## Thursday, December 13, 2012

### Minute to Win It Math Circuits

I'm supposed to be planning for a grade 8 manipulative workshop I'm holding in January so I've been researching hands-on/student centered ways to guide student learning. The problem always ends up that I find all these fabulous blogs that I immerse myself in reading and I get totally off topic. But, that's also a good thing, right? I am totally immersed in reading fabulous blogs! Well, today I came across Reflections of a High School Math Teacher and couldn't stop reading.

At this moment, my favorite entry is Minute to Win It Circuits...Move and Learn.  Here's an overview of the activity:

He set up 5 stations around the class, allowing for two groups at each station at once.  Which means, of course, that there was actually two copies of each station.

Station 1:

• Math problem written very large on a full sheet of paper.  "Write the phrase as a power and then evaluate.  four to the third power."
• Cut up the paper into 6 equal pieces (approximately 3x3).
• Randomize and clip together.
• Make sure there are two sets of this problem at the station.  One for group 1 and one for group 2.
Station 2-5:  Same idea.  Different problems.

Process:
• Groups are assigned to stations.
• Set timer for 1 minute.
• Partners work together to unscramble the pieces and then solve the problem.
• Write answer down on paper.
• After minute is over, they rotate, moving to the next station.
In the comments, someone (A. Nonymous) shared that he/she puts the answer to the problem they completed at the NEXT station.

I think this is very cool!  If you have 5 stations your time would be
• 1 min to work
• 15 seconds to clean up
• 15 seconds to move to the next station
Total time used:  7.5 minutes.

I'm throwing out some ideas here for implementing in my own classroom (when I return back to the class).
• What if I had students show work and write answers on index cards (or regular paper) and at the end of the minute, they put answer in container and move on.  Then I've collected it.
• Hmmm....to make sure they remembered name, I could number papers and assign students numbers.  Give all students a "booklet" of papers with their number on it ahead of time.  They answer, rip of paper and put in container.
• Answer provided at next station (as per A. Nonymous).  They would have to switch stations quickly to get time to read answer.
• Focus each question on an outcome I am specificially assessing.  But then each students would have to work individually.  Still would work.  More question sets at each station then.  Don't think I'd want to do more than 5 stations for time.
• Could have some stations as "group" effort.  Find a partner at the station you're at and answer the following.  Write partner's name on bottom of paper.
We'll see which ideas I actually keep when it comes down to it.

I love, Love, LOVE this idea and hope that I don't forget about it when it comes down to actually trying the activity.  Maybe I'll even have the Grade 8 teachers who are attending my session in January attempt something like this.  Ooooh....brainwave!  <evil laugh>

If you try this, I would love to hear how it goes, what questions you used, what course you tried it in.  What worked.  What didn't.  Anything and everything (except what you had for lunch).

## Thursday, November 29, 2012

### Rewrites

When I was still in the classroom, I had students complete daily mini quizzes (one or two small questions based on the work done in the previous class).  This allowed me to see what they got and what they didn't get right away.  I "assigned" homework each day but told them that they had the answers in the book so they could check it themselves.  If they needed help, they could come see me before school or at lunch.

My students were allowed to rewrite these mini quizzes as many times as needed to get a full 5/5.  Now that I look back, I know that there are a few things I would change.  Number 1:  I would allow students to review with me and then write the new mini quiz right away.  One blogger said that her students can't review with her and rewrite on the same day.  Very cool.  Another teacher has his students email him a request for assessment detailing
1. What they want to reassess
2. Reasons why they didn't do well the first time
3. What they have done (not plan to do) to make sure they get it now
4. What date/time they want to rewrite
They must complete these steps for each and every reassessment they want to complete.  If a student does not sufficiently answer the questions or they give lame responses (ie. I looked over the mini quiz), he replies to the email detailing where they need to be more specific.

You can find his specific email form letter on his blog.

I would also have students sign up for a rewrite during class but not actually show up to do it.  grrrr...  This would definitely help.  I can't imagine that they would spend the time writing all the detailed information in the email and then not show up for the rewrite.  Also, I'm not going to call it a rewrite anymore.  I'll be using the term reassessment as I love the connotations that this word evokes.  It even sounds more serious.

