To open today's lesson, I showed a quick bear video to inspire interest!
I then explained: Today, we are going to solve bear word problems involving the 8 major bear species in the world! I pointed to the Bear Pictures with Labels on the board (created using this document: Bear Pictures). To provide students with problem solving opportunities, some weights are provided while other weights are unknown.
Reasoning for Teaching Multiple Strategies
During this Addition and Subtraction Unit, I truly wanted to focus on Math Practice 2: Reason abstractly and quantitatively. I knew that if students learned multiple strategies of adding and subtracting numbers, I wouldn’t only be providing them with multiple pathways to learning, but I would also be encouraging students to engage in “quantitative reasoning” by “making sense of quantities and their relationships in problem situations.” By teaching students how to use a variety of strategies, such as using number lines, bar diagrams, decomposing, compensating, transformation, and subtracting from nines, I hoped students would begin to see numbers as units and quantities that can be computed with flexibility.
Goal & Poster Introduction
To begin this lesson, I introduced students to the goal: I can solve and represent multi-digit addition and subtraction word problems. Showing the Three Problem Solving Structures poster I explained: Today, we will begin by solving problems about bears. We will be looking at three different problem solving structures: Part-Part-Whole Problems (Missing Whole), Part-Part-Whole (Missing Part), and Comparison Problems (One part Less or More).
Modeling Part-Part-Whole Problems (Missing Whole)
I explained and modeled Bear Problem 1 and asked students to follow my steps on their white boards: Student White Board (Problem 1). Look at this first problem. I know that this is a part-part-whole problem because we are asked to find the combined weight of two parts (or two bears). Whenever I have a part-part-whole problem, I always draw one box and split into two parts. Do you see how we already know the weights of both parts? One part, the black bear, is 650 pounds. The other part, the brown bear, is 1,500 pounds. Notice how the whole weight is unknown. Let's represent the unknown whole with a question mark. What do you think we need to do to find the unknown whole? Students said, "Add the parts together!" Perfect! Let's use the standard algorithm to find the sum of the parts.
We then followed the same process: modeling altogether, talking, and solving Bear Problem 2. Only this time, I released more responsibility to students by providing students with time to work ahead:Student White Board (Problem 2).
Modeling Part-Part-Whole Problems (Missing Part)
We then moved on to Bear Problem 3. I explained: Now, let's go on to part-part-whole problems that have an unknown part. I modeled the problem on the board while students solved the problem on their white boards: Student White Board (Problem 3). Students caught on quickly and were eager to go on to the next problem: Bear Problem 4 with less teacher guidance. Each time we found the weight of a bear, students continually reminded me to Label Bear Weights. It became sort of like a puzzle or game! Here's an example of a student's board: Student White Board (Problem 4).
Modeling Comparison Problems (One Part Less or More)
Finally, I explained comparison problems: Comparison problems are problems that have two or more parts that are compared. For example, one part is less or more than the other part. In this first example (Bear Problem 5), a panda bear's weight is being compared to a polar bear's weight. With comparison problems, I always draw two boxes, with one box bigger than the other. The biggest box always represents the larger part. Let's reared this problem and figure out which part (or bear) weighs the most. Again, we completed this problem together, students repented their thinking on their boards: Student White Board (Problem 5).
With the last problem, Bear Problem 6., I provided even less support, hoping to gradually release more responsibility to students so they could soon successfully complete problems without any teacher guidance: Student White Board (Problem 6).
At this time, I knew students were ready to try representing and solving multi-digit word problems with partners.
Assigning partners is always quick and easy as I already have students strategically placed in groups of 4-5 students throughout the room (based on abilities, behavior, communication skills, etc.). I simply divided these larger groups into smaller groups of 2-3 students. During partner work, sometimes students choose to work alone, but they frequently check answers with each other.
I passed out the Student Zoo Problems and modeled how to cut and paste the problems in student math journals: Pasting Problems in Journal. Next, I passed out an Animal Weight Student Resource to provide students with pictures of each animal and some known weights.
Right to Work!
As soon as students were ready, they eagerly began solving the first problem: Students Representing Problem 1. I loved watching these two students make sense of the problem, draw a bar diagram, label their work, and solve the problem using the standard algorithm. With each problem, students referred back to the Animal Weight Student Resource. to find the weights of animals. During this time, I also encourage students to use problem solving structures vocabulary: part-part-whole, unknown whole, comparison diagram, missing part, etc.
Here are Students Working Together to Solve Problem 2. This problem was a bit trickier as there are three "parts" instead of two "parts." I continued to ask guiding questions such as, How many parts are there? Do you know the whole? Is this the answer? What is the problem asking?
After solving the part-part-whole problems with a missing whole (problems 1 & 2) as well as part-part-whole problems with a missing part (problems 3 & 4), students then moved on to comparison questions (problems 5 & 6).
I supported many students as they made the transition between problem solving structures: Representing a Comparison Problem.