Math Unit Four

Grade 4 Module 4: Angle Measure and Plane Figures

This 20-day module introduces points, lines, line segments, rays, and angles, as well as the relationships between them. Students construct, recognize, and define these geometric objects before using their new knowledge and understanding to classify figures and solve problems. With angle measure playing a key role in their work throughout the module, students learn how to create and measure angles, as well as create and solve equations to find unknown angle measures. In these problems, where the unknown angle is represented by a letter, students explore both measuring the unknown angle with a protractor and reasoning through the solving of an equation. Through decomposition and composition activities as well as an exploration of symmetry, students recognize specific attributes present in two-dimensional figures. They further develop their understanding of these attributes as they classify two-dimensional figures based on them.

 Acute angle (angle with a measure of less than 90°)

 Acute triangle (triangle with all interior angles measuring less than 90°)

 Adjacent angle (Two angles ∠𝐴𝑂𝐶 and ∠𝐶𝑂𝐵, with a common side 𝑂𝐶 , are adjacent angles if 𝐶 is in the interior of ∠𝐴𝑂𝐵.)

 Angle (union of two different rays sharing a common vertex, e.g., ∠𝐴𝐵𝐶)

 Arc (connected portion of a circle)

 Collinear (Three or more points are collinear if there is a line containing all of the points; otherwise, the points are non-collinear.)

A Lines and Angles

Lesson 1: Identify and draw points, lines, line segments, rays, and angles. Recognize them in various contexts and familiar figures. Lesson 2: Use right angles to determine whether angles are equal to, greater than, or less than right angles. Draw right, obtuse, and acute angles. Lesson 3: Identify, define, and draw perpendicular lines. Lesson 4: Identify, define, and draw parallel lines.

B Angle Measurement

Lesson 5: Use a circular protractor to understand a 1-degree angle as 1 360 of a turn. Explore benchmark angles using the protractor. Lesson 6: Use varied protractors to distinguish angle measure from length measurement. Lesson 7: Measure and draw angles. Sketch given angle measures, and verify with a protractor. Lesson 8: Identify and measure angles as turns and recognize them in various contexts. 4

C Problem Solving with the Addition of Angle Measures

Lesson 9: Decompose angles using pattern blocks. Lessons 10–11: Use the addition of adjacent angle measures to solve problems using a symbol for the unknown angle measure.

D Two-Dimensional Figures and Symmetry

Lesson 12: Recognize lines of symmetry for given two-dimensional figures. Identify line-symmetric figures, and draw lines of symmetry. Lesson 13: Analyze and classify triangles based on side length, angle measure, or both. Lesson 14: Define and construct triangles from given criteria. Explore symmetry in triangles. Lesson 15: Classify quadrilaterals based on parallel and perpendicular lines and the presence or absence of angles of a specified size. Lesson 16: Reason about attributes to construct quadrilaterals on square or triangular grid paper.