I love it!  I will definitely be implementing the email Request to Reassess when I return to the classroom next year.  I think I will add this to the course outline that I stole borrowed from him in yesterday's post.  Either that or put it on my class blog.  Actually, that's probably the best place for it so that students can just do a copy paste and focus on filling in the details.    Oooohhhh....maybe even a google form.  I will have to play with those two ideas and see which one better fits the situation.  (All my students have a google education account so I don't have to worry about creating google email addresses.)

## Wednesday, November 28, 2012

### Course Outlines

This morning, I spent quite a bit of time looking for activities/lessons on rational expressions.  I got distracted and veered way off topic when I discovered Continuous Everywhere but Differentiable Nowhere's blog.  After reading through a few posts, I found links to his course outlines.  I have only read the first one but absolutely love how it begins.  I definitely plan on stealing borrowing the introduction.  Don't panic...he gives permission for anyone to do this on his blog!

Here's the portion I love but feel free to check out the course outline in it's entirety here.

Greetings!

Howdy! This year we are going to discover beautiful, useful and extraordinary islands of knowledge.  I’m going to be challenging you consistently as you build bridges from island to island – from lines to quadratics to polynomials to matrices. These islands will provide resting places for our adventures, while we explore what great things these paradises have to offer. Still, any adventure isn’t an adventure unless there is uncertainty, unexpected perils. I can promise you that you will not be immune from confusion, wandering dazed and confused.

But don’t worry! Yes, at times it will be hard – all good adventures are – but rest assured that I’m always going to be right there with you. I am here to tell you now: we are in this together and we can conquer all. In fact, I’m going to make sure we make it to the end of the year with lots of sparkling mathematical treasures to your name: graphs of neat functions, complex numbers, quadratic functions, the remainder and factor theorems, compound interest, and other surprises.

teaching goes both ways
With this said, you are now at a point in your education where you are responsible for your own learning. You are old enough to know what you need to do when you are having difficulty. Wait, are you? Pop quiz.

When you are feeling lost in class, you should:
(a) wait until the next class and hope that it will all begin to make sense.
(b) not do anything… it’s only one concept and you know you’ll be tested on a bunch, so it won ‘t be a big deal to not learn it.
(c) ask someone else for help – whether it be Mr. Shah, your desk partner, or a friend.
(d) watch America’s Next Top Model and hope that the concept will be explained during a photo shoot.

You are in this class to learn some math – and even though we are in this journey together (remember: I am always on your side), that does not absolve you of responsibility. For this class to operate smoothly, for us to have a good time, to get all we need to get accomplished in mere months, you need to
… come to class prepared every day
… spend quality time working on your homework daily
… not be afraid to ask questions about concepts or homework problems you are struggling with
… be an engaged participant in every class
… be kind and respectful to the other members of the class

If you keep your end of the bargain, I guarantee you that your mind with be brimming with intellectual riches at the end of the school year. You will have learned a lot.

Just as I expect only the best from you, I want you to expect the best from me. I promise to come to teach class well-prepared, ready to embark on our daily adventures. I promise to try my best to make my presentations clear and interesting. I promise to respect you.

I can't wait to get back in the classroom and add this to my course outlines.  LOVE IT!

## Friday, October 19, 2012

### Modelling One to One Correspondence Lesson in Kdg

Yesterday, I had the pleasure of modelling a One to One Correspondence Lesson in Kindergarten.  I love kindergarten.  They are so eager to learn!  Wouldn't it be fabulous if we could bottle that eagerness and implant it in all students?

Outcome:  Number 5:  Compare quantities 1 to 10, using one-to-one correspondance

Activity #1:
Materials:
• Dice
• Bingo Chips
• Plastic Container

The Process:
I started by rolling a die to obtain a random number (although sometimes if a number showed up too many times, my die would accidentally and quietly get knocked over onto a different number).  Let's pretend a 3 showed up.  I would loudly and slowly clap three times.  Students would hold up fingers to show me how many times they had clapped.  Then, we would clap and count the same number together (so, if you're following along...that was 3 times).  We repeated this activity several times until everyone knew what they were supposed to be doing.

The next stage was exactly the same except for one difference.  This time, they had their eyes closed while I was clapping and while they were holding up their fingers.  This allowed me to see which students were having difficulty as they weren't able to look at other students' responses for support anymore.  I would sometimes repeat the claps if it looked like too many had trouble.  "I'm going to repeat the claps again so that you can check your work!".

