I asked my students to solve these brownie problems individually before sharing answers with a partner:
1. Share 12 brownies with 4 people
2. Share 6 brownies with 4 people
3. Share 3 brownies with 4 people
This revealed a lot of misconceptions about the meaning of fractions. On the third problem, Janessa thought each person would get 2 pieces, forgetting that one piece is 1/2 of a brownie and the other piece is 1/4 of a brownie for a combined total of 3/4 of a brownie.
Cristal also looked at these parts as 2 pieces. However, she called it 2/3 of a brownie because she saw "2 of 3 parts of a brownie," forgetting that thirds of the same whole must be equal.
On the second problem, Gabriela forgot that she was sharing 6 brownies with four children (instead of 3 children).
Jason showed me how he moved one corner from each brownie to form another 3/4 of a brownie for the fourth person.
Angel and Ediverto, who mainstream daily into my classroom from 11:30 AM to 2:24 PM, both had interesting solutions.
Angel could see that the brownie parts were 1/2 and 1/4, but didn't know how to combine these. He finally saw that 1/2 was the same as 2/4. This helped him write "2/4 + 1/4 = 3/4."
Mrs. Fuerte, Ediverto's Educational Aide, wrote the names of his friends across the top of the paper to help the boys understand the problem. Without any further coaching, Ediverto cut the paper brownies apart, and wrote 1 2/4 on his paper and underneath it simplified this to 1 1/2.
Later, he and Angel proudly showed the class their solutions for sharing 3 brownies with 4 people. Ediverto, who never speaks a word, points to each part and then holds up 3 fingers to show 3 of 4 equal parts.
Great job, men!! :)
Every time I present a new fraction problem, it amazes me how much the children still struggle with the concepts of correctly naming the fractional parts and realizing what represents the whole.
Patricio, who recently got a new calculator, was fascinated to see that 3 divided by 4 on his calculator was the same as 3 brownies shared with 4 children--or 0.75 which equals 3 quarters or 3/4 of a brownie each. He was very proud to present each of these ideas to the class.
Very fun, Mariana! :) Well done.