Posted by: jwhiff | October 21, 2016

Digging a Hole: The Story of a 2-Month Inquiry on Clay

Sometimes, you just can’t plan the awesome stuff. I didn’t have a burning desire for an inquiry project to kick off the year. Nor did I have any idea (even a vague one) that I would start the year teaching (and learning) about Earth Science, but sometimes these things just fall into your lap. 

On the second day of school, an assorted grouping of children from grade 1 to grade 5 were working with me in our fairy garden.  They were attempting to dig a lake for the fairies and fill it with water. The problem: the water wouldn’t stay in the hole. I remembered having this very issue when I was a child. It was a problem I tinkered away on in my back yard for a significant amount of time. I figured if I enjoyed this problem, then so would my students.

So, once I was assigned my class, I started science outside digging holes and filling them with water. The holes weren’t very large (the volume of a large yogurt container…approx. 1.5 litres). We dug them on the edge of the playground (where twisted ankles were less likely) and timed how long they took to empty.

Boring? Weirdly, no. The holes all took any where from 2 mins to 30 minutes to drain. The kids were puzzled! Why did some holes drain much more slowly than others? 

After predictions, discussions and hypotheses, we tried again. This time, they spread out more, looking for ground they thought would drain even more slowly. One group’s hole took over an hour to drain! It drew a huge crowd of kids loudly counting off the seconds. They continued to monitor it after school. 

Of course, we needed to investigate this spot more. After a bit more digging, what did they find?? Clay!

Every student ended up with a small chunk to mold and dry. Would this clay be strong? How does it compare with natural clay sold in the store? 

I bought some so we could explore the similarities and differences. Every student was given a small ball to play around with. Would this clay be stronger than the playground clay? 

After letting both sets of clay dry, we compared the strength of each sample, by tapping, pinching and dropping it (and recording observations all the while, of course). 

Store clay seemed stronger, but wasn’t as strong as they thought. One student thought we should test how they compared after being submerged in water. Which type would be stronger then?

The result of this experiment and the conclusion of our inquiry will be revealed in my next post!

Posted by: jwhiff | October 12, 2016

Number Practice Activities

With all of the project work my class, it is important that I have thoughtfully designed number practice activities.  Here are a few that you are welcome to use and modify as you like:









I used Comic Life to create the place value activities, by the way.  It’s pretty handy for creating all kinds of handouts.

Posted by: jwhiff | October 11, 2016

Inuit Class Game

My class has been working away, researching about the Inuit and creating trivia cards.  It is the first phase of a great Social Studies game format that I have tinkered with over the years.

Here is how you start:

  1. Organize your class into 2-4 large teams
  2. Find reading, film and web-based materials your class can use to research about the Inuit.
  3. Cut tag into trivia card-sized rectangles (or squares)
  4. Have the kids work at creating a series of trivia decks that they will use with a partner to challenge partners from other teams.

Once the kids have done enough research and created decent trivia decks, time to get playing.  Every time they play, they should have a different partner from their team.  That way, kids are constantly working and stretching their social muscles.

Here are some materials that I have created that explain the game.  I print off one copy of the instructions for every group of 4 kids and place these–along with trivia decks, dice, health points (coloured beads), animal, family and technology cards–into bins for each game group.  You are welcome to use any or all of my materials.




By the way, this game becomes more complex as the term progresses.  I will post the materials I create for the phase in which Arctic explorers start to enter the story.

Posted by: jwhiff | October 8, 2016

Learning Large Numbers Part 2: Human Cities

screen-shot-2016-10-08-at-8-26-08-amWe began this phase of the project by sorting population numbers from the various members of Metro Vancouver.  These are less interesting than animal numbers, but they are a handy point of comparison that the kids felt they could visualize because they live here.  12,000 cheetahs in the whole world doesn’t seem like so many when there are 34,000 people living in the city of Port Moody.  Port Moody doesn’t even seem all that big!

screen-shot-2016-10-08-at-8-26-28-amNext comes searching for the most populated cities in the world.  The kids brainstormed ideas for the largest cities they thought exist.  Then I took them into the lab and they looked them up.  By the way, it is difficult to get a straight answer for a population of a city.  This ended up becoming another critical thinking task.  Why do different websites have different populations for the same city (in the same year)?  Why are some website’s top ten most populated city lists quite different from others?

The kids are blown away (as am I) by the size of some of these cities, by the way.  Some students become a little demoralized by the whole thing, especially when you start exploring car, pollution and sewage numbers.  We listened to podcasts (, watched a depressing Youtube video ( and found data on the number of cars out there.  My job is not to demoralize children, however.  They need hope, right?

So this is where we started looking at density as a solution for preserving habitat.  This is actually quite fun.

First, I taught them how to estimate the population of a high-rise.  Well, I actually didn’t teach them at the start.  I threw them into a small problem task first.  Here it is: apartment-problem

This was quite tough, actually.  I realized they needed some more practice with this, so I had them take a hundred square and, using washable marker, map out a series of apartments that could comfortably fit rice “people” (pieces of rice).  This hundred square becomes a standard floor in a high-rise.

d531eea0c68b11e38ee85161e8abc65b-rotated-57ec5b48c408fb1f42aaf927-pxgg4_28-09-2016-05-07-35Then they worked together to create apartment buildings by stacking hundreds and thousands blocks together to create high-rises.  They placed their standard floor design on the top and put the rice people into the apartments.  The assumption here is that every floor of the high-rise is a duplicate of their standard floor plan.  That way, they simply need to figure out the number of floors and multiply it by the number of rice people living on each floor.  They moved around the classroom and figured out the population of each model high-rise.  They then figured out the population of the whole city.

