![]() ![]() The distance from the center to any point on the circle is called the radius, and the distance across the circle through the center is called the diameter. ![]() A circle is a closed shape that is defined by the set of points that are the same distance from the center of the circle.This angle relationship, along with complementary and supplementary angle relationships, can be used to determine missing angle measures in diagrams. When two lines intersect, a pair of congruent vertical angles are created.Pacing: 23 instructional days (21 lessons, 1 flex day, 1 assessment day) They will also continue solving real-life applications of surface area and volume, with the addition of cones, spheres, and cylinders. In eighth grade, students will zoom in on right triangles and apply the Pythagorean theorem to determine side lengths in right triangles. Sixth-grade students also began to distinguish between the three-dimensional space an object takes up and the surface area that covers it. In fifth grade, students developed an understanding of three-dimensional volume, which they further built on in sixth grade. In fourth grade, students studied the concepts of angle measurement and understood angle measure to be additive. The foundational skills for the standards in this unit stem from fourth through sixth grades. Students should have access to several tools they may opt to use throughout the unit, including rulers, protractors, compasses, and reference sheets (MP.5). Students will also encounter complex diagrams of angles and 3-D figures where they will need to understand what information they can glean from the diagram and plan a solution pathway before jumping in (MP.1). Many of these words enable students to be more precise in their communications with each other (MP.6). Throughout the unit, students encounter several vocabulary words, such as complementary angles, vertical angles, radius, and circumference. Students will also use their expressions skills to write numerical expressions that can be used to find surface area and volume of three-dimensional figures. Investigating circles, students discover the proportional relationship between the circumference of a circle and its diameter, and understand π as the ratio of these two quantities. In the beginning of the unit, students use and solve equations to represent relationships between angles and find missing angle measures. The seventh-grade Geometry standards are categorized as additional standards, however, there are several opportunities throughout the unit where students are engaged in the major work of the grade. In Unit 6, seventh-grade students cover a range of topics from angle relationships to circles and polygons to solid figures. ![]()
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