Are you teaching your kiddos how to solve fraction of a group problems? My co-worker came up with a fabulous name for the tried and true strategy that we probably all use:
The Backwards Zorro! It's visual and fun to say and it really seemed to stick in the minds of the kiddos. Here's how it works:
Starting at the bottom, draw a line from the 4 to the 24 (4 goes into 24 six times). Draw the line to the 3 (six times three is 18). Draw the top line and write the answer. Presto!
One of my students called it Ping Pong. We went with that!
ReplyDeleteI like! Thanks! Easy to explain too!
ReplyDeleteBut does this actually teach the students WHY it works? That the word OF means to multiply, and that you can use cross factors to simplify before multiplication? Shortcuts are great... but only AFTER there is a strong understanding of the process! I think we do a dis-service to our students if we teach them an 'easy way out' of learning the concept of fraction operations.
ReplyDeleteABSOLUTELY CORRECT!
DeleteDifferent Anon here. I think it does explain it. Once you have established fractions as part over whole. The first step says how many are in each part when your whole is 24. (6) The second part says you want three of those parts (3 groups of 6 which is 18). I like this trick because it helps kiddos (with a littl esupport) think about the math behind the process.
ReplyDeleteAnon 1: I totally agree that students should understand the WHY of mathematical procedures. I think, just as with any tool, it depends on how the teacher presents it (As Anon 2 pointed out). What I didn't blog about were the two previous lessons in which students actually divided themselves into thirds, fourths, and sixths. They then drew pictures representing fractions and learned through the pictures how to find one-sixth (or whatever) of a number, and also two or more fractional parts of a number. The "shortcut" was reserved until after we had thoroughly gone through the "basics."
ReplyDeleteanonymous, if I was taught how to do fractions this way in school I might have learned it. I can multiply and divide, add and subtract but never understood fractions. No maybe I can help my daughter with fractions.
ReplyDeleteI saw this on Pinterest, and just love it. I teach remedial college math, and anyway I can get them to learn is great. Yes, we go over and over that "of" means multiply, but sometimes we just need the trick, especially if you are a freshman in college!
ReplyDeleteI couldn't find a way to contact you, but what would you think if I reposted this idea on my math blog but featured your blog and a backlink to it? Let me know. You can find my contact info on my blog:
ReplyDeletehttp://gofigurewithscipi.blogspot.com/
Thanks, Scipi! I'd be honored for you to repost on your blog, and I'm your newest follower!
ReplyDeleteMath teacher here - tricks work for the moment but when kids get to higher maths, you realize that those tricks screwed them. They do not understand harder concepts because they never truly understood the easy ones, like fractions. If you want your kid to learn, don't do these "trucks.". Truly doing the kid an injustice.
ReplyDeleteAs a former high school math teacher who now teaches teachers how to teach math, I completely agree. I am a huge proponent of the "why before how" principle --- making sure students understand why the math works in a particular problem. I focus less on getting the right answer and more on the process taken to find a solution. A book I recommend in all of my classes/workshops is by Jana Hazekamp and it's called "Why Before How." Algorithms have their place, but it is crucial that our students first understand why the math works before being shown any tricks to simplify the process. I would probably use this as a challenge or extension problem and see if my students can come up with the algorithm before showing it to them. If students can discover or create algorithms on their own, their mathematical competencies will grow by leaps and bounds!
DeleteAnonymous, Please see comment #5. I would agree with you if this was the only way I'd taught it, but this was the culminating activity.
ReplyDeleteAnd what will they do when the second factor is not a multiple of the denominator of the first factor?
DeleteSometimes "understanding" needs to be put aside for being able to do it. Sometimes after memorization comes understanding. As a high school math teacher there were many things I could mathematically do, but it was when I had to use them later that I understood.
ReplyDeleteI have NEVER been good at math. Having a shortcut to get the right answer first, and not being frustrated so that I couldn't "grasp" the lesson would have been so much better. Build confidence, then explain the HOWS and WHYS. I'm not a teacher, just always hated math. Thank you for showing me this short cut. Making a subject fun and associating to real life makes learning and comprehending so much better and more likely to be remembered.
ReplyDeleteI do fractions in my head and use them daily. I think this is weird and confusing.
