Montana Math MT.PLUS.ALG.TRIG.2

MathGrades 9–12Trigonometric Functions

The Standard

Understand and use the radian measure of an angle and convert between degree and radian measures.

2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning

Teacher's field guide

What Students Need to Do: Students use radians to describe angles by comparing arc length with a circle's radius. They convert angles between degrees and radians using 180° = π radians.
What Mastery Looks Like: Students recognize that an arc as long as the radius makes a one-radian angle. They convert 135° to 3π/4 radians and 5π/6 radians to 150°.
Common Misconceptions: Students may treat a radian as a fixed arc length instead of an angle. They may use the conversion factors backward or think a half turn is 180 radians.
How to Assess It: Exit ticket: A circle has a 4 cm radius and a 4 cm arc. Find its central angle in radians, then convert 150° to radians and 2π/3 radians to degrees.

Lesson moves

Give pairs paper circles, string cut to each radius, and protractors; have them mark one-radius arcs and measure the central angles.
Ask why a one-radius arc makes the same angle on a small circle and a large circle. Have students write two sentences.
Give bingo cards labeled 30°, 90°, π/6, and π/2; call equivalent measures for students to mark.
Draw a bicycle wheel with a 35 cm radius; have students find the distance along its rim for turns of 2 radians and 180°.

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