6th grade CCSS (6.G.A.1 - 6.G.A4) Perimeter Area Volume

Solve real-world and mathematical problems involving area, surface area, and volume.

CCSS.MATH.CONTENT.6.G.A.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

CCSS.MATH.CONTENT.6.G.A.2
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 = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

CCSS.MATH.CONTENT.6.G.A.3
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

CCSS.MATH.CONTENT.6.G.A.4
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.

These should be a Godsend to 6th grade math teachers.  Perimeter allows you to have your students practice addition (and if you are creative subtraction as well) and area does the same for multiplication. Allows you to remediate while applying a previously learned skill.  I'll admit my students do well up until surface area and then it just isn't pretty thereafter....

I have decided that this will be my first concept to polish.  I have a good lesson, I have the students square a piece of construction paper (diagonal fold, remove bottom piece) and then they cut the square into other shapes, a square, two smaller rectangles, a large triangle and two smaller ones.  We then use these shapes to discuss area and fractions and percentages (I also use these same shapes in discussing variables with my 8th graders and I even use them to discuss systems with my Algebra students).  I have a few versions of this lesson, and will share it if asked.  
Giving the students partial nets, and then complete ones to find the areas might make more sense to my students rather than starting with the 3D and then trying to backtrack.  

I showed a tissue box and then construction paper cup outs to correspond to the differently area'ed sides of the box and then introduced nets.I think starting with partial nets, then nets will more easily allow my kids to see that a net is only individual shapes added together.  Getting them comfortable with adding areas as shapes are added might be easier than trying to see adding areas while translating a 3D shape to 2D faces. 

Remediation:
I've asked nearly every class I've had for the past 15 years and only rarely have I had students who remember being taught that multiplication can be modeled beautifully through the use of blocks. When I show students that the numbers we call squares are called this because if you build the multiplication out with blocks you get a square, they are amazed.  I have a small amount of cm cubes and a small number of wood 1in cubes and I used to use these more than I now use powerpoint, or google.  When asked this year if there was any office supply I wanted for next year, I asked for 2 things.  #1 graph stamps and #2 half-inch square paper.

 I want my students building rectangles and seeing the multiplication.  I want them adding the sides in time and eventually telling me the surface are and volume of the shapes they are making.  

I see lots of multiplication practice.  I see lots of being able to visualize what the math is showing.