Posted on 09/15/2010 8:41:36 PM PDT by Fundamentally Fair
Right! And then the answer is THE GIRL jumped further. Can’t be another answer. That’s the rules.
The rules of diversity math.
No. The indented purpose was to show the kids that they could use a number line to determine which fraction was greater.
Have they been taught how to determine the lowest common denominator and then convert the fractions to that denominator?
Yes. That was the second part of the lesson. They were taught to methods for working the problems, then had to work some problems with a number line and others by finding a common denominator and comparing.
See post 18. Agree? I’m senseing some sarcasm...
I think they are meant to be misleading. When using number lines, it’s specifically taught that they are not to scale, so students should not just try to “eyeball” a comparison like this. They’ve had similar visually misleading questions on the SAT for years.
Number lines are never meant to be taken as “drawn to scale”. Expecting them to be equal in length because they represent the same physical length is a common mistake, but it’s still a mistake.
Good grief! You can’t have the boy winning. Even if I didn’t know a blessed thing about fractions and common denominators, I’d still be able to pick the girl as the winner. Only in real life can a boy possess the ability to outjump a girl.
Second, who the heck names their kid "Maisie" besides Uncle Buck's sister?
Refuse the assignment. The way the libs have pushed the metric system is that it is easier because it is based on 10s. Dividing metric measurments int 6ths and 8ths is so asinine it must come from public educators.
You can't compare two fractions on two number lines unless they are exactly the same scale and perfectly partitioned.
Try using a number line to determine which is greater 5/9 or 9/16.
That's really the point; you can use a number line to demonstrate the process, but mandating that the kids use the number line to solve the problem will only confuse them.
That's goofy, given that the lines were at different scales. Besides, as someone else pointed out, people on the metric system don't use fractions for meter. They use a decimal number.
Yes. That was the second part of the lesson. They were taught to methods for working the problems, then had to work some problems with a number line and others by finding a common denominator and comparing.
Anybody can find a common denominator, but it's more convenient to find the least common denominator. Are they teaching the kids how to do that?
I demonstrated in post#25 they need not be the same scale.
Perfectly partitioned, yes.
I doubt solutions using geometric construction is typical 5th grade curriculum.
Yes.
Do you know the name of the book your daughter is using?
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,
Thank you.
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.
So this works for me. I am surprised they don't have colored pictures with all sorts different ethnic people in it explaining the problem.
The notches aren't the same distance though...
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