Developing Courses

My question for all you fantastic teachers out there is why I can't find any of your course calendars  It is so hard to plan a new course without having even a small idea about the time it is supposed to take to teach certain concepts!

So as a favor to you, I have been working on my course outlines and lesson plans! And I have been doing it all online.  When I am finished you will have complete access to all my work! And for those particular courses, if you are using the same material, you will not have to create your own!  You can literally just copy and paste into your own document.

Here is what I've gotten so far:

Math 10-3 Course Calendar


Math 20-3 Course Calendar


Science 14 Course Calendar


Math 31 Course Calendar


The goal is to complete these resources by June.  When they are finished I want t to include links to completed lesson plans and links to all the resources I can possibly provide.

I've taken and modified these lessons from various places.  Math 10-3 and 20-3 are from Learn Alberta resources and the Mathworks textbooks.  Science 14 is from the ScienceConnect.1 textbook and learn alberta.  Finally, Math 31 is taken straight from my mentor teacher.  He did a great job developing it and deserves all the credit, all I'm gonna do is make a calendar for it and include lesson plans for it all.

My goodness, why are things not organized like this to begin with.  It is absolutely painful fishing my way through blogs upon blogs to find lessons that aren't necessarily there.

As a beginning teacher, even if I get offered a really great lesson from a more experienced teacher, it is useless unless I really know where it belongs in a set of lessons.  Even trying to get a guest in to speak to a class the first time I teach it is absolutely painful because I can never match it up quite right to the classes.

Math 10C Measurement Unit Plan

Thanks to my mentor teacher Debbie, I now have a working template for Unit Plans. I thought I would share it for the world to see how awesome she is!
 

I've been using this template to complete a Calculus Unit Plan as well as a Math 9 Unit Plan.  As I keep teaching I am certain that they will slowly get filled in! I'm convinced that filling these in as I go is way easier than filling them all in at once.

Here's a link to my live document on Google Docs.

Enjoy!

The Product Rule

This whole teaching thing is just so fantastic I really don't know where to start!  I think though that there is  an obvious lack of hands on activities out there! For inequalities for example, I was able to find one activity that happened to be a story reading activity that I'm totally going to turn into a story writing activity.  You'd think by now that enough universities have forced students to write lesson plans that there would be an online database of hands-on activities for nearly every concept in mathematics!

This week was teachers conference! Wow! There was a lot of great ideas being thrown around.  I went to a great 4 hour session on physics labs, argued about how things should be measured, watched a fantastic comedy act, and started to wish I had a class set of iPads.  But not everyone can be that lucky.  

I'm starting to realize that most of the ideas covered in physics can become great mathematics activities! Especially considering the new curriculum here in Alberta.  So here are a couple ideas I came across and highly recommend turning into math labs!

Focal point calculations!  Graphing diameter vs. distance gives a linear relationship!

Using isometric fabric to explain gravity wells and charges!  I'd have to look into this more but it's a fantastic hands on explanation of electric fields and point charges.

Lasers to find the distance between data on a cd! I should really have a program of studies out right now.

A box and candies to explain half lives! I'm thinking calculus or exponential functions!

Toy trains to explain vectors and vectors with velocity! Cheap and awesome! Math 30 material.

There was one more that I didn't get a picture of.  It involved some springs hanging from chairs to calculate spring constants.  Just too cool!  I'm excited because my math classes are gonna be awesome!

To continue my calculus geogebra interlude I have here the product rule examples I'm using.  Now because not all the examples are super interesting to look at I don't go over the uninteresting functions with geogebra in my class. A great idea that I haven't been able to make work yet (thank you Audrey @a_mcsquared) is to insert a geogebra sketch google gadget into a google doc (spreadsheet) so that I can watch as students play around with it!  In this manner anyone could play with it and all the students could see their riends playing with it live. 

 If anyone figure it out please let me know! And if you take any of these ideas and turn them into labs please please please send them to me!

No Smartboard Allowed!

After talking to my 10C Mentor Teacher I have decided to try something a little different.  Mainly because she has challenged me to teach without a smartboard.  WHO TEACHES WITHOUT A SMARTBOARD?! This is the twenty-first century! With twenty-first century teachers! Breath Darcy Breath.  Okay I'm calmed down now... so apparently sometimes projectors break down or smartboards crash and there is no other choice than to work with a whiteboard.  So in lieu of it all breaking down she has asked me to teach without one.  All I'm allowed to use it for is to put up questions.  Bleh.  

