Geometry 6 G 2

[elivesey]

Eleanore Livesey says:

June 7, 2012 at 12:38 pm

 I havea question that  relates to 6.G.2 which refers to the volume of a right rectangular prism. It states “Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found  by multiplying the edge lengths of the prism. Apply the formulas v=lwh and V=Bh to find the volume of right rectangular prisms with fractional edge lengths in the context of real-world problems”.

Since it says apply the formulas does that mean that a student might be given the volume and two sides and be asked to find the other side? Also if it is a cube would they then be expected to find the cube root to determine the side given the volume? I would appreeciate hearing your thoughts on this matter as it has been brought to my attention by a sixth grade teacher. The Model Content Frameworks and the Illustrative Mathematics websites do help but we need more examples to clarify the depth of knowledge needed at each level.

[Bill McCallum]

It says “apply the formulas to find volumes”, so no, this does not include applying the formula to find side lengths given the volume. However, the Expressions and Equations domain in Grade 6 gives expectations for solving equations, including

6.EE.7. Solve real-world and mathematical problems by writing and solving equations of the form $x+p=q$  and $px = q$ for cases in which $p$, $q$ and $x$ are all nonnegative rational numbers.

So, for example, you could have a problem about finding the height given the area of the base and the volume that fits with this standard. Cube roots do not appear until Grade 8.

[kathy25]

Hi Bill,

Want to start by telling you how much I appreciate this opportunity to ask questions. A teacher I work with has asked the following,

Delete

“I was looking ahead to the standards covering geometry.  It seems to me the only 3-D shape mentioned in the standards is cube.  The rest of the material regarding 3-D shapes focuses on the attributes not the specific names.  Is this how everyone else reads the CCSS for Geometry?”
I am wondering how to answer since there is a lack of 3d shapes mentioned in the second grade standards. Thanks for your time, Kathy

I guess teachers are struggling with the lack of 3d being mentioned in 2nd grade.

[Bill McCallum]

Well, they are right that there isn’t much about 3-dimensional shapes in Grade 2. The focus in Grade 2 is on achieving mastery of addition and subtraction, so students can move on to multiplication and division in Grade 3. To achieve this you have to make room in the curriculum, which means giving up something else.

[nathan118]

Bill, love your site! Question about your first response regarding 6.G.2. You said a student could be asked to find a height given a base and volume (then solve the equation). Wouldn’t this be similar to Eleanore’s example of finding a missing side given volume and 2 sides? Or are you simply giving an example of an extension of the standard…something that’s not actually IN the standard? (And Eleanore’s initial question is also an extension of the standard then.)

 

Thanks for the clarification!

[Bill McCallum]

I was thinking of both of these as being linked to 6.EE.7, since you could use the formula to set up an equation of the form $px=q$ for both my example and Eleanore’s example. I thought mine was a bit simpler because in Eleanore’s case you would get your $p$ as the product of two of the side lengths. But both fit with 6.EE.7, given that you already know the formulas from 6.G.2

[carlymorales]

A group of us working on writing curriculum noticed that the standards have the formula is written v=bh noting that the B is not capitalized. We wondered why it isn’t a B?

[Anonymous]

Please see this post: http://commoncoretools.me/2013/01/28/to-b-or-not-to-b/#more-1634

[Author]

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