At the end of the session, the classroom teacher told me that she liked the idea of having students close their eyes while listening.  I had to admit to her that I stole the idea from HER.  Two days prior to this lesson, I had been in her classroom modelling a 3-D shapes lesson.  I was early and caught the tail end of her rhyming lesson.  She had her students close her eyes and named two rhyming words, then had students repeat back those rhyming words.  I thought it was a great idea to remove the visual so I stole borrowed it.

Activity #2:
Materials per group of 2:
• Brown paper lunch bag
• Numerals 1-9 (9 fit nicely on a piece of paper, 10 did not otherwise I would have done 10).  (One side had the numeral, the other side had an arrangement of circles or squares matching the numeral)
• Envelope (to hold the numerals)
• 9 bug foam stickers

The Process:
Obviously I modeled this process before having students do the activity.

Students removed the envelope containing the numerals and placed it off to the side.  They emptied the bag so that all the bug stickers were on the table.  Each student counted the bugs.

Partner 2 closed their eyes or turned their back.

Partner 1 pulled a card out of the envelope.  They counted out the correct number of bugs to match the numeral and placed them in the bag.  They hid the numeral card.

Partner 2 opens their eyes, empties out the bag and counts the bugs.

Partner 1 checks their work.

Now, the roles reverse.

When the activity was finished, I told students they could each keep one bug foam sticker.  They cleaned up and returned everything else to me.

The classroom teacher mentioned that this would be an easy activity to adapt to other themes, using different objects, stickers, etc.

Activity #3:  I did not have time to get to this activity but thought I would share it anyways.
Again, prior modeling would have to be done.

Materials per group of 2:
• Numerals 1-9 (9 fit nicely on a piece of paper, 10 did not otherwise I would have done 10).  (One side had the numeral, the other side had an arrangement of circles or squares matching the numeral)
• Envelope (to hold the numerals)
The Process:
Partners sit one behind the other, partner 1 in front; partner 2 behind them.

Partner 2 pulls out a card and then taps slowly, gently but firmly on partner 1's shoulder.

Partner 1 counts and reports the number of counts.

Switch.

This activity was meant to be a repeat of the first activity.  I thought clapping would be too difficult to distinguish once all the groups were doing it.  Obviously there would have to be a conversation about quality of tapping.  Wouldn't want any injuries!

I hope that you find these low tech activities useful!  I'm sorry that I don't have pictures to share of the students in the class but the FOIP forms would have been complicated.

## Thursday, September 6, 2012

### Introducing Probability to 30-2

I will be modelling a lesson in two weeks, introducing probability to Math 30-2 students.  I brainstormed a bit and knew that I wanted to do a hands-on activity based on the Monty Hall problem.  I raced to the internet, did some research and came up with a rough-draft below.  I would love some input regarding a) better questions I could be asking and b) the ordering.  It seems a little weird to throw the card question in the middle.  Not sure if I want it there are at the end.  Would love your input!

Note:  I still need to check that it's ok to bring candy for students.  I've never been told no in the past as I'm a guest but...I haven't been to this school yet and better dot my i's and cross my t's and all that.

My rough draft lesson plan.

30-2 Probability Intro
Monty Hall Problem
Based on:
·         Monty Hall problem
·         And blog write up and comments listed at Point of Inflection
·         And lesson plan shown here:  http://www.ms.uky.edu/algebracubed/lessons/Monty_Hall_Lesson.pdf

Materials:
·         Candy - would be a toy car if not allowed to use candy
·         Bowls with lids, labeled 1, 2, 3
·         Blocker so they can’t see which one I’m changing
·         Cards
·         Envelope you can’t see through
·         3 cups per group
·         1 object per group (represent candy) – or candy

Instructions:
·         Place 3 bowls on table.  One has candy inside of it.
o   Don’t give out rules yet
·         “One of these three bowls has candy in it.  If you can guess which one, you get the candy.”
·         Play
·         “Who else wants to play?”
·         Play a few times.
·         “What’s the probability of winning?”
·         Next time, say “Your guess was as good as any other.  But I want to give you another chance.  I will show you that this bowl <lift an empty one> is empty.  Do you want to keep your original guess or switch?”  Finish
·         Play again but this time stop after showing an empty bowl.
·         Ask “what are the odds now?”  They will probably answer 50%.
·         “Interesting” Finish game.
·         Play again, stopping again after showing the bowl.
·         Ask “when you chose at first, you had a 1/3 chance of winning.  Now you say that the same bowl you picked has a 50% chance of winning.  How could flipping over an empty bowl over here improve the chances that this bowl is a winner?”
·         Allow for discussion.

