This week, our focus was learning how to compare and order fractions using different models and strategies. Before beginning to explore different strategies, I knew from previous lessons that my students were struggling with knowing when it made sense to compare two fractions. For example, it is not fair to compare 1/2 of a large pizza to 1/2 of a small pizza because the wholes are different sizes. Last week, I began to notice that my kids jumped to compare fractions without taking into account the size of the whole. They were really struggling with remembering to identify the whole before comparing two fractions. After teaching this fun (my kids loved the candy relation) one -day lesson, I noticed a quick change in my students thought process.
Last week, I mentioned that a group of kids came to the realization that it takes two 1/8 pieces to make up 1/4. Following that, a group of kids came to the conclusion that the larger the denominator the smaller the fraction piece and the smaller the denominator, the larger the fraction piece. Well, we used that discover to help us compare two fractions with like numerators. For instance, when comparing 2/3 and 2/5, my kids explained to me that 2/3 is greater because it only takes three pieces to make up the whole verses five- so those three pieces are larger than the five.
That being said, it was really important to me that my kids truly understand the "rule" (the larger the denominator the smaller the fraction piece and the smaller the denominator, the larger the fraction piece) that they came up with and were not just memorizing the phrase to solve the problems. I ensured they had a deep understanding by constantly asking students to explain their thinking and asked them to show me how they solved the problems in more than one way. I'm really trying to make sure that my kids are getting a deep understanding of the content, rather than just memorizing procedures.
Next week we will begin pieces missing and comparing the wholes to compare fractions.
Last week, I mentioned that a group of kids came to the realization that it takes two 1/8 pieces to make up 1/4. Following that, a group of kids came to the conclusion that the larger the denominator the smaller the fraction piece and the smaller the denominator, the larger the fraction piece. Well, we used that discover to help us compare two fractions with like numerators. For instance, when comparing 2/3 and 2/5, my kids explained to me that 2/3 is greater because it only takes three pieces to make up the whole verses five- so those three pieces are larger than the five.
That being said, it was really important to me that my kids truly understand the "rule" (the larger the denominator the smaller the fraction piece and the smaller the denominator, the larger the fraction piece) that they came up with and were not just memorizing the phrase to solve the problems. I ensured they had a deep understanding by constantly asking students to explain their thinking and asked them to show me how they solved the problems in more than one way. I'm really trying to make sure that my kids are getting a deep understanding of the content, rather than just memorizing procedures.
Next week we will begin pieces missing and comparing the wholes to compare fractions.