visualizing fractions

I think this is fairly normal,but keep an eye on it. Also, I have found some of the fraction relationships are a little easier for kids to see if you use a circle instead of a rectangular bar.

It often takes kids a little while to get used to something that has a larger number in it (1/3) being a smaller amount than something that has a smaller number in it (1/2). I think this is far less likely to happen if they have been taught properly and incrementally, but my experience is that this is rare in elementary school. Teaching young kids does not appear to be a profession that attracts those who are good in math. They often just rely on the text and most are really not very good.

My non-LD daughter actually had a problem with this initially. She is in the advanced fourth grade math and her teacher seems to believe that advanced means they don’t need teaching. He assigns workbook pages and class time is spent going over the answers—no preteaching at all. Just the other night I used square colored tiles with her to demonstrate estimating whether fractions are closer to zero, 1/2, or 1 and equivalent fractions. If you don’t have any colored tiles, pick some up—they are a really hand math teaching aid.

I used foods, Hersey bars for rectangle problems, and english muffins for circle problems, and we cut them up and divided into parts for fractions. Have you looked at the Landmark School’s arithmetic book…it’s terrific!(Landmark school in Mass., has a great web site with resources to order on line.)

I use egg cartons, colored cotton balls, and yarn. I have the students take the string across half either length wise or width wise and fill up half of the egg carton with cotton. I do this for thirds, 6ths, fourths, etc. I do this for a few lessons. We then do group problems. I have for example each kid in classs fill up their egg carton to one third full and 2/3 empty using the string to show areas. Then I have 4 kids come up front. We add 1/3 +1/3+1/3+1/3. We redistribute up as many full cartons as possible. Now we have 1 1/3 altogether. I have overheads to model. This lesson came from Visualizing Math. The kids really get this so much easier than pies and bars.

It is great for improper to proper. multiplying etc…

I use this as the intro for a week or 2. Then I go to the other manipulatives, then fianlly paper/pencil. It is amazing how they understand fractions.
I hope this made sense.

Michelle

I esp like the egg carton idea. I have used pies—last year we tortured our son by making him tell us if he wanted 1/4 or 1/5 of the pie to eat!!! He had the emotional investment to start to figure it out. He just still doesn’t “see” what 1/2 and 1/3 ect are automatically.

Beth

I think this is very normal and a very good strategy. Instead of sitting there confused, he drew another rectangle and a line through half of it. I like the initiative he took and the problem solving skills he showed.

Children this young want to see that line and study it a bit. He didn’t want to draw the line in his textbook. He’s still learning fractions and you’re not. It’s easy for you to visualize where that 1/2 line would go but that’s exactly what he’s still learning to do - he’s learning to understand what is 1/2 of something. By drawing the line through his own rectange, he was teaching himself.

Good for him!

I have often wondered if egg cartons would help students learn about literal numbers. Each location could be labeled with a letter or other symbol. Then you could say, “Add a and b and put the answer in k?” Or it might be,” Add Pooh and Rabbit and put the answer in Piglet.”

I’ve never had a chance to try it, but I wonder if it would work.

Sara McName

I have used a program called hands on equations that are WONDERFUL for getting kids to understand algebra. It works so well. You could probably can do a search but it would be worth it . My 5th graders were all doing algebra. Even my low kids when I taught regular ed.. It was easy too.
Michelle

http://www.borenson.com/

I highly recommend anyone teaching regular ed or general ed. to try this. It looks pretty cheap too considering.
Michelle

This is GOOD. It is a real practical solution to a problem, it is quick and gives a solid answer. Unfortiunately it isn’t typical enough since too many kids are trained out of using visualization, but please encourage him to continue in this way.

BTW, I speak as a math major and math teacher and math tutor.

Actually, the circle or pie diagrams are harder, not easier. They’re OK for half, or quarter and most people can do a lopsided third, but once you get to fifths, forget it. If you make a rectangle 12 centimeters long you can make many fractions easily and at least come close to fifths. Or do 60 millimeters and you are good for almost anything but sevenths. Most of us think things are “easy” if that is what we were taught in our youths. But since math is so often so badly taught, it is helpful to nre-examne your assumptions.

I forgot to mention that there is a free 2 minute video clip to show you how it works. Young kids really get this.
Michelle

My dad thought of this analogy independently — I’m longing to do a computer graphics version of it… hmmm…. Flash is calling…

I think this is fairly normal,but keep an eye on it. Also, I have found some of the fraction relationships are a little easier for kids to see if you use a circle instead of a rectangular bar.