Switch to cards:
·         Let’s try this with cards.  <Student> pick a card but don’t look at it.” Put in envelope.
·         “Who do you think probably has the Ace of Spades?
·         “What’s the probability that it’s the Ace of Spades?” 1/52
·         “I’m going to get rid of a card that is not the Ace of Spades.”  Look at 3 and discard 1.
·         “Do you think you’re more likely, equally likely, or less likely to have the Ace of Spades now?”
·         Run through deck, discussing probability as you go.

Back to the bowls:
·         Ask students “We’re going back to the question - Should you switch or stay?  In partners, I’d like you to discuss how to PROVE if the contestant should switch or stay.”

Provide groups of two with student handout, 3 cups and candy/other object.  Explain that they will be creating data based on the Monty Hall problem.  Make sure they understand that they need to do the test 50 times each (a total of 100 times) - 50 for switching and 50 for staying.

Student Handout

Names:_________________
_________________

Let’s Make a Deal

1.       Do you think you will win more often if you switch or stay?  Explain.

2.      Play the Monty Hall Game with a partner. Record your results in the table below. Be sure to play 50 times WITH switching doors and 50 times WITHOUT switching doors.
 Strategy Switch Doors Stay WINS LOSSES Winning Percentage

1.      Do your results display a difference in your chance of winning based on whether or not you switched doors?  Explain.

3.      What is the probability of winning the Monty  Hall Game?  Explain.

4.      Do you believe that you have a better chance of winning if you switch doors?  Why?

## Friday, June 15, 2012

### Exploring the Laws of Logarithms

I was looking for a more student directed way of learning the Laws of Logarithms for Math 30-1 and 30-2 students in Alberta when I found a tweet by RobAnthony01 talking about his process.  I used his 140 characters and turned it into something I can give to my students to work on independently, with my guidance as necessary of course.

It's not a very complicated activity but sure would be a heck of a lot more interesting than me saying "When adding two logs...do this.  When subtracting two logs...do this."

## Wednesday, June 13, 2012

### Reflection App - Well sort of...

Yesterday, I discovered a cool new tool and just had to share it.  It's called Reflection and can be found on the Reflection App website.

What it works on:
Platforms:  PC (Windows XP or greater), Mac (OS X 10.6.8)
I was testing on a Windows XP using my iPhone 4S.

What does it do?  It's a projection "app".  It allows you to wirelessly project what is happening on your iPhone or iPad onto your computer.

Right now, if you want to show what's happening on your iPhone or iPad, you have a few choices.
1. You can AirPlay it to an Apple TV.  Not sure how many classrooms have that.  Mine didn't.
2. You can also purchase the Apple dongle at a cost of about \$35. I've used the dongle.  Honestly, I had trouble with it.  I would have to take my cover off because I couldn't get it to attach securely.  Even with the cover removed, the second I moved around it had a tendency to jiggle loose.  Then, if it had jiggled loose too often, it would stop projecting my iPad completely.  So frustrating.  Especially when you're doing a presentation about how great iPads can be if used properly.  Thirdly, I was tied down and limited to the length of my VGA cable.  Frustrating.
3. I've heard people talking about other apps that will project as well but have not researched them.  I was really looking for something that would allow a class of 20-30 iPads to project inexpensively.

So far, this is my favorite...Let me tell you about it.

I installed the software on my laptop.  It was fast and easy, about a 9Mb download.   Then I went to my iPhone 4S, (make sure your laptop/desktop and iPhone/iPad are on the same network) accessed AirPlay and started projecting.  That's it.  There's nothing to install on the iPhone or iPad.  That means anyone on the same network as my computer can instantly project through my computer to the projector.  Awesome!

Wait!  You scream.  Does that mean ANYONE can tap into my computer and start projecting?  Well technically yes unless you take the following action.  You can set a password.  This way, you can either 1) turn it off at the beginning of class or 2) give it to your students for that class and then change it afterwards.  Again, easy-peasy to do.

What can you use it for?  Let students show videos they've found, work they've done, anything they've created, brainstorming they've completed in groups.  It even projects sound!  So, if they're showing a video, the sound automatically transfers with it.  I did notice a slight lag when I ended the YouTube video.  It showed up on the computer screen for about 5 seconds after I closed the YouTube App.  It will not display the video on your device at the same time, however.  Oh, and apparently multiple devices can connect to the computer at once.  The website states that it will start to slow down as you increase the number of connections.  I didn't bring my iPad to work today so I will have to test it and see how it goes. This spot here will be updated as soon as I have tested multiple devices.

