When Will I Ever Use This In "Real-Life".....

 The most common question I think many teachers receive is "When will I ever use this in real life???" I get this question from students, from my own kids, my wife (when have I ever used...)

First, I always find it funny that math is generally the main target for this question. The one subject that arguably is needed for any profession.  So let's look at math skills and where they are used in real life.

"When will I ever need to know that a^2 + b^2 = c^2?" 

Let's look at the skills needed to solve this problem:

1) Following Steps in Order.

In order to solve this problem you have to follow steps in the correct order. Assuming you are solving for a leg, you need to square then subtract then take the square root. If you are solving for the hypotenuse you need to square then add then take the square root. If you don't follow the steps in order, you end up with an incorrect answer. 

Now, reflect on the times in your profession or in your life you had to follow steps in the correct order to complete a task. Recently I was tasked with putting together a squat rack with a lat pull-down attachment. There were over 20 steps and hundreds of different pieces of hardware. Following the steps in the correct order was key to putting it together. 

2) Attention to Detail

Looking at the Pythagorean problem, you need to know if you are solving for a leg or a hypotenuse. You need to label your values correctly and put them in the correct part of the equation. You have to notice if you are adding or subtracting a constant.  25 + 36 = c^2  is a different problem than 25 + b^2 = 36. Students get training on noticing small details and the importance of those details. How many times have you heard someone say, "I only forgot the negative sign, why did it get marked wrong?" That one symbol is the difference between MAKING $40 and LOSING $40.  

Obviously when putting together the squat rack, this skill was vital. There were bolts of different sizes, including a 72mm bolt and a 76 mm bolt. These are almost identical in size, but different enough that putting the wrong one in the wrong place would make the equipment non-functional. 

3) Building Social Skills (especially to ask for help!) 

The math classroom is the prime place for students to practice social skills and language to ask for help - not only from an adult but also from peers. Students solving for the missing value of a right triangle can check in with each other, practicing good social questions such as, "What did you get for the answer - I got 15."  They can work on respectful dialogue when answers do not match "Oh, I got 9." From there they can use respectful, responsive language to determine who made a mistake. 

This language is a skill and needs to be taught. Students do not inherently know how to handle conflict, especially if they are the one that made an error. 

You can bet I was asking for help when I needed to attach the two vertical sides of the cage.

4) Using Resources

Sometimes you don't have the answer in your brain. Sometimes you need to use a resources. In the math classroom this can be a tool card, a notebook, a digital reference... each classroom has their own system. I can't think of a single profession where this skill isn't valued. Doctors have scores of medical text, mechanics have diagrams and reference cards for various vehicles. No profession requires you to know all of the answers to all of the questions off the top of your head. In teaching, like other professions, our greatest resource is each other - getting ideas on how to help students from other teachers that have had similar situations is vital, which connects right back to having the social skills to talk to others.

So many skills in one skill!

This is just a small selection of thoughts that came to mind as I have thought about this question. I've left off other skills such as patience and perseverance.  Math is more than a list of algorithms. The math classroom should be a fluid, open classroom with dialogue and discourse. Students should be engaged in discussion and asked to defend their answers. Incorrect answers and appropriate-levels of struggle should occur. Those skills translate to the real world in many important ways. 

The Fun of March Mathness!

This is, arguably, the most wonderful math-time of the year. I just happen to be teaching probability during the NCAA tourney. It is the perfect one-two punch - math with a high level of engagement!


This all starts with a game of coin flipping. Who can be the best of the best at flipping coins? We discuss probability, make connections to powers of two, create tree diagrams... then March Mathness begins.


"Did you know that Warren Buffett has offered $1 billion to anyone that picks a perfect bracket?"


"Wow, that's crazy!"


"How can he afford that?"


"Can you do more than one bracket? That improves your chances!"

We go back to the probability of picking 4 flips correctly (1 in 16) and make some predictions. I have each student complete a region of the bracket, which is 15 games. They predict what the theoretical probability will be for getting all 15 games correct. Guesses range from 1 in 100 to 1 in 20000.


I let them on the calculator and they discover the answer: 1 in 32,768.


Ok that's a big number. so then we talked about the entire tournament: all 63 games. What is the theoretical probability of picking all 63 correct?


Students used some logic to say about 1 in 128,000 since 32*4 (regions) is 128. others went slightly higher: 1 in 1 million, 50 million. One student said 1 in 37 trillion. Students laughed and he did too, figuring he was way over the mark.


