math

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Update – Escalator links are no longer active…I think this program has been discontinued.

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.

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

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.

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.

Sep

2011

This week, in math class……

So what did my students do in math this week? Lots.

In grade 7 math we solidified understanding of factors and multiples and then moved on to divisibility. I also introduced some great challenges to them this week that they had fun exploring.

Courtesy of @Mathnasium, they tried this problem:

If two monkeys can eat three bananas in two minutes, how many monkeys will it take to eat 18 bananas in six minutes?

I gave them a few minutes in class to attempt it. Some students figured it out quickly, while others thought they had the answer, only to be disappointed when I told them it wasn’t correct. Their homework for the evening was to continue to work on the challenge, and to clearly write out the strategy that they used. The next day everyone came back to class with the answer. I am not saying that they all figured it out independently, but they left class more curious and enthused than I ever could have hoped for. What is important, too, is that they all came back with strategies. So even if they had received help, they got to a point where they could explain the reasoning behind the solution.

From the nRich website, on Friday they tackled Take Three from Five. For the weekend, I left them thinking about why this challenge always works. I don’t expect them to come up with the solution provided by nRich, but I am curious to see what they discover.

In grade 8 math we have been working on prime factorization and I also introduced scientific notation. The students are slowly working their way through the Power Mad challenge from nRich, which is a great follow up for the concepts that we have been covering. I find that even in grade 8, the most common mistake students make with powers is multiplying the base by the exponent. If anyone has any tricks that help students avoid this, I am all ears.

I love all of these challenges that I can directly incorporate into the curriculum, but I also know that students have other interests, as well. So I brought out about ten to fifteen different resource books of math puzzles, logic, and games, and had students put sticky notes with their names on the books with the puzzles that interest them. Next week I will go through their choices and personalize some extra challenge booklets for each student. I haven’t quite figured out when that is happening, as it seems like a daunting task, but I know that the reward of having engaged students will make it all worthwhile.

Aug

2011

More Rich Math Tasks

I have just spent time looking through the Rich Maths Task resources on the East Midlands Maths Network, and have found some great tasks to incorporate. They are organized by strand, and some of the tasks are taken from the nRich site, which I have also spent many hours perusing.

Thanks to @ColleenYoung for this sharing this resource with me. This site is listed on her blog under Diigo Rich Tasks List, and the site is labelled Rich Maths Task. There are many other sites to visit on her list, and if they are all as helpful as this one, then I know I will spend many hours exploring.

Aug

2011

Rich Performance Tasks

The London (that’s London, Ontario folks) District Catholic School Board has a website called Rich Performance Tasks, or RPT’s for short. The website is no longer updated, but the tasks are still there for others to access. They are real-life tasks that bridge different subjects. There are tasks for all grade levels and most subject areas within the Ontario curriculum. Each task has both a student and a teacher page. If you click on the teacher page, then you have access to pre-task activities, exemplars, and curriculum tie-ins.

If you click on the science tasks link, then you are brought to divisional science projects. There are tasks designed for primary, junior, and intermediate grades, and it appears that the goal was for students to work together across grade levels.

If you are only looking for science-based tasks, then I have some of my projects posted for all to use. Enjoy.

Note – This website is no longer accessible to the public…..sigh…..

math

The Escalator

Pascal’s Triangle and Magic Squares

Division of fractions…beyond the algorithm

Mathemania

So You Think You Can Budget

Problems of the Week

Numbers, Numbers Everywhere….Again

This week, in math class……

More Rich Math Tasks

Rich Performance Tasks

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