As far as I can tell, only two things didn't work on it.  1) Facebook wouldn't play embedded videos or at least not the one I had tried.  2) Skype didn't transfer.  There may be other apps that don't work but so far so good with the ones that I've tried.

One other small glitch:  Once when I had told it to connect, I had this blog open in edit mode.  When it displayed my iPhone it was itty bitty on the screen.  I just canceled the airplay and reconnected and it was fine.  So far that has only happened once.

Cost:  The free version only allows you a total of 10 minutes time and that's it to explore the app but within that time, you can pretty much guarantee that you'll love it.  Full Disclosure Here:  Once I ran out of my free time, I contacted the company, explained who I was and that I work with teachers across Central Alberta sharing resources, activities, apps and ideas that they may find useful within their math classroom and then I very politely requested a free copy of their app.  I want to be able to actually SHOW people how easy this app is to use.  The current cost is \$14.99 per license or \$49.99 for 5.  Contact them for more than 20 licenses for another discount.

Check out the Reflection App website to watch the video and find the download file.  Let me know if there's anything serious that I missed when playing with the app - either good or bad.

Edited to add:  I was asked where I'd heard about the Reflection "app" and I couldn't remember at first but now I suspect it was because of this post.  Not sure why I would have kept reading about it since she states that only works on Macs but it definitely works on PC's now.  So, thank-you, Kathy, for pointing me in this direction!

## Tuesday, June 12, 2012

### Assessment - Killing the Overkill

Students Can Demonstrate Understanding with a Shorter Assessment Piece

I've been working on changing my assessments.  Marian Small has been a huge influence on this ever since I attended her session on the High School Math Institute.  Now, every time that I am creating a new assessment, I search "Marian Small" +topic in google to help generate some ideas rather than always recreating my own.  I always try to change the question so that I'm not just stealing her ideas, especially since I share so many of the things I create with the teachers around Central Alberta during Assessment sessions.  However, I certainly use her framework as it makes the questions so much more interesting and checks for a deeper understanding.

When I present a session on assessment, one of the first slides I show asks

What Does...
 Solve 34

on a test tell us about the student?

The inevitable response is that "They can operate a calculator".  It terrifies me that when I first started teaching, I would strongly populate my exams with questions like this...ones that tested their ability to operate a calculator.   Of course, I would have to have many questions like this to test whether they could do it in multiple settings.  So, my students were answering a bunch of repetitive questions and I was stuck marking a bunch of repetitive questions.  Of course, it was easy because a simple answer key worked but what did it tell me about my students' understanding?  Pretty much nothing.

Once I began my assessment journey, I realized how easy it would be to change these questions to better get at their true understanding.  Yes, it makes my answer key pretty much useless.  Yes, it might take me extra time to mark the question.  However, I was then able to cut down 20-50 questions to just a few deep questions so it balances out in the end.

Giving up a little bit of control during the assessment process allows students to demonstrate their knowledge more fully.

I wanted to know if students truly understood that 34 is really 3x3x3x3.  Why not let them pick the numbers they used?  By wording the question carefully, I could prevent "easy outs".  This is how I changed the first question:  (The bold portions would not be bolded on the test.  They're bolded so you can see how I tried to ensure I didn't get situations like 11
.  The others are samples of how I would assess the other outcomes.

Question 1:
Choose a base greater than one:  ____________

Choose an exponent greater than the base:  ______________

Create a visual representation for the power you produced.

Question 2:
You simplified an expression.  The result was (3/4)1/2.  What could the original expression have been if you were using the following operations?
(am)(an) = _____________________

am/an = _______________________

(am)n = _______________________

Question 3:
Choose one of the following operations:               (ab)m     OR     (a/b)n

Choose your own bases and exponents, however "m" and "n" can NOT be a whole number.

Explain TWO ways to determine the result without using any "rules".

Question 4: (From Marian Small)
Write an expression that you would likely use three power laws to simplify.  Use a variety of exponents.

Simplify it.

Question 5:
Jamie states that a0 is a.  Pat says that it is 1.  Jessie says that it is 0.  Casey says that none of them are correct.  Who is right and how would you convince everyone else without saying "The rule is..."

