Whole numbers are a familiar concept, one we can wrap our brains around. Consequently, whole number number talks seem to be pretty simple. However, when it comes to fractions, most of us have an anxiety about them, even in our everyday life.
Think about the last time you baked something. The recipe calls for 1/3 cup…you look the drawer and you only have a 1/2 cup measure and a 1/4 cup measure…what do you do?? Fractions often throw up a mental block for many of us because we learned procedures and memorized a series of steps to cope with this foreign concept (“don’t ask why, just invert and multiply” or “cross-multiply to find the common denominator”). When we consider the 8 Math Practices, today’s students need to understand fractions on a deeper level.
In my recent Facebook Live video about fractions, I touched on helping our students really understand what they’re doing with fractions. This requires a good foundation of number sense. Many students’ problems with fractions stem from a weak understanding of whole numbers. So, when students are trying to think about something that is a part of one whole, whether it’s decimals, percents, or fractions, it’s a struggle.
Enter: fraction number talks. This great book (one of my new favorites!) helps us apply a familiar strategy to a new area of math: Number Talks for Fractions, Decimals and Percents, by Sherry Parrish and Ann Dominick, published by Math Solutions.
This book features over 1000 purposefully designed number talks and also includes a link to an online video library of number talks in action in actual classrooms. There is also a reproducible packet that supplements the book that includes the area set and linear models. We’ve blogged before about Parrish’s Number Talks – check out our post on that great resource!
Starting in grades 3-6, having number talks about fractions will help kids start to understand fractions on a conceptual level using the same strategies used in whole number number talks, such as the open number line, compensation, decomposing and composing.
Take this problem:
Most of us look at that and immediately the default “fraction move” is to try to find the common denominator. So, we skip count by 2 and end up with 8 as a workable number, multiply, and get 4/8 to add to 5/8.However, we want students to really think about the actual numbers and what they represent. Think about it this way instead: if we were to decompose 5/8 into 4/8 + 1/8. We know that 4/8 = 1/2, so we can bond together the two halves to make a whole, and we can see that we are left with 1 and 1/8.
Normally, the way we learned fractions, we wouldn’t think to decomposing fractions and the number sense that goes along with it. Number Talks for Fractions, Decimals and Percents helps teachers think differently about number talks and expand this useful concept to a new area of math instruction.
This number talk rubric is one I usually give to principals, and helps us look at how student centered we are in our instruction. We don’t want our students to just regurgitate procedures. 21st century education demands a shift towards more student-led instruction, however, about 95% of the teaching we see in classrooms as part of our coaching projects is teacher-directed. Teachers are trying to make this important shift away from the teacher being the giver of all knowledge, but I’ve found that part of the challenge is that teachers, especially in the elementary sectors, don’t have a strong understanding of fractions and decimals for themselves. If they could have a deeper understanding of the concept, it would help their teaching, and in turn make them more confident in helping students direct their own learning. This book is a giant step in building that understanding, and ultimately, that confidence.