So I'm gonna try this:

And I think it will work, I've never tried it.  We shall see... I have to do a whole review session so I'm gonna do it like 7 times in the same class and see how it goes.  Crossing my fingers here!

Also This teacher has some great ideas and this cardomatic is one of them!  I think I'll try it!

Derivitive Shortcuts

So I've kept creating my geogebra files after spending two days figuring out how to upload them.  I'm going to use this one next monday for my calculus students.  5 examples showing off the exponential, sum, and constant shortcuts of derivitives.  Thanks to my mentor teacher I've a set of notes that goes over why we would ever want to use these rules and how we came to find them.

Not sure if I will spend any time whatsoever proving those rules but I will bring my calculus textbook just in case somebody wants to see the proof after the lesson.

In other news, I am super pumped about our whole school project as well, it should be pretty awesome but all we have so far is an idea in our heads.  Look out world, here come the student teachers!  I've been super lucky in finding friends in my colleagues and am looking forward to working with them more! Look forward to a report on what we have planned and how it went!

So I've kept creating my geogebra files after spending two days figuring out how to upload them.  I'm going to use this one next monday for my calculus students.  5 examples showing off the exponential, sum, and constant shortcuts of derivitives.  Thanks to my mentor teacher I've a set of notes that goes over why we would ever want to use these rules and how we came to find them.

Not sure if I will spend any time whatsoever proving those rules but I will bring my calculus textbook just in case somebody wants to see the proof after the lesson.

In other news, I am super pumped about our whole school project as well, it should be pretty awesome but all we have so far is an idea in our heads.  Look out world, here come the student teachers!  I've been super lucky in finding friends in my colleagues and am looking forward to working with them more! 

Understanding Tangents as Limits of Secants.

This took way too long to figure out... and yet... I did it.  

Explanation: Export as dynamic webpage, change advanced setting to whatever you like, under advanced/files go clipboard: google gadget, press clipboard.  Copy code to the file that comes up, save it as a file, press publish, then get code, copy the code, put it in blog html, publish to blog.  Ta da!

Which cup is better?

My mentor teacher is awesome and let me design one of his calculus labs! With the help of John Scammell and the Twitter Community, and a little push from the school chemistry teacher, this is what I've come up with!

My school just got a set of CBL probes and I am totally excited to use them!  I'll let you know how it goes!



Hopefully it's not a complete bomb!

Coming Late to Class?

Lesson Starters!

So I've been working on some lesson starters in class every day and here are the results!  We were practicing different problems and then marking them holistically.  They are for a bunch of different classes  and stretched our thinking a lot! Have fun trying them for yourself!

Math 30-1: Settlers of Catan!

By popular request I have asked my friend Christine if I could post her lesson on Settlers of Catan and she said yes! So here it is!



The worksheet she used for us to record our observations and predictions:



And finally here is the excel worksheet! This is probably the most awesome part of this great lesson!



I think the only thing I might do is add this to the logic and puzzles unit somewhere and have them actually play the game afterwards!  Thanks Chistine!

Polynomial Engineering

This was presented to me by Renee Jackson and is absolutely incredible.  I want to develop it further to include negative tiles!

Here are the templates for the algebra tiles! It will probably take a while to make a class set so start early!

I should just say, for about an hour and a half about thirty math teachers were entranced by this!

Algebra Tiles - A Developing Concept Plan

This isn't a particularly useful outline of an activity we presented.  However, there are very useful resources attached throughout the paper and the papers we researched and included in the bibliography are incredible!  Plus, all the research we did gave me an idea about how to teach negatives in algebra through area explorations, rectangles, and squares!  I'm really excited to develop it and will post it when I finish putting it together!  I promise it will be awesome!



Right from the start of our presentation we had some pretty big issues with the technology we wanted to use. One of the problems with setting up on the spot is that there is no time to test and make sure everything is going to function properly. Initially, the Notebook software we needed would crash every 15-30 seconds after opening it, so our SmartBoard aspect was almost completely useless. Fortunately we got it to function just as we needed it, but the SmartBoard was out of calibration and it wasn’t calibrating properly. Overall though, once we got past these couple bumps and bruises with the technology, it all worked smoothly for the most part. It definitely would have been helpful to have a backup plan for a scenario such as this, as technology can at times be finicky, and there is not always time to fix it.  

