Geometry and it's uses

If you've ever considered where to find real life examples to be used in your geometry lessons you have to look no further than the companies who develop Mechanical CAD or Computer Added Design software. These websites are filled with several video and image examples of how geometry is used in design to build devices that are used in everyday life. Simply by going to google and typing in Mechanical CAD provides links to limitless examples.

Here are a few;

 

Examples of their use in a classroom could be at the beginning of a lesson as a hook or breaking down the image to define the various solids, cube, cylinder, sphere, triangular prism, cone, cuboid etc. You could use images and make a game of "finding the solids" and then relate that back how it is used in real life.  
Other opportunities to involve these images into your lessons is to underline how important language is involved in communicating the information presented. Some of the images show dimensions and relationships between parts., units of measure and scale.
With so many various images you can differentiate what is shown by providing more and less complex images.

Number Riddle

I've always been a fan of this riddle. Although not truly math related, the students will assume it is because of the numbers.

Examine carefully the following sequences of numbers:

1

11

21

1211

111221

312211

13112221

1113213211

31131211131221

Although the sequences appear to behave totally at random, in fact, after the first sequence, each sequence is constructed in a precise and methodical way based on the previous one. What is the next sequence?

To solve, simply say the quantity of each number. Ex. in the first line, there is one 1, hence why the second line is 11. Now, the second line has two 1's, hence what the third line is 21.

Get it?

Olympics and Math

Every four years in Canada we are given a wonderful opportunity to mix our Canadian tradition and heritage into the classroom.  Canada has a long and storied history of doing well in the winter version of the Olympics.  In 2010 our class utilized the Vancouver Olympics to study in-depth a variety of math strands.  The activities used also worked during the previous Olympics as well.

Our unit started with looking at Canada's history in past Olympics.  The data management strand offers some very easy connections to this part of the unit.  Students begin by collecting data from a variety of websites (ex. olympic.ca) and creating a variety of graphs.  Data is also used to create and test hypothesis using scatter graphs in grade 8 (ex. Does the money given for a gold medal equate to more hardware for a given country?).  These activities serve to give the student relevant real world data and also create an increase in national pride.

Once the Olympics begin, the students continue to collect data throughout.  In intermediate they analyze the variety of data (medal winners, historical trends, # of athletes, etc.) and determine which type of graph best suits their needs.  This of course leads to the discussion about the purpose of their data and how data can be leading or 'mis'leading.  Students then need to make inferences and convincing arguments base on their data collection.

There are many curriculum connections in the number sense also factors heavily in our discussion throughout the games.  The students can move beyond simple textbook and worksheet questions that may have little connection to their lives by using math they are immersed in throughout the study.  Students use percentages to calculate which countries are doing well (% of medal winners) versus countries that are disappointing.  It is always a lively discussion when we talk about disappointment and how 4th place may seem disappointing, but means you are still fourth in the world.

The students favourite unit involves the unit on percentages and tax.  We try to figure out what a vacation to watch the Olympics would generally cost by making a budget based on data.  Vancouver (yikes!) ended up being very expensive.  Using data from a variety of sources students need to find flights, lodging and of course tickets to watch their favourite events.

Having completed this unit over the past three Olympics, my main reflection is the increased use do technology.  Students are able to follow live Olympic updates, use programs such as Tinkerplots and spreadsheets for graphing, and I-pads or computers for research.  The two seem to go hand in hand in bringing out meaningful math and making the students interested and intrigued in concepts that can get tired when using out of date information.

It also goes without saying that this unit fits quite nicely in other subject areas well.  Teachers can easily incorporate language arts, health and science topics with the Olympics.  The unit also includes completing the events in phys. ed.  class complete with medal ceremonies.  Every time the students complete the unit their reflections always speak highly in regards to fun and interest in math during the Olympic activities.  Every four years I look forward to utilizing the Olympics and in 2010 our Olympians didn't disappoint.