Topic: Grade 7 Module 3 Topic B

Topic B Unknown Angle Measurements

In topic A, students use the distributive property to write expressions in equivalent ways. Students build on this work in topic B when they write and solve equations to find unknown angle measurements.

Students begin the topic by recalling how to name angles and identify angle relationships from a diagram. Students use prior knowledge of angle relationships and their understanding of a new term, complementary angles, to write equations. As students look for efficient methods to solve these equations, they are introduced to the use of if–then moves. Students practice checking solutions to equations by using the original equation and the problem context.

In a digital lesson, students continue to write equations to represent angle relationships. Students apply their understanding of a new term, supplementary angles. Students find unknown angle measures by using tape diagrams and equations. Students determine that when solving an equation, they can divide both sides of the equation by a nonzero number or multiply both sides of the equation by its multiplicative inverse and get the same result.

Students continue to write and solve equations that represent angle relationships. They are introduced to two new angle relationships: vertical angles and angles at a point. In the last lesson, students apply the new learning from the topic to solve more challenging, multi-step angle relationship problems.

In topic C, students continue working with equations, gaining fluency in solving equations containing all types of rational numbers. In grade 8, the if–then moves are formalized as the properties of equality. Those properties are used in solving more rigorous equations throughout the high school grades.

If–Then Moves

Assume a, b, and c are numbers.

If a = b, then a + c = b + c.

If a = b, then a - c = b - c.

If a = b, then a ⋅ c = b ⋅ c.

If a = b and c ≠ 0, then a ÷ c = b ÷ c.

Vertical Angles and Angles at a Point

D

E (5x)° (7x + 96)°

A 35° C

B

Progression of Lessons

Lesson 7 Angle Relationships and Unknown Angle Measures

Lesson 8 Strategies to Determine Unknown Angle Measures

Lesson 9 Solving Equations to Determine Unknown Angle Measures

Lesson 10 Problem Solving with Unknown Angle Measures