We discussed fraction sense, for instance:
Write/draw everything you can that represents the fraction 3/4
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Both of the above would be examples.
We then discussed multiple rules that are necessary in the understanding of fractions.
Spatial Relationships: (The pictures above are both examples of spatial relationships)
Having a picture of the number, including where it lies on a number line.
One/Two(Units) More and Less:
If I have 5/4 what is 1/4 more or less? What is 2/4 more or less?
Benchmarks:
1,1/2,1...is it above or below 1/2. How far away from 1?
ex. is 3.4 more or less than 1/2? It's more. How much more? 1/4.
Part-Part Whole:
Knowing 3/4 can be into parts; 1/2+1/4=3/4 or 1/4+1/4+1/4=3/4
These rules applied to the fraction 7/5:
Spatial Relationship:
 |
| The above would show spatially where 7/5 is on a number line (the line in red) |
One or Two More/Less:
one more is 8/5 or 1 3/5 one less is 6/5 or 1 1/5
Part-Part-Whole
3/5+4/5=7/5 or 1/5+1/5+1/5+1/5+1/5+1/5+1/5=7/5
Thursday 4/4/13
On Thursday we discussed how to add and subtract fractions with different denominators. We discussed how it makes a lot more sense in many problems not to just find the simplest common denominator and add fractions that way, but instead to find a common denominator that represents something in the problem and actually makes sense to children (and college students).
Take this problem for example:
If I ran for 1/3 of an hour and then walked for 1/4 of an hour. How much time would that be? What fraction of an hour is that?
My first instinct would be to convert 1/4 and 1/3 to fractions with a common denominator so I could just add them (resulting in 4/12+3/12=7/12). This was very easy, but results in a fraction that isn't easily understood in relation to the problem.
So what should I do instead?
Well since this is a problem that has to do with time, there are 60 minutes in an hour. I could instead convert 7/12 into a fraction with a denominator of 60. To do this I multiply both top and bottom numbers by 5. My resulting fraction is then 35/60. Not only is this fraction easy to understand in relation to the problem, but it also tell me how much time I was active for, 35 minutes.
This lesson taught that kids need to understand that when solving a problem the whole unit is more important that just the lowest common denominator.
Take the problem above for example, leaving the answer with correct units (60) instead of simplifying tells you more about the problem.
Hope this was helpful!
Great Blog!
ReplyDeleteI liked how you described the other way to add fractions. I know I still have trouble converting fractions into the appropriate unit. Especially when the whole isn't a number that we are used to, like 10 or 100. And this is definitely a great way to teach children instead of the way that most of us were taught.
-Mercedes
This was a great blog!
ReplyDeleteyou broke everything down very nicely and easily. I also like the illustrations that added to help out people like me who are visual learners! I thought it was nice that you gave examples as well as definitions; some people find one or the other helpful and others find both necessary. This is definitely at a elementary level and I found your informations very helpful and helpful for teaching children.
-Shae
Very great blog
ReplyDeleteI really understood what you were saying and explaining, you broke down everything so well and the pictures were very helpful and brought everything together. Your information was helpful and was easy to understand and gave me a complete understanding to what we learned that day. Good Job and keep up the good blogging
- Estefania Flores
This was a awesome! You covered all information that was highlighted throughout the week. The pictures that you utilized were very helpful and easy to understand. You communicated all of your ideas very well. It was nice that you defined the terms for us as well as showing examples. The way you described the different addition strategies was great. Keep it up!
ReplyDeleteGood job with your blog this week! You explained the two different ways to add fractions with different denominators very well. I know it will be difficult for me to try new methods for adding, subtracting and multiplying fractions because I have used one specific way my entire life, but you did an excellent job of breaking down how it could be done.
ReplyDelete- Sam Gaume
Good job showing all the different ways to solve the fraction problems. By knowing all these different it will be way easier to get through the tough fractions. Nice blog.
ReplyDelete