How to improve upon the Common Core (old)

Typo. Should read "as transformations," not "as a transformations."

(+) Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.


These aren't high school level concepts.

HSG.CO.A.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.


Way too vague!

5.G.B.4: Classify two-dimensional figures in a hierarchy based on properties.


Shouldn't these all belong to one topic? What is the meaningful distinction, if any?

5.G.B.4: Classify two-dimensional figures in a hierarchy based on properties.

5.G.B.3: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

3.G.A.1: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.


What's the difference?

4.MD.C.5.a: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles.

4.MD.C.5.b: An angle that turns through n one-degree angles is said to have an angle measure of n degrees.


Aren't these just one topic?

5.MD.C.3.a: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.

5.MD.C.3.b: A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.


Aren't these just one topic?

3.MD.C.5.a: A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area.

3.MD.C.6: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

3.MD.C.5.b: A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.


This standard should be broken into two sections. The first is measuring angles, and the second is drawing angles.

4.MD.C.6: Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.


I think this should be two topics. One about comparison and order, and the other about transitivity.

1.MD.A.1: Order three objects by length; compare the lengths of two objects indirectly by using a third object.


This standard should be broken into two sections. The first is to make sure kids understand the last number they said is the number of objects. The second is to make sure kids can count objects in different arrangements. They can probably count in a row or column, but can they count in a grid? What about scattered? What about arranged in a circle?

K.CC.B.4.b: Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.


This doesn't make any sense:

7.NS.A.2.a: Understand that multiplication is extended from fractions to rational numbers...


This is so vague that it's useless:

6.EE.A.4: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.


I can't see any difference between these two:

8.SP.A.2: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

HSS.ID.B.6.c: Fit a linear function for a scatter plot that suggests a linear association.