Teaching to the nth Degree

Oct

2012

A Day for Social Action

On Friday I took a group of students to We Day. It is a day organized by Free the Children, a charity which inspires youth to take action and be agents of positive change in the world. Founded by Craig Kielburger, the main missions of this charity are to assist the impoverished with education, clean water and sanitation, health, alternative income, agriculture and food security. Full day events will occur this year in Toronto, Vancouver, Alberta, Manitoba, Waterloo, Montreal and Saskatchewan. The day is filled with musicians and motivational speakers who want to inspire youth to get involved in social action. In Toronto, we listened to Jennifer Hudson, The Tenors, Al Gore, Justin Trudeau, Hedley, Martin Sheen, Nelly Furtado, Spencer West, General Romeo Dallaire, K’naan, Justice Sinclair, and The Honourable David C. Onley. Our students left feeling inspired by the stories they heard and energized to rally for others less fortunate than themselves. In the spirit of the day, I would like to highlight a few math resources that focus on social action.

I discovered a new resource called “Real World Math: Engaging Students through Global Issues” from Facing the Future. I tried one of their sample activities in the spring, which linked sustainability to surface area and volume. I decided to order a copy for this year, and I am excited to try more of their tasks. The resource focuses on issues such as waste and recycling, poverty, population growth, youth conflict, global health and carbon emissions. There are a variety of other resources to explore on their website, including web-based and print resources.

For many years I have been a fan of an organization called The Southern Poverty Law Center, whose mandate is to fight hate and intolerance. Their Teaching Tolerance program assists educators in preparing youth to live in a diverse world.

The Global Education website is based in Australia, and contains resources for a variety of global issues such as clean water, cultural diversity, human rights, sustainability, poverty, international aid, food security and the environment.

It is also worth checking out a few other resources that I have previously mentioned. “Math that Matters” from the Canadian Centre for Policy Alternatives focuses on connecting math and social justice so that students can make connections between what they learn in the classroom and the world around them. Radical Math is a website resource for integrating economic and social justice issues into the math classroom.

Have a great week.

Aug

2012

Tech Toolbox

As part of my job this year, I will be helping teachers integrate technology into their classrooms. This includes anything and everything, such as blogging, website creation, digital presentations, digital tools, iPad use and Smartboard use. I have spent a lot of time this summer researching resources, and I have created a list in my updated tech toolbox page. There you can find various links to resources for iPad use, screen capture and audio/video/image editing, infographics, posters and charts, digital storytelling and comic creators, interactive whiteboards, presention methods, and other miscellaneous tools.

As I continue my research, I realized that there is so much more available to explore, and I will continue to do so regularly. If I have missed something that should absolutely be on the lists, please let me know.

Jul

2012

Sustainable Thinking

I was looking for math resources one day, and I came across a neat organization called Facing the Future. It is a non-profit organization whose goal is to educate students on global issues and how to make positive changes in the world. They have a series of resources that cover topics such as poverty, the environment, global health, and population.

When looking through their site there are a few key areas to explore. The curriculum link takes you to their Global Issues and Sustainability curriculum. Most of them are for purchase, but there are free samples from many of their books. I used a sample lesson from “Real World Math: Engaging Students Through Global Issues”. It incorporated sustainable design into a surface area and volume question. It was a great assignment, but I learned that my students need more practice with these type of problems. I have ordered the book for the school next year, as I think it is a great addition to the middle school math resources.

You can also explore the Global Sustainability Issues link. Within that section, the Global Issues Tours give some background information on some of the global issues facing our world. The Newspapers in Education link shares some global issues newspaper articles and related lesson plans. The Action Project Databases give students some ideas of how they can get involved to make a change in the world.

I am always looking for good resources for educating students on global issues. If you have any, send them my way.

Enjoy the sun.

Update: The website has been updated and most of the links mentioned are no longer working, but the website is still worth exploring.

May

2012

Playing with Probability

I had to plan for the last 6 teaching days with my grade 8 math classes, and after that we are into exam review and end-of-year trips. We had not yet covered probability, so I thought that I could design some mini-activities to carry out over these six days.

Here is my plan for the six days:

Day 1:
-Introduce terminology (probability, theoretical probability, experimental probability)
-Each student is given an activity to carry out with either dice or spinners (see attachment below)
-Discussion of theoretical and experimental probability as related to the dice and spinner activities

Spinner and Dice Activities

Days 2/3:
-Introduce game assignment (see attachment below)
-Allow time for students to decide if they are working alone or in small groups
-Planning time for students to organize the activity

Game Assignment

Days 4/5/6:
-Students lead activities for class
-Class discussions of how each activity went and how other factors might have come into play. Classmates suggest ideas for improvement.

