Rather than shopping or packing up holiday décor, our family spent Boxing Day as we have come to by tradition these past few years, with our friends, the “twins/triplets” family.

For fun photos and a write-up of the event, please visit this page.

Tangrams, a set of 7 figures that --arranged in a certain way -- form a large square, provide a fun and engaging opportunity for students to explore various measurement and numeracy concepts, all while developing their spatial sense.

This morning we spent considerable time "playing" with these ancient Chinese puzzles.  Students worked through a number of guided activities, doing lots manipulating of shapes.  Oral language was used in abundance, and allowed us to develop a bank of high-frequency academic vocabulary.

Some students demonstrated their solutions to various "problems" on the document camera, others drew their solutions on scrap paper and shared with me, or with a partner.

The activity allowed for considerable focussed observation on my part, and assessment was quick and easy.

For more information on Tangrams, or to play with them online, check out the links below:

http://www.mathplayground.com/tangrams.html
http://pbskids.org/sagwa/games/tangrams/
http://games.ztor.com/tang/

Have fun exploring Tangrams!

On this day in 1994, my mother, Carola Beate Teschow, died in the palliative care unit at Toronto Grace Hospital. 

In order to commemorate her life a bit, and share the family history with Alex & Simon, I kept the boys home from school this morning for a special breakfast and to look at photos of their “other grandma”, as they call her.

The boys had questions:  Why did she take a boat instead of a plane from Germany to Canada?  Were the small black and white photographs of her as a child stamps?  Why were they so small?  Why was Auntie Jeanette in some of the photos? Who took the Easter Egg Hunt photos?  Why did Auntie Adele's hair look different? If stress was a contributor to cancer, why didn’t Daddy have cancer?!

After our photo and question session, the boys gave me a big hug, helped clear the table, and then headed off to their room to make playdate invitations for friends at school.  Then we walked to school, and I biked off to work.

Below are some photos taken in the days before digital cameras and the possibility of deleting the appalling shots and keeping the good ones only, when bad hair and imperfect smiles were just a part of everyday photography.  Enjoy!

I'm glad to be a mom myself now -- Having a first hand understanding makes some aspects of my grief more painful, but it also gives me a richer appreciation of my mother.

Last week I got into a bit of a "discussion", for lack of a better word, with someone quite irritated with "angels" as portrayed in the media.  The typical chintzy, cherub babies with wings, it seems, present a "look" that my friend does not find appealing.

It got me thinking...

The word "angel" originates from the Greek "aggelos", meaning "messenger".  Many scriptural references exist describing these messengers.  Interestingly, none of them is portrayed as a winged, chubby, baby-like figure.  On the contrary, as Dr. John Bechtle points out, Biblical angels "are always full-grown adults. When people in the Bible saw an angel, their typical response was to fall on their faces in fear and awe, not to reach out and tickle an adorable baby."

Certainly, the angels I have met are full grown adults.

Recently, my colleagues and I took our students to a "caring and sharing" holiday brunch at the Liberty Grand, put on by Spinmaster Toys in affiliation with Breakfast Clubs for Children.  As part of the event, our students got to go "shopping" in a GIANT ballroom, for toys -- one for themselves, and another to give away to their Kindergarten buddy back at school.  Each student was led around the donated toy-filled hall by an "angel", who helped the kids choose an appropriate toys for themselves and their buddies.  The angels did not have wings. But they did have huge smiles and lots of compassion and tonnes of patience as they answered the children's many questions about the various toy options.

Another angel has come to me by email over the past several years at Christmas Time.  An at-risk family we volunteer with has 10-year-old twins and 6-year-old triplets (all boys!!!)  Some years ago, I put out a call for help with Christmas gifts for this family.  A total stranger emailed me, offering to buy a gift for each child as well as the parents.  She and her family did this, and mailed the package to me, and I delivered it to the family, along with some other items we had fundraised for.  The next year, this angel initiated contact with me again, and again, we were able to add her parcel to the small pile of gifts we were collecting for the family.

