Posted by: jwhiff | June 12, 2016

Quadrilaterals and Shape Shifters

IMG_0167I thought this lesson might be a little boring for my students. Really…how surprising and delightful can four-sided shapes really be?

Fortunately, Shape Shifters always allow for some puzzling and interesting challenges. Can you build a square using your Shifters? Can you prove it really is a square? How about a rhombus? Is a trapezoid possible?

By the way, I knew that it was possible to make 2 regular trapezoids, but thought it was impossible to make 1 regular trapezoid with all 12 Shifters. My clever students, however, figured out a way. See if your students can too.

As always, you are welcome to use and modify my PowerPoint on this topic. Remember to “view slideshow” as I created it to reveal tasks and answers a step at a time. Enjoy!


Posted by: jwhiff | May 13, 2016

Learning about Symmetry with Shape Shifters

I think that the next logical stop after learning about regular polygons is looking at symmetry.  Why?  Some shapes that are not regular polygons are still special,balanced and pleasing somehow.  All sides and angles may not be equal, but it hurts me to simply call them irregular.

How do you describe these pleasing shapes?  You call them symmetrical.

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Understanding Shapes 2

You are welcome to use my Powerpoint in any way you wish.  Make sure that you choose “slideshow” and “play from the start” as I made my powerpoints to be interactive.

Posted by: jwhiff | May 12, 2016

A Mathematical Starting Place for Shape Shifters

Now that your class has created their Shape Shifters and had a chance to play around with them, they should know that they are engaging in some very serious math!!  You will find that they won’t believe you, even after you start into your geometry lessons.  They like it that much.

I start out by giving them language to describe the shapes they have created.  The first question we answer is “What is a polygon?” and then proceed to exploring angles.  I have created a powerpoint with discussion prompts and activities that you can use with your class in exploring this beginning concept.

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Understanding Shapes 1

You are more than welcome to use what you like.  When you play the slide show, much of the text is hidden to allow students to focus on the image and answer the question in their own way.  Touch the space bar to make different parts of the slide appear.

Hopefully it will be interesting and fun for you and your students!


Posted by: jwhiff | May 1, 2016

How to Make Shape Shifters

IMG_0037What are Shape Shifters?  They are twelve little right-angle triangles, designed for the purpose of engaging in transformational geometry.  And they are designed to bring story and culture into mathematics.

IMG_4287At the start, they were made by cutting and colouring triangle graph paper mounted onto card.  Although students were able to discover a surprising number of shapes through transformation, the pieces lacked substance.  They needed something.

This past year, however, I was struck with an idea.  My little set of right angle triangles would find a perfect home in Northwest Coast Aboriginal art. I could picture 4-right angle triangles nested together to form a rhombus on which characters would be drawn and coloured.  Each set would then consist of 3 such characters who would dance and transform into all kinds of delightful creatures.  And perhaps each dance could have a storyline.  What a wonderful thought…story in mathematics!

I also discovered that if you glued the pieces onto a combination of craft foam and felt, they were thicker and more of a pleasure to use.  The felt helps them slide and the pieces come together nicely without overlapping.

If you are interested in making your own Shape Shifters, check out this short powerpoint: Making Shape Shifters

You are also welcome to print out and use my designs.  Or if you wish, challenge your students to draw their own rhombi (using triangle graph paper) and then create their own designs on the plain side.

shape shifter character sheets


Posted by: jwhiff | July 20, 2014

In Den Bosch, Safe and Sound

We’re all a little groggy, but are here in one piece!

Posted by: jwhiff | November 7, 2013

Remembrance Day at Anmore

Today we had one of the most poignant ceremonies we have ever had at this school.  It was quiet, solemn and connected with our school.

A former student in the school, Corporal Tim Laidler, spoke to us about his story.  It began in Anmore and he recalled sitting on the gym floor just like all of the young students were doing today.  He then recalled his journey to becoming a soldier and making the decision to go to Afghanistan.  He spoke of sacrifice, bravery, and service.  He spoke of how difficult it can be coming home after experiencing war.  The need to keep serving.  The challenge of connecting with family.

Our choir sang, “In Flanders Fields” and did a beautiful job.  I am so glad I made the decision to include the gr.1’s and 2’s this year.  They really made the difference.  So many lovely little voices with such a powerful song.  They did a beautiful job.

