Preface: My posts are usually narrative, but this post is going to be analytical. A lot of the challenges I face, as a teacher, and you can read about here are managerial and personal and people-oriented. This difficulty I am having teaching fractions is an instructional challenge. Sometimes those are like second nature to me because of who I am and what I do, but tonight you can see my thinking on this.
What are my primary objectives for this group of students?
*My students' knowledge of basic fraction vocabulary (half, whole, third, numerator, denominator, equivalent) will be automatic.
*My students will have a thorough knowledge that fractions are equal parts of a whole.
*My students will develop concrete strategies to reason about fractions.
*My students will be proficient in the process of comparing fractions by drawing accurate representation of fractions.
What makes fractions a challenge with this group?
The standards suggest that my students should reason abstractly about fractions, but in this particular group of students there are a significant number that are not yet able to do that. My challenge becomes to give them concrete strategies to deal with abstract processes. (Understanding why 2/3 is less than 3/4 is abstract, but there is a way to make it concrete.)
My students lack the foundational knowledge and skills they should have entered third grade with as it relates to fractions. They did not come to me able to name fractions or recognize them.
So, what is my plan?
Automatic Vocabulary Knowledge: I am going to use short repeated phrases and motions to reinforce vocabulary at the beginning of every lesson and to remind students throughout the lesson. Here is the repertoire.
Class, what is a fraction?
A fraction is a part of a whole number, Miss Understood.
Then, I will put up a slide that says 1/2; 1/3; 1/4; 1/5; 1/6; 1/7; 1/8; 1/9; 1/10; 1/11; 1/12. The students will count through these fractions out loud with me before we begin the lesson.
Every single time that I say the term numerator at any point in a lesson, they will have to say, "Numerator, number on top, target number," with a motion. Every single time I say denominator, they will have to say, "Denominator, number on bottom, total number," with a motion.
Concrete Strategies: I already have my speech planned, and it is going to work because I tell the kids I have this year all the time that this or that isn't hard and they will see. As we go on in fractions, I will say the following, "Boys and girls, I always tell you that the things we do aren't that hard if you pay attention and keep trying, but I will tell you something new today. Thinking about fractions is really hard, but I will tell you a secret to make it easier. Whenever you see a fraction imagine food. You can pick. Imagine either a pizza or a cake and we'll look at it in terms of the pieces and the part you get to eat." I am hoping that with this line of thinking being encouraged over and over again they will be able to look at something like 2/3 and 2/4 and see why two big pieces are more than two smaller ones.
Proficiency in the Process of Comparing Fractions: We are going to repeatedly practice drawing fraction boxes and using them to compare fractions. I will grade their work on neatness and showing equal parts. I will repeatedly remind them that if they don't draw these accurately this won't work.
As far as helping them develop a conceptual framework for fractions, I want to make it relevant. I'm going to play a game with them called fraction scavenger hunt. I will make a worksheet that says things like 9/24 of our class are this gender, 10/24 of our class have this color of hair, 2/24 of our class wear these. I'll put my attendance roster with pictures on the smartboard and the kids will use their knowledge of numerators and denominators to figure it out.
This is my game plan and a lot of it came out of the comments I just read. THANK YOU SO MUCH FOR THE HELP!