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The Eleventh Hour?

The mathematician magician is still here, sharing her tricks.  This week it is the elevens.  Before we demonstrate the trick, I have to get on my soap box for just a moment.  In my humble opinion, all students should know their times tables through 12 even though the Common Core Standard for third grade says through 10 x 10.  Remember, Common Core is the minimum or base line of what is to be learned.  In Algebra, I insist that my students know the doubles through 25 x 25 and the square roots of those answers up to 625.  It saves so much time when we are working with polynomials.

Now to our our amazing mathematical "trick".  Let's look at the problem below which is 231 x 11. 

First we write the problem vertically. Next, we bring down the number in the ones place which in this case is a one. Now we add the digits in the ones and tens place which is 3 + 1 and get the sum of four which is brought down into the answer.

Moving over to the hundreds place, we add that digit with the digit in the tens place 2 + 3 and get an answer of five which we bring down.  Finally, we bring down the digit in the hundreds place which is a two.  The answer to 231 x 11 is 2,541. 

Now try 452 x 11 in your head.  Did you get 4,972?  Let's try one more.  This time multiply 614 by 11.  I'm waiting......  Is your answer 6,754?

Now it is time to make this process a little more difficult.  What happens if we have to regroup or carry in one of these multiplication problems?

We will multiply 784 by 11.  Notice that we start as we did before by just bringing down the number in the ones place.  Next, we add 8 + 4 and get a sum of 12.  We write down the 2 but carry or regroup the one.  We now add 7 + 8 which is 15 and then add in the 1 we are carrying.  That makes 16.  We bring down the 6 but carry the 1 over.  We have a 7 in the hundreds place, but must add in the one we are carrying to get a sum of 8.  Thus our answer is 8,624.

Let's see if you can do these without paper or pencil.  965 x 11   768 x 11    859 x 11   After working the problems in your head, write down your answers and check them with a calculator.  Try making up some four and five digit problems because this is a non-threatening way to have your students practice their multiplication facts.  Have fun!

The Dreaded Math Curse

I love books that link math and literature, and one of my favorites is Math Curse by Jon Scieszka. Published in 1995 through Viking Press, the book tells the story of a student (I’m not sure from the illustrations if it is a boy or a girl) who is cursed by the way mathematics works in everyday life. It is a tale where everything is a math problem, from tabulating teeth to calculating a bowl of corn flakes.  Everything in life becomes a math problem.
I thought the plot for this story was so interesting. Somehow, this book has made math almost fun and interesting. I liked that there are different stages to the plot, first you see the initial spark, “You know, almost everything in life can be considered a math problem.” Then you watch as the narrator becomes a “math zombie”. The story continues like this until the curses is broken, but wait! The science teacher then says, “Almost everything in life can be viewed as a science experiment.” I lik...moreTAFirst you see the math teacher, Mrs. Fibonacci, (don’t you love that name?) declare, “You know, you can think of almost everything as a math problem.” Then you watch as the student turns into a “raving math lunatic” since s/he believes “Mrs. Fibonacci has obviously put a math curse on me.” 

From sunrise to sunset, the student anxiously mulls over the answers to countless calculations such as: How much time does it take to get ready and be at the bus stop? (a problem the reader can solve.).  Estimate how many M&Ms you would eat if you had to measure the Mississippi River using M&Ms. There is even an English word problem: “If mail + box = mailbox, does lipstick – stick = lip? Does tunafish + tunafish = fournafish?”   (silly, but funny.)  A class treat of cupcakes becomes a study in fractions, while a trip to the store turns into a problem of money. The story continues until the student is finally free of the math curse, but then again Mr. Newton, the science teacher, regrettably says, “You know, you can think of almost everything as a science experiment.”

Math Curse is full of honest to goodness math problems (and some rather unrelated bonus questions, such as "What does this inkblot look like?"). Readers can try to solve the problems and check their answers located on the back cover of the book. The problems are perfect to get students’ minds working and thinking about how math really does apply to their everyday life.

The illustrations by Lane Smith are one of a kind. They are busy and chaotic to reflect the “math zombie” this student becomes. Many resemble a cut and paste project, with some images touching or overlapping others. Mostly dark colors are used especially when the student begins to dream s/he is trapped in a blackboard room covered with never-ending math problems.  (a nightmare for many) Smith’s art work makes Scieszka's words come to life and helps to paint a picture of what is going through the mind of the main character as s/he deals with the dreaded math curse.