ReplyDeleteJust found this on Pinterest! So glad I did! Yay! This is great!!
ReplyDeleteI love finding other 4th grade bloggers!!
Amanda
Collaboration Cuties
very clever! I've pinned it.
ReplyDeleteMandy
Small Fine Print
Gosh....so many thoughtful ways this could be approached rather than resorting to a trick. How can we split 24 into 4 equal groups? How many would be in three of those groups? Or...what's 1/2 of 24? So, our answer has to be more than what? Tricks are never ok to teach kids. If we only teach tricks and steps, we are missing the boat.
ReplyDeletewhy does every one see this is a trick? It's not! 3/4 of 24 is and always will be (24/4) x 3. Just like 2/3 of 12 is (12/3) x 2. Why bother with any other way of figuring it out? I've received As in all of my math classes, including college level CALC. I always figured fractions this way, and still do to this day.
ReplyDeleteAnd how would you do 3/8 of 15?
Delete(15*3)/8
DeleteSo you have 45/8
Wich would be 5 5/8
Or about 5.625
I agree with Mom2Coy! It does explain it! It simply does it 'visually'. I am VERY math-minded and at 36 years old this is how I have always done it (without the super cool Backwards Zorro name...stellar addition ;) ) And I remember the EXACT day in jr high when our substitute teacher told me that although I got the answer right using this method...it was wrong. No...it isn't. It just isn't the way YOU do it. It is VERY right for some of us...and in no way hinders our ability to 'understand' fractions.
ReplyDeleteWhat about 1/2 of 15? it's rounded?
ReplyDeleteIt's simply 15/2 or 7 + 1/2
DeleteI just finally "got it" with this illustration and anon #2 March 16, 2012 at 10:21 PM I did really well in school and pushed through but just now I actually see what steps I was doing. This isn't a short cut, it is just an easy way to SEE it.
ReplyDeleteI understand the passion in all of the posts. What I don't understand is why someone can't share an idea without being criticized for it. She clearly said that she did not just teach a "trick"...she put it together in conjunction (in fact...later on) after teaching the concepts. I am a middle school math teacher and when I am teaching about a fraction multiplied by a whole number, I have the students look at the diagonals to see if they can simplify before they multiply...which is essentially the same thing as the "trick". I would caution, however, that this would only work if the whole number can be divided equally by the denominator of the fraction in the problem. This could easily be taught as an analyzing/observation skill as the students would carefully consider the numbers they are working with.
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ReplyDeleteI agree with what a lot of people have said, on both sides of it. It is only a "trick" if students do not understand why it works. In that case it's like a magic trick that mysteriously works every time and has no logic or reasoning as far as the students are concerned. If they understand the concept, then giving it a name like the backwards zorro is just a helpful mnemonic device for remembering the procedure in the future when it's not so fresh in their minds. I do feel that even giving a name to a procedure that makes sense can be tricky though and if students are not consistently asked to explain the procedure after they learned it. Then they can forget the mathematical principals that go into it and only remember the procedure. Even though it started as a logical and meaningful thing to the students, it turns into a "trick" since all they remember after a few months is the procedure part. Which happens if that's all they've been required to remember. So I think it's important to hold students accountable for the understanding as much as it's important to hold them accountable for being able to use the procedure effectively in a problem.
ReplyDeleteI use a trick called "my calculator watch". I either convert the fraction to a decimal mentally, or divide the numerator by the denominator, whichever seems faster. Then I multiply by the target number and PRESTO! A correct answer. Fortunately, since I've understood fractions for about 50 years, I've got LOTS of options. However, I applaud those willing to risk showing their classes (or home-schooled children) more than one way of doing something, knowing that the route to learning is not the same for every young mind! Teach the tricks, AND the processes, and have them write stories about math, draw pictures to show understanding of numbers, and put on skits to explain decimals. More is caught than taught, and you will know by the sudden "lightbulb look" when comprehension has dawned.That's why I'm still teaching after 36 years!
ReplyDeletecan be drawn without the zig zag but only one vertical line next to a 6 and another line to show 18
ReplyDeleteHi, this look really good. It would be even better if there was a bit more in the way of an explanation, and some more examples; particularly with larger numbers (3 or 4-figure numbers etc.).
ReplyDelete