Common Core Learning Standards
GRADE 6 Mathematics
GEOMETRY
Common Core Learning
Standards
Solve real-world and mathematical
problems involving area, surface
area, and volume.
6.G.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.
Concepts
Embedded Skills
Area
Calculate the area of right triangles and other types
of triangles.
Calculate the area of special quadrilaterals and
polygons by composing them into rectangles or
decomposing them into triangles.
Apply techniques of finding the area of polygons to
solve real-world problems.
Vocabulary







right triangle
triangle
quadrilaterals
polygons
area
compose
decompose
SAMPLE TASKS
I.
The Dudley family built a raised garden bed. The base of the deck is 22 feet long. The height is 17 feet. They planted roses in the
shaded area of the garden as shown below. How much area of the garden is covered by the roses?
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
II.
Tammy is sewing a quilt whose pattern contains right triangles. What is the area of one triangular quilt piece when the base is 4
inches and the height is 6 inches?
III. Explain how you would decompose the shape to find the area of the living room below.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Concepts
Embedded Skills
Volume
Calculate the volume of a right rectangular prism
with fractional side lengths.
Compare finding the volume of a right rectangular
prism by packing it with unit cubes to finding the
volume by multiplying the side lengths.
Apply the formula of V = l x w x h and V = B x h to
find the volume of right rectangular prisms with
fractional side lengths to solve real-world problems.
Solve real-world and mathematical
problems involving area, surface
area, and volume.
6.G.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.
Vocabulary






volume
right
rectangular
prism
base
width
height
length
SAMPLE TASKS
I. Find the volume of the rectangular prism.
4
1
2
2
1
2
2
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
I.
Compare finding the volume of a right rectangular prism with packed unit cubes and finding the volume by multiplying the side lengths
5 cm
3 cm
4 cm
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
II.
Tim wants to buy a fish tank. He needs to fill it with water and needs to know how much water the tank holds. Use the formula,
V = l x w x h to calculate the amount of water the tank holds when the
dimensions:
l = 5.5 in.
w = 7in.
h = 3 in.
Part 2: Explain what would happen to the volume if the height of the fish tank
was doubled.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core
Learning Standards
Solve real-world and
mathematical problems
involving area, surface area,
and volume.
Concepts
Embedded Skills
Polygons in
the
coordinate
plane
Graph polygons in the coordinate plane given the
vertices.
Calculate the length of a side of a polygon graphed
in the coordinate plane where the vertices have
the same x-value or same y-value.
6.G.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.
Vocabulary





polygons
length
coordinate plane
vertices
ordered pairs
SAMPLE TASKS
I.
Part 1: Plot the following ordered pairs on coordinate
plane to create a polygon:
A (3,4) B (-3,4) C (-3,-2) D (3, -2)
Part 2: Calculate the length of side AB
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Solve real-world and mathematical
problems involving area, surface
area, and volume.
6.G.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.
Concepts
Embedded Skills
surface area
with nets
Calculate the surface area of a 3-dimensional figure
by using nets made up of rectangles and triangles.
Solve real-world problems involving surface area of
3-dimensional figures.
Vocabulary



nets
3-dimensional
figures
surface area
SAMPLE TASKS
I.
Determine the three dimensional figure that can be made from this net
 6 faces
 12 edges
 8 vertices
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
II.
Calculate the surface area of the cube.
8ft.
8ft.
III. Sandy is wrapping a box that is shaped like a cube. The box has a length of 5 inches. What is the least amount of wrapping paper
that Sandy needs?
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
IV. Find the surface area of the pyramid. The base of each triangle is 16in. and the height of each triangle is 17in.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.