The Matter of Fractions!

Math

Matters

by Ginger Stiner

Another thing I want to remember from my time spent learning to become a math teacher is that all concepts build on themselves.  Fractions are no different and I know people who struggle with this who have been out of school for years!

I want the concepts my students learn in my classroom to not only help them pass standardized tests, but also to help them in real-world situations, wherever they find themselves beyond the four walls of the school.  I want them to think of math as something they can do, instead of feeling unsure of their abilities and insecure as a result.  That is what really matters in the grand scheme and big picture of life for my students.  My goal is that nothing will hold them back from reaching their potential!

Fractions can appear to be more difficult than they are to people who are just learning them, or seeing them again after a long time.  Here are some basics to remember!

What to KNOW about Fractions! 

 First, let’s define the term FRACTION!

What?

What is a fraction?

A fraction is a part of a whole.  Think of it like the pieces that make up ONE.  A fraction is ALWAYS less than one!

Here is an example:                                                      
                                                                    Here is an example:

 

                       Fractions have 2 parts!

A Numerator- the number above the line (fraction bar) shows how many pieces of the whole are being used.

A Denominator- the number Down below the line (fraction bar) shows how many pieces the whole is broken into.

What else?

Fractions can be proper or improper!

A proper fraction- is a fraction where the numerator is a smaller number than the denominator.

Here is an example:  3
                                  4

An Improper fraction- is a fraction where the numerator is a larger number than the denominator.

Here is an example: 4
                                 3

Fractions can also be seen next to whole numbers, this is called a mixed number!

Here is an example: 

Building Blocks of Math

Math 

Matters
By: Ginger Stiner

Every week in my Teaching Math class this summer we are given a list of objectives; things that math teachers must be knowledgeable about and capable of doing in order to teach math to our future students.  This week, among other things, we are to be able to identify when a number is prime or composite and find prime factorization of a number.

I think of it this way:

Numbers are the building blocks of math!

 

What?

There are many ways to show a number and BIG numbers are made up of smaller numbers!  We can divide numbers up into smaller parts. Sometimes these smaller numbers are easier to work with and can tell us things about the big number we started with.

How?

One way to break down a number is called Factorization.

Numbers can be expressed by their factors.

Factor- a part of a multiplication problem

Product- the answer to a multiplication problem

We can show factorization through something called a factor tree.

A Factor tree looks like this:

                            

                                 

Here is a helpful video:

                                    

Important!

It is important to remember that EVERY number has factors!

The amount of factors a number has determines if a number is a prime number or a composite number.

What?

Prime- The only factors of that number are 1 and itself.  EXAMPLE: 7

7 is prime because the only two numbers that go into 7 without leaving any remainder are 1 and the number itself, 7.

Composite- The factors of that number are MORE than just 1 and the number.  EXAMPLE: 8

8 is composite because more than just one and 8 can go into 8 without leaving any remainder. 2 and 4 can also go into 8.

Lattice Method of Multiplication

 
 
 
 
 
Math 

Matters

By: Ginger Stiner

One of the best things about math is that there is more than one way to solve a problem!  This creates critical thinkers.  In order to teach math accurately I will need to be aware of and comfortable with several methods of computation.  

An algorithm is the process used to solve a problem.

One algorithm for multiplication is the

Lattice Method of Multiplication.

This is one method that was discussed in my Teaching Math class this week, and one that I want to be sure to remember!

I will teach my students that in math a LATTICE is a box with squares and diagonals that is used for multiplication.

This is what it looks like:

I will explain that the number of digits in the factors being multiplied together will determine the size of the box they will create.  

After demonstrating how to decide the size of the box I will make the diagonal lines that are the final requirement of the set-up of the lattice. 

Once the lattice has been constructed, the numbers will need to be plugged in at the top and along the side in order to begin the multiplication process.

Students will need to be aware of place value in order to put the answers in the correct triangle that was created by the diagonal lines. 

Once all multiplication is complete, addition must take place along the diagonal lines supplying one digit at a time for the solution.

This video shows the Lattice Method of Multiplication: