In what ways can shapes be related using conservation of area?

Students analyze areas of parallelograms and triangles.

A parallelogram is any quadrilateral with two pairs of parallel and equal sides.

Any side of a parallelogram can be interpreted as the base.

The height of a parallelogram is the perpendicular distance from its base to its opposite side.

The area of a triangle is half of the area of a parallelogram with the same base and height.

Two triangles with the same base and height must have the same area.

Area of composite shapes can be interpreted as the sum of the areas of multiple shapes, such as triangles and parallelograms.

The area of a parallelogram can be generalized as the product of the perpendicular base and height.

The area of a triangle can be interpreted relative to the area of a parallelogram.

An area can be decomposed in infinitely many ways.

How can volume characterize space?

Students interpret and express volume.

Volume can be measured in non-standard units or standard units.

Volume is expressed in the following standard units, derived from standard units of length:

• cubic centimetres

• cubic metres

A cubic centimetre (cm3) is a volume equivalent to the volume of a cube measuring 1 centimetre by 1 centimetre by 1 centimetre.

A cubic metre (m3) is a volume equivalent to the volume of a cube measuring 1 metre by 1 metre by 1 metre.

The volume of a right rectangular prism can be interpreted as the product of the two-dimensional base area and the perpendicular height of the prism.

Volume is a measurable attribute that describes the amount of three-dimensional space occupied by a three-dimensional shape.

The volume of a prism can be interpreted as the result of perpendicular motion of an area.

Volume remains the same when decomposed or rearranged.

Volume is quantified by measurement.

Volume is measured with congruent units that themselves have volume and do not need to resemble the shape being measured.

The volume of a right rectangular prism can be perceived as cube-shaped units structured in a three-dimensional array.