6.G.4 - About the Math, Learning Targets, and Increasing Rigor

Full Standard

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.

Learning Targets (I can)

• Represent three-dimensional shapes with two-dimensional nets.
• Justify why a net represents a three-dimensional figure.
• Find the surface area of three-dimensional shapes using nets.

About the Math

Students learning Grade 6 mathematics standards build on their work with area in the previous grades by reasoning about relationships among shapes to determine area, surface area, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, student discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areas of polygons and surface area they can determine. They reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths. They prepare for work on scale drawings and constructions in Grade 7 mathematics by drawing polygons in the coordinate plane. Essential vocabulary for this standard includes: area, length, net, polygon, quadrilateral, rectangle, right triangle, surface area, three dimensional figure, triangle, and width. Visit the online dictionary Links to an external site. or visual math dictionary Links to an external site. for vocabulary support.

Progression of Standard within Grade 6 (5 AGL)

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

TASKS

These tasks can be used with small group or whole group instruction.

• Look at the net (to the right). How could you add one more square to this net to create a cube? Explain your thinking.
• Find the length, width, and height of a rectangular prism that has a surface area of more than 200 square inches but less than 300 square inches.
• I wrapped a rectangular box in a piece of wrapping paper that was 11 inches by 17 inches. I had no paper left over but I did have some minor overlaps. What might have been the dimensions of my box?
• What is the relationship between area of a rectangle and the surface area of a rectangular prism? What is the relationship between area of a triangle and the surface area of a triangular prism and/or a triangular pyramid?
• Bring in empty food containers that look similar in size. Ask students to predict which container will have the largest/smallest surface area. Calculate the actual surface area.
• Google and display a picture of the glass pyramid at the Louvre in Paris. This is a modern example of a pyramid in today's world. The length of one base side length is 35 meters. The height of each triangular face is 27.8 meters. Sketch and and then calculate the surface area of this glass pyramid (3171 square meters) .If window washers can clean 243.25 square meters per day, how many days does it take to clean all the glass surface area of the pyramid. (Remember to only use the glass surface area of 1946 ÷ 243.25 = 8 days.)

SLIDE-BASED TASKS 

  These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Additional Tasks 

  These links provide instructional ideas connected to this standard. [NOTE: NCTM membership required for access to Illuminations lessons.] 

• Nets for Pyramids and Prisms (Links to an external site.) ( Links to an external site.Illustrative Math) 
• Nets (HCPSS Lesson Collection)
• Surface Area Download Surface Area (HCPSS Lesson Collection)
• Building a Box Links to an external site. (NCTM Illuminations Lesson)
• Fishing for the Best Prism Links to an external site.(NCTM Illuminations Lesson)
• Geometric Solids and their Properties Links to an external site. (NCTM Illuminations Lesson)
• Junior Architects Links to an external site. (NCTM Illuminations Lesson)

Tasks From Print Resources

  These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.

Print Resources

Book Thumbnail	Book Title	Grade	Pages
	Teaching Student-Centered Mathematics	6-8	293 (Net Challenges, Activity 13.19)
	Teaching Student-Centered Mathematics	5-8	224 (Viewpoints, Activity 7.29) 225 (Perspective Drawings, Activity 7.30)
	Groundworks: Measurement	4   5	112-119 (Boxed In)   80-87 (Surface Area)
	Hands-On Standards Common Core	6	110-117 (Lesson 6 & 7)

Centers

  These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

• Cube Nets Links to an external site. (printable resource) 
• How Many Feet of Lights Do I Need? Links to an external site. (Yummymath print resource)

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

  These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

• Nets of 3D Shapes Links to an external site.
• Surface Area Links to an external site.
• Find Surface Area of a Rectangular Prism Using a Net Links to an external site.
• Find Surface Area of a Rectangular Prism Using Dimensions Links to an external site.

Learning Targets

• Represent three-dimensional shapes with two-dimensional nets.
• Justify why a net represents a three-dimensional figure.
• Find the surface area of three-dimensional shapes using nets.

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading. 

Rubric for Tasks Links to an external site.