Teaching to the nth Degree

Feb

2012

Pascal’s Triangle and Magic Squares

We have been working on patterning in Grade 7 math. We spent a lot of time looking for patterns in Pascal’s triangle and seeing how the numbers in the triangle work together. I asked my students to each try to find a different pattern in Pascal’s triangle, and they rose to the challenge. They came back to class excited to share what they found, and each student was hoping that no one else had found his/her pattern. At the end of the first day of presentations, most students had claimed a pattern, but there were a few students whose patterns were claimed by others and needed to explore further. The next day I decided to help them out, and gave a short lesson about figurate numbers and asked the students to find tetrahedral and hexagonal numbers in Pascal’s triangle. We then looked into fractals and how the Sierpinski triangle can be created in Pascal’s triangle by blacking out all of the odd numbers. I left them with another challenge – to see what happens when you block out even numbers, and numbers that are multiples of 3 and 4. I also showed them some of the Pascal patterns discussed in The Number Devil, a book I mentioned in a previous post.

Here are some of the links that I used for this series of lessons:

Pascal’s Triangle and its Patterns

Pascal’s Triangle from Math is Fun

Patterns in Pascal’s Triangle from Cut the Knot

Pascal’s Triangle from Math Forum

Wolfram MathWorld Fractal Page

Wikipedia Fractal Page (Scroll down to see the changing fractal beside the history section.)

Sierpinski’s Triangle from Math Forum

As we were having so much fun with numbers, we went on to look at the Magic Square in Albrecht Durer’s paintings. In his magic square, the sum of all rows and columns is 34. We used the Powerpoint below (source unknown) that was sent to me by a friend. To start, I only showed the first five slides, and then I left it to the students to determine where else they could find the sum of 34 in the square. They made me proud and found all of the sums mentioned in the Powerpoint, as well an additional sum found through a zig zag pattern.

Albrecht Drer’s Magic Square

Hope you have as much fun exploring numbers as we did.
Have a great week.

Feb

2012

Division of fractions…beyond the algorithm

I am currently working with multiplication and division of fractions with my grade 8 students. I have never been one to have my students just learn a set of rules, and so we always have discussions about the concepts and why the algorithms work. Year after year, the same issues surface. They have no problem conceptualizing multiplication of fractions, but division of fractions is always troublesome. They can follow the algorithm easily enough, but there are always those that have difficulty understanding why it works.

Here are some of my favourite resources for helping my students grasp division of fractions. If you have found others that work, I would love to hear about them.

First up is a neat little widget from Math Design in the Juniverse. I found this several years ago, and have kept it bookmarked ever since. I started using this before I had a Smartboard, and now my students can interact with it, as well.

Next is the division page on the Visual Fractions website. The first page gives one example, but when you click on “Investigate Division” you are taken to a PDF with several pages of examples to use. Although not interactive like the previous site, we can still put this up on my Smartboard and outline parts of the circles in various colours so that students see how many times I can take the pieces of the divisor out of the dividend.

The last resource is a lesson plan from the Ohio Department of Education that I only found recently. It gives several examples to do with students, along with prepared paper manipulatives for use along with the lesson. When I have more time, I intend to check out their vast database for other math lessons and activities.

Happy dividing.
Have a great week.

Jan

2012

Mathemania

Today I would like to share some great ideas from my Twitter PLN, which I hope to incorporate into to my lessons in the coming months.

The first is the traditional Locker Puzzle. I came across the Locker Puzzle a few years ago, although I first saw it under the name “A Thousand Lockers” from the Math Forum. I recently found this exploration of the problem that James Tanton describes on his blog, Thinking Mathematics!, and I love what I read and saw. I can’t wait to try it with my students.

The second is a post from Nat Banting on his blog, Musing Mathematically. He posts a question, courtesy of Andrew Kelly, that tackles the concepts of surface area and volume. It is not the standard surface area and volume problem that I have seen, and although his work seems mostly to be with high school students, I think that it will be a great challenge for some of my grade 8 students.

The last is a great way to get your students excited for the Superbowl next weekend. This Superbowl lesson on Yummy Math leads students to investigate the cost of advertisements for the Superbowl and how they have changed over the years.

Have a great week.

Jan

2012

Systems in Action

I have accepted the fact that I am not superhuman, and so I cannot always accomplish everything that I want. There was a time where I would feel guilty for not writing for the past month or so, but I have become wiser and now understand that I must retain my sanity. Report cards and another school project (Climate Spark) have kept me on hiatus, but I am back…

We have begun our Systems unit in grade 8 science. I introduced the unit by having my students play Fantastic Contraption, one of my favourite online physics games. The site has been a little finicky lately, but my students still had a lot of fun with it. After they had a chance to play for a while, they shared some of their favourite designs with their classmates. I then showed some videos of neat inventions that work as systems. First, we watched a few videos that highlight the innovations of Theo Jansen, creator of PVC sculptures in the Netherlands (see the BBC news video and the Ted Talk). Next I showed them some of the machines designed by Rowland Emett, which were used by the character Caractacus Potts in the movie Chitty Chitty Bang Bang. This week I will also show them some examples of Rube Goldberg machines, videos of which can be found on my July 3 post. When we are a little further in the unit I will share some websites for work and mechanical advantage.

Until then, have a great week.

