The multiplicative inverse of a number is its reciprocal. When a number is multiplied by its multiplicative inverse the product, or answer, is 1.

The reciprocal, or multiplicative inverse, of x is 1/x .

For example, the multiplicative inverse (reciprocal) of 12 is 1/12 because

 12/1  X  1/12 = 12/12 = 1.

The multiplicative inverse (reciprocal) of 3/5 is 5/3.  3/5  X  5/3  = 15/15 = 1.

 

The additive inverse of a number is its opposite. The sum of a number and its additive inverse is 0.

 

 For example, the additive inverse of 12 is –12.           12  +   -12 = 0

The additive inverse of –3 is 3.       -3   +   3   =  0

 The additive inverse of y is –y.      y    +   -y  =  0

 

My Mathography

 

My very earliest memories of math are in learning basic addition, subtraction, multiplication, and division facts. Because I was strong in rote memory this was fun for me. I especially liked when my teachers would make the drill we had into a contest because it felt that my classmates and I were playing a game to see who would win. As I continued through elementary each new process was introduced as a new challenge and skill to learn. I associated very pleasant memories of math through learning fractions, decimals, and percent.

In sixth grade I was selected to be one of the students in an experimental group studying what was called “New Math”, basically independently work using manipulatives to study set theory. Through high school I was put into advanced placement math classes where my rote skills basically enabled me to earn good grades. I could plug numbers into formulas but really did not have a concept of why the formulas worked. Algebra I and II and well as Geometry courses made sense for me but beyond that in Calculus and Trigonometry I resorted to using formulas without really having a clue.

My favorite math teacher was my second grade teacher, Mrs. Terminello. She had a way of supporting us as learners, cheering our attempts while gently correcting mistakes. She made me feel that errors were opportunities for learning. Mrs. Terminello also used small group work and manipulatives along with partner practices which allowed me time to internalize the steps in a process or the facts we were learning.

I have never considered math my favorite subject. It seemed to come easily to me but it was basically linear and cut and dried the way I was taught. You were either wrong or right, there were no gray areas and one right way to complete your work. Being able to use my imagination as well as my verbal strengths in English made that my favorite subject. With many schools today shifting to a more exploratory and application based  mode of math instruction, I would probably feel more positive and might consider math my favorite subject because there is more room for using divergent approaches and a variety of strategies.

Real Life Math Story

 

I needed to buy enough topsoil to cover my small vegetable garden to a depth of four inches. I knew that this required a math computation prior to shopping for the topsoil.First I measured the length and width of the area that I needed to cover. The measurements were 10 feet 4 inches in width and 9 feet 6 inches in length. I used the volume formula of length X width X depth to figure out how much volume I needed to cover.

First I converted all measurements to fractions so that L X W X D became

9 ⅟2  X 10 ⅓ X  ⅓=

19/2 X 31/3  X  ⅓=

589 / 18  = 32.72 cubic feet

Since the bags of soils I wanted to purchase contain 1 cubic foot each, I had to purchase 33 bags to obtain the coverage I needed. 

Every year it seems that there is one particular area where my students are extremely confused by specific vocabulary. This year they have a very hard time grasping the concept of absolute value. I have explained it as the distance from zero on a number line, or the distance an integer is from zero on the number line . I have given them the more formal dictionary definitions of  1. Also called numerical value. the magnitude of a quantity, irrespective of sign; the distance of a quantity from zero.  Or 2. The absolute value of a number is symbolized by two vertical lines, as |3| or |−3| is equal to 3. The value of a number without regard to its sign. For example, the absolute value of +3 (written |+3|) and the absolute value of -3 (written |-3|) are both 3.

Absolute Value  The absolute value of a number as its distance from zero.   The absolute value of x, written as ”| x |” (and which is read as “the absolute value of x“), is the distance of x from zero. This is why absolute value is never negative; absolute value only asks “how far?”, not “in which direction?”. This means not only that | 3 | = 3, because 3 is three units to the right of zero, but also that | –3 | = 3, because –3 is three units to the left of zero.

Hi, all! My name is Pat Hutton. I am a middle school special education teacher who has experience teaching English, math, science, and social studies. My experience in teaching math has been in both resource room and in-class support settings. Our curriculum emphasizes problem solving. I love to travel and have driven cross country quite a few times. My favorite vacations, though, have been to Italy and Alaska. I live in central NJ, near the beach and the culture of New York City. I enjoy spending time watching the ocean, reading a book, or playing with my black Lab, Koda.

I am taking this course because I hope to gain new strategies for making meaning for my students. I also hope to expand my own view of how to teach math concepts, particularly more abstract ones. My eighth grade students must pass a state test, NJ ASK, that emphasizes algebra and geometry so I want to better understand the concepts they need to learn.