We then head over to Wolfram Alpha where we investigate large numbers.


Eyes go wide as jaws drop. Students try to decode how to say the number in front of them: 9,223,372,036,854,775,808


I line it up with the 37 trillion value to show the magnitude of a quintillion.

How do we quantify such a number? Well let's start with space. The distance from the sun to Neptune is about 2.8 billion miles. So how many inches is that? wow. that's a HUGE number. Why don't we write those as a ratio. What is the unit rate? 59,000?


Oh, so that means you are 59,000 times more likely to guess which inch I am thinking of than making a perfect bracket.


Well let's get crazier. The universe is 13.7 billion years old. Let's calculate how many seconds the universe been around? (mathy mathy converting process). Oh wow, that is about 432,043,200,000,000,000 seconds... That still isn't bigger than 2^63. But what does it mean?


TO RATIOS!


So if we compare the amount of seconds to the amount of brackets we get 4.68%.


WHAT DOES THAT MEAN?


That means... if... you started completing this 64-team tournament the moment the universe came into existence... and you kept filling them out, finishing one every second since the universe began. You'd be less than 5% of the way done.


They ponder, they think. They can't comprehend. How could they?


Eventually we'll get to compound probability where we multiply probability values to get the probability of two independent events. Then we'll take the probability of winning the Powerball and MegaMillion Lotteries on two consecutive days... and realize you are 100 times more likely to have that happen than pick a perfect bracket.


So. Why can Warren Buffett afford to give away $1 billion to a perfect bracket creator? Because so can you.

Who Knew Rice Could Be SO Powerful?

Exponents are a fascinating topic to me.  They rank up there with probability in the category of "unexpected answers that make no sense." With exponents students are amazed at how big numbers get and how fast they get there.  I have a number of activities I do to hook them in, but the first one I do involves some rice...

I started with an ancient parable of a farmer in Ancient China.  The parable has many different origins, most commonly in India, but I chose Ancient China because the students just finished a unit on this region and I felt it would be a great way to review the vocabulary and geography of the area. 

The story goes like this...

Once upon a time a farmer found a way to vastly increase the amount of rice produced on his farm.  He shared this information with his Noble who in turn told the Emperor.  The Emperor was very happy, for growing rice was one of the ways to get wealthy in ancient times.  It wasn't like they could just go to Kroger and buy rice, you know.

The Emperor insisted on an audience from the farmer, who showed the next day.  The farmer, being only a peasant, approached his Emperor with his head bowed the entire time.  The Emperor commended his subject and said as a reward he would grant him a reward of a pound of rice a day, every day, for a year.  This was an astronomical amount of food.

We then measured what a pound of rice looked like.  I always keep tupperwares of rice in the classroom - they come in handy for many different activities.  I also got out our science beakers and digital scale.  The pound of rice we measured had just more than 500 ml of volume.  We also estimated there were between 7,000 and 10,000 grains of rice in that pound.  Looking at a serving size, we learned that this would be between 8 and 10 servings of rice by today's standards. 

Doing some more math revealed that at the end of 30 days the farmer would have about 300,000 grains of rice. 

... Then the story continued...

Being a humble peasant, the farmer refused the reward.  Instead, he said, he wished for merely one grain of rice, doubled each day for the 30 day period. 

The Emperor laughed, but was impressed by his subject's modesty.  He granted his wish.

Students then discussed if this was a good plan.  Many of them had heard this story before, and so knew that the farmer made a good choice, but the challenge was to estimate how many grains of rice he would end up with after 30 days.  Estimates ranged from "a few hundred" (from students that had never heard the story) to "about a million." 

So to emphasize the deal I got out the rice again and said, "OK, day 1... ONE grain of rice" and I put the grain of rice on a random student's desk.  "Whew... ok... day TWOOOO.... two grains of rice..." (another student) "day three... four grains! that looks SO FILLING!" (another student.)  I do this through the first 5 days getting up to 16 grains.

Students were then challenged with proving which deal was better.  To do this we decided to use chess boards and post its to help organize our thinking and planning.  Students were put in groups of two or three students to record the results. 

The numbers started small...

... but they started growing...

and kept growing...

