HCPSS Curriculum Framework
Common Core Mathematics 6
Unit 4: Geometry
Overview (Big Ideas):
Students in Grade 6 build on their work with area in elementary school by reasoning about
relationships among shapes to determine area, surface area, and volume. They find areas of right
triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or
removing pieces, and relating the shapes to rectangles. Using these methods, students discuss,
develop, and justify formulas for areas of triangles and parallelograms. Students find areas of
polygons and surface area they can determine. They reason about right rectangular prisms with
fractional side lengths to extend formulas for the volume of a right rectangular prism to
fractional side lengths. They prepare for work on scale drawings and constructions in Grade 7
by drawing polygons in the coordinate plane. (adapted from CCSC Grade 6 page 39-40)
Enduring Understandings:
1. Decomposing and rearranging provide a geometric way of both seeing that a measurement
formula is the right one and seeing why it is the right one.
2. In addition to decomposing and rearranging, shearing provides another geometric way of
both seeing that a measurement formula is the right one and seeing why it is the right one.
3. Geometric images provide the content in relation to which properties can be noticed,
definitions can be made, and invariances can be discerned.
4. Symmetry provides a powerful way of working geometrically.
5. Geometric awareness develops through practice in visualizing, diagramming, and
constructing.
6. Tools provide new sources of imagery as well as specific ways of thinking about geometric
objects and processes.
7. Geometric thinking turns tools into objects, and in geometry the process of turning an action
undertaken with a tool into an object happens over and over again.
8. Naming is not just about nomenclature; it draws attention to properties and objects of
geometric interest.
9. Definition can both generate and reflect structure: definitions are often dependent on a
specific classification.
10. Conjectures can emerge out of a problem-posing process that generates claims that need to be
justified.
Source:
Sinclair, N., Pimm, D., & Skelin, M. (2012). Developing essential understanding of geometry for
teaching mathematics in grades 6-8. Reston, VA: The National Council of Teachers of
Mathematics, Inc.
Essential Questions:
o What types of units are necessary for finding the area of two dimensional figures and
surface area and volume of three-dimensional figures? Why are these units appropriate?
o What is the relationship between rectangles and triangles having the same base and
height measure?
o How are the areas of parallelograms and trapezoids related to the area of rectangles?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
o How is the formula for the area of rectangles used in finding the volume of rectangular
prisms?
o What is the distance between points (x1,y1) and (x1,y2) and (x1,y1) and (x2,y1)?
Curriculum Standards:
6.G.A Solve real-world and mathematical problems involving area, surface area, and
volume.
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.
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  lwh and A  bh to find volumes of right rectangular prisms with
fractional edge lengths in the context of solving real-world and mathematical problems.
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 realworld and mathematical problems.
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.
Common Misconceptions:
 Students often forget or confuse the formulas for area, surface area and volume. Exposing
students to these concepts in a manner in which they understand the meaning behind the
terms as the standards suggest will be important in fostering their conceptual
development.
 Care should be given to ensuring students understand the units that each of these terms
require:
perimeter-linear units (cm, m, in, yd)
area and surface area- square units(sq. cm, sq. m, sq. in, sq. yd)
volume- cubic units (cm3)
 Common errors when plotting points in the coordinate plane include transposing the x
and y-coordinates, mistaking a vertical or horizontal line on the plane by miscounting or
struggling visually with the difference between the lines, and confusing the positive and
negative parts of the perpendicular number lines when plotting points.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.