 Hello, my amazing math minds and welcome to this week's math tip Monday. My name is Heidi Rethmeyer. I am a staff developer at ESU 8. And this week, we're going to continue our conversation on rules that expire, which is from an NCTM article by Dr. Karen Karp, and it reminds us to make sure we are using precise vocabulary and promoting conceptual understanding so that we don't cause confusion later on in a student's math career. So this week, we are going to talk about the phrase, you cannot take a bigger number from a smaller number. And usually this phrase is often encountered when we are working within whole numbers. So between kindergarten and fifth grade, because then in sixth grade, when we introduce integers, it expires. So we don't want to set kids up for failure by stating that you cannot take a bigger number from a smaller number because you most certainly can. So here's just an example I took from a first grade example. So Beth has 13 flowers in her garden. Kate has eight. How many more flowers does Beth have than Kate? So that's a typical question you might have. I like the fact that they have a number line, and I will point out a couple of things. I like that they have arrows on each end, and we'll talk more about that. There's probably one thing I wish we would add to this number line to help kids in the future, but I'll show you an example here in a moment. But then the kids are given the opportunity to draw it using some representation, tally, and then write it. And you may get kids that write 13 minus eight, and you may get kids that write eight minus 13. And there is a distinction, and we want to use our words carefully in helping kids understand which is the correct notation for this particular problem without leading to misconceptions later. So if you want to have a conversation with a student about, you know, something less than zero, and you're thinking about a number line, temperature is probably the easiest way to do that. Kids have probably heard temperatures in the negative. So that's something they're familiar with. So, you know, you could introduce thermometers if, you know, kiddos are having conversations. This one looks obviously more like a number line over here on the left. Now the reason I put this giant cross out cancel sign on this number line is for two reasons. One, I don't like that it gives the impression that the number line ends at zero and it ends at 20 because it does not. And it, you know, doesn't give you the opportunity to represent anything over here. So here's another example. I know you often use number lines even early on as helping students to get a conceptual understanding of adding and subtracting. I think a very simple thing that we can do is when we're working with number lines, just as a teacher, you don't necessarily have to have students do this, is to instead of starting at the very left with zero leaving a space there and making sure you have the arrows, knowing that these number lines continue. Now, as a teacher, you don't have to write what goes here, but it does certainly give the impression that there is something beyond zero to the left of zero or smaller than zero, if you will. And if kids want to talk about that, you can reference things such as a thermometer and negative numbers in that regard. So that is just a very simple change that you can make now. And your sixth grade teacher will thank you for that. So when they come, they don't have a misconception about something that's less than zero. So again, we want to be careful with our mathematical language. We want to be consistent so that something doesn't expire in a few years, accurate and use precise vocabulary. So stay tuned next time for more rules that expire. And until then, stay well, be kind.