About The Algebra Stories

Sara, the Math whiz is the heroine of the Algebra Stories. Sara is the daughter of Vijay and Sonia – both software engineers who had moved from India to North America.  Sara has been practically raised by her Nana (grandmother) who lived with them.  She is a bright student – a slim girl who keeps shoulder length hair.  She dresses well but modestly. Most of the stories are about Sara’s romance with her boyfriend Johnny who belongs to an upper middle class family.  Although he is not that great academically, he is always well dressed. She comes whenever her sweetheart calls because she always wants to be with him. Sara and Johnny are fictitious but the high school romance is real.  All the other characters and the data used in the book are also not real.

In my opinion, everyone is capable of learning Math.  A deterrent is  a lack of interest in this subject. These stories are written to generate and enhance this interest.  With a life time of experience in education, the author is not delusional to think that reading this book will convert  a student into a Math genius.  This work would serve its purpose if even a fraction of the readers of these stories get more interested in learning Math.  Finally, it is not an accident that a girl named Sara is the Math whiz in these stories.  I hope this creates an interest in Math in those girls who currently think that Math is not for them.

               At the end of a story, there may also be a Challenge.  The objective of the challenges is to broaden or firm the concepts presented in the story.  The Appendix contains solutions to the challenge questions.

            About Individual Stories

Often a starting algebra student gets thrown off just by seeing letters and equal signs instead of sentences and numbers.  Sara Loves Nana illustrates that algebraic notations are nothing but abbreviated forms of what they already know from arithmetic.  I used this idea with my son when he began to learn algebra.  At that time, he was interested in baseball cards.  So we talked about prices of the cards of different players.   Subsequently, I wrote the player’s initials instead of full names and made an equation for the total price of two different cards.  He was okay with it. Then we wrote only the first letter of the name and repeated the process. After that he just started writing equations with x and y instead of the player’s names.  That’s what Sara does in this story. The story just introduces the concepts of algebraic notations and equations, and ratios and proportions. It would be useful if a student were to read it before the first algebra class.

Students learn arithmetic, algebra and geometry as different subjects.  Very few of them see a relationship between them.  Sheldon And Topanga – The Battle Of Nerds bring forward such a relationship.  I have used this story to challenge colleagues from several countries where they think that they have superiority in Math.  The results did not attest to their belief of such a superiority.  This story encourages students to think outside the box rather than look at each branch of Math separately.  This idea should be explored by a student on their own or in a group setting.   An emphasis can be provided by a teacher bringing it up early on in an algebra course.

Trip To Langley Park is a story to introduce the students to arithmetic, harmonic and geometric means. One day, my 10 year old son asked me what a geometric mean was. When I gave him the definition, he blurted out “So the geometric mean of two positive numbers can never be greater than their arithmetic mean.”  Obviously, we had a longer conversation about it. I had never thought of it before. So, I had to provide him the proof for it. This story shows that a harmonic mean of two positive real numbers is also smaller than their arithmetic mean.  It should be introduced before the first lessons on different types of means. Bright students should be able to prove this superiority of the arithmetic mean with the clue that the square of a real number cannot be negative.  The answer to this challenge is also in the Appendix.

Nana’s Bedtime Story For Sara and Cheerleader’s Sweet Tooth are about properties of exponential functions and the rules for dealing with them. Nana’s Bedtime Story For Sara is based on a Silo story I used to tell my son when he was in junior kindergarten.  There was a silo filled with grains.  A sparrow found a hole in it and flew away with one grain in its beak.  It came back with a friend to get the grains. Next time, both the sparrows brought friends so that there were four of them now.  The numbers kept doubling, and the kid would fall asleep when there were 32 birds or so. He must have been doing calculations in his dreams.  By the age 8, he used to continue the doubling process mentally to get to 16384.  Nana’s bed time story introduces this concept of divergent exponential functions.  In this story Sara also teaches the approximation of large numbers.  Cheerleader’s Sweet Tooth is about an exponential decay. I used a similar story in my pharmacology lectures to explain the difference between the zero and the first order rates of clearance of drugs from the body.   Maharaja Suryaman – a story for logarithmic functions was more difficult to write. An ancient Indian king named Maharaja Suryaman and his court of intellects were created, and the difficulty of plotting the values of the exponentials in the previous two chapters was also exploited. Johnny’s Question elaborates on the Log functions and their rules.

Text books often deal with quadratic equations in a rather drab manner.   ” Can Smart Phone Use Enhance Academic Performance?” is a result of my conversation with a high school Math teacher.  The teacher was frustrated because the students were busy during his class on smart phones when he was teaching the rather dry subject of quadratic equations.  The story deals with a possible meaning of two solutions of a quadratic equation.  The teacher then uses it for lessons in this area.  A student named Jun excites the students about the concept of vertex.  Finally, several students give examples where such equations may help.  In order to illustrate wide applications of this area, the examples came from two cheer leaders, a basketball player, and students with interest in gardening and business. These examples are based on textbook word problems for the quadratic relationships.  It is debatable as to how the whole story should be used – as a whole or in parts which precede the corresponding lessons.  Carmen’s Question uses the quadratic equations to introduce the concepts of imaginary and complex numbers.

Sara And Johnny’s Graduation Party is one of the final events in the high school romance of the two love birds. They decide to have a joint graduation party.  They have to decide who to invite and what the seating arrangements would be.  They go through a discussion of permutations and combinations.  However, they end up not using it because personal choices prevailed.

Even the best of couples have differences.  Sara and Johnny are no different.  Sara Gets Mad At Johnny because he hides a secret from her.  It turns out Johnny is not hiding anything but his ignorance of a lack of understanding of the  concept of continuous compounding.  Once Sara knows this, with her dad’s help she goes through the concepts of Binomial Expansion,  Euler’s Constant and Continuous Compounding and then happy days between them return.

Priya, another student in the school had befriended Sara Priya’s Homework deals with the basic principles of probability. Jenna and Priya’s T-Shirt Shop exploits the principles of probability.  Priya helped her mother Jenna to create and use a unique service.  They have a patent pending on the unique service of their T-shirt shop.  Their success is sweet but it presents a concern.  Now, they are scared because they think that a multibillion dollar clothing empire called Boondoggle is after their patent.  This story focuses on how the probability principles can help in making rational decisions.  It also highlight the principle of independence of probabilities of different events and the exceptions. The chapter is simplified so much that it may make an actuarial cry. The story would be ideal if the students read it slowly with the whole class participating in its discussion at each step.