No Sports, Just Multiplying

Hello all,

I know the usual readers of the blog may be disappointed that today's entry is not centred around sports, but I had to share a math teaching ah-hah moment.

As a lot of my colleagues my students have been struggling mightily with two digit multiplication.  Of course this usually leads to the discussion that today's students just don't know their facts.  "In my day..." Ya, I know you had to walk uphill both ways in your bare feet, is what the students usually tell me.

Back to math, our junior intermediate divisions have decided to have a mini focus on math facts during the month of October.  The students are completing daily activities (times table challenge) and games (multiplication bingo) for prizes and 'bragging rights'.   This is having a real positive effect on our students ability to quickly manipulate single digit multiplication.

However moving to two digit multiplication, there seemed to be no carryover.  Most students were unable to transfer their knowledge of single facts to the standard multiplication algorithm.  Multiplying and carrying at the same time were proving to be a chore.  The students and I had just about given  up, when I happened across Big Ideas from Dr. Small.

She explains in detail, the lattice algorithm (pgs. 37,38) for multiplying multiple digits in a visual sense. 

The lattice system worked exceedingly well for the students.  Each digit is automatically placed in the proper place value column.  In the example above, the pink represents the ones column, the orange the tens column, and so on.

The ah-hah came after ten minutes of dissecting the strategy with the students and their applying the strategy.  We went from two students being able to multiply two digits to 15 students being able to consistently and accurately multiply two digit numbers.  The other beauty is the lattice also works as the numbers get even larger and also work for decimals as well.

I have included a link to a you tube video showing the lattice algorithm in action.  This does not mean that this is the only way to multiply, but if students are struggling with the standard algorithm, this will certainly increase their confidence and lead to increased participation during your lessons.

Some student before and after samples are shown below.

Olympics and Teaching 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.

Detroit Lions Lose in Overtime

Should the Lions have gone for the first down last week?  Trailing by three, the Lions opted not to send out Jason Hanson to tie the game with a chip shot field goal, instead opting to use a quarterback sneak for one yard.  Of course this didn't work and they lost.  It was ultimately the wrong decision as they lost, but what does the math say?

Based on my research, using the book, Scorecasting, which borrows data from a 2005 study of the NFL among other places, the answer is YES the Lions were right is attempting to gain a single yard.  "Regardless of field position, on anything less that fourth and five, teams are always better off going for it." (pg.36)

Another study analyzed 1068 fourth down attempts.  The NFL teams punted 959 times.  Which means 90% of the time they are giving the ball back to the other team with no chance to score points. 

Ultimately it looks like Jim Shwartz went against the math opting not wanting to put his tired defense back on the field.  There's always next week!

While I'm here, I can't help but put in a plug for the book.  If you love sports and like (even if you don't love) math, this is a book you have to read.