Students were shocked at how large the final answer was (over 500 million grains of rice on day 30 alone!)  At the end we did some reflection on exponents. Here are some responses from the closing:

• The numbers start off really small, but got big REALLY fast after like day 20.
• The emperor must have been really upset!
• It didn't seem like a good deal, but on day 19 he already had more than all 30 days from the other deal. 
• That was WAY more than I thought it would be. 
• How many pounds of rice is that??? 

The last part of the assignment was for them to write how the story ends.  What happened to the farmer? Ideally they would use their knowledge of social structures to answer the question (would the Emperor kill the farmer? Honor the agreement? something else?) 

It was a very fun lesson and really emphasized the power of exponents!  

Escape the Math Classroom

This I made my first attempt at an 'escape room', but I decided to do it digital style.  Students came in and saw an on the front board with the message that said, "Escape the Math Classroom." 

We had a quick talk about "escape rooms" and I asked if anyone had experience with these. To my surprise a number of students have done these activities.  I asked what qualities escape rooms had.  Students answered with "puzzles, clues, a time limit, and teamwork."  I agreed with all of those.

I explained that today would be a little different than a traditional escape room.  Today's would be all digital.  Clues and answers would be solely on the computer.  Students would still have to figure out clues and work with a partner to solve the puzzles to move on, and they would only have until the end of class to finish the room. 

This escape room was designed around a math review for integers and the coordinate plane.  Each clue was designed on Google forms. Using the response validation option when I set it up, students had to correctly answer each question before being allowed to move on to the next response. 

Students were excited to get started and were engaged from the start.  It was fascinating to watch them work together to solve each review question - there were levels of frustration and perseverance, and absolute excitement when they finally moved on to the next clue. 

Some students finished before others and went on to other academic choices, but all groups ended up solving the room by the end of class.  For homework students had to complete a reflection survey to help me get some feedback as to how well they felt it went.  Overall they enjoyed it and were looking forward to doing it again (with more clues than just digital.)   Here is the survey they had to complete: Reflection Survey. (TTQA = turn the question around)

I plan on expanding this activity soon to include many more multi-sensory activities.  I purchased programmable combination locks and plan on storing some clues in lockers throughout the division.  Also, the next one will be multi-class and incorporate many clues from language arts as well as science and social studies.  I'm excited to team up with my teaching partner to create this game!

Here is the room for those of you that want to try it out! Escape the Math Room

Thanks for reading!

Explore Like A Pirate: Pandemic Based Game!

Last week a dangerous infection was let loose in math. Nobody knows the source or the cure (well except the teachers, of course), but class has been on edge trying to solve the mystery.

Students walked in on Monday and saw they had a 1 in 5 chance of being infected. They had no idea what this meant, but they were told that by completing problems in class they could start to find clues as to who is infected and how to cure it.

One of my favorites. Why not put it into class?

It was interesting to watch because even though they figured out the theoretical number of students currently infected (four), most chose to work alone because they didn’t want to risk sitting by someone that was infected. This led to a great social studies connection about how fear creates walls.

Students worked on problems related to simple and compound probability and were told that they could draw 2 cards for every 5 problems they got correct (which allowed them to connect ratios from a previous unit.)  If the student draws a heart card, they would get some information about the game.  This allowed students to complete work at their own pace while still being engaged.  Work could be done at home optionally for draws the next morning.  I have never had more students do optional homework than that night.

The right column is very filled with names now.

On Friday I conferenced with students one-on-one while they took a formative assessment. The meeting gave me an opportunity to do many things. I asked them how they felt about the learning targets, how comfortable they were, where they needed to improve. I also informed them whether they were infected or not.  Students that were infected had two choices: They could work for the light side and try to discover a cure to help the class, or they can play the role of antagonist and join the dark side to spread the infection.

Tomorrow they will come into class with a list of actions on the board, some for the light side and some for the dark side.  Actions include trying to cure the disease, spread the disease, mutate the disease to make it stronger, or protect someone from becoming infected.

The Game ends when one of these things occur:

• Everyone is cured (light side wins) 
• 80% of the class is infected (dark side wins) 
• Mr. Taylor or Mrs. Menker says “the game is over”

(that last option allows us to end the game should students lose sight of the objectives or forget rules about physical and emotional safety.)

Students will complete problems (this will be a general review of the term so far) and after each problem they will fill out a google form to choose one action. From there teachers will discern the outcome and let them know the result.

