you'll know that I really feel you need it.") 

If your child is in my math group, you should start hearing about weekly math assignments, usually given in the form of a sticky note placed in their books. 

Of course, we do more than just Textbook and Workbook in our math groups, which we will discuss in a future post! 

A quick note about subscribing by email

A technical note: If you've signed up to receive entries of the blog delivered to your email, you might occasionally be missing some content. I just realized that videos that are embedded from Youtube don't show up in the email version. (And in the case of the most recent entry, that means that a lot of the post doesn't make much sense...) 

So you may want to pop over to the actual blog on occasion to check in! 

Have a lovely weekend! 

Greetings from Juna and Eva

Thursday's substitute Music teacher: Jason

Beloved Music teacher Josh is out this week, so I filled in for him on Thursday. Josh's pedagogical gifts and skills are different than my own, so I didn't dare attempt to deliver his curriculum. Instead, we ran our own version of Music class in homeroom. 

The embodiment of Spring works magic in a scene from Fantasia 2000

It started out with a viewing of the 1953 Disney short animated film Toot, Whistle, Plunk and Boom. It's a fun short that traces the origins of the various orchestra sections to their prehistoric roots. It's stylized and fanciful, and even squeezes in a small bit of engineering (I didn't really understand how trumpets worked until I saw this film). Of course, being from 1953, there were also some caricatures and stereotypes to discuss as well. 

After that, we watched a couple of selections from Fantasia 2000. We started with the sequence Firebird Suite by Igor Stravinsky. It's a lovely piece of animation, and it's very dramatic. It's the final piece in the film, and it's a doozy. It instantly prompted conversations about the personification of Spring, and everyone jumped when (SPOILER ALERT) the volcano erupted. The sequence is intense, and it generated a lot of discussion afterward (and, despite my best efforts, during). We talked about volcanos, forest fires, and prairies, as well as the "story" of the piece. 

View it here (though be warned that this isn't a particularly high resolution version of it. If you have Netflix, it's currently streaming there. Even better, get the DVD or Blu-ray at the library!) 

Everyone seemed engaged and intrigued by the concept of Fantasia (take an existing piece of music and create a story that goes along with it), so we watched another of the pieces: Pines of Rome by Ottorino Respighi. 

Here's a clip of the climax of the piece, but it's better to seek out the full version (I couldn't find a copy online.) 




After marveling at how or why the creators of Fantasia 2000 came up with the idea to animate that particular piece of music with fanciful flying whales, I decided to try an experiment. Everyone got paper and pencils, and then I played them the audio of one of the segments that I hadn't shown them. While it played, I asked them to draw what they were picturing. What story would they tell while listening to this particular piece of music? We listened to it twice. 

Here's the audio without visuals. Listen to it! What do you picture? Play it a couple of times and sketch out what you visualize. Try it!




Well? What did you picture? It's bouncy and jaunty, and everyone in our class had a different vision to accompany it, from sword-fighting to clumsy crabs. 

Here's what the creators of Fantasia came up with: 





Listening to a piece of music can be a great way to create a piece of artwork, be it visual arts or a story. It's a method that we'll return to again later in the year. 

Science: Building the digestive system

As part of our Identity theme, we're learning about the different human body systems during our Science classes with Lisa. Check out her recent blog entry to see how we're learning about the digestive system!

Measuring and recording the lengths of our innards

If we could stretch our digestive systems out, they'd be about this long (and much bigger and messier).

In addition to the yarn models, we created models of our stomachs using plastic bags, complete with juices to replicate the conditions inside of them. We inserted torn up ("chewed") bread and corn, then spent some time mashing the food up to observe the results. It was both interesting and gross! 

Art field trip to the UMMA

A tradition: taking a group shot of the 5/6s at the Cube

On Thursday, the entire 5/6 took a trip to the University of Michigan Museum of Art (UMMA) to view some exhibits that related to their developing portrait work. Monica has written a bit about it on her blog, which can be found here. (Check it weekly! She updates every Friday!)

(In her entry discussing this field trip, she mentions that photography was forbidden, which meant that she couldn't get any photos of the kids working. I was unaware of the no photography rule at first, so I inadvertently violated that policy. If you keep it quiet, I'll show you a few of the photos that I got before a security guard politely asked me to put away my camera. SHHHH.... IT'S OUR SECRET.) 

Monica had us spend about fifteen minutes sketching our own versions of a piece.