We just finished the first day of activities in one of the classes, and already students are learning how to modify their activities based on how the first ones went.

We will play some more tomorrow.

Apr

2012

Pythagorean Theorem…Take 2.

This week I begin Pythagorean Theorem with my grade 8 students. I intend to use many of the same applets as last year (see Fun with Applets), with a few new additions.

Illuminations Proof without Words – This is similar to Puzzle 1 from the National Library of Virtual Manipulatives. The difference here is that this applet runs for you and asks you to figure out the proof from what you see. In the NLVM applet, you manipulate the pieces yourself. I still prefer the NLVM applet, but this is a nice alternative.

IES Applet – This is similar to their applet that I shared last year. In this applet, one of the squares gets transferred whole, while the other one is broken into pieces. The whole square and the pieces must fit into square “c”. (Update – this link appears to be broken)

Learning Math – This site from learner.org has some features that I like. In Part A, students are led through some inquiries and then the theorem is explained. Part B then leads students through a few different proofs. Part C and the Homework section have some interesting questions to solve. (Update – site disabled)

Wolfram Math World – This site has some of the proofs already mentioned on other applets and sites, they are all just put together in the same place.

I plan on showing my students a few of the proofs, and then providing them with the websites so that they can explore. They will need to choose one that makes sense to them, and then find a way to display it with reference to a real-world problem of their choosing. In the past, students have used foam board or bristle board and made pieces that they could move around and fit with Velcro. Other students created their own digital demonstrations of one of the proofs. Some simply created diagrams. Again, I will leave it up to them to choose a method they can work with.

I can’t wait for the fun to begin.
Have a great week.

Apr

2012

Playing with Platonic Solids

This week I am starting to explore platonic solids with my grade 8 students. The key question that I want them to answer is “Why are there only five platonic solids?” (For a brief explanation, see the MathsIsFun website. For a more detailed explanation, read this entry from The University of Utah.)

I want this to be a true exploration activity, and as such, I will give my students limited information. I will not volunteer this information, but I will give it only after they determine the right questions to ask.

First, the students will be given nets of the platonic solids so that they can build them and use them in their exploration. I will be giving them the copy from the learner.org interactives.

They will also get scissors and a handout with the regular polygons. They may cut out the polygons and use them as manipulatives. There are eight copies of each polygon, from three-sided to eight-sided figures.

Regular Polygons Handout

I have also created a Notebook file for the Smartboard. This will be open for the students to come and explore with, as well. It is not fancy. On one side of the page are the platonic solids for the students to see. On the other side of the page are the regular polygons, set up as infinite clones. In the middle of the page is a play area. Students can thus pull out copies of the polygons, turn them around, and see how they fit together. (The polygons were created from the tools in the program, and the platonic solid images were taken from Wikipedia. If you click on each image on the second page of the file, you will be taken to the home site for that image. )

Platonic Solids Notebook File (Unfortunately, this is what the Notebook file looks like as a PDF. WordPress will not allow me to upload the Notebook file. Help anyone?)

Should students get frustrated, I will begin to lead them through the following thought process:

Consider the regular polygons. Starting with the triangle, what is the measure of each interior angle? Continue for the rest of the polygons.
What do you notice about the sum of the interior angles of the polygons, as you go from three-sided figures up to eight-sided figures?
Which of these polygons are able to tessellate? Why are they able to tessellate?
Which of these would be able to be constructed into a polyhedron? Why wouldn’t all of the regular polygons be able to be constructed into a polyhedron?

They can then go play on the Learner.org website.

The final task will be for them to submit an explanation as to why there are only five platonic solids. I will accept written work or digital work – students can choose which method suits them best.

Have a great week.

Apr

2012

The Escalator

I came across a neat resource from the University of Toronto. As an educator who lives in Toronto and a University of Toronto alumnus, I am surprised that I had never heard of it before. The resource is called The Escalator. It is an outreach site from the University of Toronto, with an emphasis on math and science.

Under the Math tab at the top there are two options: Mathematics and Fields. Click on the Mathematics link and you are taken to the University’s Department of Mathematics page. Here you can find links to math competitions, teacher resources, and other tidbits.

There are two links under the Physics tab. The Physics link takes you to information for the Physics Outreach program and the Physics Olympiad Preparation program for high school students, complete with practice problem sets. The Candac link takes you to the Canadian Network for the Detection of Atmospheric Change, which has a variety of links and information, as well as a teacher resource page. The Chemistry tab also takes you to an access page for the Canadian Chemistry Olympiad for high school students, again complete with practice problem sets. The Engineering tab takes you to a list of robotics competitions and a variety of summer programs for students in grade 5 and up.

