Last week, I took a week off from doing any number talks/number strings. I had a visit from the superintendent to work in, and I felt like I was juggling too many other new things. One of my coworkers seems to be able to do number strings intuitively with her kids, based on questions that come up in the moment. For example, when she introduced her students to probability, they asked about a roulette wheel, and so she asked them to consider the chances of getting 00 (which is 1/38). To estimate that percent, she had them first do 1/4 >> 1/40 and notice a relationship, then 1/2 to 1/20, 1/3 to 1/30, and a few others before she had them estimate the 1/38 and then check via a calculator. I was impressed, but I don’t think I’m ready to do it without planning it yet.
I’m trying to figure out how to incorporate some number strings this week for my students. I’m struggling in some ways because I want to be sure that I’m addressing the skills that the kids need in my current unit, but also not giving them strings that require them to make use of strategies from strings we haven’t looked at yet…
In 6th grade, we’ve “finished” our addition and subtraction of integers and we’re in the midst of multiplying and dividing with integers. We’ve done multiplication so far and we’re about to introduce division this week. I’m wondering if there’s a multiplication string that would be appropriate for me to use with them. And I’m also wondering if there’s a problem if I introduce some of the strings with negative factors! Or if I should keep the focus of the multiplication strings on the products themselves, and leave the signs to the day’s lesson.
In 7th grade, we’re working on probability, and there are a few things that have come up that I think could be good for number string work. First, I noticed that while my students have fluency with converting some fractions into percents (more than most kids – not only do they know their 1/4s and 1/2s, they also know their 1/3s, and 1/9s and even their 1/8s!), but the students aren’t fluency with multiple eighths, nor are they fluent with some of the “odder” fractions into decimals/percents yet. I’m wondering if there’s a way to get the students to be able to calculate the percents of 3/8, 5/8 and 7/8 easily (i.e. noticing that 1/8 + 1/4 = 3/8, or that 5/8 = 1/2 + 1/8 and leveraging those skills somehow – or multiplying 12.5 x 3 or x 5).
Second, tomorrow, we’re going to begin proportional reasoning with percents, so I’m wondering if I should do a string where we find “friendly” percents of a number to build a more complex one.
Third, we’ve had to multiply fractions by each other (but mostly “easy” ones), so I don’t know if this is worthy of a whole string right now.
I’m still struggling not only with how to implement these strings, but also how to design and decide on the best string for a given lesson. I know there’s been some back-and-forth about whether the strings should relate to the day’s content or not, and while I’m okay with it not relating directly to that day’s content, I do feel it necessary to relate it to the general topic of the week/unit.