We’re right in the heart of the game and I have no idea how it will turn out. Will students unite to destroy the infection, or will darkness win? I’m excited to see what happens!

If The Piece Doesn't Fit, You MUST Acquit!

In math class we have started investigating triangles.  My good friend, running coach, and teaching partner, Erika, suggested to give them a bunch of straws, some vocabulary, and let them go off and running.

Who am I to say no to such a wonderful structure?

We reviewed some geometric terms: Acute, right, obtuse, scalene, isosceles, and equilateral.  Then we gave them a challenge: create a triangle with each of the vocabulary terms: one for sides and one for angles.  They realized that they had to create nine total triangles.

Students got started by building an equilateral acute triangle.  It was a solid beginning with students easily conquering that task:

Many thought they'd finish all of them inside of 10 minutes... then they tried the next one.

Feeling confident, they went on to another triangle on their list: equilateral right.  Students used the straws and tried to build it, but no matter how they arranged the straws they just couldn't manage:

If the piece doesn't fit, you must acquit!

Students became frustrated and annoyed. There was some fantastic and frank mathematical discussion amongst themselves. They discussed lots of options.  Some said it was impossible, others argued that can't be the case, but then had second thoughts... Is it possible?  After conferring and discussion, they decided such a shape was not possible to build because "there will always be a little piece of triangle missing on one side, and that side will always be longer."

Why do these teachers constantly try to trick us?

Students continued on to build the other triangles, obtuse scalene, isosceles right, but then  got stumped with 'obtuse equilateral'.  The students went back to their previous thoughts and ideas that were built from 'right equilateral' and concluded that such a triangle could not be built.  Students also made amazing observations:

"...when I built an isosceles triangle, it looks like there are two angles that are always the same too.... So maybe when sides are the same length the angle is the same degrees?"

Those two acute angles look eerily similar

We followed this lesson up with one that used protractors.  Students have begun to confirm similar thoughts and hypotheses, as well as showed that the angles of triangles "always seem to add up to about 180 degrees."

I loved all of the discussion and discovery this lesson gave the students.  Erika and I facilitated discussion, but we never clued them into the 'impossibility' of building a right equilateral triangle.  They came to this conclusion on their own and were successfully able to argue (in a middle school way) why it wasn't possible to build such a shape.

I'm excited to see how they apply this knowledge to the rest of our geometry unit!

Collaboration for the win!

Get in the Game!

I love board and card games.  They are incredibly fun and social. They get me to think.  They give me an excuse to hang out with friends.  And, best of all, they get me off of the screens!

Board and card games also give me an opportunity to learn by playing - a part of education that seems to be frowned upon in today's world.

This year I have used games in the classroom as often as I can.  There are a few games I regularly use in my classroom. This blog will explain two of them: Settlers of Catan and Blokus.

Settlers of Catan
This game is great for math and social studies integration.  Students begin by exploring the map which represents different geographical features and resources.  I explain that the number value represents the die roll needed to produce a resource from that land.  Each land tile produces a specific resource.  Recalling their knowledge of dice and probability, they have to determine what are the best locations to settle.

During this game students are faced with many challenges that early explorers faced - acquiring resources, controlling trade routes, and finding quality places to settle.  They quickly learn that the 'best' settlement areas are quickly claimed by rivals.  If their settlements aren't productive, they need to come up with creative ways to meet their resource needs, either through diplomacy or settling less desirable areas.

Students also learn that as the game goes on, the relative value of a resource changes.    

Four students start - only one will win.

After the game students reflect on their play.  Yes, I said reflect.  As is true in any learning activity, the learning occurs in the reflection aspect of the lesson.

What resources, number values, or trade routes did they control?  How did they start and finish the game? Was there a missed opportunity or a great play by an opponent? This is a great way to tie students back into tracing settlement over periods of time, the randomness of probability in short experiments, and long term goal planning.

Blokus
The Boston Globe recently published an article about Why the US is falling behind in Math.  In it the author discusses the lack of logic curricula as a key reason.

Blokus is a chess-type game (abstract strategy - no luck, all information is given) so players constantly need to think ahead.  It develops a student's geometric and spacial reasoning - being able to see how certain pieces fit in the negative space - as well as developing logic with tactical thinking and strategies.  The students learn what pieces are most important to play early, mid, and during the end game.

Students also just take their pieces to 'fill the space' to make a perfect square or rectangle.  They all do this - I'm convinced that it is built into their DNA.

