Mathematical Bingo

The other day, I wanted to run a bingo game using math equations and verbal descriptions.  That type of game is not always easy to find on the internet so I figured a way to do it myself.  It wasn't all that hard to set up.

First thing I did was find a bingo card templet on the internet.  One that allowed students to write in their choices.  I made copies for people so they could fill in their choices from a huge list on the front board.

I found a wonderful random name drawing generator at Name Picking Ninja because it allowed me to input a list of terms and I could eliminate the answer and not use it again.

It took students about 10 minutes to select 25 out of 40 algebraic expressions on the board.  I let them customize it so they'd have more buy in. 

The add names is where I added my list of predone choices I typed up in word.  I had to delete a list of writers but that took a short time.

When ready, I hit the go button, the choices spun and it stopped on one as you see in the photo.  I read the verbal phrase out loud.  For some of the classes who struggled more with this, I asked what product meant or second power to help them talk about the math more. 

The first one who managed five in a row got a small piece of candy as a reward.  Overall, it went well because it helped encourage conversation and it gave students practice in connecting the verbal with the algebraic expressions.  The down thing is that it was a bit slower since it involved discussion.

I will be able to use this in other classes to just as easily and I can use vocabulary, slope, linear equations, etc to test their knowledge.  I chose this venue so when they have a quiz on Friday, they might do better since we actually used it in a situation.

Let me know what you think, I'd love to hear.  Have a great day.

Complex Probability

I love simple probability but complex is a bit harder to do because many students have difficulty with the idea of recalculating probability for each case.  I admit when I was in high school and had the topic, I wondered why if you had two bags and selected from one bag why you needed to worry about the one you weren't using.  It wasn't until college I realized one of the probabilities was choosing one of two bags.

My high school teacher didn't explain much in detail because he thought it should be obvious to us as we looked at the situation.  I always hated the "Its Obvious" train of thought.

One nice way to introduce the idea of complex probability is to use the video Menu Tossup which looks at calculating the total number of combinations on the menu.  Something students can easily relate to since they like eating at any of those fast food places.

Another way to show more about complex probability is to set up a probability bingo game.  The math equals love site has a great explanation of the game and where it originated. The idea is to fill out a bingo card covered with various combinations such as blue/green, green/red, red/blue, green/green, blue/blue, or red/red.  Students tend to prefer playing games to completing worksheets.

In addition, you could create or purchase compound probability task cards which can be placed around the room so students can get movement while working their way through the activity.  You could also create QR codes with compound probability questions or create or buy a compound probability scavenger hunt.

Scholastic has a nice little unit on compound probability with everything needed to teach the lesson including the 5 accompanying worksheets.  Its geared for 6th and 7th grades but it could easily be used in the high school, especially if working with ELL students.  It has students use a tree diagram to help derive the formula.

On the other hand, Better Lesson a nice lesson for 7th graders to learn more about complex probability and sample space.  In addition, it has students determine probability using an arithmetic strategy.

Unfortunately, many times including probability and statistics in the Algebra, Pre-Algebra, or Geometry classes is a bit hard because they do not fit nicely into the flow of the classes.  The topic is almost a disruption in the flow but I save it for short weeks like Thanksgiving, the end of the semester, spring break where a natural break falls in the class.

Let me know what you think, I'd love to hear.  Have a great day. 

How do you teach it?????

At some point we have to teach either probability or statistics either as a part of our regular math classes or as a stand alone class.  Not many of the books I use have really interesting lessons to use other than the standard penny flips and possibly the rock, scissors, paper game. 

I'm always open for some ideas to use in my classroom.  I've found a few and its time to share them with you. 

Fortunately, the American Statistical Association has some lovely peer reviewed lessons for teaching statistics.  The lesson are designed for grades K to 12 so if you have students who are not up to grade level, you can choose something designed for younger students or take a lesson and adjust it upwards. 

For middle school, a couple of lessons really caught my interest.  The first is "How random is the iPod's shuffle" which many students easily relate to because they use the shuffle button.  The other is "How long is 30 seconds?" which appeals to me because most students I know who try to count 30 seconds tend to rush it so they finish about five seconds ahead of the time.

High School has a lesson "Confidence in Salaries in Petroleum Engineering" examines the salaries in a field which is said to have one of the highest starting salaries for any profession.  Another one, "10,000 steps" examines one of the newest fitness trend which states you need 10,000 steps per day to stay healthy.

These are not one page lessons but more like 15 to 30 pages depending on the lesson.  They come complete with the objective, standards, materials, student sheets, etc. Everything needed to carry out the lessons properly.

