I hand students a piece of paper. I ask them to write down all the names they are called by. I demonstrate by using my full name, my first name, mom and my nickname. I have 4 names that people call me. Can you write down your names?
Now I ask them to circle their favorite name to be called. I circle mom on my list. I now ask them to write a fraction of all their names in the dungeon and their favorite name escaping north.
Ok, it looks as if many of you have more than 1 name you are called. Today we are going to look at how fractions may have more than one name for the same amount. (MP7)
I hand each students several small squares (6x6) of paper.
Ok, lets take a piece of paper and fold it in half. Label each half. Now turn the paper over. How many parts do you see if we don't trace the line? (1) Ok so the one whole sheet of paper is the same as what on the other side? 2/2. I write 1 = 2/2. I remind them of the shapes they sorted yesterday to make whole circles. Were there other fractions that covered the whole circle? I ask students to come and write a few of those on the board (3/3, 4/4). I put equal signs between them because they are all names for 1 whole.
I ask them to take the first piece and to fold it in half. I ask them to open it and trace over the line. Now I ask them to label each side with its fraction name (1/2). Ok, now turn that paper over, trace the fold and now draw a line the other way to divide the square in half. How many pieces do you see on that side? (4) Can you label each piece with its fraction name. Now I would like you to cut the paper in half on the original fold. What is one side labeled? (1/2). What is the other side labeled? (2/4 - make sure that they see that there are 2/4 that make up the half of the shape.) I write on the board 1/2 = 2/4 and ask if that is true? So now I have 2 names for the same fractional amount. (MP7)
I repeat this process with thirds and sixths on the one side and 3/3 and 6/6 other so students see that there are other fractions that have different names for the same part of the whole.
Today I hand students a circle template and a piece of blank paper. I ask them to draw the same shape twice and to divide it in 2 different ways and then to color the same amount of the circle and label the fractional part that is colored in in 2 different ways.
I do remind students that I can't mix halves with thirds and we look at the shapes of the pieces and figure out why that won't work. I do suggest to students that they divide the shape one way, and then cut each piece in half again to get a new fraction. I demonstrate on the board drawing a square and dividing it in half, and then dividing each part again, and even again.
I make sure that students understand my directions. I tell them that they will make a display of fractions with the same name and that we will hang up our display to help others remember that fractions can have more than one name.
I tell students that they will work for about 15 minutes and then we will share out.
I ask students to cut their paper so the partner shapes are together, but they are separate from the other partners. I ask that they bring up anything that is halves, quarters, fourths, eighths and glue them onto that sheet.
Next I ask them to bring up anything that is thirds or sixths and glue it on that sheet. We now have a display of fractional parts, names and equivalents.