John Scieszka does a remarkable job of breaking down the typical school day into math problems while also adding some tongue-in-cheek and light hearted humor which every mathphobic needs.  The math is perhaps a little advanced for elementary students, but the problems are perfect for middle school or high school students. 

Math Curse also demonstrates how a problem may seem difficult, but if you are persistent, you can find the solution to the problem. The book teaches not to fear or be anxious about math or for that matter, any other subject in school.  Despite the fact the main character is completely overwhelmed by mathematics, it allows students who struggle with the identical feeling to know they are not alone. Any student who has ever been distressed over numbers, fractions, word problems and the like will certainly identify with the main character.

As a math teacher, I think this book makes math fun as well as interesting. Although I recognize math is everywhere in everyday life, I never realized just how much until I read the Math Curse and mathematically saw the day of a typical student.  I believe what sets Math Curse apart from other books is that it accurately illustrates and explains how math is actually used and applied in day-to-day life.  I love the story, the message, and especially the content.

Never Too Old to Play Games!

I currently teach remedial math students on the college level. These are the students who fail to pass the math placement test to enroll in College Algebra - that dreaded class that everyone must pass to graduate.  The math curriculum at our community college starts with Basic Math, moves to Fractions, Decimals and Percents, and then to Basic Algebra Concepts.  Most of my students are smart and want to learn, but they are deeply afraid of math. I refer to them as mathphobics.
We all have this type of student in our classrooms, whether it is middle school, high school, or college. When working with this type of student, it is important to bear in mind how all students learn.  I always refer back to the Conceptual Development Model which states that a student must first learn at the concrete stage (use manipulatives) prior to moving to the pictorial stage, and well in advance of the abstract level (the book).  This means that lessons must include the use of different manipulatives. 

I use games a great deal because it is an easy way to introduce and use manipulatives without making the students feel like “little kids.” I can also control the level of mathematical difficulty by varying the rules; thus, customizing the game to meet the instructional objectives my students are learning.   However, as with any classroom activity, teachers should monitor and assess the effectiveness of the games. (Refer to the December 13, 2011 posting about Lesson Plans and Research.)   

When using games, other issues to think about are:
1)      Excessive competition.  The game is to be enjoyable, not a “fight to the death”.
2)      Mastery of the mathematical concepts necessary for successful play.  Mastery should be at an above average level unless teacher assistance is readily available when needed.  A game should not be played if a concept has just been introduced.
3)      Difficulty of the rules.  If necessary, the rules should be modified or altered in order that the students will do well.
4)      Physical requirements (students with special needs).  These should be taken into account so that every player has an opportunity to win.

In addition to strengthening content knowledge, math games encourage students to develop such skills as staying on task, cooperating with others, and organization.  Games also allow students to review mathematical concepts without the risk of being called “stupid”.  Furthermore, students benefit from observing others solve and explain math problems using different strategies.
Games can also….
1)      Pique student interest and participation in math practice and review.

Games that Teach
2)      Provide immediate feedback for the teacher.  (i.e. Who is still having difficulty with a concept?  Who needs verbal assurance?  Why is a student continually getting the wrong answer?)
3)      Encourage and engage even the most reluctant student.
4)      Enhance opportunities to respond correctly.
5)      Reinforce or support a positive attitude or viewpoint of mathematics.
6)      Let students test new problem solving strategies without the fear of failing.
7)      Stimulate logical reasoning.
8)      Require critical thinking skills.
9)      Allow the student to use trial and error strategies.
Mathematical games give the learner numerous opportunities to reinforce current knowledge and to try out strategies or techniques without the worry of getting the “wrong” answer. Games provide students of any age with a non-threatening environment for seeing incorrect solutions, not as mistakes, but as steps towards finding the correct mathematical solution.

For a complete listing of the games I have available on Teachers Pay Teachers, click on the page above entitled Games That Teach or click under the quote by George Bernard Shaw.

A Little Math Humor

I just love to laugh in math class.  When I do, my students are surprised because they believe math is no laughing matter.  I like to have a small, humorous snippet on my tests or a cartoon hanging in my room.  Here are a couple I found on Pinterest which I absolutely love!

Apparently, x is lost!

Thank goodness, x has been found!
P.S.  Do you know the value of x in the above problem?