Fractions: Adding fractions using grids

Using Grids to add fractions

 

    

  Every year one of our greatest struggles is teaching the addition of fractions.  There are a variety of reasons for this.  Weak basic skills, following multiple steps and in general a bad attitude about all things dealing with fractions.  We believe that one of the biggest struggles for students is the inability to visualize how fractions interact with each other.

 

     The solution for us was to teach fractions using a grid system.  We originally started using this with our math intervention students (see http://thelandofmath.blogspot.com/2013/06/our-middle-school-math-intervention.html).  We later expanded its use in our regular classes with positive results.

     The benefits of the grid system:

• Very inexpensive
• Just paper, a couple of markers or highlighters, and some blocks or chips
• It is hands on
• It is visual
• You can work individually, with partners or in small groups
• Set up time is short and requires minimal effort
• Easy to model on white board or smart board
• This lesson compliments our lessons on subtracting fractions and equivalent fractions (see http://thelandofmath.blogspot.com/2013/10/teaching-equivalent-fractions-using.html).

     We usually focus on fractions with denominators ranging from two (2) to eight (8).  We use this range of numbers because of ease of use, but you can go as crazy as you want.

    

Step one

     Give the students an addition problem such as 1/4 + 1/3.  Have the students draw four (4) columns with one of the markers. and three rows with another color. The four columns and 3 rows are the two denominators we are using. We like to use different color markers to help students see the fourths and the thirds on the grid.





 



Step two

Teaching Equivalent Fractions using grids

Very few things cause more misery for students than fractions.  Over the years we have developed a very easy and effective way of teaching equivalent fractions by using grids.

There are a lot of reasons why we like this method:

 

·         Very inexpensive

o   You only need paper, a couple of different color markers or highlighters and some blocks or chips

·         It’s hands on

·         It’s visual

·         You can work individually, partners, or small groups

·         Set up time is minimal

·         We use this to build into a lesson on addition and subtraction of fractions

 

When we are using grids we will usually focus on 4 x 4, 3 x 4, 3 x 5 and 4 x 5 grids.  We select these because of the many equivalent fractions but there is no limit on grid combinations. 

We also model these grids on the smart board or white board.

Step 1

The first thing we do is give each student a plain white sheet of paper. Have the students create the desired grid (for example 4 x 4).  Tip: Check to see if students set up grid ok.  Many times students draw four lines, but this creates five rows (or columns) instead of four.

We like to use different colored markers (or highlighters) for vertical and horizontal lines.  For example, all vertical lines might be blue and horizontal lines are red.

 

Step 2

We give the students a situation they need to create on their grid.  A good starting point is placing four blocks on their grids.

 

Step 3

We then ask what fraction of the grid is shaded.  The answer of course is 4/16.  We then have the students look at other fractions that can be shown on the grid.  Usually 1/4 is the next fraction “discovered.”

Step 4

 

We show the students a variety of ways to represent 1/4 on the grid.  We really like to have students come up to smart board or white board and show their arrangement.

 For example, if a student puts four blocks in a column we will talk about how one of the four columns is filled in with blocks.  Next, with the same arrangement, we show how each row has one of four squares with a block.

We also arrange the blocks in one row.  This shows one of four rows have a block or each column has one of four squares with a block.

 

Other arrangements include diagonal (one of four columns & rows) and dividing grid into quadrants and putting one block in each quadrant.

Step 5

Usually 2/8 is the last equivalent fraction mentioned.  We show how to divide the grid into half (8 squares each) with two blocks in each half.

Step 6

We continue to use the 4 x 4 grid a few more times. Any even number of blocks will have an equivalent fraction. At least once we pick 3 or 5 blocks because there is no equivalent fraction on the board.

Step 7

We repeat the process using different grids such as 3 x 4, 3 x 5 and 4 x 5.  These grids give us a nice combination of different equivalent fractions.

Extension

Give the students different colored blocks (or chips, etc.) to place on grid.  Have the students write the simplified fraction of each color on the grid.

Creating a Successful Math Newsletter for your class

 



 

     One of the things we try to do each year is to create a math newsletter to share with parents, students and administration.  The main reason is to help develop better communication with parents.  The development of our newsletter is an ever evolving process, but we feel like we have hit on some key things that make our newsletter very effective.

 

     At the start of the year we focus on gathering the email addresses of different parents, students and any one else that might want the newsletter.  We have been able to get around 90% of our student's families to sign up.  When we send out the newsletter we just email a PDF to the different people on our email list.  We mail copies to families that did not sign up for email.  We also make extra copies and leave in the classroom for students that might not see the email version. In the past we sent out newsletters each month.  This year we are attempting to send out one a quarter.

 

     Below is a sample of a newsletter from last school year. The rest of this article will focus on the content, features and structure of the newsletter.



 

 

Page 1 of the math newsletter
 

 
#1 Headline: The first thing we do on our newsletter is state what it is and for what time period.  In this case we call the newsletter the "7th grade math newsletter" (yes we know, verrrrry creative).  If we had newsletters for each individual teacher we might have use something like Mr. Mitchell's Math Class (also very boring) or perhaps something slightly more interesting such as Math Mania.

#2 Contact Information: This part of our newsletter includes information such as Names, email address, school phone, planning period times, website, etc.

#3 Quote: We like to have a quote about dealing with one of two topics: 1) Importance of math and/or 2) Motivational.

#4 Greeting: We address this to the parents despite the fact that many of the readers of the newsletter are our students.

#5 Dates to Know: Just like it sounds. We focus on big events such as early releases, no school, end of grading period, parent - teacher conferences, etc.


    
#6 Classroom Activity:  In this section of the newsletter we highlight an activity that takes place in the classroom. For example, this newsletter mentions our "Fab 5" which is a basic skills review at the start of each class.  In this section we might mention a math program we are using, special projects, or discuss our invention program.

#7 Upcoming Topics:  In this section we list what we are currently working on in class and what parents can expect in the next few weeks.

#8 Math Careers: One of our goals is to let parents and students know about the many career options available in mathematics.  It seems obvious to us, but many students have no idea about the math needed in different careers.  A couple of weeks ago a student told me how he wanted to be an architect but was stunned to find out math was required math.

Solving Math Word Problems

    One of the biggest struggles for math students each year is solving word problems – especially if they involve setting up equations.  Below I have included a few tips on successfully attacking these problems.

First: Read the problem!

This seems so obvious, but many students only read a small portion of the problem.  I believe that many students anticipate what the problem is asking and try to solve before they know all the facts.  Some students are intimidated by word problems and give up before they even read the problem. 

Second: What is the question? What does the problem want to know?

            It is hard to answer a question if you don’t know what is being asked.  The question usually is found at the end of a problem.  For example:

            Three friends go to a restaurant and spend $30 on food. The tax on the food is 5%. The friends leave a combined $5 tip.  How much will each person spend at the restaurant?

            The problem wants to know “how much each person spends at the restaurant.”

Third: Play detective and look for clues.

            What are the important pieces of information found in the problem? In the above problem we know the following information:

·         3 friends

·         Spent $30 on food

·          5% tax

·         A combined $5 tip

A very effective strategy is to highlight or underline these key pieces of information.