Most of us have to introduce students to probability in a way they don't get bored or allows them to get up and move around.  What about setting up a QR game with 16 QR codes spread around the room and each QR code asks a probability question.  The question might be something like "You flipped two coins, what are the four possible answers?"  The student then writes the answer down on the answer sheet.  If you don't have the digital device, you could create the 16 questions and post them around the room.

Shodor.org has a really nice interactive spinner which the student to change the number of segments so students change check out the probabilities for different scenario's.  In addition, there are activities on fair chances, coin toss, theoretical vs experimental probability, and random number generators.  There are also worksheets and discussions. 

In addition, you could introduce probability using Bill Nye the science guy.  Episode S04E08 can be found on School Tube or You Tube.  Bill Nye is a fun person to watch as he explains an assortment of topics. 

The above probability activities are to teach simple probability but what about complex probability such as you have to remove two marbles without returning them to the mix.  How does that change things?  Tomorrow, we'll look at activities for complex probability.

Let me know what you think, I'd love to hear.  Have a great day.

How Do You Tell?

We all know that statistics can be in a positive or negative way and we've seen when they are not being properly used. Unfortunately, we can't always tell at a glance that the numbers presented are right. 

Often we hear when statistics are not being used properly, when two graphs are shown with different scales to convince us one product is better than another or one company is better than another. 

Yet there are other numbers out there that are used properly.  How do you help students understand which stats found in life are good and which can be ignored.  Part of teaching mathematics is to help them build a mathematical sense.  A sense of which things such as stats are reasonable and which are not.

If the statistics are used to promote something such as a solution to a problem or a course to help people, chances are the numbers provided may not be fully accurate because advertisers do not meet the same standards that a researcher does.  This means the "Three out of four dentists" recommend the protective power of this particular toothpaste might be suspect because the company wants you to buy it.

Second, if a statistic is used, can it be verified.  Where can I find the "Three out of four dentists" research showing this.  Any statistic that is worth anything can be verified because you should be able to find the study it is based on.  If I hear that some basketball player is able to shoot 4 out of 7 free throws, I should be able to go find that stat in a reputable site such as put out by the NBA.

Third, if the statistic does not seem to line up with reality, question it.  For instance, when I hear that three out of four marriages dissolve in divorce and out of everyone I know most have not divorced but there are a couple who may be on their third, fourth, or fifth marriage, I'd question it.  The multiple divorced people might change the statistic so it seems as if there are more than actually occur.

On the other hand, most sports teams tend to provide verifiable statistics on all players because these stats provide the owners with the necessary information for them to keep, trade, or release players.  Other groups tend to be insurance companies, actuarial companies, census bureaus, and other companies who use the finished data for setting rates.

Insurance companies have had a lot of data to come to the conclusion that females who reach 21 should pay less than their male counterparts since this is a standard practice across the board.  On the other hand, when I read the number of children killed has doubled every year since 1950, I can question that because its easily disproved by simple mathematical equations.

We need to help our students learn to distinguish good stats from bad stats and help them learn to tell the difference.  Let me know what you think, I'd love to hear.  Have a great day.

Doubling Pennies Etc.

  I researched the history of chess and one of the legends on its origin made me think of the doubled penny problem we often pose students in class.

The problem is the one where you ask a student if they want $1,000,000 or a penny doubled each day for a month.  After exploring the math, they discover the second is the better option.

The story I read said a wise man invented the game of chess to show the king how important each person in his kingdom was.  He enjoyed the game so much, he required all his subjects to learn the job and as a reward, he offered the wise man gold and silver but the man turned it down.  Instead, he requested one grain of wheat on the first square, two on the second, three on the third etc until all 64 squares had been used.  This would have given the wise man quite a lot of grain.  As a matter of fact, the story says the servants scrambled to find enough grain to do this.

Another place this particular doubling problem is found is in bacterial growth.  It is often expressed as starting with one that splits into two, each hour or day and you are asked to find the final numbers at the end of a specific period of time.  Its the same type of problem as the previous two.


All three problems fall under the general term of a doubling problem or exponential growth which is usually applied to how long it takes for a certain population to double.  One way to explain this to students is that it takes over one million microorganisms per milliliter to make water cloudy or contaminated so if it starts with one organism, it may not take long for the bacteria to split into one million organism.

So harmful bacteria grows at the same rate as good bacteria. If one harmful organism enters a pot of stew and splits every hour, the population would have grown to more than eight million which is enough to make someone sick.  This is one reason why you should not leave a pot of food in your trunk on a hot day.

I've seen the bacterial growth problems but I've never seen them applied to harmful bacteria in food which is a real life application of math and explains why there is an occasional outbreak of food poisoning at community potlucks.  It gives students a perspective on why you might want to care about bacterial growth.

So the next time I teach this topic, I'm going to include the example on harmful bacteria which people might find more interesting.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

Warm-up