Equivalent fractions - a visual model of splitting the pieces further

With learning fractions, there is always the problem of "so many rules to remember". I offer this visual method of splitting the pieces further, and using the arrow notation as a remedy; hopefully this would help fix the method in students' minds.

Making equivalent fractions is like splitting all the pieces further into a certain number of new pieces. For example, if I split all the pieces in 3/5 into three new pieces, there will be 9 pieces. And, instead of 5th parts, they will be 15th parts. If you have an image and you split even the "white pieces" into three new ones, you'll see those 15 parts. So, 3/5 = 9/15.

The arrow notation shown in the video has one arrow between the numerators and another between the denominators. It also has a little "x3" written next to it. This is to signify into how many pieces we split the existing pieces.

This notation can help students not confuse equivalent fractions with fraction multiplication. The two fractions are equivalent or the "same amount of pizza"; one is not three times the other.

Please also see this free sample worksheet: Equivalent Fractions worksheet. This worksheet shows the same notation and the same idea as the video. It is a sample from my book Math Mammoth Fractions 1.

Please let me know what you think of this notation. I haven't see it anywhere else, but maybe it does exist somewhere. Do you think it confuses or helps students?

New math blog carnival: Math Teachers at Play

Denise has just posted the inaugural edition of a new blog carnival: Math Teachers at Play.

According to her, it is a "collection of tips, tidbits, games, and activities for students and teachers of preK-12 mathematics."

She said she wanted to start this kind of carnival because of not finding any blog carnival that would exactly fit what she wanted: a collection of blogposts concentrating on preK-12 math and also specifically on math teaching.

I definitely can second that feeling, being in the math education field and loving even the "lowly" K-6 math. I found several nice posts in the carnival, go check it out!

A little algebra problem

Just to "flex your algebra muscles" a bit; it's not too hard:

Raju is 19 years younger than Ram.  After 5 years, their ages will be in the ratio of 2:3. Find their present ages.

Solution:

Let Raju's age be J and Ram's age be R. We can make two equations:

J + 19 = R (Raju is 19 years younger than Ram)

J + 5

R + 5
=
2

3
(The ratio of (Raju's age in 5 years) to 
(Ram's age in five years) is 2/3.)

We will cross-multiply the latter equation:

3(J + 5) = 2(R + 5)

At this point, one can either resolve the parenthesis, or substitute from the first equation R = J + 19 in R's place. It won't matter which you do. I'll substitute R = J + 19.

3(J + 5) = 2(J + 19 + 5) Now, add 19 + 5.

3(J + 5) = 2(J + 24) Then use distributive property.

3J + 15 = 2J + 48

J = 33.


Then check: If Raju is now 33 and Ram is 52, then in five years they will be 38 and 57. And, 38/57 = 2/3. So yes, it checks.