My note to the teacher:
My wife wrote a note in XXXXX’s assignment book, but I wanted to make sure that you got the message. We worked with her for over 2 hours on her math homework last night. She was having some real trouble with the work. We will continue working with her each night, but last night we got to a point of diminishing returns and put an end to it.
I also wanted to ask you about the number line technique presented for determining if fractions were equal or if one was greater than the other. I understand using the number line to give the students a visual representation of the fractions and their order. I am curious about the utility of the number line in working problems.
Some of the problems required the use of the number line. In order for the number line method to work, the lines must be of the same scale (equal length) and accurately partitioned. For a 5th grade student to draw two accurate number lines and precisely place the fractions on the two for comparison is unrealistic. For example, try using the number line technique to determine which is greater 5/9 or 9/16.
The weakness of this method is demonstrated on the back of the homework page in the workbook (the question about who jumped farther in the long jump). For an accurate comparison, the two lines would need to be equal (i.e. 6/6 of a meter should align with 8/8 of a meter). However, Maise’s ‘meter’ is shorter than Dan’s.
I found a page that I think will help her here: http://www.mathsisfun.com/flash.php?path=%2Fnumbers/images/fraction-number-line.swf&w=930&h=885&col=%23FFFFFF&title=Fraction+Number+Line
And, as a complete aside, the choice of meters as the unit of measure makes little sense. The beauty of the metric system is that it is based on multiples of ten, rather than fractions. ;)
Thanks for your time,
I will post a method to determine which fraction is greater in a moment, but allow me to chime in on this technique line technique (that is, if I have enough info - there seems to be an image in your original post that is not coming through on any one of the three computers I have at my disposal).
I thought about the book technique you’ve shown for a little bit. At first, I had a great problem with it, but now, I think this method is sound.
Your letter to the teacher is reasonable, in that this method really fails when the student has to divide a line of an arbitrary length on the page into odd fractions, as in ninths, or sevenths, and so on.
The method I’ve used to teach my daughter for comparing fractions is to cross multiply. Has your school taught that technique first? It’s exceptionally straight forward, and since it uses straight multiplication, can be done by ANY fifth grader who knows how to multiply.