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Bobs Math

Bobs Math

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And now for something completely different...

As anyone who reads my blog regularly, I often put forward items that come from the classroom where Valorie works.

Well, today's no different.

For the season break, I thought I'd share one of their homework problem, also known as "The Christmas Tree Problem".

For context, this is a split class of 5th and 6th graders, they're presented with a challenging curriculum that diverges from many of the traditional 5th and 6th grade topics.  One aspect of that curriculum is known as "Bob's Math" (for the teacher, Bob Whittemore).  He covers stuff that's usually far beyond the normal course of study for 5th and 6th graders, some of them are high school subjects.

Just before the winter break, Bob traditionally assigns this homework problem...

Find the volume and surface area of the following Christmas Tree:

One pyramid with L=W=2’ S=2’

 

A stick with no dimension.

 

An equilateral triangular prism with L=8’ and W=2’.

A cylinder where r=1’ and w=2’ is cut out

An equilateral triangular prism with L=1’ and W=2’ is cut out

Two cones with H=1’, r=.5’  Find the slope or slant height

An equilateral triangular prism with L=9’ and W=2’.

Two cylinders where r=1.5’ and w=2’ are cutout.

An equilateral triangular prism with L=1.5’ and W=2’ is cut out.

Two cones with H=1’, r=.5’ Find the slope or slant height

 

A triangular prism with L=10’ and W=2’.

A cylinder where r=2’ and w=2’

Two cylinders where r=1.5’ and w=2’ are cut out

An equilateral triangular prism with L=1.5’ and W=2’ is cut out

Two cones with H=1’, r=.5’ Find the slope or slant height

 

A base consisting of a single rectangular prism with L=W=2’ and H=3’

 

 

Terms: L=Length     W=Width     H=Height     S = Slant Height    R=Radius

 

On this note, I'm off for vacation.  I'll be back late December, but until then, I don't know how spotty my internet access will be.  I'll see what I can do to keep the blog moving forward given the moderation (which I can't remove unfortunately), but ymmv.

 

  • Seems like a great place to use multiple-integral calculus(sorry if that is the wrong term, hope you know what I mean), if I only could remember how :)

    Have a nice vacation, Larry!
  • I had nothing better to do, so here's what I think the answers are:

    Surface area:
    469.795
    Volume:
    135.329

    (three decimal places). Can anyone confirm that? I used a quick python script, and may have forgotten something...

    I've assumed that the rectangle where the base meets the lowest triangle is not included as part of the surface area.

    If I'm right, hooray! What's the age of children I am matching here? :D At least it was more challenging than those pathetic SAT tests ;)
  • > A stick with no dimension.

    Bob fails. If the stick had no dimension it would be a point. A stick has one dimension and has length, but has no volume.

    (If Bob were a student instead of a teacher, the number of marks Bob would lose for that would not result in failure.)
  • Problems like this one are a great way to make sure kids will hate math when they grow up.
  • I got something a bit different than Not Bob:

    SA: 496.998 (ft^2)
    V: 134.905 (ft^3)

    Nice to see we're in the same ballpark for Volume, anyway. Did you handle the SA by subtracting the area on the triangles that was cut out, and adding the area that was added internally?

  • I got the same volume as Not Bob, however I got 473.795 for the surface area. Did you include the bottom square on the pyramid?
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