1/2 = 2/4
2/3 = 4/6
First draw out your fraction models draw out 3/3 and then right under that draw 6/6. Once you have drawn those models out color in 2 of the 1/3 pieces and 4 of the 1/6 pieces. Do those look equal to you? well that is because they are! You have completed an equaltiy problem. to check your illustration of the equation just check it with the drawing below.
for more practice on fraction equality you can go to the following website by clicking the on the word fraction.
I think the pictures you have explain fraction equalities really well. They allow us to visually see what we are comparing. I think it's important for kids to see fractions like this.
ReplyDeleteI think fraction bars and cuisinaire rods are great. I don't even faintly remember them from grade or middle school but i think they are great illustrators of both equalities and inequalities. Great way to make math hands-on.
ReplyDeleteUsing the fraction bar to figure out the fraction amounts are really helpful, I especially the pictures in this blog to illustrate the fractions.
ReplyDeleteYou can take your teaching to another level by using these pictures to explain the standard way of finding equivalent fractions. The pictures help your students move beyond them, to a deeper understanding.
ReplyDeleteLet's look more carefully at the 2/3=4/6 picture. In going from 3rds to 6ths, the denominator doubles, because it takes twice as many pieces to make one whole thing. At the same time, the numerator doubles, because these pieces are each half as big as the pieces before, which means it takes twice as many of them to name the same amount of stuff.
Is this because of anything special about 3rds and 6ths? NO! It will be true of ANY equivalent fractions.
If we wanted to change 2/3 into some number of 15ths, then it would take 5 times as many pieces to make one whole thing. And at the same time, each piece would be 1/5th as big as before, so we would need 5 times as many pieces to name the same amount of stuff.
Similarly for any equivalent fraction. Let your students suggest weird fractions to try, like 39ths or even 99ths!
So in equivalent fractions, the numerator and denominator always increase (or decrease) in proportion --- multiplied by the same amount.