 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've created some files with strings of problems based on the ideas of Kathy Fosno. They're designed to help your students develop strategies for multiplication facts, and I'd like to share some ideas for using them with your students. 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 math behind the strings, and suggestions for presenting the problems in the classroom. I'll be talking about some of these ideas during the webcast. In this particular file I want my students to be thinking about how the five times facts can help them with the seven times facts, and I'm hoping they'll suggest the strategy during the lesson. They don't, it's up to me whether or not I want to bring it up at this time. So let's have a look at the problems. First of all you'll notice that I'm supporting each problem with an array. The array is a really powerful model for multiplication, and I want my students to become as familiar with it as they are with the number line. I hope you'll understand why I think so as we move through the string. I've chosen five times four as my first problem because I think it's one that all my students will be able to answer. As well, adding two more groups of four to twenty is pretty straightforward, and it's within the reach of my struggling kids. It's really important that you begin in a place that's within reach of your lowest kids, and try to go to a place that's challenging for your strongest kids. Now ask, how much is five times four? How do you know what was your strategy? Write the answer when it's given, and model the strategy by circling sections of the array. If your kids suggest counting by fives, you can show it this way, and I like to label the sections of the array. Now you may have another student that sees this one as two groups of ten. So in this case I would circle it just like this, and again label that, and in this case you might also want to point out that now we have a five times two and another five times two array. You might have another child that suggests that they could count by fours and get the same answer of twenty. Now this isn't a strategy that kids are likely to use to answer this multiplication fact, but having a student suggest it is great because it shows that they're making connections to the way you can break those numbers apart. The next problem is seven times four, and you'll notice a couple of things. First of all, I always leave the previous questions up 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, this array still shows five times four. I'd ask, what would a seven times four array look like? Can I use this five times array to help me think about that? Now watch this. I can actually pull down two rows from that array and turn my five times four array into a seven times four. So who knows how much seven times four is? How do you know? Adding two rows is designed to push them towards the strategy that I'm thinking about and in a not so subtle way, but as always, I'm going to accept as many strategies as they can come up with. I may have a student suggest that they see this as a seven times two and another seven times two. They know seven times two is fourteen, so seven times four is going to be twenty-eight, and actually that's a terrific strategy for that problem. Of course, the strategy that I've been sort of looking for here is that they can see the five times four is twenty, and then they have a two times four is eight, and that'll give them the answer, twenty-eight. I've added this page especially for the webinar because I want you to consider why this is so much better than memorizing basic facts in isolation. If your students understand why seven times four can be thought of as five times four and two times four, then they'll be ready to think of six times twenty-three as six times twenty and six times three, and that's a really big math idea. The next facts I chose were five times six and seven times six. The arrays work the same way. Most of my kids know two times six, so that's another easier one. Adding twelve to thirty is again pretty straightforward for most students, but now I have a chance to talk about strategies for adding those two numbers for the kids that need it. Remember how we want to include our struggling students in this conversation. I then chose five times eight and seven times eight. If my kids are still wanting to count by fives for this fact, I'm going to push them a little bit towards seeing it instead as four groups of ten. Now this is a great strategy for this tough fact, but remember doubling eight might be hard for those struggling students, so it's also going to give me a chance to talk about strategies for adding eight to another number. It isn't about getting everyone to the same place at the end of the lesson. It's about helping everyone move forward one step. Finally I like to end with the challenge fact. This time seven times seven with no helper fact. The bottom rows are already on this array, but you can pull them down during the discussion if you want to. And that's it. Again, I owe a great debt to the ideas of Kathy Fosno, and I highly recommend you check out her work if you found this interesting. Remember, keep it quick. Don't expect everyone to master the strategy this time, and please promise me you will not resort to mad minutes with your kids. We want our kids to see the math behind the facts and work flexibly with numbers, not to believe that rote memorization is the key to math power. Thank you for spending the past few minutes with me, and I hope you and your students can make use of these files.