Using the model of the Pink Rectangular Prism, today's entry ticket is a quick check on student understanding of how to determine the volume of a rectangular prism.
How many cubic units?
This independent work is discussed, as a class, and I collect the different ways students determine the answer. It is important to "notice" that there are more than one way to reach the answer.
Using the Blue Rectangular Prism, I first guide students through a connection between what we see, and the steps needed to make sure we have all of the information to determine volume. Then we apply these steps to solve a problem. I provide guided notes, colored coded with step-by-step instructions and examples so that students have notes to refer back to in their Journals.
The problem is set in a real world context of soccer ball sales, because I know that a lot of my students love soccer. We work on the sample problem together. This is not direct instruction, this is an interactive dialogue where I encourage students to try and solve using what they've learned and their results and to feel safe in sharing their thinking. We do the problem step-by-step.
Step 1: Count the number of inch cubes in the first layer of the figure. There are _____ inch cubes in the first layer.
Step 2: Count the number of layers. There are _____ layers.
Step 3: Add the cubes in each layer to find the total number of cubes. ___ + ___ + ___ = ___
Step 4: The volume of the figure is _____ cubic inches.
Some of my students pick up on this quickly, and multiply instead of add, which is a very good thing!
Using MP 3, students think-pair-share to solve the following problem.
Robbie wants to measure the volume of this figure. He says that there are 4 cubic units in the bottom layer of the figure. Since there are 2 layers in the figure, he thinks he can add 4 + 4 to find the total volume of the figure. Is Robbie correct? If he's not correct, then explain how you can find the volume.
Here, I really want my students to: refine mathematical communication skills through participation in mathematical discussions involving questions like “How did you get that?” and “Why is that true?”, explain their thinking to others, and respond to others’ thinking.
Partnerships are made with students of like ability today. Sometimes I use "table partners"--these are groupings that are Low-Medium, Medium-High typically. Depending on what we're doing I have students get into different groups. I support ESL students (and all students) by realia, a word wall, and an L1 English student partner.
After pairs have shared their answers together, I use cold calling to ask partners how they got their answer. I allow them to utilize technology to show their thinking; they can choose from using the whiteboard or SmartBoard to show (and teach) their classmates the way they solved the problem. This is very important because the students presenting are developing their mathematical communication skills, other students are exposed to a variety of ways to make meaning, and everyone is practicing respect of others' viewpoints and differences.