Thursday’s grade 4 math afternoon session covered lessons from the Grade 4 Module 4: Angle Measure and Plane Figures. This module introduces students to seven new geometry terms in the first lesson that set the foundation for their progression to high school geometry. They draw points, lines, segments, rays, and angles and learn how to identify them with geometrical notation. By using a right angle template, students are taught to easily identify right, acute and obtuse angles in Lesson 2.

Physiometry fluency tasks are introduced in Lesson 2 and involve using arms to construct types of angles, which is fun and engaging. Continuing with the use of the right angle template, students study the relationships of perpendicular and parallel lines. A fun activity involves using the letters of the alphabet to identify segments that are parallel and perpendicular. Students will come to realize that points are needed in order to name segments. Attending to precision and communicating/critiquing the reasoning of others play a key role here.

Students are introduced to the concept of degree after visualizing the progression of ¼ turns, ½ turns, and ¾ turns using the two-circle manipulative that makes angles pop out and come alive. Students transition from using the two-circle manipulative to using a circular protractor, and then to using the 180-degree protractor when identifying angle types and measuring.

A hard-to-grasp concept is angle measure vs. arc length measure. When is an angle larger? Students will explore this concept using two circles, one smaller than the other. Each circle is folded into quarters, showing a right angle. Students will notice that the arc-length of the larger circle is larger than the arc-length of the smaller circle, even though the right angles forming the arcs are the same. The circles are excellent visual aids in this example.

Paper folding exercises that students will be using to understand angle addition and subtraction were demonstrated. These exercises will lead classrooms into the discussion of complementary, supplementary, and vertical angles and students will be able to solve missing angle problems based on these relationships that they can visually recognize. The vocabulary here is not part of the 4th grade, but provides great exposure and provides students with the skill of being able to visually recognize these relationships leaving 4^{th} grade.

The remainder of the module focuses on classifying two-dimensional figures and lines of symmetry. Classifying quadrilaterals is always challenging (i.e., is a rectangle a square, or is a square a rectangle?). A nice presentation on the hierarchy of the “trapezoid” family was drawn out to help the audience. Students/teachers should start with drawing trapezoids based on the fact that they have at least one set of parallel sides. From there, progress to drawing just parallelograms, then just rectangles, then squares. This is a great activity to help students see the progression. The module is loaded with fun, engaging, and solid activities that will build the strong foundation needed for the geometry to come in later modules and grades.

This is a great activity to help students see the progression. They lines, segments, rays, and angles ausing a right angle template, students are taught to easily identify right.

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