Like I said, when I first started teaching, I would overkill on questions.  I believed an assessment was supposed to take all class which meant I would have to put a LOT of questions on it.  Then, of course, when you have a class of 16-30 students, you had to MARK all those questions.  I would now use this assessment to check students understanding in Math 9:

Side Note #1:  These types of questions are excellent discussion starters, review questions, exit slips, "homework checks" and formative and summative assessment questions.

Side Note #2:  Students should NOT see this style of question for the first time on a final assessment!  They should experience it ahead of time.  I would worry that they would feel like they were being "tricked" otherwise.

I've considered including the outcomes on the assessment to give students and parents a better idea of students' success within each outcome.  I'm trying to decide between two formats:

Option 1:
I could attach the table included below to their paper after the assessment.  I would highlight the questions they were successful (or not successful) at.

 Number 1 Q1 Q5 Q4 Demonstrate an understanding of powers with integral bases (excluding base 0) and whole number exponents by Representing repeated multiplication, using powers Using patterns to show that a power with an exponent of zero is equal to one Solving problems involving powers 2 Q2 Q2 Q2 Q3 Q3 Q4 All Demonstrate an understanding of operations on powers with integral bases (excluding base 0) and whole number exponents (am)(an) = am+n am÷an = am-n (am)n =amn (ab)m=ambn (a/b)n=an/bn, b ≠ 0

OR, I could add a column to the assessment (something like below) but then I would have to make sure to blank out the pieces that give answers.

Exponent Laws Assessment

 Question 1: Choose a base greater than one:  ____________ Choose an exponent greater than the base:  ______________ Create a visual representation for the power you produced. Demonstrate an understanding of powers with integral bases (excluding base 0) and whole number exponents Question 2: You simplified an expression.  The result was (3/4)1/2.  What could the original expression have been if you were using the following operations? (am)(an) = _______________________ am/an = _______________________ (am)n = _______________________ Demonstrate an understanding of operations on powers with integral bases (excluding base 0) and whole number exponents (am)(an) = ___ am÷an = ___ (am)n = ___ Question 3: Choose one of the following operations:               (ab)m     OR     (a/b)n Choose your own bases and exponents, however "m" and "n" can NOT be a whole number. Explain TWO ways to determine the result without using any "rules Demonstrate an understanding of operations on powers with integral bases (excluding base 0) and whole number exponents (ab)m= ___ (a/b)n= ___ Question 4: (From Marian Small) Write an expression that you would likely use three power laws to simplify.  Use a variety of exponents. Simplify it. Solving problems involving powers Question 5: Jamie states that a0 is a.  Pat says that it is 1.  Jessie says that it is 0.  Casey says that none of them are correct.  Who is right and how would you convince everyone else without saying "The rule is... Show that a power with an exponent of zero is equal to___

So there it is. A short assessment piece I could use to check my students' understanding of the power laws. What do you do in your classroom to assess students' understanding of the power laws? I would love to hear ideas for a performance assessment piece, other assessment questions (ie. a fabulous word problem), etc.  How would you share the connections between their responses and the outcomes (like I was attempting in option 1 and 2)?

Share and link in the comment section!

## Friday, June 8, 2012

### Chomping Down with "Screen Chomp"

Free

I absolutely adore Screen Chomp.  Any time anyone asks me for a great ipad app, it's the first one I share.  Why?  First of all, it's so easy my Kdg niece can use it without help.  The easiest way to use it is to just hit record and then draw on the screen and speak.  When finished, you'll have a perfect recording of what you drew and said!  You can even prepare the screen ahead of time by adding images if you want.  Preview the recording immediately after making it.  Then it's next to nothing to share that recording on twitter, facebook or just grab the link and share that!

What a fabulous tool for schools working with digital portfolios.

How would I use this?  Digital portfolios, assessment for learning, assessment of learning, students creating tutorials for school website, projects, and so on and so on...  Can you imagine having a student reading a passage of text and posting it beside how they did on the same text a month ago?  Students don't even have to be in the room to share their understanding or thinking.  Struggling student?  Watch them thinking through a math problem pre-written on the screen.  My brain goes into overload every time I think about how it can be used in the classroom.

The second reason I absolutely love this program is that it is completely and utterly free!

Third, as long as you have a wifi connection, you don't have to worry about how to download that video.

