Posted by: jwhiff | July 24, 2018

The Experts!

An expert’s job is to read ahead and absorb information about the chosen mystery numbers topic. They will help their classmates uncover the mystery by being there to take questions. Experts can also create power points or some sort of presentation for the big reveal (Sample: Basketball Points)

The first time around, this should be your job. You are modelling it for your future student experts. By the way, I will post up the necessary links!

Posted by: jwhiff | July 24, 2018

MN6: GDP of Underprivileged Nations

Now that your class has examined the earnings of the wealthiest people in the world, time to look at 10 nations that are nowhere near as wealthy as those 9 people. Remember to click on each heading if you need an explanation of the process.

Here are the GDPs of 10 Mystery Nations:











Unit: Billion dollars. Thought I would do the reverse this time. What would the numbers look like if they were expressed in dollars instead of billions of dollars?

Experts: Your expert can find the correct matches by searching in this GDP list from the CIA World Factbook.  It is going to take a little searching, so you want a patient expert this time.  Plus, your expert may get confused about the 0.0015 number.  It is expressed as 1.5 million dollars in the original list.  I just converted it to billion dollars to make it more challenging and consistent with the other items.

By the way, you might want to supply all of the students with the following links this time.  They won’t know much about these places to begin with and so will resort to blind guessing.  You could also project this map to help them with the task.  These websites will help them to narrow the list down at least.





South Sudan





Democratic Republic of Congo (DRC)


Central African Republic



I chose these nations not because they have the lowest GDPs, but because they have the lowest GDP per capita rates. This means that if the GDP of these nations were split evenly (and they aren’t, of course), their citizens would have the lowest individual wealth in the entire world.

As it is, it is pretty shocking to see the wealth of the ten nations in comparison to the wealth of the top nine billionaires (MN5). It is claimed that the wealth of these individuals is not only greater than the combined GDP of these nations, but of the combined “wealth” of more than half the world’s population! Is this true? I recommend investigating this one. What is the total wealth of these billionaires? How many countries’ GDPs equal their wealth? What are the populations of these countries? Here a couple of handy CIA World Factbook links to help you out:



Posted by: jwhiff | July 23, 2018

MN5: Richest People

This is the start of a very interesting story. I highly recommend NOT doing this lesson as a stand alone. Follow it up with MN6: GDP of Underprivileged Nations. It paints a very stark picture of wealth inequality. Remember that if you would like to understand the Mystery Numbers process better, please click on the headings.

Here is the list:










Unit? Dollars. In the article, the unit is billion dollars. This is, of course, much easier to read. Recognizing the value of the 8 in 3.8 billion dollars, for example, is a very important numeracy skill that I would practice here. Change the unit and get the kids to practice recording the number. What if the unit were million dollars? Thousand dollars?

Expert source: Independent Article (Richest People)

This article was written in January 2018, so it is relatively current. Individual wealth fluctuates very quickly, so it won’t be perfect, for sure. It’s an accessible article for middle school kids, however. Another article that is quite accessible and provides good good biographical info for your expert is from Time Magazine: Richest People. I didn’t go with this article because the numbers are more highly rounded. The differences between the articles make for an interesting discussion, though.

Richest People: Who earned what?

Jeff Bezos (founder of Amazon)

Carlos Slim Helu and Family (controls Latin America’s largest mobile telecom firm-America Movil.

Mark Zuckerberg (founder and CEO of Facebook)

Tim Sweeney (founder of Epic Games and creator of Fortnite)

Warren Buffett (successful investor and owner of over 60 companies, including Dairy Queen and Duracell batteries)

Larry Ellison (co-founder of database company, Oracle)

Bernard Arnault (owner over 70 exclusive brands including Louis Vuitton, Sephora and Dom Perignon)

Queen Elizabeth (British monarch and owner of property, rare items and investments)

Bill Gates (co-founded Microsoft)

Larry Paige (founder and CEO of Google)

Amancio Ortega (co-founded Inditex, parent company of fashion retailers such as Zara)

Remember that not all of these people are the real deal. It bugs me a bit the Independent article doesn’t include the Koch brothers, because they are on a bunch of other lists. I figure this could be a part of the discussion as well.

Ethical concerns about amassing such wealth? This will make for an interesting debate, especially when you move on to the GDP of Underprivileged Nations.

Posted by: jwhiff | July 19, 2018

MN4: Population Density

This Mystery Numbers really needs to follow the lesson on Largest Countries (Area) and Largest Countries (Population). You can either get the whole class to investigate this topic at once, or commission your early finishers to start on it first.

I’m not going to provide a list of numbers this time…just a question: Which countries are the most crowded?

The kids can return to their population density maps to generate their initial lists. Then, we need to start looking at some math. What can we do to know exactly how much space every person would have if we split up a country’s land equally? 

Start with Canada. Is Canada crowded? How much space would every Canadian have if we split the land up equally?

