References to geometry in the Washington State Math Standards


(All content on this page has been taken from the text of the Math Standards)

Explanation of terms used in the Standards:
Core Content areas describe the major mathematical focuses of each grade level or course. A limited number of priorities for each grade level in grades K–8 and for each high school course are identified, so teachers know which topics call for the most time and emphasis.
Additional Key Content contains important expectations that do not warrant the same amount of instructional time as the Core Content areas. These are expectations that might extend a previously learned skill, plant a seed for future development, or address a focused topic, such as scientific notation. Although they need less classroom time, these expectations are important, are expected to be taught, and may be assessed as part of Washington State’s assessment system.
Core Processes include expectations that address reasoning, problem solving, and communication. While these processes are incorporated throughout other content expectations, they are presented in this section to clearly describe the breadth and scope of what is expected in each grade or course.
Explanatory Comments and Examples accompany most of the expectations.... The comments expand upon the meaning of the expectations. Explanatory text might clarify the parameters regarding the type or size of numbers, provide more information about student expectations regarding mathematical understanding, or give expanded detail to mathematical definitions, laws, principles, and forms included in the expectation.

Pages 78-79 in the Standards: 6.4. Core Content: Two- and three-dimensional figures (Geometry/Measurement, Algebra) Students extend what they know about area and perimeter to more complex two-dimensional figures, including circles. They find the surface area and volume of simple three-dimensional figures. As they learn about these important concepts, students can solve problems involving more complex figures than in earlier grades and use geometry to deal with a wider range of situations. These fundamental skills of geometry and measurement are increasingly called for in the workplace and they lead to a more formal study of geometry in high school.

Students are expected to:
6.4.A Determine the circumference and area of circles.
6.4.B Determine the perimeter and area of a composite figure that can be divided into triangles, rectangles, and parts of circles. Although students have worked with various quadrilaterals in the past, this expectation includes other quadrilaterals such as trapezoids or irregular quadrilaterals, as well as any other composite figure that can be divided into figures for which students have calculated areas before.
6.4.C Solve single- and multi-step word problems involving the relationships among radius, diameter, circumference, and area of circles, and verify the solutions. The intent of this expectation is for students to show their work, explain their thinking, and verify that the answer to the problem is reasonable in terms of the original context and the mathematics used to solve the problem. Verifications can include the use of numbers, words, pictures, or equations.
6.4.D Recognize and draw two-dimensional representations of three-dimensional figures.
6.4.E Determine the surface area and volume of rectangular prisms using appropriate formulas and explain why the formulas work. Students may determine surface area by calculating the area of the faces and adding the results.
6.4.F Determine the surface area of a pyramid.
6.4.G Describe and sort polyhedra by their attributes: parallel faces, types of faces, number of faces, edges, and vertices. Prisms and pyramids are the focus at this level.

Page 92 in the Standards: 7.3. Core Content: Surface area and volume (Algebra, Geometry/Measurement) Students extend their understanding of surface area and volume to include finding surface area and volume of cylinders and volume of cones and pyramids. They apply formulas and solve a range of problems involving three-dimensional objects, including problems people encounter in everyday life, in certain types of work, and in other school subjects. With a strong understanding of how to work with both two-dimensional and three-dimensional figures, students build an important foundation for the geometry they will study in high school.

Students are expected to:
7.3.A Determine the surface area and volume of cylinders using the appropriate formulas and explain why the formulas work. Explanations might include the use of models such as physical objects or drawings. A net can be used to illustrate the formula for finding the surface area of a cylinder.
7.3.B Determine the volume of pyramids and cones using formulas.
7.3.C Describe the effect that a change in scale factor on one attribute of a two- or three-dimensional figure has on other attributes of the figure, such as the side or edge length, perimeter, area, surface area, or volume of a geometric figure.
7.3.D Solve single- and multi-step word problems involving surface area or volume and verify the solutions. The intent of this expectation is for students to show their work, explain their thinking, and verify that the answer to the problem is reasonable in terms of the original context and the mathematics used to solve the problem. Verifications can include the use of numbers, words, pictures, or equations.

Pages 101-102 in the Standards. 8.2. Core Content: Properties of geometric figures (Numbers, Geometry/Measurement) Students work with lines and angles, especially as they solve problems involving triangles. They use known relationships involving sides and angles of triangles to find unknown measures, connecting geometry and measurement in practical ways that will be useful well after high school. Since squares of numbers arise when using the Pythagorean Theorem, students work with squares and square roots, especially in problems with two- and three-dimensional figures. Using basic geometric theorems such as the Pythagorean Theorem, students get a preview of how geometric theorems are developed and applied in more formal settings, which they will further study in high school.

Students are expected to:
8.2.A Identify pairs of angles as complementary, supplementary, adjacent, or vertical, and use these relationships to determine missing angle measures.
8.2.B Determine missing angle measures using the relationships among the angles formed by parallel lines and transversals.
8.2.C Demonstrate that the sum of the angle measures in a triangle is 180 degrees, and apply this fact to determine the sum of the angle measures of polygons and to determine unknown angle measures.
8.2.D Represent and explain the effect of one or more translations, rotations, reflections, or dilations (centered at the origin) of a geometric figure on the coordinate plane.
8.2.F Demonstrate the Pythagorean Theorem and its converse and apply them to solve problems. One possible demonstration is to start with a right triangle, use each of the three triangle sides to form the side of a square, and draw the remaining three sides of each of the three squares. The areas of the three squares represent the Pythagorean relationship.
8.2.G Apply the Pythagorean Theorem to determine the distance between two points on the coordinate plane.