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Wedding Cake Ribbon

47
skips
53
questions

Act One

• Robert Kaplinsky

December 06, 2012

How much purple ribbon will you need to make a wedding cake exactly like this one?

• 1.

How much purple ribbon will you need to make a wedding cake exactly like this one?

• 2.

What unit of measurement will we use?

• 3.

What is a guess that is too low?

• 4.

What is a guess that is too high?

• 5.

• 6.

What information would be useful in figuring this out?

• 7.

Do the measurements we have for our cake dimensions seem reasonable?

Act Two

• Teacher note
There is a 3 to 4 year gap in the Common Core State Standards between when students are expected to learn perimeter (Grades 3 and 4) and circumference (Grade 7). As such, you may need to modify the question to make all cake layers squares or other polygons.
There are two overhead views of the cake: one with a scale and the other without. The dimensions of each layer of the overhead view of the cake are:
Bottom circular layer = 7.5â€³ diameter
Middle square layer = 5â€³ side length
Top circular layer = 4.5â€³ diameter
As the cake dimensions are listed in inches, it is probably easiest if you guide your students to list their answers in inches as well.
My expectation is that if you give the students the overhead view without scale, they will take measurements based off the drawing without considering whether 7.5 inches is a reasonable size for a wedding cake and come up with an answer of approximately 57.7 inches (7.5pi inches + 20 inches + 4.5pi inches).
This is a good time to ask them â€œDo the measurements we have for our cake dimensions seem reasonable?â€ Once they determine that it is not reasonable, you can provide them with the scale of 1â€³ = 3â€³. That gives us the actual dimensions of each layer of the overhead view of the cake:
Bottom circular layer = 22.5â€³ diameter
Middle square layer = 15â€³ side length
Top circular layer = 13.5â€³ diameter
With these new dimensions, you get the actual answer of approximately 173.1 inches (22.5pi inches + 60 inches + 13.5pi inches).
I am also fine with answers that are larger than the ones listed if they can separate out how much is extra and articulate their reasoning by saying something like:
â€œWe will need the ribbon to overlap a little bit.â€
â€œWe need some extra ribbon in case we make a mistake.â€
• ImageOverhead view of cake without scale
• ImageOverhead view of cake with scale

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