Covering and Filling: Surface Area and Volume of Rectangular Prisms

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Objective

SWBAT determine whether to calculate surface area or volume to solve a given problem, solve problems involving surface area and volume.

Big Idea

Students apply their knowledge of surface area and volume to solve some problems for a box company.

Do Now

7 minutes

See the Do Now video in my Strategy Folder for more information about how I begin my class.  Often, I create do nows that have problems that connect to the task that students will be working on that day.  For this lesson I strategically ask students to think about the order of multiplying numbers.  I selected these problems to get students to think about what is easiest for them when they are multiply a series of numbers.  This will connect to finding volume and multiplying multiple numbers.

While checking the do now, I ask students to reflect on the relationship between 2 x 5 x 15 and 5 x 15 x 2.  Is one way better than the other?  Students should see that they can re-order multiplication of numbers to make their multiplication easier.  If students don’t mention the commutative property in their reasoning, I will bring it up.  I ask students to share strategies for finding ¼ of 240 and ¾ of 240?  Some students make divide 240 by 4 to get 80 and then multiply 80 by 3.  Others may multiply ¼ x 240.  I selected these problems so students could review finding a fraction of a set.  Some of my students have struggled with this in the past. Students will encounter problems that require these skills in their group work

Surface Area and Volume Review

5 minutes

I ask students to define surface area and volume and brainstorm why someone would have to find surface area or volume.  Students do this independently for a minute.  Then they share out with their partner for a minute.  Then I will call on students to share out their definitions and refine them as a class. I will post our refined definitions on the whiteboard.  This way students can revisit the definitions during their partner work.  I will ask students to share out situations where they would need to find surface area and volume.  The most common mistake is that students confuse surface area and volume.  It is really important that students have a solid understanding of these two concepts and how and when to use them.

For finding volume, many students will come up with V=lxwxh.  I ask if there is another way to find volume of a rectangular prism.  If students don’t come up with it, mention volume of a rectangular prism can also be found by finding the area of the base and multiplying by the height.  This idea of finding the area of the base and then using the height connects to the volume problems in lesson 6.8 when students worked with layers of blocks in boxes.  

Group Expectations

6 minutes

Group Work

32 minutes

During this time I will be moving from group to group to ask questions and make sure students are meeting group expectations.  I have a rubric for students that I use and fill out during group work.  See the Group Work Rubric video in my Strategy Folder for more details.  

To check for understanding I ask groups questions about the task.  My main questions are: “What is the question asking you to do? How do you know?”  This way I could understand what students were thinking at the time and what challenges they were facing.  It also sparked debate among some group members who had conflicting ideas.  Students are engaging with MP1: Make sense of problems and persevere in solving them.

If groups are struggling, I bring them back to the definitions of surface area and volume that we created at the beginning of the lesson.

During this time I am also looking to see what strategies students are using to calculate surface area and volume.  Some students will create nets, others will draw individual sides.  I am looking for students who find a strategy for finding the surface area, like recognizing that there are 3 sets of congruent faces and using that knowledge to more efficiently calculate the surface area. I note students who use one of these strategies and have a couple share their work during the lesson closure.  I anticipate that some students will struggle to draw and label nets or sides to match their box. For volume I anticipate that some students will strategically multiply the whole numbers first before multiplying by a decimal. 

Closure

10 minutes

For closure I ask a student who used knowledge of matching sides to efficiently calculate surface area.  The students share how they knew to calculate surface area and how they did it.  I ask another student who strategically multiplied whole numbers and then decimals to find the volume to share with the class.  These students will come up to the front and put their work under the document camera so that students can see their work while they explain.

I also ask students what challenges they confronted during the work time and how they overcame them.   I also said that students could talk about a misunderstanding they had and how they clarified it.  In one of my classes a student shared that her group struggled at first and found volume to answer the question that asked how much paper it would take to cover the box.  She shared that her group had to work go back and figure out what the question was asking.  This was great because many of the other groups had similar struggles and related to this student’s reflection.  Students seemed relieved to hear that other groups had struggles similar to the struggles of their own group. 

I took this opportunity to praise my students on their perseverance and the strategy of going back and digging into the question.  I gave them a class compliment, telling them that I was proud of their perseverance and persistence in problem solving.  I also take a minute to highlight specific positive behaviors I saw in groups.  For instance, I might share, “I saw that Jerry was stuck on #2 and he made sure he asked his group members to explain what they were thinking and why” or “It was great in Ashley’s group that the group members were discussing what they thought the problem was asking and why.  They didn’t always agree, but they listened to each other and found a way understand each other and figure out what they needed to do.”  I am always messaging to my students that they will come across problems that are challenging and confusing – it is okay to struggle, but you have to figure out a way to keep going!

Rather than give a ticket to go for this lesson, I collect the students’ work to analyze their strategies and their level of success in differentiating between volume and surface area as well as calculating them.

Second Block (optional)

60 minutes

For my students, around 30 minutes was not nearly enough time to get to all of the problems in the packet.  I used a second block on the following day to have students work in the same groups on the same tasks. 

 

The class followed the same structure as the first block: do now, quick review of the task, group work, and a summary of students sharing.  I gave groups a new group work rubric for the day.  If groups successfully completed their work they can work on the “Additional Problems”.

 

At the end of the block I asked students to reflect on challenges that they encountered and how they worked through them as well as actions that occurred in their group that they are proud of.  I also give them the Ticket to Go to complete it independently.  See the Ticket to Go video in my Strategy Folder.