I put the following problems on the board for students to solve in their math journals. I say little about the different layouts of the problems right now. I want students to look for clues about what they need to do, without me actually telling them. I am hoping that they will notice the structure of the problems and find a way to solve them (MP7).
36 + 15 = _____
36 - 15 = _____
15 + _____ = 36
36 - _____ = 15
I give students a few minutes to solve all 4 problems. I circulate around to ask students questions and to try to clarify their thinking.
When I see that most of the students have at least attempted the problems, and I have noted who is having a great deal of difficulty with the problems so I can work with them later as needed, I ask students to turn to the board, put pencils down and to see if we can solve the problems together.
I ask for students to come up and share with us their answers and their solutions to the problems. I am expecting that students will use the number grid or number line, or add the tens and the ones such as 30 + 10 = 40 and 5 + 6 = 11 so 40 + 11 = 51.
When we have reviewed all 4 problems, I ask students if they notice anything about the problems. I am wondering if they will notice that I have put up the same 2 numbers in each problem, but because of the order of numbers (again the structure of the problem - MP7), that the number they add is not always the same.
I tell students that today we will develop a suitcase of ways we might be able to solve problems so that if we have a problem to solve, we can open our suitcase, pull out a strategy and figure the problem out.
I ask students if they have ever packed a suitcase. What kinds of things do you put in a suitcase? (clothes, toys, etc.) Why do you pack these things? (you will need them, you like them...)
Well we are going to pack a suitcase today with all the things that you might need to solve a math addition or subtraction problem. You are going to make some choices about what might help you when you are solving problems. We will put those things in the suitcase. You will keep the suitcase with you and when you are stuck, I want you to open it and look at your choices.
Who can think of some tools first of all that might help you to solve math problems? We will brainstorm a list first and then put these things in our suitcases. I write down the things students suggest such as number grids, number lines, blocks, addition/subtraction houses, calculators, rulers, templates, columns, graph paper, hands to represent counting up or down, etc.
Next I hand each student a pocket folder with a handle on it (the suitcase). I ask them to put their name on the outside of their suitcase. I tell them that they can decorate their own suitcase to be theirs. Next I spread out pictures of the objects students have suggested (hopefully I anticipated most of their suggestions and have a copy for each one - if I missed any, I write the name down on a piece of paper and promise to copy it while they are working.)
I tell students to think about the tools they might need to solve a math problem. I then let students come up table by table and pick up the tools/strategies they think will help them. They do not need to take every tool up on the table, nor do they need to have the same tools as everyone else. The idea is for them to have some reminders about strategies that will help them solve problems. Just as we all pack different things in our suitcase to go on a trip, their math suitcases will look different inside. We can add to our suitcases during the remainder of the year as we add additional strategies to our repertoire.
I tell students that now that they have the suitcase all packed, we are going to take a trip with it. I am going to read some travel math problems. I want them to open their suitcase, take out the tool or tools they can use to solve the problem, set it on their desk and use it to figure out the answer. The idea is for students to choose an appropriate tool for solving the math problem and then use it as they make sense of the problem and persevere in solving it (MP1, MP5). If they have chosen something like base 10 blocks, they may go and get the actual blocks to solve the problem. I remind them that the picture is just a reminder for when they are stuck. When they have used one of the tools to find an answer, they can write it on a piece of blank paper that is in their suitcase already.
1. We are going on a long trip. In the morning we drive for 3 hours. At the end of the day we know that we have gone a total of 11 hours. How many hours did we drive in the afternoon?
2. We stop for lunch at a restaurant by the highway. You order a piece of pizza for 79cents, a drink for 15 cents, and a cookie for 25 cents. How much did you spend in all?
3. Our hotel has 3 sections. There are 18 rooms in the first section, 22 in the second section, and 19 in the third section. How many rooms are there in all?
We work problem by problem to share what strategies and tools we used. I ask students to hold up the tool/strategy they used. I call their attention to the different tools and strategies used for this problem. Finally we share our solutions and students demonstrate how they used the various tools.