This is my favorite game to watch the learning happen. Games are relatively quick so they get to play multiple times.  Students go through specific learning stages with similar reflections after each time they play the game.  These reflections include where to play, what pieces to play early, and how to recognize and build "escape routes."

You can't stop red, you can only hope to contain her. (They didn't)

After the game has concluded, students also tally the size of each piece they have remaining and the total percent of 'bloks' they have left.  They then reflect on the board, their game play, and what strategies or lessons they have learned to improve their gameplay.

With all this reflection, students think I'm trying to build master players.  The truth is that many of these reflections tie right back into our 'regular' curriculum.  Did you use your resources wisely?  Did you take your time?  Were you thinking and planning ahead, or were you just making decisions in the moment?  How did these decisions work out for you?

I really enjoy these games because of their multiple tie backs to different learning standards, but also due to the fact there is not just "one way" to win. You can't memorize the 'answer' because there isn't one solution.  This ties back into The Globe's article - students need to think creatively, logically, and two-steps ahead to achieve victory.

There are other games I use on a regular basis in the classroom as well including Dominion, Dixit, and Ticket to Ride.  What games have you used and how have you successfully implemented them in your classroom?

Multiplying Decimals at the Casino.

Hello everyone!  I'm really excited as we just started spring break here, so instead of my weekly post I've decided to do a bunch of short success stories from the year.  These are all ideas that I've wanted to blog about, games I've played, or just a-ha moments.  

The first one is a card game I played earlier in the year that helped students reinforce the concept of multiplying decimals.  

Protocol: Decimal Blackjack (or 21 if Blackjack is taboo at your school)

Quick summary: This activity has students practice multiplying decimals.

Materials needed: decks of cards with the 10s, Jacks, Queens, Kings and Aces removed.

Procedure:

1. Put students in partner groups (see my blog on my beliefs of getting into partners here)
2. Give each student a modified deck of cards
3. Ask students who knows how to play 21.  Explain the differences in this game:

• Your goal is to get to .21 or HIGHER without going UNDER.
• You will be multiplying, not adding, your values
• Each card represents a decimal, so 8 is actually .8
• The person closest to .21 without going UNDER wins.

4. Students each draw one card from the deck.  The player with the higher value goes first
5. The student draws a card and multiplies the two values:

This student started with .9 and had to multiply that by .3

6. Play continues until one player goes under .21 (twenty-one hundredths).

I really enjoyed this game.  Rounds went fast (sometimes ending in just one card) which meant lots of repeated practice.   Students quickly made lots of connections to the number line, the algorithm, and reviewed basic facts, but also increased their number sense... Here was one of the big take aways from MANY of my students:

Low numbers "suck" - They learned that when you  multiply by .2 or .3 the value goes down QUICKLY!

Mr. Taylor! I had .9 but then I LOST IN ONE CARD! *SCREAM*

This was by far my favorite unintended consequence of the game.  Building that number sense helps them estimate answers much more accurately and find errors in their thinking in more complex problems.

Students have really enjoyed this game - I've kept it in my game center and they often ask if they can play.  I'm looking for ways to increase the application and metacognition of this activity.  If you have thoughts, please let me know!

Welcome to the Math Art Gallery!

So we are closing in on that spring break, which of course means that because of this and the fact we just finished PARCC testing,  our students are all but checked out.  Perfect time to introduce geometry concepts, right?

Right.

Looking at the CCSS, I go through some of the key terms and words that my students will have to know to continue their mastery of learning targets.  A few are ones they have mastery of, some are ones that are familiar, but most are ones that will need some review.

On Wednesday, I start the lesson.  The students walk in and see a stack of white paper, compasses, and rulers.  They also notice bins of colored pencils and markers up front.

I begin the lesson explaining how hard they have been working and I really felt we needed a day to just relax.  No major lesson today - they will have the period to just draw.

An aura of suspicion goes up, but I continue:

Seriously, all I have planned today is for you to draw.

One brave soul speaks up - "Mr. Taylor, you have something up your sleeve."

OK, there are two conditions.  First, whatever you draw has to be school appropriate.  Second, you have to use these tools as intended for their regular use to draw.  You can not draw freehand at all.  I mean I need to add SOME element of challenge, right?

I then introduce the compass and explain how to use it.  I tell them there is some learning curve (hah) to it, and they will need some practice to build the muscle memory.