Our peers were already well versed in algebra tiles thanks to the previous days activities.  The time that they spent exploring squares and their properties was invaluable to our presentation.  After some reflection I could not help but think the concepts that we presented were far too vast for a 45 minute presentation.  However, if we were to have split the activities that we had into four different presentations then the product of our presentation would have been far more effective in teaching our peers about the properties of algebra tiles.  A more focused exporation of positive algebra tiles, a more intense activity involving the properties of negative tiles, and a single activity exploring the properties of lattice multiplication that tied into a factoring activity later on would have created an atmosphere that allowed the students to explore the tiles themselves later on.  Concerning the properties of positive tiles, there was a need to allow students to further explore the concept of multiplication as represented by area.  Adding further tiles of different shapes and sizes to this activity would have expanded the learning potential.  However, having students build squares and rectangles from predetermined sets of trinomials allows them the opportunity to get comfortable and familiar with the materials before getting into the more difficult ideas of negative area and factoring.

In regards to teaching students about trinomials containing negative terms, we found that it would be useful to review the concept of operations involving integers.  During our presentation is was somewhat difficult even for our classmates to understand why it is needed to keep all negative algebra tiles together along one side of the trinomial representation and all positive tiles along the other side.  Renée brought up a great point which we could have explained.  That is, when multiplying a negative integer with a negative integer we get a positive product (same with a positive integer multiplied by a positive integer).  But when we multiply a negative integer with a positive integer we get a negative product.  If we were to represent our trinomial with negative and positive tiles interspersed, even if the tiled representation generates a square or rectangle, the placement would not satisfy our mathematical rules for integer multiplication.  This would have aided in addressing any confusion that our students may have when investigating with algebra tiles.

After using tiles to build squares and rectangles to factor since grade nine I have only one new suggestion.  The idea of negative area, as presented by Andrew and expanded upon using tile activities, would allow students the opportunity to explore the concept of algebra tiles even further.  Using black negative tiles, colored positive tiles, and a black backdrop could enable us to teach about polynomials using direction.  Statements such as “the black negative tiles cover up portions of the grid that we don’t want to find the area of” would be possible and the need for integer multiplication of negatives would not be needed to determine which color tile is needed to complete the rectangle students are building.  Instead we could use questions such as “do we want to find this area or is this part of the section we don’t want to find the area of?”  However, consistency is important in mathematics and allowing students to use integer multiplication in order to factor is a useful and familiar tool that students can use without too many misconceptions being made.

When working in a group it is hard to have a proper flow. In group work, I think there needs to be more practice on the actual presentation, to ensure timing and flow of thought is clear. This is also true in individual teaching. It may take more then one try to present a lesson properly. This is why it is important to have a detailed lesson plan to follow, or for others to follow. It may also be helpful when presenting a new topic/lesson on the first time it might be helpful to have notes or an outline handy. It is important to remember that a concept may take more/less time then you had originally thought to cover in a period. It is important to remain flexible and allow for some changes. Having problems or an extension activity is a great idea for making up for any shortcomings. Also, keeping an eye on the clock and managing the time properly is very important.


Written by Christine Crowe, Andrew Johnson, Kim Simon, and Darcy Bundy

A Math 10C Resource Analysis!

We put a lot of work into making this a real, viable resource for any teacher's using this textbook!  Included is an analysis of the textbook, its strengths and weaknesses, and links to supplemental resources to compliment the textbook where it falls short of the curriculum!

Mathematics 10C on Prezi

Enjoy!



And a quick look at how exactly the textbook matches the curriculum along with more resources!

Me vs. The Man

This video is intended to be a teaching supplement.  If a teacher makes a lesson out of the idea presented in this video then students will be able to experience a hands-on approach to percentages and taxation.  It is meant to empower both students and parents to learn outside the classroom and not as a direct teaching tool or a replacement for proper instruction.  I have often found that when a student is struggling in mathematics and there is no further time available for me to spend with them then parents or other educators must step in and help them.  Normally at this point it is too late for a teacher to help with the catch-up work that the student must do but by providing students and parents with the resources and insights that they need to discover the material for themselves we are increasing their chances of success in the classroom later on.  With that in mind, the creation of this movie signifies the beginning of a career long search and collection of resources that can, and will, be used both inside and outside of my classroom.

Grade Stream & Strand:  Mathematics 8

Topic:  Number   

Timeline: 1 - 8 Minute Session

Big Idea:  Teachers, parents, and students alike will become become aware of new ways to understand and teach GST.

NCTM Principles and Standards for School Mathematics covered in this presentation:

1.  Number:

A)  Understand numbers.

In Grades 6-8 all students should:

- develop meaning for percents greater than 100 and less than 1;

- work flexibly with fractions, decimals, and percents to solve problems;

B)  Compute fluently.

