The benchmark(s) of focus is the primary focus for student learning and instruction to be taught or reinforced and provides an intentional opportunity for students to work with that concept or skill.
MA.912.GR.1.4
Prove relationships and theorems about parallelograms. Solve mathematical and real-world problems involving po...
Clarifications:
Clarification 1: Postulates, relationships and theorems include opposite sides are congruent, consecutive angles are supplementary, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and rectangles are parallelograms with congruent diagonals.Clarification 2: Instruction includes constructing two-column proofs, pictorial proofs, paragraph and narrative proofs, flow chart proofs or informal proofs.
Clarification 3: Instruction focuses on helping a student choose a method they can use reliably.
MA.912.GR.1.5
Prove relationships and theorems about trapezoids. Solve mathematical and real-world problems involving postul...
Clarifications:
Clarification 1: Postulates, relationships and theorems include the Trapezoid Midsegment Theorem and for isosceles trapezoids: base angles are congruent, opposite angles are supplementary and diagonals are congruent.Clarification 2: Instruction includes constructing two-column proofs, pictorial proofs, paragraph and narrative proofs, flow chart proofs or informal proofs.
Clarification 3: Instruction focuses on helping a student choose a method they can use reliably.
MA.912.GR.3.2
Given a mathematical context, use coordinate geometry to classify or justify definitions, properties and theor...
Clarifications:
Clarification 1: Instruction includes using the distance or midpoint formulas and knowledge of slope to classify or justify definitions, properties and theorems.
Supporting benchmarks either make a connection or may help students achieve the focus benchmark(s) and increase students’ opportunities to make connections within the subject or to other subjects. The information included in this section is not a comprehensive list, and educators are encouraged to find other supporting benchmarks.
MA.912.GR.1.1
Prove relationships and theorems about lines and angles. Solve mathematical and real-world problems involving ...
Clarifications:
Clarification 1: Postulates, relationships and theorems include vertical angles are congruent; when a transversal crosses parallel lines, the consecutive angles are supplementary and alternate (interior and exterior) angles and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.Clarification 2: Instruction includes constructing two-column proofs, pictorial proofs, paragraph and narrative proofs, flow chart proofs or informal proofs.
Clarification 3: Instruction focuses on helping a student choose a method they can use reliably.
MA.912.GR.1.6
Solve mathematical and real-world problems involving congruence or similarity in two-dimensional figures.
Clarifications:
Clarification 1: Instruction includes demonstrating that two-dimensional figures are congruent or similar based on given information.
MA.912.GR.3.3
Use coordinate geometry to solve mathematical and real-world geometric problems involving lines, circles, tria...
Clarifications:
Clarification 1: Problems involving lines include the coordinates of a point on a line segment including the midpoint.Clarification 2: Problems involving circles include determining points on a given circle and finding tangent lines.
Clarification 3: Problems involving triangles include median and centroid.
Clarification 4: Problems involving quadrilaterals include using parallel and perpendicular slope criteria.