Several young students spoke about their thoughts on war and this was very powerful!  I was so surprised and touched to hear their thoughts…how war is scary, how we can help…what it means for them.

We also have a wreath-laying ritual at our school.  Two students from each class placed a class-made wreath at the front of the gym while we sang the song “Till the Boys Come Home” (a school tradition).  It always makes me sad-pround.

Each part made me cry.

Posted by: jwhiff | November 5, 2013

Object Study as Math Enrichment

A great math centre is something I call “Object Study”.

Basically, interested students explore a range of collected items (shells, fossils, bones, rocks and minerals) through measurement and observation.

Here’s what you’ll need:

  • a balance scale with various gram weights
  • a large beaker marked with millilitre increments
  • rulers and callipers (cheap at Lee Valley Tools)
  • paper, pencils, erasers
  • a selection of interesting collected items
  • field guides and information books on your items (if possible)

What the students do:

  1. select an object to study
  2. weigh it using balance scale and record weights and total mass on their paper.
  3. measure maximum length and width in cm/mm.  Record these by drawing a horizontal and vertical axis matching the measurements and writing the number and unit beside them.
  4. Complete a detailed sketch of the item inside the axis lines.
  5. Figuring out the volume of the item through displacement (filling beaker with water up to a certain point, submerging the object, recording new water mark, and taking the difference between the new and original water mark).

I find that certain students love this station and visit it all of the time.  Some really slow down and study their object, locating it in the field guides, and even recording extra information about it.

I am still looking for a big enough beaker, by the way.  I have a couple of smaller measuring containers, but some of my rocks and shells simply do not fit inside!  I’ll take a picture and post it as soon as I have one.

Posted by: jwhiff | September 23, 2013

Allowance Project Extras

I should have done this earlier, but better late than never!

I just wanted to make sure that the parent letter and the bank book were ready to go for anyone to use.

Here is the content of the parent letter (just and copy and paste what is relevant):

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I wanted to tell you about a new math project I have started.  It is all about money, counting, saving, spending and giving to others.

Everyday the students have a chance to earn pennies by remembering to complete helpful classroom tasks such as cleaning up after lunch and playtime, hanging up their coats properly, and remembering to put pockets into the bin in the morning.  They will keep these pennies in money pouches that I purchased for them.  Eventually three things can happen with these pennies:

1-they are traded in for other coins.  These are saved in piggy banks that we will be making.  

2-they are spent in the class store.  The class store will have small donated items or items that I have purchased.

3-they are spent on donated items for the food bank.

 Here is where I need your help:

For each child I require: about 10 nickels and 10 dimes.  Please send these in a bag or container labelled with your child’s name.  These will be the “bank” where pennies are traded in.  These coins will be the ones saved in piggy banks and will be sent home at the end of the year.  

 I also need items for the school store.  I was hoping that you might be able to sent a few small items that seem to accumulate and never get played with.  Extras from birthday party goody bags are just the kind of thing I am looking for.  I will be rounding up items at my house as well.  Please make sure that the items are small.  Items can be small toys, balls, pencils, erasers, stickers.

Finally, I am hoping that all families can send in 2-3 non-perishable items for the food bank.  On our charity focused day, the children will shop for these items with their own earned pennies.  All item that they purchase will be given directly to food bank.  Extras will be saved to continue the project after Christmas.

Thanks, everyone!

And, of course, here is the bank book too!

My Bank Book

Quarter page

Remember, that you can visit some of my old entries for some writing on the project and a little tinkering that I did along the way:

Allowance Project blog archive

Posted by: jwhiff | August 7, 2013

Pretty Prague

imageI forgot all about Berlin the afternoon I stepped off the train and beheld Prague–an absolutely breathtaking beauty.

We flirted for an evening and into next morning.  I couldn’t take my eyes off the elegant spires, quaint alleyways  and graceful bridges.  What detail! What perfection! Like a fairytale dream city.

Then the repetitive trinket-shops started to get on my nerves.  Then the crowds.  Thai massage parlours.  TGI Fridays.  Hooters.  What a shame. I wanted to go back to Berlin.

