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Fractions are Division

The seventeen messages in this discussion were originally posted over the course of one month starting in February of 2001.

Monday, February 12, 2001 5:54:17 PM
Guy
Fraction, decimal activities

Anyone have any cool fraction, decimal activities for 5th graders?

Monday, February 12, 2001 8:47:14 PM
Sandy
Re: Fraction, decimal activities

Check out the NCTM Addenda book for Rational Numbers.

Monday, February 12, 2001 10:18:16 PM
Heather
Re: Fraction, decimal activities

Have you tried the Mathline lesson, "Alphabits"?

Monday, February 12, 2001 10:22:34 PM
Emma
Re: Fraction, decimal activities

The Investigations fraction modules for grades 3 , 4 and Name that Portion in Grade 5 is excellent -- teaches fractions, decimals and percents together, not in isolation.

Tuesday, February 13, 2001 1:55:58 PM
Debbie
Re: (2) Fraction, decimal activities

I don't know if this might be what you are looking for, but what about cooking? There are recipes for no bake cookies, etc. that you can double, halve, quarter, convert the fraction (1/2 cup) to decimals... My children did this beginning in first grade and it provided a great visual to parts of the whole.

Saturday, February 17, 2001 9:34:14 AM
Jane
Re: (2) Fraction, decimal activities

Sandy writes:
Check out the NCTM Addenda book for Rational Numbers.

Or check out the grade 5 Addenda book.

Cuisenaire rods work well for developing understanding of fractions and equivalant fractions. Dale Seymour probably has a book on the subject. Since I am no longer at work, I can't go to the shelf and look this one up. I'm sure that are C. rods somewhere in your school.

Saturday, March 10, 2001 9:45:16 PM
Jerri
Re: (2) Fraction, decimal activities

Emma writes:
teaches fractions, decimals and percents together, not in isolation

Could someone please tell me why you don't also teach kids from the very beginning THAT A FRACTION IS A DIVISION PROBLEM. I'm a science teacher and we don't have much use for fractions in the metric system. They are division problems and kids rarely seem to understand that!

Sunday, March 11, 2001 7:59:56 AM
Lance
Re: (3) Fraction, decimal activities

Jerri writes:
Could someone please tell me why you don't also teach kids from the very beginning THAT A FRACTION IS A DIVISION PROBLEM.

I just had this eye-opening experience this week, that some kids don't know that a fraction is a division problem. One of my students in an accelerated geometry class asked how they know 2/3 is .666666.... It stumped me at first and then I told him to divide 2 by 3 and it was like the light bulb turned on. I just took it for granted that they knew the relationship.

Sunday, March 11, 2001 9:55:51 AM
John
Re: (3) Fraction, decimal activities

Jerri writes:
I'm a science teacher and we don't have much use for fractions in the metric system.

The conversions of meters to centimeters to millimeters is a hard one for students. Understanding the division process involved is essential to their converting the units. How many meters is 274 centimeters? Division problem I think, or is it fractions?

Sunday, March 11, 2001 10:01:03 AM
Donna
Re: (4) Fraction, decimal activities

Lance writes:
I just took it for granted that they knew the relationship.

I think that in the past we have all taken it somewhat for granted that kids UNDERSTAND mathematical relationships!!! To me, that's the beauty of the NSF curricula and STANDARDS-BASED INSTRUCTION, kids are given numerous opportunities to explore and build a true UNDERSTANDING of mathematics that is connected to EXPERIENCE!!!!!

As I have spoken to a number of groups of teachers this year, I keep reiterating how important it is that we, as elementary teachers, really see our mathematics goals to include BUILDING UNDERSTANDING and LAYING A STRONG FOUNDATION for mathematics.

Sunday, March 11, 2001 9:18:32 PM
Eileen
Re: (4) Fraction, decimal activities

John writes:
The conversions of meters to centimeters to millimeters is a hard one for students. Understanding the division process involved is essential to their converting the units. How many meters is 274 centimeters? Division problem I think, or is it fractions?

I just worked on this with my fifth grade students. We had built understanding with fractions that the more pieces a whole is divided into, the smaller each piece is. Therefore, 1/8 is smaller than 1/2, even though students initially think that 8 is more than 2.

Once this understanding was in place, it wasn't too difficult to talk about converting a larger unit of measurement to a smaller one and vice versa. If you are converting from a larger unit to a smaller one (meters to centimeters), there will be more pieces of the smaller unit. Therefore, to convert a large unit to a smaller unit, we would multiply. Converting cm to m (smaller unit to a larger unit) requires that you divide.

You're right, it isn't an easy concept to grasp, but, at the end of the week, most seemed to understand the concept and were doing quite well. Conversion in the metric system isn't really fractions, but multiplying or dividing by multiples of 10, but it helped to have an understanding of the relationship of fractions to teach it.

Monday, March 12, 2001 7:10:39 AM
Karen
Re: (3) Fraction, decimal activities

Jerri writes:
They are division problems and kids rarely seem to understand that!

I teach seventh grade math and I do make sure my students understand that a fraction is a division problem. However, I believe this is the first that they learn it at my school, and I agree it needs to be taught from the very beginning. It is essential they know this because it is used so often when solving algebraic equations in which a number needs to be divided to both sides (in which I teach to divide both side in the fractional sense).

When I teach "turning" a fraction into a decimal I use the phrase "tip and divide". I relate this to tipping over a stack of boxes. When tipped, the top box will fall further than the bottom box. So when given a fraction, you tip it (always to the right) and the top number falls inside the division box and the bottom number falls outside. I use this because it is difficult to remember which number goes where.

Monday, March 12, 2001 5:59:30 PM
Jane
Re: (3) Fraction, decimal activities

Jerri writes:
Could someone please tell me why you don't also teach kids from the very beginning THAT A FRACTION IS A DIVISION PROBLEM.

I think you've hit on one of the reasons why factions are often so difficult for kids. They are so multi-dimensional. You are certainly right that kids don't recognize that a fraction can be interpreted as a division problem.

Monday, March 12, 2001 8:12:05 PM
Connie
Re: (4) Fraction, decimal activities

I teach second graders, and I try hard to provide them with enough experiences to develop a fraction sense. They should know confidently that 2/3 is not a whole something. A whole or a set has somehow been divided into equal parts and those parts are thirds. They should have a solid sense that thirds means three parts.

Parts means something has been divided. It could be an any size something that is being divided, but there are always three equal parts. There are many, many activities to help build this type of thinking.

Tuesday, March 13, 2001 5:34:13 AM
Corrine
Re: (4) Fraction, decimal activities

Hi J,
I like the "tip and divide" suggestion. It will help the children remember.
Thanks.

Wednesday, March 14, 2001 4:55:09 PM
Don
Re: (4) Fraction, decimal activities

I made a visual aid showing the fraction 1/2 at a twelve o'clock position (with a fraction bar not a slant), then again at the one o'clock position with the fraction bar tilted, again at the two o'clock position with the fraction more tilted and finally at the three o'clock position with a ")" replacing the fraction bar.

I put it on the wall in the Title 1 CAI area. I never got any feedback and have no idea if it ever helped.

Thursday, March 15, 2001 11:18:40 AM
Joe
Re: (5) Fraction, decimal activities

Needless information, the fraction bar (division bar) is known as a vinculum