In Grades 6-8 all students should:

- develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Specific Outcomes:

1.  Demonstrate an understanding of percents greater than or equal to 0%, including greater than 100%. [CN, PS, R, V]

Vocabulary Focus

GST: A 5% tax on the supply of most goods and services in Canada.  

(Canada Revenue Agency)

HST:  A harmonized sales tax replaces both the five percent federal goods and services tax (GST) and the provincial sales tax and is applied on the same basis as the GST.  

(Canada Revenue Agency)

PST: a provincial tax imposed on the consumers of most goods and particular services in a particular province.  (Canada Revenue Agency)

Works Cited:

Alberta Education. (2008). The Alberta 10-12 Program of Studies. Edmonton: The Crown in Right of Alberta.

N. C. T. M. (2012, February 9). Principles and Standards for School Mathematics. Retrieved February 9, 2012, from National Council of Teachers of Mathematics: http://www.nctm.org/standards/content.aspx?id=3742

Ward, Susan. (2012, February 9). GST. Retrieved February 9, 2012, from Small Business: Canada: http://sbinfocanada.about.com/cs/taxinfo/g/gst.htm

Special thanks to Vi Hart, Dan Meyer, and John Scammell for their inspiring work.

Angle of Elevation and Depression!

I want to put out a special thanks to John Scammell for providing me with this lesson!  It was amazing and quite honestly, very entertaining!  Some of the images are his, one of them is Dan Meyer's, and I sort of mashed everything together to recreate a lesson that John taught to a class somewhere here in Alberta! It was fantastic!


Here is a link to the notebook file I used: honestly, the activity was not tech based at all and the students still loved it!



Finally, the activity sheet I used so students could record their observations, measurements, and calculations!



Was this activity successful?  Absolutely.  One student said “it managed to be applicable to real life.”  Another said it was “interactive, engaging, and inquiry based.”  Yet another said that it “showed an application that 20-3’s will be excited to complete and learn.”  However, in my opinion, the most useful comments are the ones that will make this lesson stronger and more memorable for students.  One of my peers pointed out that “in order to be [more] accurate you need to be farther away” when using the clinometers. “A thorough discussion of error” is needed, and “spending more time on some of the strategies and how to measure more accurately using the clinometers” both came up several times in the feedback.  Quite frankly, I agree with them.


The time provided to introduce this activity to my peers was not quite enough to fully appreciate what they encountered.  Our opening exercise would have included more than identifying trigonometric ratios and the introduction to the clinometers would have included building them and measuring the angle to an object at varying distance had there been more time available to enjoy the activity.  With more hands-on experience and more time to explore the use of the clinometers students would have observed the rules of the clinometers on their own and would have begun to think about how else these tools could have been used.  I have often felt pressured to perform while teaching in a classroom and the results during these times are always poor.  When teaching my grade eight class last year I was told that I was speaking far to fast for anyone to keep up.  Making a small leap in logic here, I can assume that it is also possible to move a class too fast through an activity.  Without the proper amount of time available to students they will have trouble making connections.


A lot of the students forgot to add their own height to their estimate while measuring the height of the Education Cafeteria.  Others didn’t use angles at all, preferring to measure the height of the windows and multiply that by three, estimating for the difference in height of the windows.  What is really interesting though is that some students preferred to use meters in their answers instead of feet.  When the answer was given in meters some of the groups cheered about how close they came and others ran to google to convert the measurement into meters.  Kieren talks a lot about teaching mathematics with a focused, yet open mind.  Not looking for a specific answer and yet keeping the class moving towards the final goal, ie. the program of studies.  We need to think about teaching with respect to how our students are thinking about the subject.  A good discussion to add to this lesson is one that explores the way that different groups found their answer and the strategies that they used.

While teaching during my IPT, I gave students an assignment to explore the NASA website.  However, after looking at the assignment, two of my students decided to write their own fictional story and base their calculations on the scenario that they described.  Their zeal for the assignment went from nearly no interest to extremely interested when they were allowed to explore the material in a manner that appealed to them.  I find the same thing often happens to me while completing assignments.  Pedagogically, this lesson became an inner argument of control in the classroom.  Allowing the students the freedom to leave the classroom and giving them the responsibility to return to the designated meeting spot can motivate students who would otherwise feel micromanaged and creates an atmosphere of open ideas and solutions.  This can be the basis for building mathematically confident and inspired learners.  Students who feel empowered within a classroom are more likely to share, communicate, and practice the skills that they’ve learned; which will in turn creates a healthy student/teacher relationship with my students!