Benchmarks really help with comparing fractions without finding common denominators. Who wants to find a common denominator between 23rds, 14ths, and 127ths? Definitely not me. Here's where benchmarks come in handy. They're typically 0, 1/2, 1, 1 1/2, 2, etc. If we have 7/14 6/23, and 125/127 to compare, I can tell you very quickly which is biggest and which is smallest based on how close it is to a benchmark. For example, 125/127 is very close to a whole, so it must be a large fraction. 7/14 is half, so it isn't as big as 125/127. 6/23 isn't even close to a half (11.5/23), so it must be the smallest one. No common denominators needed.
The image above may help you understand this concept. Two 1/3 pieces is more than half, but four 1/9 pieces is not. Four may be more than two, but 9ths are smaller pieces.
Parts. There are different ways of adding whacky fractions. Traditional is very confusing. What if you could separate each of the fractions into nicer pieces? You can! See?
While adding to zero is very easy, your starting point could be at any other fraction you want to add. For example, if you were adding 2 2/3 to 3 2/3, you can split up one of the 2/3s and add a single third to the other one to make a whole. 2 2/3 can become 2 1/3 and the other 1/3 makes 3 2/3 into 4. Now you're adding 4 and 2 1/3. Much easier. No? Any fraction can be broken into smaller parts to make them easier to add. You can even add 5/6 and 1/2 without finding a common denominator. If you know that 3/6 is equal to 1/2 you can take 3/6 from 5/6 and add it to the half. Then you're adding 1 and 2/6.
What about time? We have minutes and hours that make up our time system. 24 hours in a day and 60 minutes in an hour. How do you add 2 5/6 hours to 1 3/4 hours if you want the answer in minutes and hours?
If you fill in a few of the missing lines, you can see that the clock makes these fractions (5/6 and 3/4) for us. In terms of 6ths, you reach the 5th piece at 50 minutes. The 3rd piece of 4 is at 45 minutes. So I'm adding 2 hours 50 minutes to 1 hour 45 minutes. If minutes start over at 60, then you have to add 1 whole hour to your total. The end result is 4 hours 35 minutes.
These were the things that really helped me this week. Hope they help you too!
Good blog!
ReplyDeleteI thought the start of your comment was great by starting off with asking a question. I thought it was a good idea that after every phot you put up you briefly explaned the photo instead of just sticking it wherever without and explanation. The overall way you explained was brief but to the point where everything was understandable. Overall it you have a good blog and keep up the good work.
I loved how you made your blog humorous and interesting. You really kept my attention throughout the whole thing! I think its good to play around and have fun with math so the kids we are teaching will enjoy it more. I liked how you covered all the material but did it in a kind of non-conventional way. All the pictures (especially the clock one) really helped to solidify your point. I struggled a little bit with using fractions when it came to the clock so it was nice to have it explained again. Good job!
ReplyDeleteI really like how you broke the ice at the beginning of your blog with a joke. Through out your whole blog you kept the tone light and entertaining. I really enjoyed the pictures that you used, they helped clarify some of the points you were making in the blog. Overall I feel that this was a well put together blog and I cant wait to read yours next week. I would suggest that you use some pictures or examples of the steps to solve the problem though, I think it would be a good thing to add into your blog.
ReplyDelete