## Tuesday, June 5, 2012

### I'll Be Back...

next year in my role as CARC's Mathematics Lead Teacher/Facilitator.  Woot Woot!  I miss my students but look forward to working with K-12 Math teachers in Central Alberta again.  I had so much fun running around to different schools providing PD and modelling lessons.  However, I have a whole new respect for substitute teachers.  I had no idea how hard it would be!  I've never subbed a day in my life and this year I modelled lessons in classrooms.  The only difference was that I had to create my own lessons rather than following a predetermined one.  When I return to my classroom, I'm going to make sure to leave chocolate and let them know how much I appreciate their hardwork, especially those who have to come in to my -1 courses with little or no math background.

Summary for this year:

Favorite Session I offered:  Hands on and Virtual Manipulatives
Although this often became a contentious issue when dealing with high school -1 teachers, I really enjoyed sharing some of the ideas I have gathered over the years.  My favorite has always been "Using Algebra Tiles to teach Factoring Polynomials and Completing the Square".  You can find the information about this in my previous post. I also learned a lot from the teachers who were willing to share their ideas for using the manipulatives. Many teachers at the high school level are concerned about the lack of basic skills (such as multiplying in their heads) so I also created a lot of games for practicing basic skills at any level.

Favorite Learning:
When I started this job, I spent a day running around to schools meeting teachers, taking notes about sessions they would like, questions they had, etc.  By the end of the day, my hand was cramped and you couldn't read my handwriting.  (I wasn't hauling my laptop around and my phone was too small to take extended notes).  That weekend, I went out and bought the iPad 2 with bluetooth keyboard.  What a lifesaver!  Now, I can take notes and still read my writing.  I'm also a much faster typer than writer so I could keep up much better.

Just after I bought the iPad, I was asked by a school to come in and help with an Early Numeracy Intervention Program using iPads that they wanted to set up.  Perfect!  So, off I went to explore and download a variety of iPad apps for improving math skills.  Luckily, almost every developer I contacted was willing to give me free samples!  Woot woot!  You can find a list of my favorites on my delicious account

My Goal for next year:
To post more on my blog.  Not sure what happened this year.  I guess it had a lot to do with learning and becoming comfortable with my role.

I'm also going to work on posting as much as possible specifically about Alberta 30-1, 30-2 and 30-3 math curriculum. So, if you have something to share, I would love to see it!

Well, I should probably get back to planning for Grade 12 math now.  Will see you again soon!

## Thursday, February 2, 2012

### Completing the Square Smart Notebook Activity

I've uploaded another Smartboard lesson to Teachers Pay Teachers entitled "Completing the Square".

Students will use algebra tiles and the student handout (found in the attachments of the file), guided by the teacher using this file, to create the formula for Completing the Square.

Below I have included three sample pages from the file.

There is an intro story - I had created worksheets for today's lesson but accidentally spilled ink all over it.  Since I didn't have time to remake the worksheets, you need to help me figure out the missing numbers.  I set up all the expressions so that you could build a perfect square out of each expression.  What number is missing?  We would build the first factored form together once they have built the square.  After than they should have no problem writing it for the perfect squares.

A discussion would then need to occur regarding patterns.  Students are then asked to...

Since they can't build it using algebra tiles (I remind them they are not allowed to deface school property by breaking any of the pieces), they should be aware they have to do it just with paper and pencil although they might try to draw it.

Then we start to deal with expressions that have too many and too few pieces.  The story is that a little munchkin snuck into my classroom and either added to or took away unit pieces out of the algebra tile bags that I had created again for class.  They originally started with the exact number needed to make perfect squares. Help me figure out how many extra/too few pieces there are.  Once they have built it and determined the number of extra pieces (write that in the circle), we would discuss that it is a perfect square - which would be (x + 3)^2 but has 2 extra pieces so we represent it as (x + 3)^2 + 2.

We repeat the discussion again for "missing" pieces but when we are missing pieces we have a perfect square minus whatever we're missing.

Aligns to Alberta Curriculum:  Math 20-1
This lesson addresses the process for "Completing the Square" in order to address the following outcome:
*Analyze quadratic functions of the form y=ax^2+bx+c to identify characteristics of the corresponding graph, including vertex, domain and range, direction of opening, axis of symmetry, x and y intercepts and to solve problems.

This resource can be located on my Teachers Pay Teachers store AT NO CHARGE!  Make sure to post a review in my store.  Let me know if you have any suggestions for improvement!