 Hello, my name is Pat Lohr, and I'm a member of the Edmonton Regional Learning Consortium's math team. Thank you for joining me. Today I'm going to share four examples of number strings based on the ideas of Kathy Fosno. These examples are designed to give you some ideas about how you could use strings like these to encourage your students to develop good addition strategies. You're watching the first of two parts, and in part one I'm going to discuss the first two strings which make use of a 10 frame visual. In part two I'll discuss the last two strings, and they use an open number line. This professional learning opportunity is made possible by Grant from Alberta Education to support the implementation of the revised mathematics curriculum. The file has a page of teaching notes with information about the math behind the strings and suggestions for presenting the problems in the classroom. I'll be talking about some of these ideas during this webcast. The four example strings are definitely meant to be a starting point for you, and I encourage you to make use of the ideas to create some number strings of your own. I want to remind you that they are not meant to replace concrete experiences for your students, but I think they'll help you move your students on to more abstract ways to work with numbers. So let's have a look at the first example. This one uses a 10 frame visual based on Trevor Culkin's Power of 10 Materials. There's certainly other versions of 10 frames, and you might also be familiar with math racks. What these models have in common is the anchors of 5 and 10, and I can't emphasize enough how important it is for our students to develop a strong understanding of this concept. I'm using the Power of 10 visual because I know many of you are familiar with it, and you may already be using it in your classroom. These problems are designed to push my students to use visualization, and those anchors of 5 and 10 to combine numbers I'm going to show them. I use the screen shade on my smart board, and I give them just a quick peek at the 10 frame. So here we go. You could also use the large Power of 10 cards and flash them if that's easier for you. I want to discourage my kids from counting the squares one by one, and you can see that it wouldn't be possible here. I'll give them another slightly longer look at it. And then when we're ready to discuss, I'll take the screen shade right off. Now this one is pretty easy. I always want to start any number string at a place where I'm sure my struggling kids can be successful too, and I try to go to a place that's challenging for my strongest kids. It's about helping everyone in the class move forward rather than trying to get everyone to exactly the same place at the same time. For each problem I'm going to ask, how many squares altogether? How do you know? What was your strategy? Did anyone think of it in a different way? You can write the answer when it's given, and if you think it's appropriate, you could write an equation. You know your kids better than I do, and what they're ready for. I suggest you do the writing on the board, because this really should be a mini lesson, and you don't want it to go on too long. I'll just show you the other problems in this string. Ten and ten. Ten and ten and two. And ten and nine and nine. You can see how they're growing in complexity. I wouldn't necessarily use this exact combination of problems. It just depends on my students and what I think they're ready for. When we come to this problem, I hope you see how your students might have more than one strategy for finding the total, and asking if anyone thought of it in a different way becomes even more important. One student might see it as thirty, with two missing, while another might visualize moving one square from a nine to make a second ten, and that leaves eight more. The squares do move, but again, I would do the moving in a mini lesson. If some of your students suggest counting the squares one by one, accept that, but ask if anyone has a strategy that doesn't require counting each square. You're really trying to help them move beyond that. I think I'll actually flash this last one at you so you can think about how you would find the total. It's not a trivial problem, so get ready to pay attention. There you go. Do you think you know how many squares there are all together? Would you like another peek? All right. Now give me a thumbs up if you have your answer. We'll take a look at it all together. Why don't you turn to your partner and explain how you figured out how many squares there are? This one is challenging, but you need to remember to make your strongest kids stretch, too. With the visual right there on the board, everyone can talk about how they know the total. Now we're going to take a look at a second type of number string. In this one, I'm going to use the ten frame visual as a way to support a strategy for addition facts, and in this case, adding five to another number. My students are ready to be using equations to represent addition, so these will be part of the string. When we begin looking at strings like this one, I would probably have the ten frame visual right there, right from the start. Later on, I might use the screen shade to cover the visual, or not show the cards if I'm using those, until I'm ready to discuss the strategies. Here I've begun with five plus five, because I'm confident that everyone in my class is able to be successful here. Next is five plus seven. Remember the questions. Who knows the answer? What was your strategy? Did anyone think of it in a different way? I'm predicting that students are going to suggest two possible strategies here. So I've actually grouped the red squares to help me model them. And this is where the smart board is a really great tool. They might suggest moving five over from the seven to make a ten, and leave two more to make twelve. Or they might suggest making a ten by moving three from the five to the seven, and again leaving two more. Both are good strategies, and you can see how important it is for the kids to have a strong anchor of five and ten. They need to know that a seven is made up of a five and two, or that seven and three more makes a ten. Notice that I'm presenting the problems one at a time, rather than having them all up at once. I'm also leaving the previous problems with their answers up on the board. I'm encouraging my kids to use what they know to help them with what they don't know. When I think some of my students are ready, I'm going to leave the ten frames covered up at first, so they can visualize the numbers themselves and hopefully come up with an answer of their own. Not all of my kids will be ready for that though. So before too long, we'll uncover the frames and use them to help us with the discussion. Remember, I'm trying to help everyone in my class take one step forward. This string continues with five plus six, and finally eight plus five for my challenge fact. I think we may be too quick to assume that kids understand that five plus eight and eight plus five have the same answer, unless we give them the opportunity to really think about it. This concludes part one, where I've shown you two strings that make use of a ten frame visual. In part two, I'm going to share a couple of strings that use a number line. I owe a great debt to the idea of Cathy Fosno, and I highly recommend you check out her work if you found this interesting. I also owe thanks to Trevor Colkins for his strong ten frame visual. Remember, keep your mini lessons quick, and don't expect everyone to master the strategies the first time you present them. We want our kids to see the math behind the facts, build strong anchors of five and ten, and work flexibly with numbers. We definitely do not want them to believe that rote memorization is the key to math power. Thanks for spending the past few minutes with me, and I hope I've given you some food for thought. Thank you.