This year, our friends--who sign up each year with a local charity for a gift for each child -- were told that they had to sign up with a different branch, due to some postal-code-related policy change.  By the time they did so, it was too late:  That office's gifts were already all spoken for.  Mom told the boys "Santa's not coming this year", at which all five burst into tears.  The afternoon my co-volunteer emailed me this news, I rec'd an email from the ANGEL!!!  She was contacting me yet again to see how she could help!!!  (This family's situation has brought many angels over the few years I have know them. The above story is just one example.)

Yes, I have met many un-winged, adult angels.  Often, they arrive at the most oportune moments, bringing a home cooked meal to me when I was starving at home, at my wits' end, arms full of two screaming newborns, or appearing in my classroom suddenly to offer me an extra planning time at school when I am overwhelmed with paperwork, or arriving at my door with a drill and a willingness to hang countless hooks in my new apartment.  Sometimes, they bring unexpected news that at first seems strange, scary or insurmountable. But always, the angels are wise, much wiser and more in control than I am, in the moments they appear in my life, and I look back on the many instances of their arrival as did my counterparts in scripture, with awe!

One of the ministry monographs on problem-based learning and bansho in particular suggests using butcher paper to create a clean math “wall” on which to post solutions for the debrief phase in a 3-part lesson plan.  This was appealing to me, because I have so little teaching wall space in my classroom.

This afternoon, I tried out the butcher paper for the first time, using a problem inspired by Marilyn Burns’ “The Doorbell Rang” to introduce division.

Behold the stupendous results below:

In a desperate attempt to expand beyond the textbook, and really teach multiplication effectively, I recently put together a series of explorations with various manipulatives to help students construct an understanding of multiplication from four different perspectives.

First, we examined the area model, by making rectangles of various shapes and sizes, and calculating the total area.

Next, we made arrays out of two sided counters, rolling the dice to determine number of rows and columns, then building the array to match.  After that it was time to examine the effect of "0" on a number.  We did this by looking a plates of "cookies" (coloured cubes), and noticing that if we had 0 cookies, it wouldn't matter how many plates we had, we'd still have 0 cookies!  The set model was the perfect way to demonstrate this concept.  (That being said, I'm not sure I'd wait so long to introduce the set model next time, as I think it is an easier to access model of thinking about multiplication than the area model, for Grade 3s.)

One final thing I wanted to do was demonstrate to the students a way of applying multiplication using a combination model.  We had been reading some poems earlier that morning, and I told the students they could choose their favourite poem to copy out on some fancy paper I had purchased at Staples.  I had 3 types of fancy paper, and also one kind of lined paper, for those who preferred the simplicity of lines.  So, FOUR kinds of paper in total.

I also told them that if they wanted to give their copied poem to someone, they could choose one of THREE different kinds of envelopes I had brought for them: full page, business or a smaller size envelope.

The students were very excited, and eager to begin.

BUT... I told them they could only get started on this project after they showed me how many different possible paper-envelope combinations they could come up with.

The students appeared to be quite engaged with this task. A few of them figured out right away that you could get the answer by multiplying the number of paper types by the number of envelopes, but couldn't explain why.  Some students used coloured cubes to represent the paper types, and plates to represent the envelopes to show their thinking.  Others drew pictures to explain their thought process. 

In the end, even the one group who thought the answer was 7 (3 PLUS 4!!!) developed and shared at least two plausible solutions.

The preparation for this math unit was considerably more involved than the typical textbook-linked jot notes in my dayplan, but it was well worth it to see the light bulbs go on for so many students.

I have heard that many of our society’s great “inventions” were discovered accidentally.  For example, corn flakes, now a staple breakfast cereal in many North American households, came about by accident.  (For more on that story, check out this page.)  

This morning, I had such a happy accident.

My insulated lunch bag, which I had hitherto used to keep my freshly cooked