Dec

2011

So You Think You Can Budget

A short while ago I came across a website titled the Canadian Centre for Policy Alternatives. I found it because I came across a book published by them, Math that Matters, and I was interested in learning more about their initiative.

I went back on the site today and was exploring, and found something quite interesting under the Multimedia and Interactive link. In their interactive tools, they have a section titled “So You Think You Can Budget”. It takes the Canadian budget figures from March 2011, and allows you to decide how to spend the nation’s money. There is a detailed list of spending choices that represent the interests of the varied citizens of our country. It would allow older students to gain some understanding of the difficult choices that are involved in budgeting for a country.

And when you have some spare time on your hands, go explore their website. There are lots of goodies to be found.

Have a great week.

Nov

2011

Science Interactives

Interactive sites allow students to practice learned concepts in a fun and engaging way, especially with the increased use of interactive whiteboards and iPads. This week I have chosen to share some of my favourite interactive science websites. If you have a website that I should add to my list, please send it along.

Have a great week.

Phet Interactives

Nova Interactives from PBS

Utah Education Network Interactives

WISC Online Learning Objects

Study Jams

Nov

2011

Problems of the Week

As I continue to find ways to enrich my math program, I have been searching for good problem of the week or problem of the month sites. Here is my growing list of resources that I have found online:

University of Waterloo Problem of the Week – Grades 7 – 12

University of Waterloo Emmy Noether Circles – Grades 5-6

Mathcounts

Mathmagic

Abacus Math Challenges

Word Problems for Kids

Problem of the Month

University of Mississipi Math Challenges

As always, I welcome any suggestions of resources to add to this list.
Have a great week.

Nov

2011

Go With the Flow

My grade 8 students are currently learning about the properties of fluids. They already conducted labs on density and viscosity, and are now adding buoyancy into the mix. This will be followed with discussions of hydraulics and pneumatics. In order for them to explore how all of these properties work together, these are the activities I have planned for the next few weeks:

Build a tin foil boat that can hold as many pennies as possible:

My students have already completed this. I modified the activity that was presented in our Nelson Science and Technology resource, but a similar activity can be found here.

Float My Boat

The students were not only challenged to find a way to build a boat that held as many pennies as possible, but they also wanted to “outdo” their peers by having their boat hold more pennies. It was a fun day filled with learning and friendly competition. As a follow up, students were asked to explain how the tin foil boat design was modified as they carried out the activity and identify which design worked best, and why.

Explorations with diving balls, Cartesian divers, and density kits:

Cartesian Diver Activities from the Thunder Bay National Marine Sanctuary

Resources from The Marine Institute

Density Block Activity from Arbor Scientific

Investigation of Ballast Water:

Students will research the problems associated with using ballast tanks and some of the solutions currently in use. They will present their findings through the viewpoint of those affected, and they will be required to consider their audience. This is an IB task, and the rubrics follow the IB standards.

Ballast Water Management

Investigation of Hydraulics and Pneumatics:

After conceptual discussions, the students will have time to explore hydraulics and pneumatics while using syringes and tubing. They will then design a hydraulic or pneumatic system that will move an object a certain distance.

Make it Move

As students explore, the following interactive sites and videos will be available for them:

Balloons and Buoyancy Interactive Simulation – from PhET lab, explore by filling the balloons with different gases

Buoyancy Explorer Interactive Activity – from SEED, drop blocks into different liquids to see what will happen

Eureka Video on Buoyancy

Brainpop Science Buoyancy Site

How Stuff Works – Submarines

If you have any other great resources that I can incorporate, I would love to hear about them.
Have a great week.

Nov

2011

Holocaust Education Week in Toronto

Holocaust Education Week in Toronto is from November 1-9th. In honour of the week, I would like to share one of my favourite related websites:

The Secret Annex Online
This website teaches about Anne Frank’s house in Amsterdam, as well as guides you through a tour of a 3D online version of her house. It is part of the larger Anne Frank Museum website, which has a wealth of information shared in various digital means. It is a wonderful website to visit, both to teach students about her history and to explore the many ways to effectively share information online.

And if you are interested in learning more about Toronto’s Holocause Education week:

Sarah and Chaim Neuberger Holocaust Education Centre
A wealth of resources for the general public and educators.

Have a great week.

Oct

2011

Numbers, Numbers Everywhere….Again

I had a few minutes to spare (hah!) and so I ventured over to Vi Hart’s blog to see if any new doodles had been added. I came across one of her older doodles, “Sick Number Games”:

While I was watching I couldn’t help thinking of the book, The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger. I read this book a few years ago, and enjoyed it from the first page. It is about a young boy who is visited in his dreams by a number devil. This devil shares number tricks with the boy, night after night after night. There are many possible ways to incorporate it into your classroom. Some of the number tricks are easier than others, and so there are applications for various learners. I personally have used it when exploring Pascal’s Triangle with my students.

Here are a few resources I have found for incorporating The Number Devil in the classroom:

Reflections on The Number Devil from Math Horizons

Activities from NZMaths

Have a great week.

Pascal’s Triangle and Magic Squares

Division of fractions…beyond the algorithm

Mathemania

Systems in Action

So You Think You Can Budget

Science Interactives

Problems of the Week

Go With the Flow

Holocaust Education Week in Toronto

Numbers, Numbers Everywhere….Again

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