I ask students to take out the fraction squares that they identified several days ago. I show a picture of a shape divided into parts, with a fractional part colored. I ask students to find one of their squares that has the same amount colored in. I ask them what fractional part they are holding up? I take several responses until I have at least 2 names for the same part. Students have their fraction squares with them. These have one fraction on the front, and an equivalent on the back so I know that students will come up with at least those 2 names for a fraction. If students do not use the squares to come up with several names, I ask them if they can use their fraction squares to help them find another name. I record the answers on the board. I ask students how we could have the same part but with different names? (equivalent fractions).
I introduce the word equivalent by asking them what math word it reminds them of? (equal) If they don't come up with the word equal, I rewrite the word equivalent with the letters equi in a different color and reread the letters as equa.. and ask if that reminds them of something. This helps the students make the connections between equal and equivalent.
We talk about the ways this can be possible with several different fractional parts. I want students to visualize how the same portion of a whole can have several different names.
I give students a variety of rectangles. Each one is the same size but divided differently. I ask them to label at least one portion of each rectangle by its fraction name. I display the rectangles on the Smart Board and after giving students a few minutes to label theirs, I ask for volunteers to come up and label the ones on the board.
Now I take my paper set of rectangles that looks like theirs, and I hold it up and tell students that I am going to cut out each rectangle, but not cut them apart. I demonstrate cutting out the whole rectangle along the dotted lines so that they can fold the paper into fractional parts.
When I am done, I show students how I can fold the shape so that it looks like only 1 portion is showing (i.e. 1/2. 1/4 etc.)
Now I hold up my 1/2. I ask if anyone sees anything that is the exact same amount? I show them how I can use my 1/2 and try to cover up other choices until one matches.
I look to see if students can find those equivalent amounts. We record them on the board.
We find all matched pairs together.
In order for this lesson to work, students do need to be very careful about cutting and folding their paper squares into sections. Also when they put one shape over another they need to carefully line up the edges in order to see if the parts match. As a teacher I remind students to work carefully and to make sure that they are cutting and folding right on the lines. I want students to be able to see the equivalents, but if they are not careful, they will not be able to match the equivalents.
I give students a paper that is divided into fraction bars. It includes halves, quarters, eighths, and thirds and sixths. The parts are labeled. I ask students to cut out a larger part (such as 1/2 or 1/3) and to then find something marked in smaller pieces that is the same. I show them how they can slide the big one over the little ones to see if they match and then when they find a pair, they should cut it out and glue them on their paper.
I hope that students will begin to see how fraction parts can have different names for the same portion.
I circulate around the room to support students who may be struggling with this activity.
We close today by displaying our fraction bar equivalents on the board.