Florida B.E.S.T. MA.912.GR.6

MA.912.GR.6 is a B.E.S.T. standard. These are the benchmarks under it.

• MA.912.GR.6.1

  Solve mathematical and real-world problems involving the length of a secant, tangent, segment or chord in a given circle.

• MA.912.GR.6.2

  Solve mathematical and real-world problems involving the measures of arcs and related angles.

• MA.912.GR.6.3

  Solve mathematical problems involving triangles and quadrilaterals inscribed in a circle.

• MA.912.GR.6.4

  Solve mathematical and real-world problems involving the arc length and area of a sector in a given circle.

• MA.912.GR.6.5

  Apply transformations to prove that all circles are similar.

01

What Students Need to Do

Students use circle relationships to find missing angle measures, arc measures, and segment lengths. They apply theorems involving chords, tangents, secants, radii, and inscribed or central angles.

02

What Mastery Looks Like

Students identify relevant arcs, angles, chords, radii, secants, and tangents in a diagram. They choose the correct theorem, write an equation, solve accurately, and justify each step.

03

Common Misconceptions

Students often confuse central angles with inscribed angles or use the wrong intercepted arc. They may forget that a tangent is perpendicular to the radius at the point of tangency. They also mix up formulas for intersecting chords, secants, and tangents.

04

How to Assess It

Draw arc AB measuring 100°, inscribed angle ACB, and a tangent at A with chord AB. Ask students to find both marked angles and name the theorem used for each.

1. 01

   Cut paper circles, fold chords and diameters, then mark perpendicular bisectors to test which lines pass through the center.

2. 02

   Show two possible solutions to a circle problem and ask students to defend which theorem applies and why.

3. 03

   Run a theorem-match relay where teams pair diagram cards with angle, chord, tangent, or secant equations and solve each card.

4. 04

   Model a bicycle wheel with a tangent road line, then calculate angles formed by spokes, chords, and the road.

• MA.912.GR.7.2

  Given a mathematical or real-world context, derive and create the equation of a circle using key features.

• MA.7.GR.1

  Solve problems involving two-dimensional figures, including circles.

• MA.912.GR.3.2

  Given a mathematical context, use coordinate geometry to classify or justify definitions, properties and theorems involving circles, triangles or quadrilaterals...