Dean Ballard: Additionally, some other recommendations that we’ve found, some techniques that we’ve found very important and very helpful are to make vocabulary and concepts explicit and visual. That repetition is a good thing. Use scaffolds such as sentence frames, partnering, allowing students to talk in their native language to each other to translate ideas, to use engaging activities, and to create, manage and process opportunities for students to talk about the math with each other. On this slide, a lot of these strategies, I would say that the third bullet really gives you the most specific kinds of techniques that we’re going to share, and I’m going to share some more specific techniques along the way because I realize that ultimately it’s the specific teaching techniques that you can take into the classroom that make the biggest difference for you.
Dean Ballard: All right, so we’re going to move on, and I’m going to get into a math problem with you. This problem and the next two that I’m going to share with you are featured in the books CORE put out called Spend Some Time with 1 to 9. The problems are actually available to you in a free sampler that you can get as well, that you can download from our website. These are activities that we created to provide some engaging problems that build number sense through problem solving and mathematical reasoning. This is in itself modeling a couple of techniques for addressing language challenges. That of using gauging problems, and also the idea of minimizing the language demands in a problem, while still maximizing mathematical reasoning.
Dean Ballard: While taking you through a couple of these math tasks I’ll model and discuss techniques for helping students overcome language barriers. With this particular problem I’m going to first go through the directions like I would with a class of students. And then, we’ll process it together. I’ll have you actually input into the chat, or the question window some of your thoughts, and then I’ll give you a few minutes to try that math challenge yourself actually, and then we’ll briefly process some of your answers as well.
Dean Ballard: So, going through the math problem: Create equations for the digits 1-9. Create as many equations as you can using these digits and when I say digits versus numbers, I want you to think about the digits are like letters, and numbers are like words, just like we make words using the letters, we make numbers using the digits. The digits 1, 2, 3, 4, 5, 6, 7, 8 and 9, and 0. So, we’re going to use digits, those digits 1-9 to make some equations. So they’ll be creating numbers and equations, and we’re going to see how many of the digits we can use. For example, 8 divided by 4 = 5-3. Here’s an equation, so it’s equal, and let’s see if it’s actually a true equation. 8 divided by 4 is 2, 5-3 is 2, so we have 2=2 so we have a good equation, it works. I’ve used 4 of the digits. 3, 4, 5, and 8 creating numbers and we have a good equation.
Dean Ballard: Here’s another example. 6 x 7 = 42. Here we have again an equation that’s true. 6 x 7 does equal 42. I’ve used 4, I’ve used some of the digits, I’ve used four of them, 1, 2, 3, 4 to create 6, 7, and 42. Another example. 2 to the 3rd power equals 8. Again, a true equation, it is an equation that is true, and I’ve used some of the digits. I’ve used 2, 3, and 8 to create that equation. Final example here of ones that work. I think I’ve gotten in this equation to use all of the digits. 1, 2, 3, 4, 5, 6, 7, 8, and 9 so I used all the digits in this case to create numbers in an equation that’s true. Let’s see if it’s true. 7 x 5 is 35 + 8 is 43 – quantity 6 + 1 is seven, so we have 43 – 7 makes 36. Over here we have 29 + 3 makes 32. 32 + 4 makes 36. So we have 36 = 36, so it’s an equation, it works, it’s great.
Dean Ballard: Now you noticed I did not use any digit more than once within the same equation. Now I can re-use the digits on new equations, but within each equation I did not use the digit more than once. So you never see here, like the 3 only used one time here, 6 never used more than once here, none of these digits are repeats. None of these cases are the digits repeated. So you can’t do something like this, this does not work. 8 divided by 4 + 3 = 7 – 3 + 1. The equation is true, 8 divided by 4 is 2 + 3 makes 5. 7 – 3 + 1 makes 5, that’s 4 + 1 makes 5, so we have an equation, and it is true. 5 = 5, but I used 3 two different times, so I’m not allowed to do that. I’m also, you might have noticed, I did not use 0. 0 is not from 1-9.
Dean Ballard: So, even though it’s a digit it’s not one of the digits we agreed on using here, so you can’t do something like this. 16 divided by 2 is 8, and 40 divided by, let’s see 8 – 3 is 5 so 40 divided by 5 is 8, so we have 8 =8, that’s good, that’s the equation it works, all that’s good except I used 0, not allowed to do that. I’m crossing that out. So you can use any math operation you want. You can use add, subtract, multiply, divide, or exponents. Whatever you can to make an equation use some or all of the digits, don’t use 0, don’t use a digit more than once within an equation, and you see how many you can create. Be as creative as you can.
Dean Ballard: All right, so, everybody, all my webinar friends here that’s the end of the instructions with the class.