There is still some doubt in the room to the 'leniency' of the assignment, so again I emphasize the main points:

You can draw whatever you want as long as it is school appropriate and you must draw using the tools as designed (rulers for straight lines, compass for curves and circles.)   No freehand.

I then pass out the paper and tools.  I explain that each student gets exactly one sheet of paper - if they "mess up" they can use the back, but after that they have to incorporate errors into their art.

I give them the period, making sure students are using the tools correctly and helping them use the compass - in fact I end up setting up a mini-lesson station for this tool.  They are excited and work the period.  They ask about color, and I tell them there is no expectation of color, but if they choose to color that can be done by freehand so long as the original lines are visible.  They are also allowed to black outline by freehand (instead of re-using the tool to trace over an established line.)

Here are a few samples of what my students created:

 They ask about homework, and I tell them they can finish their products, remembering the rules.  Some students borrow compasses, others choose to hand in what they have.

The next day students come in and see their works of art hanging around the room.  I welcome them to the math art gallery and ask them to take their seats.

The girl that spoke up yesterday mentions, "I knew there would be more to this..."

I start by asking who has been to an art museum before.  Many students raise their hands.  We go over norms of art museums:

• quiet voices
• you aren't allowed to touch the art work (or even come close to it)
• walk slowly
• You shouldn't lean on the walls or use them to write on
• Don't clog up any areas

I actually had this video prepared in case students were unfamiliar with the norms, but didn't have to use it:  How to behave in a gallery.

From there I welcome them again to the Math Art Gallery.  Their assignment is to find different forms of geometry in the various works of art in the room.  They should take notes as to who's artwork it is in and where in the artwork they see it.

I also tell them there is a definition sheet in two different spots of the room - if they are unsure about a term, they should reference that sheet for help.

They then take the next thirty minutes in the art gallery looking for the terms, but also admiring each other's work.  I wander the gallery with the same worksheet, finding the same properties.  They complement each other as they pass, and I share some of my favorite observations. We all comment on properties that are easier or harder to find.  Some, we note, are quite rare!  Students also remind each other of the norms as they walk.

I really enjoyed that part of the community building - an unexpected and happy outcome :)

After thirty minutes, we all return back to our spaces and review our work.  Students share where they found the terms - scalene triangles, trapezoids, arcs, chords, and so on.  As we review, students become shocked at how many geometric terms are in their drawing - they are amazed that there is so much to their work.  Specifically, the student that did the 3d cube was amazed at what was found.  He said he just wanted to do a simple shape, but it turns out that he and other students found the following elements in his drawing:

• acute angles 
• cube
• obtuse angles 
• parallelogram 
• parallel lines 
• perpendicular lines 
• rectangle
• right angles 
• right triangle 
• rotational symmetry 
• scalene triangle 
• squares
• trapezoids

Over a dozen terms in that one 'simple' design.  They began to build awareness of geometric terms and properties in everyday objects around them, looking at them through a new lens.  From there students began attaching meaning to the vocabulary.  They gained practice using the tools to create more specific designs.  Their natural curiosity kept the momentum going, and all of this coming the week before spring break.

So for those of you closing in on a week off - keep the lessons real, make the time count, stay away from the worksheets, and keep the students enchanted.

This was my contribution to the gallery.

Today I will read your future minds...

A few weeks ago my math class started algebra concepts.   I have a fantastic lesson that I spiced up thanks from some advice from Dave Burgess and his excellent seminar on how to Teach Like a Pirate.    Students sit down, get out their notebook, look up and read the board.  However, instead of the usual warm up or friendly message, they see :  "Today I will read your future mind!"

They giggle as usual, and taunt my talents.  I play along - "Oh, doubters... just wait.  You don't even know what you are thinking yet... but I do...."

With that I take out an index card and turn my back to the class.  I look over my shoulder a few times, making sure to have direct eye contact with a few of them.   As I'm turned I write a message on the index card.  I put this index card into an envelope, seal it, walk up to one student very deliberately, and put it into the student's binder, folder, or book, warning all of them not to even touch the envelope.  I then explain how soon they will all write what I have just written on this card.

Hook?  Check.

I then lead them through the typical pick-a-number scheme where you add, multiply, and do all this magic to the number.   I encourage them to choose a lower number as there is some arithmetic to do to this number, but really any number will work.  No calculators are allowed and students must show their work for each step.

