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

Next, fill in one of the four columns with your chips/blocks.  We make sure that we reinforce how 3/12 and 1/4 are equivalent fractions.

Step three

     Use a different color (green in this instance) chip to represent the fraction 1/3.  Place the chips on one of the three rows. Once again we try to emphasis that 1/3 is equivalent to 4/12.

 

Step Four

 



     You will notice that one of the "squares" has two chips.  Just relocate one of the chips to an open square.  The result is 7 of the 12 "squares are filled in or 7/12.

Another Example

     Here is another example using the problem 2/3 +1/4. 

 

Step One

 





   After drawing a grid with four columns and three rows (same as the denominators) we fill in 2/3 of the grid.  Note: Many kids will visualize this differently. Some will see 2 of the three rows filled while others will see 2 out of every three in each column with a chip.

Step Two

     Next use a different color chip (green) to represent 1/4 of the grid.

Step Three

     Two of the "squares" have two chips.  Relocate a chip from each of these "squares" to an open square.  The result is 11 of 12 "squares" filled or 11/12.

Other Options

Two Grids

     Using two grids instead of one.  This is ideal when working with a partner.  In the above example the grid on the left represents 3/4 and the grid on the right represents 1/3.

     Next, combine the results of the two boards.

Finally, relocate duplicate chips to open "squares." This example shows how to represent a mixed number as an answer.

 

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