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This story about fractional numbers is told from the bottom picture up.
In our EDC notebooks, we have been tracking equivalent fractions. We started on day 1 with the fraction 1/16. All students were able to understand that there were 16 pieces in the top row and if we were to shade one of those boxes it would equal 1/16 of the whole. On day 2, most students immediately realized that when we added another 16th, we created an area equal in size to the the 8ths row immediately below. When we got to 4/16, also 2/8, students saw that this was equal to 1/4 of the whole. It was at that point that students started to fill in percentages for the fractions that we had created. Most students knew that 1/4 = 25%, and they concluded that 1/8 was half as large so it must = 12.5%. A few students then realized that 1/16 must equal half of 12.5% or 6.25%. This knowledge of fractions and their equivalent percents will be a key component in adding, subtracting and comparing fractional pieces. Most students know several landmark percents like 25%, 50%, and 75%, and they can easily shade an object like a circle graph correctly with those amounts. Soon, students learn to represent other amounts like 30% (3/10) with accuracy based on their knowledge of the landmarks mentioned. Putting fractional amounts into percentages just makes life easier.
The third picture up comes from our current investigation, and it shows how students come to see "out of" statements as fractions. One out of three is the fraction 1/3, which seems easy enough but is VERY important conceptually.
The next two pictures are the absolute most important concepts that we will cover in this unit. Students shade in portions of a 10 X 10 grid and report the percent (parts out of 100) that it took to cover the portion. One picture shows one fourth of a grid shaded (25 blocks and 25%). the shading is a bit "artistic" , and it probably led to the misconception about shading in 1/8 of the grid, which should be 12 1/2 blocks or 12.5% . The percent was listed correctly, but the grid does not have 12 1/2 blocks shaded. Still, I can tell that the idea of 1/8 being half of 1/4 is understood.
The top picture is the Holy Grail of understanding fractions. All of the fractions listed are considered landmark (IMPORTANT) fractions in our number system. Understanding the percentages that go with each of these is a very critical conceptual step.
So, know the fraction. Be The fraction!
Know the percent. Be the percent!
5 comments:
Fractions, percents, decimal and equivalents have always been very scary....but not as scary as your pug!! Just kidding...but hopefully this topic will no longet be scary w/ your great teaching expertise!!
Mikenzie's mom and Mikenzie and the pug we wish we had
wow thats some great revision i wish i could revise like that.
from:yuliane your favorite student "right"
wow now thats what i call revising i wish i could revise like that student i would so awesome to be able to revise as good as that.
From:yuliane your favorite student again "right" Am i right?
Yuli,
You are such a great student. Revisions are like everything else in life, as they take a bunch of practice.
I'll be glad to help you out, if you'll keep helping me con mis espanol :-}
Senor R.
i was having a really hard time with this believe it or not but my mom could understand this better than me but then when i got the hang of it i was awesome at this and now my mom is asking me how you convert them into fractions and it is really cool she is also asking me stuff like what is parallel mean and it is so cool it makes me feel so smart when i can teach my parents something new
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