Here is the algorithm I lead them through.  I haven't tried reading minds over the realm of the internet, but I'm willing to have a go.  All of you readers, math geeks and non, should play along.  I'm curious if I can use my psychic powers through wifi.  Here are the steps I give my students:

• No talking from here out - it disrupts the psychic energy.
  
• pick a number 
• double that number
• add 4 to the result
• triple that result 
• subtract 6 
• divide by 6 
• add 4 
• subtract the original number from this result (this step usually takes some clarifying)
• circle this final answer

Now I want you to look at this chart.  Find the letter that corresponds to the final answer circled on your paper and write that letter on your paper.

For instance, if you got a 8, you'd choose 'h'

I always make sure to walk around the room to see what number is circled and to clarify this step.  I also help students that may have made a mistake in arithmetic.

Once everyone has their letter I stop and build the drama a bit more.  I close my eyes - pretend to meditate... whatever. Get a good psychic vibe in that room!

When I continue I ask them to think of an animal that starts with the letter they have written down and have them write this animal in their notebook (telling them specifically that spelling doesn't count.)  For example, a student that gets an 8 could write 'hyena'.

I then ask them to think of a color that animal can be, and to write that as well.  For instance, if they got an 8 they might choose a brown hyena, but can't pick a pink hyena.

At this point I walk back to the student that has the envelope.  I look at the answer in their notebook and smile.  I ask them if they think I have the same thing written on the card in the envelope.  They always hesitate.  The anticipation is thrilling.  I ask that student to open the envelope and to read out loud what is written.

Most of the time they don't even read it out loud.  Most of the time they shout out "NO WAY!"  Generally what happens from there is the rest of the class reacts with shock and awe with a hint of fear.  Eventually the card gets read.  Students are in disbelief.  How is this possible?  Will you teach me?  PLEASE? TELL ME YOUR SECRET (seriously - students begging to be taught?)  Nobody can believe that I have done the impossible.  Same color. Same animal... well, 95% of the time.

If you are playing along you might wonder what is on in that envelope and if I've read your mind through the world of cyberspace.

You may wonder, if in fact, I will end this post with the words grey elephant.  

I think I will.

Next time I'm using one of these as a prop.

Getting in Shape One Math Problem at a Time

In my first of (hopefully) weekly installments, I will be introducing protocols that I have used in the classroom to help build authentic student engagement.  

A bit of background: I currently work in a the middle division of a school that specializes in students that have one or more learning difficulties.  These students often have high energy levels and low social skills.  As a result, many of my lessons involve movement and student interaction.  They also involve a high level of fun because, seriously, if you are going to be somewhere 40-60 hours a week you better be enjoying it! :)

So with that, here is my first installment of authentic student engagement strategies - in which someone from your class may become the next Richard Simmons!

(showing a sweating to the oldies video is a moral imperative)

Title: Math Squats and Jumps

Quick Summary : This activity will have students use body actions to help one student guess the mystery answer from a math problem.

Materials needed: none

Procedure:

1. One student is placed in the ‘hot seat’.  This seat is placed in the front of the room, facing towards the class and facing away from the board.
2. The teacher writes a problem on the board.  This problem should have an integer number as an answer.  The hot seat student is instructed directly NOT to turn around.
3. Students at their desk solve the problem.  Student in the hot seat waits.
4. When a desk student solves the problem, the student stands up. 
5. After all students are standing, the teacher tells the hot seat student a range that the answer is between (such as 50 – 500).
6. The hot seat student guesses a number in the range.
7. The students give a clue if the guess is too high or two low:
• If the answer is too high, the students jump (large jumps = much higher!)
• If the answer is too low, the students squat (lying on the floor could mean MUCH lower.)
• If the answer is correct, the students clap.
8. The hot seat student continues to guess until the answer is reached
9. If a guess is made and students do conflicting actions (jump and squat, squat and clap, etc.) students that don’t agree must conference to find any errors.

Example:

Linda sits in the hot seat and faces the class.  Students (except for Linda) solve the problem on the board (424 ÷ 4).  All students except Linda solve the problem and then stand behind their space.  The teacher gives Linda a range of 30-400.  Linda starts by guessing 350.  Students squat down (a few even lie on the floor to let her know she needs to guess way lower).  She then guesses 100.  The students do a small jump.   Eventually Linda guesses 106 and the crowd cheers!