5.MD.5.a Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. Find the volume of a right rectangular prism with whole-number side edge lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. Edited to clarify the focus of this standard to use edge length of a three dimensional prism when finding volume. 5.MD.5.b Apply the formula V = l w h and V = b h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving and mathematical problems. Apply the formula V = l w h and V = b B h (where B stands for the area of the base) for rectangular prisms to find volumes of right rectangular prisms with edge lengths in the context of solving and mathematical problems. Edited to clarify the meaning of symbols used in formulas for volumes. 5.G.4 Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. For example, all rectangles are parallelograms, because they are all quadrilaterals with two pairs of opposite, parallel, equal-length sides. Edited to include an example to clarify the expectation for student learning and to retain the mathematical rigor. world world
High School Geometry 2011 Standard Proposed 2016 Standard Revisions are in red text Rationale for Revision G.CO geometric theorems. geometric theorems and, when appropriate, the converse of theorems. Edited to incorporate a footnote that clarifies the focus and expectations of the standards in this Geometry cluster. G.CO.MA.11.a Prove theorems about polygons. Theorems include: measures of interior and exterior angles, properties of inscribed polygons. Derive the formula for the relationship between the number of sides, sums of the interior and sums of the exterior angles of polygons, and apply to the solutions of mathematical and contextual problems. Prove theorems about polygons. Theorems include: measures of interior and exterior angle. properties of inscribed polygons. Edited to provide focus and coherence within the standard and preserve the mathematical rigor. G.C.MA.3.a Derive the formula for the relationship between the number of sides and sums of the interior and sums of the exterior angles of polygons and apply to the solutions of mathematical and contextual problems. Standard The content in this standard was incorporated into standard G.CO.MA.11.A where it is more coherently aligned (Proving theorems about polygons). G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, ) lies on the circle centered at the origin and containing the point (0, 2). Use coordinates to prove simple geometric theorems algebraically including the distance formula and its relationship to the Pythagorean Theorem. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, ) lies on Edited to provide deeper focus of important and specific connections with other standards within the Model Geometry course and preserve mathematical rigor.
High School Model Algebra II 2011 Standard Proposed 2016 Standard Revisions are in red text Rationale for Revision A.SS.E.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored (x2 – y2)(x2 + y2) and further factored (x - y) x + y)(x - yi)(x + yi). Edited the example in the standard to align with the focus and expectations for Algebra II. A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Compare the system of polynomials to the system of integers when adding, subtracting, multiplying, and dividing polynomials. Edited to clarify expectations for student learning and provide coherence between understanding systems and dividing polynomials. A.APR.MA.1.a Divide polynomials. Standard moved. This standard has the same student learning expectations with the revised standard A.APR.1 (See above). A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R. Standard deleted Deleted the standard in Model Algebra II as the standard is in the Model Algebra I course.