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Lessons

Standards in this Lesson

Common Core Math Standards
6.EE.B.6

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

6.G.A.4

Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

7.G.B.6

Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

CSTA Standards
2-AP-11

Create clearly named variables that represent different data types and perform operations on their values.

2-AP-17

Systematically test and refine programs using a range of test cases

2-AP-19

Document programs in order to make them easier to follow, test, and debug.

Oklahoma Standards
OK.7.AP.A.01

Select and modify an existing algorithm in natural language or pseudocode to solve complex problems.

OK.7.GM.1.1

Using a variety of tools and strategies, develop the concept that surface area of a rectangular prism with rational-valued edge lengths can be found by wrapping the figure with samesized square units without gaps or overlap. Use appropriate measurements such as cm^2

OK.G.3D.1.1

Solve real-world and mathematical problems using the surface area and volume of prisms, cylinders, pyramids, cones, spheres, and composites of these figures. Use nets, measuring devices, or formulas as appropriate.

OK.L1.AP.A.01

Create a prototype that uses algorithms (e.g., searching, sorting, finding shortest distance) to provide a possible solution for a real-world problem.

OK.PA.GM.2.1

Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate units of measure, such as square centimeters.

Textbook Alignment

IM Algebra 1
IM.Alg1.2.3

Writing Equations to Model Relationships (Part 2)

IM.Alg1.2.2

Writing Equations to Model Relationships (Part 1)

IM 7 Math™
IM.7.7.14

Surface Area of Right Prisms

IM 6 Math™
IM.6.1.15

More Nets, More Surface Area

IM.6.1.14

Nets and Surface Area

IM.6.1.13

Polyhedra

IM.6.1.12

What is Surface Area?

Connected Math
CMP.7.7

Filling and Wrapping: Three Dimensional Measurement

CMP.6.4

Covering and Surrounding: Two Dimensional Measurement
Practices in this Lesson

MP.4

Model with mathematics

(Also available in WeScheme)

Students define the shapes used to build a rectangular prism, print them, cut them out, and build the rectangular prism. Then they use their model to calculate the surface area.

Lesson Goals

Students will be able to:

  • Demonstrate understanding of surface area and use that understanding to calculate surface area of rectangular prisms

Student-facing Goals

  • I can explain what surface area is.

  • I can use my understanding of surface area to calculate the surface area of any rectangular prism.

Materials

Preparation

  • Students will be generating files that need to be printed. If their computers are not connected to a printer, make a plan for how printing will happen.

  • Make sure all materials have been gathered.

  • Decide how students will be grouped in pairs.

Key Points For The Facilitator

  • This lesson focuses on developing students' understanding of Surface Area of prisms, such that they can build their own formulas. Instructors are encouraged not to reference any pre-defined formulas during the exploration.
Glossary
face

the flat surfaces on the outside of a solid figure

rectangular prism

a solid figure which has 6 faces, all of which are rectangular

surface area

the sum of the areas of all of the faces of a solid figure (polyhedron) or the total area that the surface of the object occupies

🔗Surface Area

Overview

Students build on their experience with writing code to define shapes. They will define shapes for all of the faces of a rectangular prism, print them, cut them out, and build the rectangular prism. Then they will use their model to calculate the surface area and write code to do the same.

Launch

Students should open the Prism Starter File (Pyret) in their browser and click run.

Click run and type prism into the Interactions Area to see an image of a rectangular prism. Notice that the faces and dimensions (Length, Width, and Height) are labeled.

Faces are the shapes on the outside of the figure. Edges are the line segments where the faces of solid figures meet in each of the three dimensions.

  • How would you describe the faces of this prism?

  • Skip down to the code on line 22. It reads lst = [list: front, ] , which defines lst to be a list of values. This list will include all of the faces of the prism, but right now it only includes front. Add the names of each of the remaining faces to the list. (Order doesn’t matter.)

  • Once you complete your list, go back up to line 20 and look at the definition for front. Type front into the interactions area. What do you get?

  • Just as front has been defined to draw a rectangle whose dimensions are width and height, you will need to write definitions for each of the other faces of the prism the you put on your list. Start adding definitions on line 21 and add a line for each definition so that all of the faces are defined between front and lst . Click run and test each of them in the interactions area to make sure that they match the prism you started with.

Facilitation Note The sample definition was written to make the image of an outlined rectangle with a black and white printer in mind. If you have access to a color printer in your classroom, you may want students to change the code of front to better match what they see in the image of prism and code the remaining faces with solid rectangles to match the image they are looking at. If you do not have access to a color printer, but think that colors would support your students, you can have them color the rectangles on the printout before cutting and assembling the prism.

  • When you’ve finished, click Run and type print-imgs(lst). What do you Notice? What do you Wonder?

  • Do you have enough shapes to cover all of the faces of the prism?

  • Read the comments in the file to learn how to customize and print the faces to build your prism.

Investigate

Have students cut out and tape together the images they defined to form a 3-dimensional paper model of a rectangular prism.

Students will then use their models to calculate the surface area.

Supporting students with learning variations

  • Labeling the shapes with face names and/or area before taping them together may help some students.

  • Printing two copies of the file (one to cut and one to write on) might best support other students.

  • Once you’ve built your prism, use it to help you calculate the surface area of the figure. Then, turn to task 2 in the Prism Starter File and define surface area to calculate the area of the prism using width, length and height.

Synthesize

Have students share the codes they wrote to define surface area. Did students all write the code the same way? Can anyone see other ways that they could have written the code?

  • How did building the prism help you to understand surface area?

  • How did writing the code for surface area help you to understand surface area?

These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, and 1738598). CCbadge Bootstrap by the Bootstrap Community is licensed under a Creative Commons 4.0 Unported License. This license does not grant permission to run training or professional development. Offering training or professional development with materials substantially derived from Bootstrap must be approved in writing by a Bootstrap Director. Permissions beyond the scope of this license, such as to run training, may be available by contacting contact@BootstrapWorld.org.