The Study of Math

Mathematics for the elementary student can bring about a variety of feelings.  Math can be intimidating, it can be exciting.  Kids can be stimulated or bored, interested and curious or impartial and distracted.  Self-confidence can contribute greatly to which way (positive or negative, greater than or less than) a student views math.

Self Esteem in school is effected by a multitude of  different sources; teachers, peers, parents, appropriate placement, school philosophy, the student's level of self-efficacy, reinforcements... the list goes on.
As a student it is important to have trust in your teachers as well as your parents, they are there to help you and often know what is best in regards to learning for your future.  It is not acceptable, though, to rely on these adults to do the thinking or the work for you.  You are your greatest advocate in your education, ask for what you need!  Do not be afraid to ask questions, request extra help, or admit if you do not understand.

Another important step to take for success in mathematics and school in general is to learn to become an effective student.  Children are not born with good study habits, they are developed.  A great level of motivation to learn pre-algebra is not an inherited trait, it is an encourage and rewarded one.  You do not have a genetic predisposition toward liking math.  I know many that would argue this, citing that intelligence can be inherited and left-brainers are simply better at math.  I agree, but I also believe that anyone can achieve success and enjoyment of mathematics.  This success takes hardwork, patience, dedication and, most importantly, willingness to learn and to ask questions.  Set goals for yourself, treat yourself to a small prize for success, but do not punish yourself for failure.  Math proficiency comes with practice, try and try again!

In this blog I have, so far, provided you with  a wealth of resources for learning and practice, but there are many more out there.  If you are a visual learner, Khan Academy provides videos and easy to understand explanations on thousands of academic topics.  Many of the websites I have provided have excellent manipulative components that help the more hands-on learners.  There are math Podcasts available for those who learn best by listening, sometimes repeatedly, to verbal explanations of topics.  My advice is to take advantage of a sampling of all kinds of teachings.  Even if you consider yourself a hands-on learner, reinforcing ideas by watching it done by others certainly cannot hurt!

 

Do your best and HAVE FUN!

Working with Fractions

Fraction Facts

A fraction is a part of a whole.

Fractions are split into parts.  The top number is the "numerator", the bottom number is the denominator and the line between is essentially a division symbol.

There are different kinds of fractions.  Proper fractions, such as one third, have a smaller numerator than denominator.  An improper fraction has a larger number on top (numerator) and can be changed into a mixed number.

 

Fractions have their own place on the number line, just like whole numbers.

 

 

Fractions have many equivalents, there is more than one way to name a fractional part, even though it is the same amount.

When working with fractions it is important to understand that there are multiple ways to express the same value.

You also must understand that there is a value that is less than one but greater than zero.

Addition and Subtraction of Fractions

Fractions, proper or improper and mixed numbers can be added and subtracted just like whole numbers.  The first step in this process is to find Common Denominators.  A common denominator is just what it sounds like, a common (same) denominator (number on the bottom).  Mixed numbers must be first turned into improper fractions before the common denominator is determined.  Common denominators are found by determining the least common multiple of the two denominators and what number that denominator is multiplied by to get to that multiple.  The numerator must also be multiplied by that number and that gives you a fraction equivalent that can be added or subtracted.  It is important that the fractions be transformed into fractions with common denominators because when adding or subtracting the denominator does not change.  Only the numerators are added to or subtracted from each other.  This entire process is nicely illustrated in the following video. 

Adding and subtrating fractions can be a bit confusing at first but once you get this system down, it can also be quite fun, the following sites have games that will help build your abitiliy, confidence, and enjoyment of fractions.

4 Fun Fraction Games:

math-play.com  mathplayground.com  FruitShootFractionsAddition  formula-fusion

Once the common denominators have been determined, the numerators also changed, and an equivalent fraction created it is time to add or subtract!  Like I said above, only the numerators are used in this step, the denominator stays the same.  For example, 18 twenty-fourths added to 22 twenty-fourths equals 40 twenty-fourths, the twenty-fourths DO NOT get added together.

Once we have our answer, in this case 40 twenty-fourths we are not done.  It is most common to give the answer in Lowest Terms.  Lowest terms means the fraction's numerator and denominator have no lower common factors (not including 1).  Lowest terms are determined by fining the greatest common factor of the numerator and the denominator and dividing each by that number, you are reducing the fraction to it's lowest equivalent fraction. Web Math gives us a handy online calculator, along with explanation of the reduction.  This resource would be great for checking work!

 

 

 

 

Introduction to my blog, Sets & Whole Numbers

Introduction

A journey through elementary mathematics…twenty years later.

By:  Mara Dahlberg

A lot has changed, or perhaps been forgotten, in the past twenty years.  When I originally decided to return to school to obtain my teaching license I was fully aware that math was not my strong point.  This aspect of my education has been a struggle since elementary school and continues to be so in college.  In this blog I will be documenting my journey through elementary math, as an adult, in hopes that I will gain some knowledge, experience, and empathy in order to better teach my future students.

Blog  

Sets & Whole Numbers

Our first section this week is about sets, illustrating the Big Idea that values can be represented using any sort of ideas and symbols, anything that can be listed or described.  Sets are composed of individual values, or elements, but are combined and looked at collectively. 

When learning about sets it is important to understand the meaning of the symbols associated with this concept.  After all, if you can’t speak the language, you cannot comprehend its meaning.

What follows are the basics.

  More information can be found at:

http://www.purplemath.com/modules/setnotn.html

http://www.rapidtables.com/math/symbols/Set_Symbols.htm

Some Simple Set Theory Symbols

∈ “is an element of”

∉ “is not an element of”

⊂ “is a proper subset of”

⊆ “is a subset of”

⊄ “is not a subset of”

∅ empty set; a set with no elements

∩ intersection     ∪ union

 

 

The pairing up of sets is called correspondence and sets are considered to have one-to-one correspondence if they each have a pair.

This is an important idea for children who are learning how to match, count, and how to associate actual value to numbers. 

Another sub-topic of sets is subsets.  A subset is a group of objects (or numbers) found within a set or sets that are the same, a set of its own, but of which all the elements are contained in another set. 

Set B is a subset of a set A if and only if

every object or element of B is also an object of A.

Is A a subset of B, where A = {1, 3, 4} and B = {1, 4, 3, 2}?

1 is in A, and 1 is in B as well. So far so good.

3 is in A and 3 is also in B.

4 is in A, and 4 is in B.

That's all the elements of A, and every single one is in B, so we're done.

Yes, A is a subset of B

Note that 2 is in B, but 2 is not in A. But remember, that doesn't matter, we only look at the elements in A.

The subset only has elements that are found in the set.

Real World Application:  Subsets are helpful in discovering possible combinations or outcomes and how many there are in any given situation.

Learn More

The following are some websites with activities for elementary-age children:

• k12math  In depth explanations & visuals

• kidzpark  Printable Worksheets

• onlinemathlearning  Videos & Online Practice Problems

• mathsisfun Easy to understand explanations

Mara Dahlberg  6/14/2013