Most of my students do not live in apartments, as we live in a rural area. Many live in mobile homes/trailers. For this lesson, I need to increase their frame of reference. I think it is also a life lesson. My sincere hope is that one day they explore the rest of the world, and learn new things at every turn. So, I want to show students here a few different styles of homes; this also supports the idea that students respect our human differences.
I show students a picture of my townhouse. Then I introduce the idea of being an architect for the next few minutes. This incorporates a career connection as well. (I also use a similar strategy in my lessons: Modeling an Office Building, & Modeling a Vacation Home.) My focus here is not to design the dream house, though that could very well be an extension of this; the students would love it! I've also included a rubric for that task if you choose to use it. I just have them fill out the questionnaire at this point; I expect the square footage to not be accurate, and that it will need to be revised. My focus is to entice my students and draw them into this task of modeling an apartment building in the next step.
(a) Uses MP4, and is a DOK 1. Here students draw lines on a model to help show its volume. First, I remind students that these are cubes. Since they are cubes, all sides are equal.
(b) Uses MP4, and is a DOK 1. Here students determine the number of cubes in a model. Students can count the cubes in the model. I remind my students here to count the cubes that aren't visible as well. Today, students experiment with representing problem situations by drawing pictures, using objects, and creating an equation. Students need opportunities to connect the different representations and explain the connections. Students should evaluate their results in the context of the situation and whether the results make sense too. They also evaluate the utility of models to determine which models are most useful and efficient to solve problems.
(c) Uses MP2, and is a DOK 1. Here students find the volume of a model using a formula. We discuss how to use the volume formula now. In (C), students write simple expressions that record calculations with numbers.
(d) Uses MP 6, and is a DOK 2. Here students determine the difference in the volumes of 2 models that involve the conversion of measurements. Here, it's important for students to note that this problem could be solved a few different ways. I suggest to students that they convert yards to feet to help solve the problem. I'm looking for students to refine their mathematical language by using clear and precise language in their discussions with others and in their own reasoning. Students use appropriate terminology when referring to expressions. They are careful about specifying units of measure.
In the Paired Practice, I'm looking for students to: make two correct drawings, correctly identify the number of cubes, multiply the correct numbers to find the volume of cubes, and accurately calculate the difference. My students are accustomed to filling in worksheets as review practice, and now as answering word problems. (I am pretty anti-worksheet, but when reviewing computation skills, they're very useful.)
It's my job to change things up, and keep it "interesting". So, for this practice, I wanted to provide a simple graphic organizer for students to fill in. In this graphic organizer it's clear to students that they will do the identical task for each model, & then compare both models. My students, especially this year, need very simple, concrete expectations. Using a rubric consistently helps to let then know what to expect, and how they will be evaluated. I typically show my students the rubric beforehand, which is something that might not be a common practice with other teachers who use rubrics in their classrooms. I feel that this is a much more effective way to teach my particular students, and it might work well for you too.
At the end of the independent practice, I have students compare the models, the most important concept of this lesson, to see which model has the greatest volume. Provided students have done the multiplication steps correctly, this task is quite easy. Here, I need students to write out in words their thinking, instead of simply writing down a final answer. Being able to read their writing makes the concept more concrete for them, but it also let's me determine where remediation may need to occur.