Click on Universe under the Astronomy tab, and you are directed to University of Toronto’s public portal. Here you can video chat with astronomers and send them questions, or book a planetarium visit or speaker. There is also a link here to the Transit of Venus. On June 5, 2012 Venus will pass across the sun. This has not happened since 2004 and will not happen again until 2117. (Alternately, you can read about the Transit of Venus here.)

The resources tab has a few areas to explore, including a link to the teachers’ resource page of the Canadian Mathematical Society, which has its own database of resources to search through. The curriculum link is still being developed, so check back to see its full potential. Currently you can find the link to the Science Rendezvous for Educators site. The Science Rendezvous is what first led me to The Escalator website. It is a one-day science festival, hosted on university campuses, research institutions and community sites across Canada on Saturday, May 12, 2012. The database on the educator page is not yet built, but again, I am curious to see what will be included there.

Have a great week.

Update – Escalator links are no longer active…I think this program has been discontinued.

Mar

2012

Building Bridges

My grade 7 students will begin building bridges next week. They will be allowed to use white glue and wooden sticks of their choosing, such as popsicle sticks, toothpicks, and stir sticks. They will model it after a real bridge that exists somewhere in the world, and so a research component will be involved. They will have to meet the following design specifications:

The bridge deck must be able to span a distance of 30cm but may not be longer than 40cm.
The bridge must be able to carry a load of at least 1kg.
The bridge can be no higher than 20cm off the ground.
The travelled portion (width) of your bridge must be at least 3cm wide, capable of transporting a Hotwheel © or Matchbox© car (each car’s dimensions are approximately 30 mm wide x 70 mm long x 25 mm high).

The following websites will help them as they prepare to build their bridges:

Bridge Building page from 42Explore

Physics Balsa Bridge Building Contest – scroll down to the links at bottom

In addition, they can also explore the following bridge building game sites:

Cargo Bridge

Nova Build a Bridge

Have a great week.

Mar

2012

Playing with Mechanical Advantage

I have finished discussing the basics of simple machines with my grade 8 classes. We have looked at the formula for work, and their weekend homework task was to play on and explore the following websites:

Edheads (update – this game is no longer free, it now requires membership)
Museum of Science and Industry

This week we begin mechanical advantage. We will start by playing with levers (materials: prisms for fulcrums, metre sticks, spring scales, and various masses). The students will investigate what happens to mechanical advantage as we change between first, second and third class levers, exploring with various lengths of effort and load arms. We will then move on to pulleys, and the students will build various systems with fixed and movable pulleys (materials: pulleys, string, spring scales, various masses, and retort stands with ring clamps). They will explore different lengths of rope and how mechanical advantage changes depending on how the load is supported.

Here are some links that I will use along the way to supplement their learning:

Wisc Online – I will have to tread carefully with this one, as the units are not metric.

Pulley Basics (from an unexpected source: Summerlift Products)

Videos:
Mechanical Advantage (from Hila Road Outdoor Centre & Educational Resources)
Eureka Video Series (1980’s cartoon series from TV Ontario) – This is the first video in the work and mechanical advantage series, which include episodes 8 through 15. For more information on Eureka, see the Wikipedia Page.
Mechanical Advantage (from Khan Academy)

If you have any other good resources, I would love to see them.
Have a great week.

Feb

2012

Analyzing Systems

In my grade 8 science classes we have been learning about systems. The Ontario curriculum unit, Systems in Action, has the students go beyond learning about physical systems and has them explore social systems and the evolution of systems.

I began this unit by having my students analyze a social system which included identifying subsystems, inputs, outputs and side effects. Each student chose a different industry and analyzed the various parts of that industry and their effect on society, economics, and the environment.

The students are currently finishing presentations for their second assignment, the evolution of technological systems and their impact on society. Together we brainstormed a list of ideas to research, and then students wrote their top five choices. They were then assigned to groups based on their topic preferences. Amongst the favourite topics, students chose to research the evolution of the telephone, the computer, the camera, and mp3 players. Each student group had to create a visual timeline of their chosen system using digital or non-digital tools. As they presented the timeline, they had to explain the reasoning for each technological change and how the evolution of the system has impacted society.

Below is a copy of my assignment sheet. As my school is an IB World School, the rubrics are IB MYP style.

Systems Evolution

Once presentations are complete, the students will move on to the second phase of this assignment. They will consider the various presentations and determine which technological system they believe to have made the biggest impact on society. To do this, we will have discussions to determine which criteria would be used to make this type of judgment. Based on the criteria that we determine, the students will compose their thoughts.

After analyzing the evolution of systems, we move on to experimentation with work and mechanical advantage.
Have a great week.

Tech Toolbox

Sustainable Thinking

Playing with Probability

Pythagorean Theorem…Take 2.

Playing with Platonic Solids

The Escalator

Building Bridges

Playing with Mechanical Advantage

Analyzing Systems

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