 Hi, my name is Pat Lohrer and I'm a member of the Edmonton Regional Learning Consortium's math team. Thanks for joining me today. I've been working on some files with strings of problems based on the ideas of Kathy Fosno. They're designed to help your students develop strategies for addition facts and I'm going to share some ideas for using them in your classroom. This professional learning opportunity is made possible by a grant from Alberta Education to support the implementation of the revised mathematics curriculum. In each file you'll find a page of teaching notes with information about the string and suggestions for presenting the problems in your classroom. I'll be talking about some of these ideas during the webcast. In the string I'm going to show you now, I want my students to be thinking about those near double facts and how knowing your double facts can help you with lots of other facts. I'm hoping they'll suggest the strategy during the lesson and if they don't, I can decide whether or not to bring it up myself. I've chosen to use a 10 frame visual for support based on Trevor Culkin's Power of 10 Materials. There are other versions of 10 frames and you might also be familiar with Math Racks. All these models are designed to help kids develop those anchors of 5 and 10 and I can't emphasize enough how important that is for our students. I've worked with plenty of grade 6 students who don't have those anchors and it makes any kind of mental math really difficult. If your students aren't familiar with 10 frames, spend some time building that familiarity before you try using them to support a string of problems. They should be able to recognize the numbers 1 to 10 at a glance as well as knowing for example that 3 is 2 away from 5, that 8 is a 5 and a 3 and that 2 more gets you to the 10. So let's have a look at the problems. I'm using the smart board to present my string but please remember you don't need a smart board to do number strings. With an overhead or blackboard and some 10 frame cards or a big math rack for support, you're ready to go. I've chosen 5 plus 5 as my first problem because I'm pretty sure all my students will be able to answer this one. It's really important to start with a problem that's within reach of even your lowest kids so that they can join the conversation as well. Then I always try to go to a place that's challenging for my strongest kids. So I ask, how much is 5 plus 5? How do you know what was your strategy? And maybe most importantly, did anyone think of it in a different way? I suggest you do the writing and modeling on the board because this really should be a mini lesson and you don't want it to go on for too long. For this question, students will likely say I counted by fives or I know double fives. And here the smart board is nice because I can just pull the 5 over to make a 10. The next problem is 5 plus 6 and you'll notice a couple of things. First of all, the previous questions are always there with their answers because I actually want the kids to use what they know to help them with what they don't know. Secondly, the 10 frame still shows 5 plus 5. I would ask, what would 5 plus 6 look like? Can I use these cards to help me think about that? Here I've actually put the extra red square on top of the square so I can just pull it over to make the 6. If I was using big 10 frame cards with my kids, I would just trade the 5 card for a 6 card. So who knows how much 5 plus 6 is? How do you know? You can guess that by giving them 5 plus 5 first and then using my little trick with the extra square, I'm not so subtly pushing them to think about my target strategy, that near double one. But I always want them to suggest as many different strategies as possible. Maybe someone will notice that 6 plus 4 is 10 and then you have one more left from the 5. So I have grouped the squares to make that easy to model. And there you can see the power of having a strong anchor of 10 knowing that 6 and 4 more is 10 is an important idea. Now here's a page I've added especially for the video because I want you to consider why this is so much better than memorizing basic facts in isolation. If your students understand how 5 plus 6 can be broken apart and recombined to make finding an answer easier, then they'll be ready to think about how you could do the same thing for larger numbers. And that is a really big math idea. What you're doing is giving your students math power. The next facts I chose were 8 plus 8 and 8 plus 7. 8 plus 8 is a much harder double fact so I'm going to have a chance to reinforce strategies for this one. Remember how we want to include our struggling students in this conversation? I also want them to realize that you can subtract one from a double fact like so to find a near double. Don't forget to ask for other strategies because there are several good ones for this fact. You could double 8 and minus 1, double 7 and add one or move from the 7 to make a 10. And of course you could always move from the 8 to the 7 to make a 10. And all of those are good strategies. The rest of the facts in the string are all near doubles with no double fact for a helper. So it's going to be interesting to see if any of my students will suggest using double facts as a strategy. Here we have 5 plus 4 and 7 plus 6. And for the last fact I want to show you something really important so pay attention. Up to now I've been showing the equation and 10 frames together but that's something I'm going to think hard about before I do this string with my kids. Maybe some of them aren't ready to recognize the 10 frames without counting those squares one by one. And in that case I'm going to start by showing them the 10 frames without the equation so I can reinforce that. Don't forget to keep your low kids in the game. Once some of my kids are getting pretty good with the strategy I'm going to want to present the equations without the visual support. You also need to keep your stronger kids moving ahead as well but during the discussion I can remove the shade so the support is there for anyone who still needs it. Again I highly recommend you check out the work of Kathy Fozno if you found this interesting and you might want to check out Trevor Culkin's Power of 10 Materials. Remember to keep the mini lesson quick. Don't expect everyone to master the strategy this time and please promise me you won't resort to mad minutes. We want our kids to see the math behind the facts and work flexibly with numbers rather than believe that rote memorization is the key to math power. Thanks for spending the past few minutes with me and I hope you'll give these ideas a try with your students.