Fractions: Subtracting fractions using grids

 

Using Grids to Subtract Fractions

 

    

  Every year one of our greatest struggles is teaching students to subtract 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 adding 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 a subtraction problem such as 1/3 - 1/4.  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

     Have the students fill in 1/3 of the grid (4 of the 12 spaces) with one color of chips/blocks (red chips below).  Next, have the students use a different color chip (green below) to fill in 1/4 of the grid.

Step three

     The next step is for the students to pair up the different color chips.  In this problem there are four red chips and three green chips.  As a result we are able to pair up three of the chips.  That leaves us with one chip all alone.  This is the answer to the problem 1/3 - 1/4 = 1/12

 

 

 

 

Another Example:

 

Step One

 

    You give the students the problem 3/4 - 1/2.  In this first step draw a grid 3 rows and 4 columns (or 4 rows and three columns).  Next, fill in 3/4 of the grid.  In this example the students will fill in three of the four columns (9 of 12 spaces are filled in).

 

 

 

Step two

 

 

     The next step is to fill in 1/2 of the grid with another color (the green below).

 

Step three

     Pair the different chips together. The result in our example is 3 red chips with out a partner.  This is our answer: 3/4 - 1/2 = 3/12.  Your goal is for the students to notice that the three remaining chips fill up one of the four columns.  So 3/12 simplifies to 1/4.





 

Yet one more example:

Step one

     You can use the chip method when working with mixed numbers.  In this example we are subtracting 1 2/5 - 1/2.  In this first step we filled in one whole grid (10 spaces) and 2/5 of a second grid.

 

 

Step two

     Next add the chips that represent 1/2 (5 total chips in this example) and place on the board.

 

 

Step three

     Next we partner the green chips with the red chips.  Start with chips that are on the second board and then move to the first board as needed.  In our example below we are able to pair up all four chips on the second board and one on the first board.  This leaves us with 9 red chips without a partner.  This is our answer: 1 2/5 - 1/2 = 9/10

 

 

 





Todd Hawk is a middle school math teacher and the co-founder of the Land of Math website (www.landofmath.com). You can reach him at landofmath2@gmail.com or follow him on twitter: @landofmath2