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.

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.