From there, generate a formula and get to work! Get the kids to work away at this for about 1 math period before looking up lists of the most densely populated countries. After seeing the list, it would be interesting to explore answers to the following question: Why?

Why are some countries so crowded? Do they have anything in common? How do you manage a big population in a relatively small space?

Explore these countries a little. How are the towns and cities organized? Do people fight over the little space that is there? Or do people happily share?

At this point, you can look at urban planning. How do you keep a lot of people feeling happy and balanced in a small space? What would you do? Compare your ideas to your own community. If you’re really ambitious, arrange a Skype call with an urban planner or invite one to come in to speak with the kids. This planner can work locally or even be from a very densely populated area out there somewhere.

Have fun exploring this one. It is a rich task, for sure.

Posted by: jwhiff | July 18, 2018

MN3: Largest Countries (Population)

If you don’t follow up the largest countries (area) post with this one on population, you are missing out on an interesting opportunity to delve deep into issues concerning population density.  More of the full explanation will follow! If this is not a follow up lesson, it is still interesting as a stand alone.

If you need more information about the Mystery Numbers Process, please click each heading for more information.

Here is this week’s Number List:











Unit = people

Expert Source = CIA World Fact Book

Country List:














United Kingdom

I would present students with a population density map to help them narrow down which regions appear to be most populated. Have them make their initial lists before presenting them with the country list. Then it’s back to the maps!

Once the final lists are done, it’s time for the Big Reveal.

I recommend moving on to an examination of population density once you are done. It’s an incredibly interesting opportunity for some deep inquiry: MN4 (Population Density)

Posted by: jwhiff | July 16, 2018

MN2: Largest Countries (Area)

This is a completely different list than last time!  It is a great one to do when you are about to cover area and perimeter. Make sure you have access to some atlases, even if they are old and out of date.  Longest coastlines will follow. Ooh…then populations and population densities!

If you would like more information about the Mystery Numbers Process, please click the headings below.

Here’s the new Number List:











Expert Source: World Altlas

Unit = square km (I recommend that you spend some time bringing this to life, too.  How big is this exactly? How big is our school property compared to a square km?)

Country List: (some correct, some put in there to throw them off.  Provide atlases to search and create their own lists ahead of time. Also a good time to introduce the idea of map projections!)


Greenland (Denmark)







United States


Democratic Republic of Congo


South Africa



I’m really hoping that the Big Reveal in this case is controversial!  It should be…map projections really fool us!  Plus, there is a good opportunity for kids to write about what surprised them here.  Greenland looks so huge!  I thought for sure it would be in the top 10.  Crazy that Australia is smaller than Brazil!  Russia is THAT much bigger than Canada?  Really?

If you have students finished way ahead of the others, get them to start looking for the very smallest countries and generate their own lists.  Use maps or atlases, not technology in this case.  Why?  Technology gives too much away and maps are so tactile and satisfying to explore.

Posted by: jwhiff | July 13, 2018

MN1: Basketball

I’m trying to keep my Mystery Number titles plain and numbered to help you keep track.  I’ve also added categories under Mystery Numbers so that you have an idea about what you are getting.

Now! I’ve started with a list that interests my youngest son right now.  My goal in this endeavour is to have as many lists as possible, covering a wide range of topics and possible interests.  I’m hoping that you (teachers) will find lists that will match topics that you are covering in class.  I would link this one up with gym class, for sure.

Here’s the first list:











Remember that the kids should demonstrate some understanding of the numbers FIRST.  Get them to order the numbers, for sure.  You could also ask them to provide word forms, expand them and represent them in some way (build them, draw them, compare them). You can also break down place value (important when you have very large numbers or very small numbers with decimals).  What you decide to do should match your teaching focus.   By the way, copy and paste this list into a plain word document for them to see or use.  Don’t give students a link to this site.  Too much will be given away!

Next, the kids need to come up with the title of the list.  Here is a link to the site I used to find those numbers in the first place: Expert Source 1

To help them, they need to have an expert. I recommend that you select a student expert (or two).  It would be great if you can choose students who are keen on the topic.  Experts should be willing to research and understand the topic well enough that they can lead 20 questions.  They can also make a powerpoint for the BIG REVEAL.  It’s nice to have pictures and a visual count down.  Here is a sample:

Basketball Points

For now, just play 20 questions and come up with the title.  You can generate a basic title, or really specific. Now either provide them with the unit (in this case points) or have this emerge from a quick discussion about what might make sense in this case.

Once that they know the basic details, they need to brainstorm what they already might know about the topic.  They can do this in groups.  Hopefully you have been sneakily exposing them to some of this information in gym class.  This will give them something to remember come brainstorming time.

