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! 

Catching up on Feburary - Hodge Podge #1

February has been a bit of a whirlwind, what with a flurry of field trips and new projects and activities. The blog has been fallow for the last few weeks, so we're going to play catch-up with new posts over the next couple of days. 

First up, a few scenes from school from this week: 

Nick and Imogen preparing for a French presentation. 

Keira and Sam discussing the properties of angles. 

Frigid temperatures kept us indoors for PE, but everyone had a good time doing cup stacking. Did you know that "sport stacking" is a thing? It's good for hand-eye coordination, cooperation, and ambidexterity. Read more here. 

Speaking of cooperation, they were pretty pleased with themselves after building this creation. (They were equally delighted when they knocked it down.) 

There was some cooking in Mandarin today. 

I (Jason) run an after-school comics and cartooning club once a week. A couple of months ago, Oliver started creating a stick figure comic book each week, often featuring the exploits of Guy Wiz.

Guy Wiz is a simple idea: A wizard-type fellow battles his enemies by casting spells that are increasingly ridiculous. For example, Guy Wiz might shout "Pig Spell!" during a brawl, which then causes a pig to inexplicably fall from the sky to vanquish his opponent (and they get much weirder than that). It's a fun little comic.

I mention it because Oliver has been cranking out issues of Guy Wiz. He showed up the other day with twenty issues, each more ridiculous than the last. It's fun to see him taking a simple, silly idea and really running with it, and you can really see his creativity exploding. He's also pretty pleased to have such a body of work, and his classmates (and teacher!) were delighted and impressed.

Warm-ups and work spaces

We often begin our school day with a Warm-Up exercise. Today, this problem was part of it: 

"Divide up the grid into four equally sized, equally shaped parts, each containing numbers that add up to 36." 

This task requires an understanding of addition, subtraction, and rotational symmetry, none of which are particularly complicated concepts for a fifth or sixth grader, but applying them to this puzzle becomes quite a challenge! The kids took to the task this morning, each in their own way. 


One of my favorite things about our classroom set up is the number of options that students have when tackling a task like this. Our home base consists of three large work spaces: "Jason's Room," "Sam's Room," and "The Middle School Commons." In general, we're able to allow kids to move to the space in which they feel the most productive. For some kids, that might mean sitting in a silent room at a desk. For others, the ability to collaborate, talk things through, and move around is vital. Having those options available to a student is wonderful. 

A large focus of the fifth and sixth grade years is encouraging increased autonomy and self-discipline. Having a silent room available to a student is great, but the really gratifying part is when a kid starts to take ownership of their own productivity by opting into the space that works best for them. At the beginning of the year, kids will generally sit with their friends when given the choice, regardless of how much they actually get accomplished. Over time (and with occasional guidance), kids start to figure out what environment works best for them, and under what circumstances. 

Some examples from this morning:

Sydney and Kaeli opted to work together on the whiteboard in the middle school commons. They eventually drew a version of the problem on the board with wet erase markers, allowing them to try several different possible solutions  

Chris and David paired up and began working through possibilities on paper. 

Lee opted into the silent room for part of the assignment, venturing out to collaborate with others when he felt it was useful. Eventually, several kids opted into this room. 

This group was particularly social, though not necessarily as immediately productive as they might have liked. After some nudging, they all made choices to move to areas that were a little more in line with their individual working style.