Next comes designing a green city.  In our neck of the woods, developers have purchased an old town site known as Ioco and plan on creating a high density community there.  The property includes much local forest.  The problem I posed to the kids is, how would you develop this land for as many people possible with the least amount of damage to the forest?

Over 3 blocks (of 1 hour each), the kids worked together in groups to create model cities:

d531eea0c68b11e38ee85161e8abc65b-rotated-57f4546ff39af46eafda1a75-rdtw8_04-10-2016-06-16-30d531eea0c68b11e38ee85161e8abc65b-rotated-57f454b4b3090246eca2c947-pdqls_04-10-2016-06-17-39d531eea0c68b11e38ee85161e8abc65b-rotated-57f453f9f39af46eafda1a44-cer81_04-10-2016-06-14-33d531eea0c68b11e38ee85161e8abc65b-rotated-57f4541cc0e14a46f56f99a3-spkp4_04-10-2016-06-15-07Note the animal over passes, green roofs and bean cars on the roads, by the way🙂  My advice: don’t go for pretty.  They need to get back to the math ASAP.  Plus, the quicker the project, the more fun it is.

Right now, we are on the population estimating phase.  I printed photos of their cities and they are labelling and calculating building population estimates.

Next comes this nice little problem: city-of-lougheed-pdf.  It is based on another development planned on the border of Burnaby and Coquitlam.

Followed by a map-making exercise:  ioco-photo

Posted by: jwhiff | September 28, 2016

Learning Large Numbers Part 1: Endangered Species

I have trouble forcing my kids to swallow any learning without making it 1. genuinely fascinating or 2. real.  Big numbers are fascinating to kids if you find the right context.

I started with sorting species of animals.  No numbers.  Just got them to show me how they would sort them.  Here is the document I used:  interesting-statistics-for-math.  I didn’t use all of the numbers on this page.  I focused on the specific species at first.  Plus, I didn’t give them any numbers at first.

I made sure to show the kids pictures of the animals, too.  I created a Powerpoint that I continued to modify over the course of the project:  animal-guessing.  Don’t reveal the numbers at first.  I added the numbers later.  By the way, you’ll see that I added human numbers after the animal slides.  Save these for later as well.

Next came population numbers for each animal.  I handed out the numbers and asked the kids to make a guess at which numbers matched each animal.  They then created a list of species from the most endangered to the least (according to their assumptions).  This was all done with a partner at first, by the way.

screen-shot-2016-10-08-at-7-43-05-amEventually the real matches were revealed.  However, these numbers pose an interesting problem:  how do I know if they are accurate?  How are animals numbers even collected?  Do all websites have the same data?

We explored this issue for a number of classes.  The students chose animals off the list and double checked a number of websites to see if my numbers were accurate.  Conclusion?  You can never simply believe the first thing you read.  There was a huge range in what websites were reporting.  This is a very interesting (and important) critical thinking task.

And is 12,000 cheetahs a large number or a small number?  How can you tell?  We tackled this problem two ways.  First, by building the numbers.  Second, by comparing the numbers to populations in human cities.

In order to build the numbers, we needed all of the base ten material in our school, orange paper and meter rulers.  We built animal numbers and we also did this:


We didn’t stop at a million.  We arranged cones in the gym to mark off ten million and hundred million.  Billion was a cube the height of the gym.  By the way, I continue to use the image above in practice tasks I design.  It is a handy reference for all students.

Next comes human populations through cities, cars, garbage and sewage.

Final word on this phase: the kids forget they are doing math.  Plus, this kind of context for learning brings learners of different mathematical strength together in a comfortable space. Kids who find number work boring because they crave bigger challenges love it because there is so much critical thinking involved and they find animals endlessly interesting.  Kids who need practice get lots of exposure to numbers in a meaningful context.  Cynicism is very low.



Posted by: jwhiff | August 31, 2016

Rock Science Ideas

Here is another Powerpoint you are more than welcome to use:

Life of Rocks

It is a good way to start kids thinking about the rock cycle and I really like its simplicity.

My students had a good time collecting rocks off of the playground and then using pebble identification guides that I purchased in order to try to figure out whether they were sedimentary, metamorphic or igneous.  I highly recommend this handy dandy guide:


We also wrote poems about our rocks.  I wanted them to know that every rock has an epic, ancient story behind it.  So, the kids worked in groups to brainstorm as many ideas about how their rocks got here.  Then, they turned their favourite ideas into poems.  They were allowed to use ideas off of the list or come up with others.  Here is what our brainstorming looked like (and a sample poem that I put together in front of the kids using their ideas):

How did you get here, Rock?

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.

Screen Shot 2016-05-13 at 2.26.32 PM

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.

Screen Shot 2016-05-11 at 6.20.34 PM

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


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