Author Archives: dbsheffer

Reflection on Blogging


Blogging was a new experience for me.  I had considered asking my computer savvy son to help me set up a blog but this course forced me to experience blogging on my own.  I rather found it enjoyable.  I plan to continue with blogging but may change to my interests of quilting and cooking instead.

By taking this course I learned that online courses are no more difficult than face to face classes.  I rather enjoyed doing my course work when I wanted to in the comfort of my own home.  Because this is a career change for me, this course helped me become more comfortable with the subject of Math in general.  I’m becoming confident that I could teach Math if I choose to next year.

I am amazed at how interrelated math is with nature.  I especially enjoyed the nonlinear patterns web quest and learning about Fibonacci, the Golden Rule and Fractals.  I think these theories help us with design principles that work when decorating our homes, designing a quilt pattern or putting together a coordinated outfit.

Yes I will use journals with students.  I see the value of students taking the time to write down their thoughts, feelings and questions about Math.  I also think it would be a great way to assess how students are grasping the content material in classrooms that are larger than ideal size. My writing responses to the students would be a way to give the students a little more individual attention, not always possible during the class period.  I especially like the idea of a blog.  Students would be more open to writing if they can do it on the computer.  I also think blogging would be more convenient because I could read the blogs while at home without dragging a stack of journals home.



Factoring Quadratics


For this blog post I will list the steps used to factor a quadratic equation.  A simple quadratic equation looks like this: Ax² + Bx + C.  Factoring means you are trying to reduce the equation into simpler terms.  For this example I will use the equation  x² + 6x + 8.

Steps:  #1.  Determine the factors for “c”. 

                        Ex. Factors for 8 are 1×8 and 2×4

            #2.  Which set of factors will add up to “b”.

                        Ex. 2+4=6

            #3.  Determine the factors for “a”

                        Ex. (x) (x) = x²

            #4.  Write the following binomial

                        Ex. (x + __) (x +__)      

                        and fill in the correct factor from steps 1 and 2.

                        Ex. (x + 2) (x + 4)


I have always been the type of person who has to write things down in order to reinforce my learning.  Writing involves thinking about the concepts just learned, putting those thoughts into my own words and writing those thoughts down.  By taking the time to organize the information and make connections to what I already know I can better understand the new material.  Many of my students would benefit from the same process.  I will ask students to keep a journal or blog when the computer cart is available to our classroom.  The writing prompt I could give to students is to explain how to factor a quadratic equation to a younger sibling or friend.

Applet Review


I’ve decided to review Algebra Balance Scales found at

The purpose of this game is to solve simple linear equations by placing virtual manipulatives on a balance beam.  When the beam is balanced, the player then solves for x.  Students soon realize that any operation done to one side must be done to the other to keep the beam balanced.

I think this applet would be excellent for students who need more practice with solving linear equations.  The site also has another version of the Algebra Balance Scales game that has problems with negatives. I find many children and adults who need extra help when working with negative numbers.  My district doesn’t have math manipulatives, so this Applet would be an inexpensive way to give those students, who learn best by working with concrete examples, the opportunity to do so.

Evaluating My Definitions of Equations and Functions


After reviewing my classmate’s definitions I need to revise mine.  To my definition of an equation I would add that equations have equal signs.  To my function definition I would add the rule that there is one output for every input.  I think these additions make my definitions more accurate.

I would add the following example for functions:

Find f(4) if f(x) = 3x +7       f(4) = 3(4) + 7       f(4) = 12 + 7         f(4) = 19

When assessing the student’s knowledge I like to use pinch cards.  Each student is given a 5×7” card with the words equation and function written in big letters.  I would ask a series of question such as “Is f(x) = -5x – 4 an equation or function?”  The students pinch near their answer on the cards and hold them up over their heads.  This technique works best if the students are conditioned to allow for a short wait time and then everyone shows their response at the same time, on a signal given by the teacher.


There is a new quilting notion I would like to purchase.  It comes in two sizes.  I will use a proportion to determine how much of a savings the larger size will be.  The wonder clips come in packaged of 10 for $5.49 or 50 for $24.99.


To do a price comparison I will figure out the unit cost for 50 clips at the $5.49 price for 10.

My equation: 5.49 = x             5.49 x 50 = 10x      274.5 = 10x   274.5 = 10x      $27.45

                        10      50                                                                 10        10

Answer:  I will purchase the 50 count package because the savings is $27.45 – $24.99 = $2.46 plus the 50 count package comes with a free storage container.


I have just started a new knitting project.  The sock pattern instructed me to knit for 8 ½ inches.  I knit 5 rows and it measures ½ inch.  How many rows will I have to knit to reach 8 ½ inches?

My equation:  5 = x             5 x 8.5 = .5x      42.5 = .5x          85 = x  

                       .5    8.5                                     .5       .5

Answer:  I will need to knit 85 rows to reach 8 ½ inches.

My Definition of Equations and Functions


My definition: An equation is a math sentence used to solve a problem.

            3 + x = 10

            V = ∏ r²h


My definition of a function:  Input a number, the number goes through a math process and produces an outcome.

f(x) = 3x² + 5  (Read by saying f of x equals 3 times x squared plus 5.)

Supplementary resources that reinforce equations and functions:

Kid friendly definitions:

Students are given simple word problem and they practice writing the equation.

This link has another version of the function machine.  Students put in an input of their choosing and the machine spits out the output.  Students then come up with the rule.

This site has a simple game to play with the function machine. 

Journal entries:  To determine background knowledge I would have students record their definitions of equations and functions before the lesson.  Following the lesson they would go back and revise their definitions and provide examples.

Reference:  Pizza image came from

My Reflection on Math Myths


Myth #3:  In order to find a correct answer, you must always know how you got that answer.

While I was in elementary and middle school the method of teaching was rote learning.  We memorized multiplication tables and formulas.  Our homework consisted of completing drills.  Because of that, I can often get the correct answer but may not be able to explain the logic behind or process of how I arrived at my answer.

This myth goes back to our discussion earlier in this course about meaning vs. method.  Students will be more successful if they understand how to perform a math skill rather than memorize a rule.  This author feels that students need both intuition and logic to be successful in math. 


Myth #10:  To solve a difficult problem, work intensely, and don’t stop until the problem is solved.

When my sisters and I came home from school we had to sit right down and complete our homework.  This had a negative affect on my assignments.  I would rush thru the problems, and be careless so I could go outside to play.  On the nights my mother checked our work I would sit there struggling over a difficult problem and become very frustrated with the amount of time it was taking.

Now I often find myself leaving a problem and coming back to it later.  I did this yesterday with a level 5 Sudoku puzzle.  After a break I can see the problem with fresh eyes and was able to complete it without peeking at the answer.

Giving students the permission to leave a difficult question on a test and come back to it, is a good test taking strategy.  Sharing the strategies we use when dealing with difficult problems, may help the students handle their problems more affectively.