Cluster Summary for: Solve real-world and
mathematical problems involving area, surface area,
and volume
Grade Level: 6
Domain: Geometry
Cluster Priority: (check)
__ Major Cluster
_x_ Supporting Cluster __ Additional Cluster
SCALE
TRIMESTER 1
TRIMESTER 2
TRIMESTER 3
4: Advanced
In addition to score 3, in-depth inferences and applications go beyond Mathematics, are applied to other disciplines, and are utilized in real-world contexts.
3: Proficient
Find area of squares and
Find area of squares and
Find area of squares and rectangles.
The student exhibits
rectangles.
rectangles.
Apply these techniques in context of solving real-world and mathematical problems within cultural contexts
no major errors or
Apply these techniques in
Apply these techniques in
including those of MT American Indians.
omissions.
context of solving real-world context of solving realFind area of triangles and special quadrilaterals and composite figures.
and mathematical problems
world and mathematical
Draw polygons in a coordinate plane given coordinates for the vertices.
within cultural contexts
problems within cultural
Find the volume of right rectangular prisms with fractional edge lengths.
including those of MT
contexts including those of
Represent 3-dimensional figures using nets made up of rectangles and triangles and use the nets to find the surface
American Indians.
MT American Indians.
area of these figures.
Proficiency Example
A rectangle measures 5 in by

Find the area of a right triangle with a base length of three meters, a height of
12
8 in. Find its area.
four meters, and a hypotenuse of 5 meters.
cm

Find the area of the trapezoid (right) using the formulas for rectangles and triangles.
3
A square has a side length of

On a map, the library is located at (-2, 2), the city hall building is located at (0, 2),
cm
5 cm. Find its area.
and the high school is located at (0, 0). Represent the locations as points on a
7
coordinate grid with a unit of 1 mile.
cm
1. What is the distance from the library to the city hall building? The distance from the city hall building
to the high school? How do you know?
2. What shape does connecting the three locations form? The city council is planning to place a city park
in this area. How large is the area of the planned park?

A right rectangular prism has edges of 1 ¼”, 1”, and 1 ½”. How many cubes with side lengths of ¼ would
be needed to fill the prism? What is the volume of the prism?

Create the net for given prism or pyramid, and then use the net to calculate the surface area.
2: Partially Proficient
There are no major errors or omissions regarding the simpler details and processes as the student recognizes or recalls terminology and performs basic processes.
However, the student exhibits major errors or omissions regarding the more complex ideas and processes.
1: Novice
With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
0: No Evidence
Even with help, no understanding or skill demonstrated.
Mathematical Practices Best Taught in this Cluster: (check those that apply)
__ Make sense of problems & preserve in solving them __ Reason abstractly & quantitatively __ Construct viable arguments & critique the reasoning of others
__Model with mathematics __Use appropriate tools strategically __Attend to precision __Look for and make use of structure __Look for & express regularity in repeated reasoning
Key Vocabulary for the Cluster:
Area, surface area, volume, prisms, quadrilaterals, polygons, right rectangular prism, vertices, three-dimensional, decomposing, edges, dimensions, net, face, base, height, trapezoid, isosceles, right
triangle, rectangle, square, parallelogram, rhombus, kites,