 Hello, my amazing math minds, and welcome to this week's math tip Monday. My name is Heidi Rothmeyer, staff developer at ESU 8. And this week, we will continue our conversation on the article by Dr. Karen Karp of 13 rules that expire again to help promote strong conceptual understanding with our students and make sure that what we're saying or encouraging our students to do does not lead to some misunderstanding later. So here are really two topics I'm going to combine combined today. One of them is when we say line up the numbers to the right when we're dealing with addition and subtraction of pull numbers. And then oftentimes the terms that we use again in addition to subtraction of borrowing and carrying. So we'll take a look at what issues we might run into and some different terminology we can use to help our students because unfortunately the line the numbers up to the right that particular concept will expire in grade five, which is when we start dealing with computations with decimals. So I'm going to go to the iPad and we'll look at some examples. Okay, so let's start with the example of 245 plus 32. So you might get some students that do this and then we might be tempted to say no, we need to line them up to the right so that it looks more like this. Well, yes, that will work when we're dealing with whole numbers, but we want to run into problems then if we have something like this. Because now when I try to line them up to the right, clearly we're going to have problems. So instead of saying line it up to the right, what's more appropriate to say is to line up like values. This will help students again reinforce the idea of place value so you can have better conversations about place values. And then it will become even more valuable when we start talking about subtraction. So let's take the example of 245 minus 87. And first I can have a conversation that I'm lining up like values. So I have my ones on the same place and my 10s in the same place. And this is obviously an example where traditionally we would say that we need to borrow. So let's go ahead and write this in expanded form. Again, I am lining up my like values, my ones and my 10s. Now, instead of saying borrowing, we're not really taking from something and then giving it back, we are regrouping some of our different place values. For example, I'm going to regroup this 40 into a 30 and a 10. And then this is going to become 30 and this is going to become 15. So I regrouped my 10s. So I can then subtract my 15 minus seven. Again, I'm going to have to regroup another time where I'm going to regroup my 200 so that I give 100 to the 10s and maintain the 100 in the 100s place. So using the terminology of regrouping will really help to reinforce the idea of place value concepts for our students. And you can do something very similar when you're dealing with decimals. We could do the same thing and write it in expanded notation and do some regrouping. So that was a real quick example of the trouble we may encounter if we use the phrase lining up the numbers to the right. We want to be consistent in our language so that whatever rule we might be talking about will apply throughout their K-12 mathematical career and not just expire. And also the precise vocabulary in terms of using regrouping instead of borrowing again will help students have a better understanding of the concept of place value in our numbers. So I hope those examples help you reflect on some of the terminology you use in your math classroom. And until next time, stay well, be kind.