Today I begin by handing out a sheet with the same math problem on the front and the back. The problem is 71 - 43. I ask students to solve the problem 2 different ways. I do not mention that the problem is the same on both sides. It is ok if they do notice that it is the same problem because I am looking more for the strategies they can employ (MP1 and MP4) I am looking to see if students notice that the problem was the same each time. I also want to look at the types of strategies students are comfortable using.
I ask for several students to come up and demonstrate their strategies for solving the problem. I ask them to explain their thinking. It is important to listen to how students are solving problems because it allows you insight into their understandings. Next I ask if there is anyone who solved the problem a different way. I invite them to come up and show us their strategies as well. I expect students will use the number grid, tens and ones (which, because they are not used to regrouping may cause them to get the answer 32), number line, drawing base ten blocks or tens frames.
Next I present a page with the same addition problem on the front and back: 74 + 68.
I ask students to solve this problem 2 different ways as well. I now ask them to turn and share their strategies with someone at their table.
I ask the students to share out anything they noticed when they talked to a partner about the strategies they or their partner used. They might note that they used the same strategies, or that they got the same answers, etc.
I tell students that we have our math suitcases that we have used this year and they have been helpful for reminding us what ways we might solve a problem, but now we need to make something more pocket sized that will help us. The suitcases are a bit cumbersome and I want them to have an easy and ready reference at hand to help them think of strategies.
Today we will take a time to make a booklet that includes all our favorite strategies. These will be our reminders when we want to solve a problem. The booklets will be small so that they are easy to take with us.
I invite students to come to the rug. I use chart paper and ask students to brainstorm the many ways they might solve a math problem. I am asking students to brainstorm here rather than look in their suitcases because I want to see which strategies they can recall on their own. I am looking for an awareness of a variety of math tools (MP5) that students know they can rely on to help them solve difficult problems. I break the ideas into addition, subtraction, multiplication/repeated addition, graphing and other. I record their ideas.
I give each person a small booklet booklet.docx (see sample that is intended to be folded, you may want to add additional pages) that contains only one 2 digit addition or subtraction math problem on each page. There are spaces on each page to solve the problem in any way that the student chooses, but they must use 2 different strategies for each problem. I ask them to solve each problem in 2 ways so they can have a reference material for when they solve a problem. I ask them to label the ways they have solved the problem by referring to the brainstorming chart we just made and to then check off the easiest way they found to solve each problem.
I let students have about 20 minutes to solve the problems and complete the booklets. They are welcome to decorate the outside of the booklets when they finish the problems.
I put a word problem on the Smart Board and ask students to read the problem and then use their booklets to find a way to solve the problem and to find the answer.
The problem I post is: "I leave home at 8 o'clock. I walk 3 miles to the library to pay my fines for overdue books. I owe 89 cents for the first book, 76 cents for the second book, and 48 cents for the third book. How much do I owe in all?
For students who quickly solve the first problem I add, If I have $3.00 to pay my fines, can I buy a popsicle for 50 cents on the way home?"
If there is time we will share our solutions to the problem. If not, we will pick it up again at the beginning of next lesson.