 Hello, my amazing math minds and welcome to this week's Math Tip Monday, the first of 2021. I am Heidi Rathmeyer, staff developer at ESU8. And this week, we're going to talk about rules that expire. This comes from an article from Dr. Karen Karp, who was actually one of our speakers at our NITM conference this fall. So if you had a chance to listen to her, she's pretty amazing. I've also included a link to the article of the 13 rules that expire if you'd like to read more about it. This is a quote from the beginning of the article that talks about why we need to be very careful with our language that we use with students because over generalizing some strategies using imprecise vocabulary and relying solely on tips and tricks really is not going to promote conceptual understanding and then we'll lead to misunderstanding later for our students. So we are going to talk about one specific rule today and I will address others in the future. So today, the rule that I want to address is when you multiply a number by 10, just add a zero to the end of the number. Or if you multiply by 100, just add two zeros, which I know has probably come out of my mouth as well and working with students. The problem is this particular rule will expire by grade five. So I'm going to go to my iPad and we'll take a look at some examples. So let's start with 25 times 10. And if you ask students to do the traditional algorithm, probably get 250. And maybe you do another one, let's say 34 times 10 and we get 340. And maybe you do a few others and you'll get students that might notice, well, hey, all I have to do is add a zero. So what might happen then if we introduce these two problems to students? Well, some answers we might get are certainly 500. We might also get 50.00, well, I just added a zero, right? So clearly we can see that this can cause some confusion and some problems when we get two decimals. So let's take another example. What if I have 0.34 times 10? And what my students be tempted to do? What answers might we get? Well, we might get 0.340 because I added a zero to the end. Maybe I'll get 0.034. Maybe I'll even get 0.34. OK, so clearly that's going to cause some confusion if I say just add a zero to the end. So if I start the conversation about multiplying with 10 with just the tips and tricks, and I skip over the conceptual understanding of place value, I'm really setting up my students for a poor understanding of number sense and some confusion in the future when they do encounter decimals. So what are some different ways maybe we could approach this as opposed to going just straight to the tip and the trick that the shortcut that we may be tempted to do? Well, maybe we can start by just having a conversation about patterns. So maybe show the students these problems and let them have conversations. And you will probably get students that say, well, all I have to do is add the same number of zeros to the problem as what I'm multiplying by. So if it's 10, I add is one zero. If it's 100, I add two. If it's a thousand, I add three. And as a teacher, I would say, well, that's interesting. So tell me what what is actually happening to the number that we started with here? What is actually happening to this number so that I get this number? Let them have some conversations with, you know, small groups or with a partner. And then I might also ask the students, is there a scenario where this doesn't work by just adding a zero to the end and see if they can come up with an example where it doesn't work? And then I can continue the conversation with this series of problems and say, OK, again, what do you notice? What do you wonder? What's happening? And hopefully then this will lead into some more conversations about place value and understanding just what we're doing conceptually as opposed to just adding a zero to the end. And I would also be very hesitant about saying, well, we're just moving the decimal. I have a concern because we're not really moving the decimal. The decimal is always between the ones in the tense. What we're actually doing is changing the place value of the numbers that we're given in the problem here. So, you know, think about the language when you're when you're doing problems like these. Now, certainly once kids have that conceptual understanding, then those tips and tricks may be useful to them. Absolutely. But I want to make sure that we're really setting them up to have a strong foundational understanding of the number sense and place value so that when they encounter problems, whether they're decimals or whole numbers, they really understand what's happening. So this rule of just adding a zero to a number when you multiply by 10 will expire in fifth grade when we encounter decimals. So in the future, as you're having conversations with students and in your teaching, think about the language you're using, make sure it's consistent and accurate and that the rules and the language that you're using are not going to expire and that we use precise vocabulary. So I will have more examples in the following weeks about other rules that expire and until then, stay well and be kind.