Designing Boxes

15 teachers like this lesson
Print Lesson


SWBAT: • Define surface area and volume. • Calculate surface area and volume of rectangular prisms and cubes. • Design boxes to meet certain requirements.

Big Idea

If boxes have the same volume do they also have the same surface area? Students explore this question while designing boxes.

Do Now

7 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to review volume and surface area.  A common mistake is for students to confuse surface area and volume.  I walk around and see how students are progressing.

I ask students what strategies they are thinking about to answer the questions.  I call on students to share what they think and why.  I push students to use precise language, including the correct units for each measurement.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others and MP6: Attend to precision.


3 minutes

I call on students to read over the definitions and fill in the blanks.  It is crucial that students understand the difference between these two terms.


10 minutes

I read over the problem.  Students participate in a Think Write Pair Share.  If students struggle, I encourage them to reference our work so far in this lesson.  I walk around and monitor student progress.  Some students may struggle with expression 2 and 3.  Expression 2 represents the surface area of Box C since 2 ½ times 2 ½ is 6 ¼ and there are 6 identical faces.  Expression 3 represents the volume of Box A, since you would multiply 2 x 3 x 6.5 or 6 x 6 ½.  Students are engaging in MP2: Reason abstractly and quantitatively and MP6: Attend to precision.

I call on 2-3 students to come up and show and explain their work.  

Designing Boxes

20 minutes


  • Before this lesson, I use the ticket to gos from the previous lesson to Create Homogeneous Groups.
  • I give each group a set of 24 cubes.
  • I give each group a Group Work Rubric.
  • I Post a Key for these problems around the room.

I read over the task and introduce the blocks.  We go over directions and expectations.  My goal is that students complete the table and answer the “Analyzing Your Designs” questions.  If groups struggle to draw the boxes on the isometric paper, I tell them to come back to it after their finish the questions. 

 As students work I walk around to monitor student progress and behavior.  Students are engaging in MP5: Use appropriate tools strategically and MP6: Attend to precision.

 If students are struggling, I may ask them one or more of the following questions:

  • What do you know? What are you trying to figure out?
  • What do you notice about the dimensions of each box?
  • What strategies do you have for finding surface area?
  • Does your answer make sense?
  • Which design do you think is best?  Why?

For the table, I created an extra row in the table that students will not be able to fill in (there are only 6 different boxes).  I want students to double check to make sure they have found all of the boxes, rather than just stopping when they fill the table.  A common mistake is that students turn the same box onto its side and call it a new design.  If that occurs, I ask them to compare this box with the others they already have. 

When students complete their work, they raise their hands.  I quickly scan their work.  If they are on track, I send them to check with the key.  If there are problems, I tell students what they need to revise.  If students successfully complete a practice set they can move onto the next set.  If they complete the problems they can move onto the challenge problems. 

Closure and Ticket to Go

10 minutes

For the Closure, I have students return to the “Analyzing Your Designs” questions.  I ask students to share their thinking about which box would use the least amount of cardboard.  I ask, “How does the box you picked compare to the other boxes?”  I want students to realize that this box is more like a cube than the other designs, and it has a smaller surface area.  I ask, “Why do you think the company wants to create a box using the least amount of cardboard?”  I want students to realize all the materials that the company uses costs money and that a company always wants to minimize their costs. Students are engaged in MP6: Attend to precision and MP7: Look for and make use of repeated reasoning. 

If I have time I ask the question in part (d).  I want students to realize that there are only two rectangular boxes that fit 26 blocks, and they have larger surface areas.

I pass out the Ticket to Go and the Homework.