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.