It often takes kids a little while to get used to something that has a larger number in it (1/3) being a smaller amount than something that has a smaller number in it (1/2). I think this is far less likely to happen if they have been taught properly and incrementally, but my experience is that this is rare in elementary school. Teaching young kids does not appear to be a profession that attracts those who are good in math. They often just rely on the text and most are really not very good.

My non-LD daughter actually had a problem with this initially. She is in the advanced fourth grade math and her teacher seems to believe that advanced means they don’t need teaching. He assigns workbook pages and class time is spent going over the answers—no preteaching at all. Just the other night I used square colored tiles with her to demonstrate estimating whether fractions are closer to zero, 1/2, or 1 and equivalent fractions. If you don’t have any colored tiles, pick some up—they are a really hand math teaching aid.

I used foods, Hersey bars for rectangle problems, and english muffins for circle problems, and we cut them up and divided into parts for fractions. Have you looked at the Landmark School’s arithmetic book…it’s terrific!(Landmark school in Mass., has a great web site with resources to order on line.)

I use egg cartons, colored cotton balls, and yarn. I have the students take the string across half either length wise or width wise and fill up half of the egg carton with cotton. I do this for thirds, 6ths, fourths, etc. I do this for a few lessons. We then do group problems. I have for example each kid in classs fill up their egg carton to one third full and 2/3 empty using the string to show areas. Then I have 4 kids come up front. We add 1/3 +1/3+1/3+1/3. We redistribute up as many full cartons as possible. Now we have 1 1/3 altogether. I have overheads to model. This lesson came from Visualizing Math. The kids really get this so much easier than pies and bars.

It is great for improper to proper. multiplying etc…

I use this as the intro for a week or 2. Then I go to the other manipulatives, then fianlly paper/pencil. It is amazing how they understand fractions.
I hope this made sense.

Michelle

I esp like the egg carton idea. I have used pies—last year we tortured our son by making him tell us if he wanted 1/4 or 1/5 of the pie to eat!!! He had the emotional investment to start to figure it out. He just still doesn’t “see” what 1/2 and 1/3 ect are automatically.

Beth

I think this is very normal and a very good strategy. Instead of sitting there confused, he drew another rectangle and a line through half of it. I like the initiative he took and the problem solving skills he showed.

Children this young want to see that line and study it a bit. He didn’t want to draw the line in his textbook. He’s still learning fractions and you’re not. It’s easy for you to visualize where that 1/2 line would go but that’s exactly what he’s still learning to do - he’s learning to understand what is 1/2 of something. By drawing the line through his own rectange, he was teaching himself.

Good for him!

I have often wondered if egg cartons would help students learn about literal numbers. Each location could be labeled with a letter or other symbol. Then you could say, “Add a and b and put the answer in k?” Or it might be,” Add Pooh and Rabbit and put the answer in Piglet.”

I’ve never had a chance to try it, but I wonder if it would work.

Sara McName

I have used a program called hands on equations that are WONDERFUL for getting kids to understand algebra. It works so well. You could probably can do a search but it would be worth it . My 5th graders were all doing algebra. Even my low kids when I taught regular ed.. It was easy too.
Michelle

http://www.borenson.com/

I highly recommend anyone teaching regular ed or general ed. to try this. It looks pretty cheap too considering.
Michelle

This is GOOD. It is a real practical solution to a problem, it is quick and gives a solid answer. Unfortiunately it isn’t typical enough since too many kids are trained out of using visualization, but please encourage him to continue in this way.

BTW, I speak as a math major and math teacher and math tutor.

Actually, the circle or pie diagrams are harder, not easier. They’re OK for half, or quarter and most people can do a lopsided third, but once you get to fifths, forget it. If you make a rectangle 12 centimeters long you can make many fractions easily and at least come close to fifths. Or do 60 millimeters and you are good for almost anything but sevenths. Most of us think things are “easy” if that is what we were taught in our youths. But since math is so often so badly taught, it is helpful to nre-examne your assumptions.

I forgot to mention that there is a free 2 minute video clip to show you how it works. Young kids really get this.
Michelle

My dad thought of this analogy independently — I’m longing to do a computer graphics version of it… hmmm…. Flash is calling…