STANDARDS

CCSS: 6.G.A.4, MP4, MP6, MP7

TEKS: 7.9D

The Perfect Wrap

Get expert tips on how to use math to wrap presents—no matter the shape!

R_Koopmans/Getty Images (Poorly Wrapped Present); Shutterstock.com (All Other Images)

Tis the season to wrap presents . . . which is harder than it looks! Cut the paper too short and you leave a gap. Cut it too long and you have bulk to fold over. Is there a way to optimize the amount of paper you use?

Making a geometric net to wrap a present would be the most paper-efficient way in theory. “This means it’ll exactly cover all the faces and not have any overlap anywhere,” says Katie Steckles, a mathematician based in the United Kingdom. But cutting paper from a wrapping paper roll often leaves some waste, and cutting out nets would create even more scraps. “Nets make for very strange shapes, and if you’re trying to use a roll to wrap a pile of presents, you’d need to find a way to fit all the nets onto the sheet without wasting too much space!” Steckles says.

Read on to learn more about Steckles’s mathematical methods for wrapping gifts with just the right amount of paper, leaving minimal scraps. Whether you’re wrapping a rectangular prism or a cylinder, her tips can help you tackle any present!

Have you ever wrapped a present? It’s harder than it looks! If you cut the wrapping paper too short, you’ll leave a gap. But if you cut it too long, you have a lot of extra to fold over. Is there any way to use the perfect amount?

In theory, you could make a geometric net of wrapping paper. A net is a flattened version of a cube or other three-dimensional shape. A net would exactly cover all the faces of a present without any overlap, says Katie Steckles. She’s a mathematician based in the United Kingdom.

Cutting wrapping paper from a roll often leaves some waste. Cutting out nets would create even more scraps. “Nets make for very strange shapes,” says Steckles. “If you’re trying to use a roll of paper to wrap a pile of presents, you need to find a way to fit all the nets without wasting too much space.”

Luckily, Steckles has some mathematical tricks for wrapping gifts with just the right amount of paper. She can wrap cubes, rectangular prisms, or cylinders—and leave very few scraps. Her tips can help you tackle any present. Read on to learn more!

Here are three shapes and Steckles’s recommendation for how to wrap presents. Use paper, a ruler, and a pencil to draw nets for these gifts. Record your work and answers on our answer sheet.

Here are three shapes and Steckles’s recommendation for how to wrap presents. Use paper, a ruler, and a pencil to draw nets for these gifts. Record your work and answers on our answer sheet.

TRIANGULAR PRISMS

A: Must wrap around the long faces and base
B: The length of the base plus the heights of both triangular faces

A.  Make a net for this chocolate bar that’s a regular triangular prism with the dimensions below.

A.  Make a net for this chocolate bar that’s a regular triangular prism with the dimensions below.

Triangle height = 0.87 in.

Length = 6 in.

Base width = 1 in.

Triangle height = 0.87 in.

Length = 6 in.

Base width = 1 in.

B. How long and wide would your paper need to be to wrap it using Steckles’s method?

B. How long and wide would your paper need to be to wrap it using Steckles’s method?

C. Draw a rectangle showing the ideal length and width of the wrapping paper around your net.

C. Draw a rectangle showing the ideal length and width of the wrapping paper around your net.

RECTANGULAR PRISMS

A: Length of the base plus half the height of each short faceMust wrap around the long faces and base
B: Must wrap around the long faces and bases

A. Make a net for this present that is a rectangular prism with the dimensions below.

A. Make a net for this present that is a rectangular prism with the dimensions below.

Width = 2.5 in.

Length = 4 in.

Height = 1 in.

Width = 2.5 in.

Length = 4 in.

Height = 1 in.

B. How long and wide would your paper need to be to wrap it using Steckles’s method?

B. How long and wide would your paper need to be to wrap it using Steckles’s method?

C. Draw a rectangle showing the ideal length and width of the wrapping paper around your net.

C. Draw a rectangle showing the ideal length and width of the wrapping paper around your net.

CYLINDERS

A: Must wrap around the long face
B: The height of the cylinder plus a little more than half the diameter of each circular base

A. Make a net for this water bottle that comes in a cylindrical tube with the dimensions below. (Hint: Circumference = 3.14 × diameter)

A. Make a net for this water bottle that comes in a cylindrical tube with the dimensions below. (Hint: Circumference = 3.14 × diameter)

Height = 7 in.

Diameter = 2 in.

Height = 7 in.

Diameter = 2 in.

B. How long and wide would your paper need to be to wrap it using Steckles’s method?

B. How long and wide would your paper need to be to wrap it using Steckles’s method?

C. Draw a rectangle showing the ideal length and width of the wrapping paper around your net.

C. Draw a rectangle showing the ideal length and width of the wrapping paper around your net.

videos (2)
videos (2)
Skills Sheets (6)
Skills Sheets (6)
Skills Sheets (6)
Skills Sheets (6)
Skills Sheets (6)
Skills Sheets (6)
Lesson Plan (1)
Article (1)
Text-to-Speech