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Solve mathematical problems, including those is real-world contexts, involving area of two-dimensional shapes. (6.G.1)

Solve mathematical problems, including those in real-world contexts, involving volume and surface area of three dimensional objects. (6.G.2, 6.G.4, 7.G.6)

Concepts and Skills

* Power Standard Content

* Find the area of triangles

* Find the area of quadrilaterals

* Find the area of composite shapes (e.g., can be decomposed into rectangles and triangles)

* Find the volume of rectangular prisms (with whole and fractional edge lengths) by filling and using formulas

* Find surface area of 3-dimensional figures (rectangular prisms, triangular prisms, some pyramids) using nets

Draw on a coordinate plane by plotting points

Use coordinate pairs to find side lengths of a polygon

Draw/construct nets using rectangles and triangles to represent 3-dimensional figures (rectangular prisms, triangular prisms, some pyramids)

Critical Language

Language Usage

A student in 6th grade will demonstrate the ability to apply and comprehend critical language by describing how two-dimensional shapes can be used to represent three-dimensional figures, interpreting a problem to determine which measures are involved, explaining how formulas are related to the shape itself, and explaining a solution strategy.

Content-Specific Vocabulary

Area

Volume

Surface area

Two-dimensional

Three-dimensional

Net

Length

Width

Height

Square

Rectangle

Triangle

Quadrilateral

Polygon

Parallelogram

Rectangular prism

Triangular prism

Square prism

Square pyramid

Triangular pyramid

Coordinate plane

Coordinate pair

Process-Specific Vocabulary

Represent

Apply

Draw

Construct

Create

Fill

Wrap

Cover

Surround

Measurement

Square units

Cubic units

Concept-Based Connections

Essential Understandings

Shapes and objects can be measured in a variety of ways.

Volume is a measure of filling an object.

Surface area is a measure of wrapping an object.

Area is a measure of covering a shape.

Two-dimensional shapes can be used to create three-dimensional objects.

Factual Guiding Questions

How do you find area of triangles? Quadrilaterals? Composite shapes?

How do you find volume of rectangular prisms?

How do you find surface area of prisms? Pyramids?

Conceptual Guiding Questions

Do all rectangular prisms with the same volume have the same surface area?

How do you know when to find surface area? Volume?

How is finding the area of a parallelogram similar to find the area of a triangle? Rectangle?

Engaging/Debatable Guiding Questions

How can you use familiar shapes to find areas/volumes/surface areas of composite shapes and figures?