Fortunately, the story doesn’t end there.  We decided to retreat to our hotel room partway through the day to figure out some meaningful way to spend the rest of our time in Prague.  It was hot, sunny and humid when we left the crowds.  When we returned and hour later, a huge storm had cleared the crowds and completely changed the atmosphere of the place to spooky and cool.  We ran from one carriageway to the next, giggling and soaked.

We watched a black light theatre show (famous in Prague) and the kids thought it was a riot. They also found a small pup in one of our many refuges and fell in love.  They went to bed at a reasonable time and left Stephen and I to enjoy a glass of wine and a nip of Becherovka (good for burning nostril hairs). So, after the disillusionment earlier in the day, we ended the evening feeling placated.

The next day was Quentin’s birthday and went really well.  Here is what we enjoyed:image

  • The lady at the Danish bakery.  She sang Happy Birthday to Quentin 3 times, gave him a special cookie and 2 plates of strawberries (one decorated with a whipped cream heart, the other with a number seven), and forced an American tourist to take our photo with her twice.  She also insisted on us buying a giant apple juice and chased us down the sidewalk to hug and kiss Quentin.  We were both delighted with the experience and happy to get out of there.
  • The space observatory. We hiked up a small mountain (a hill, really) to get there.  Two ladies ran the old telescopes (100 years +) and we saw Venus, solar flares and sunspots.
  • Being hot, tired, grumpy and hungry and then devouring smoked pork ribs, roasted duck, cabbage and lots of cold beer.
  • Playing “Guess what time it is now, mom!” with Quentin who was absolutely delighted with his new digital watch.

imageThat about does it! We flew back to the Netherlands the next day and now are savouring our final week here.

Posted by: jwhiff | August 2, 2013

7 Days in Berlin

Not enough!  Despite a few rough patches (noisy nights, the odd record breaking temperature day, and a weird stomach bug), we have had a great time here.

imageWe picked the perfect neighbourhood for enjoying the city with kids (somewhere between Mitte and Prenzlaur Berg).  It is on the old East German side of the city very near the centre, but it feels off the beaten track.  There are tons of well-loved parks, art and fashion shops (all very home-made hip), and a variety of unique inexpensive cafes.  Lots of kids, lots of bikes and lots of opportunity for play.  A very cool place, but inclusive and light-hearted too.  It has been fun puttering around and imagining living here.

The kids carry around a backpack with a soccerball in it (you never know when you’ll need one) and have been able to use it often here.  We have had a couple of great family matches (they can’t stop giggling when mom finally joins in) and even some games with neighbourhood kids.  This means kids of all ages and genders…from barefooted teens to fully-outfitted four year olds and everything in between.  Although many kids are really impressive to watch, playing well is not a prerequisite for participation.  Our kids had a lot of fun, to say the least.

imageOf course we’ve needed to do a little sight-seeing. Berlin has a lot of subtle, but important sights relating to the wall.  We enjoyed interpreting the ground symbols (literally simple lines and numbered circles on the ground) showing escape tunnels paths and individual stories around Bernaur Strasse. We also went to Check-Point Charlie and viewed old sections of the wall.  However, the city has grown incredibly over the past 24 years and most of the wall has simply been swallowed up by development.

We also visited several museums including the amazing Pergamon (with such things as Babylonian city gates and Greek temples reassembled to give scope and dimension to the ancient wonders) and the Deutsches Technikmuseum (with an interactive German history of technology, perfect for the kids).  I also enjoyed taking in the Neues Museum, not for its artifacts so much, but for the building itself.  It was demolished at the end of World War 2 and then carefully reconstructed with all salvageable columns, frescos and brickwork.  All new materials were used to fuse the original parts together.  They match the original parts in their form, but are completely basic in terms of colour so as to highlight the original battle-damaged parts.  The effect is solemn and grand.

The story of Berlin during the Nazi regime is told in bits and pieces all over the city.  Everywhere are photos and short stories of great artists, scientists, musicians, activists, business people, authors…that were lost to Berlin (a once vibrant, liberal, diverse city) as a result of Nazi persecution.  We also saw the remaining foundations of the Gestapo headquarters and the ruins of a train station from which Jewish people and others targeted by the regime were deported.

Altogether, Berlin has a depth that most cities lack.  It is not as beautiful as many European cities, but that doesn’t matter.  It has a positive, creative energy coupled with the psychology of a really complicated past..  It’s one of my favourite cities.

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