Play it out a little and see how the kids do.  Stuck?  Provide them with this randomized list of people, some correct and some way off:

Kobe Bryant

Sydney Crosby

Dirk Nowitzki

Elvin Hayes

Sergio Aguero

LeBron James

Brock Boeser

Moses Malone

Kareem Abdul-Jabbar

Michael Jordan

Shaquille O’Neal

Wayne Gretzky

Karl Malone

Wilt Chamberlain

John Horgan

See if they can whittle this down to the ones that make sense and then match the ones that make sense up with their numbers.

After you have played this out, time for the big reveal!  Remember that it would be nice to use a student-generated powerpoint to help with this. Then, follow up as student interest dictates!  There are a lot more interesting stats on the topic, plus all kinds of opportunities for reading and research.


Posted by: jwhiff | July 10, 2018

Shape Shifters: Reflection and Rotation Symmetry

I worked away to update this one.  I added some rotation animations and a couple of guided practice pages to help out.  I hope they help!


Practice Pages:

Reflection Symmetry Worksheet

Rotational Symmetry Worksheet


Posted by: jwhiff | July 8, 2018

Mystery Numbers!

This is an excellent intermediate (grade 5-8) routine! This will take at least 2-4 math periods to complete at a time. It involves developing and practicing number sense across whole numbers, fractions and percents. Devices are handy (especially for accessing and recording information), but not totally necessary. It can all be done on paper, too. Have base ten materials ready for representing and building numbers, if you can. The kids will need to read, write, hypothesize, discuss, offer and listen to opinions, make connections and hopefully be blown away.

Step 1: The Experts

An expert’s job is to read ahead and absorb information about the chosen mystery numbers topic. They will help their classmates uncover the mystery by being there to take questions. Experts can also create power points or some sort of presentation for the big reveal (Sample: Basketball Points)

The first time around, this should be your job. You are modelling it for your future student experts. By the way, I will post up the necessary links!

Step 2: Introducing the Mystery Numbers

Show students the raw numbers randomized in a list. Their first job is to simply organize and break these number down a little. They should be able to read them, build or visualize them, expand them, explain place values and place them in some sort of order. They can do this on paper or on their devices. Handy tip: after students have built the numbers, they should take a photo with their devices and link it to their work.

Step 3: Game Time

Once the kids feel comfortable with the numbers, they’ll need to determine the topic. This is where your experts come in. Play a little 20 questions as a class. The experts can only answer yes or no to these questions. Keep going until the topic is uncovered! They range from light and fun to really serious.

Step 4: Story Details

Now that the topic is uncovered, the kids need to revisit the numbers. Any thoughts on what these numbers are describing? Write down hypothesis/guesses. Compare these through discussions (whole class, small group, partners or a bit of everything!). You may want to generate a list of units that make sense. Dollars? Grams? Might some numbers actually represent percentages? At this point, you can reveal the list with the units attached. Does this make the story clearer? Time to give the kids a second chance to revise their thinking. They should do some research during this phase, too.

Final Step: The Big Reveal

Time to compare results! Once the real list is revealed and kids have had a chance to see how close they came, they can dig into the story a little further. For example, once the kids know the GDP of various nations, they should be introduced to wealth sharing percentages. It creates a fuller, more complex picture. They should have a chance to ask and wrap their heads around possible answers. Why are there two completely different lists for the top 10 box office earning movies of all time? Why are civilian casualty numbers for World War 2 rounded to the nearest thousand? How did they determine world populations ten thousand years ago? They say that numbers don’t lie, but how can we trust them for sure?

These are all interesting and important questions. Stoke your students’ enthusiasm the best you can during this phase. Pay close attention to conversations, mining them for insights and questions. Be curious yourself. This is my favourite part and will be your’s too.

Stay tuned for the next posts…I’ll be laying out topics and number lists next.

Posted by: jwhiff | July 4, 2018

What Students Bring: Observing During Math Play

You know when you’ve planned this really great lesson and you place those colourful, hands-on materials in the middle of each group and the kids just dig in and start building a bunch of stuff that has nothing to do with your lesson?

We all anticipate this, right? A lot of wise teachers actually make sure they allow for some of this free play at the start of lessons. Why fight it?

You can actually build a really useful math routine around this natural urge to play.

Ever heard of math talks? You know- you place up an image of something in the real world like a couple of full egg cartons and you lead a discussion on the math that the kids notice? It’s a great routine. This just builds on this routine.

All you need to do is snap pictures of the things the kids are building while exclaiming “Woah! It’s so weird, but I’m noticing a lot of interesting math in the things you are building! Did anybody else notice this?”

Then you load up the images and show them one by one on the screen. Check it out! Leah! Did you realize your were making math this whole time? Crazy! Can anyone tell what kind of math Leah was making?

And they are in! The kids want to astound everyone with their math creations. You just need to pay close attention and order up some serious investigations when something interesting comes up.

This is a perfect intro to math at the start of the year. And it’s a gift that keeps on giving.

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