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GEOMETRY READINESS 6.8D Determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers. 6.10A Model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts. 6.11A Graph points in all four quadrants using ordered pairs of rational numbers. STANDARDS SUPPORTING 6.8A Extend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle. 6.8B Model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes. 6.8C Write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms, where dimensions are positive rational numbers. BIG IDEAS A figure can be decomposed into other polygons. The volume of a rectangular prism is the amount of space the object occupies. The area of a 2D figure describes the covering of the shape. The coordinate plane is an intersection of two number lines. The coordinate plane is used to measure distance and location of points. ESSENTIAL QUESTIONS Why do different shapes have different formulas to describe the area? How are the interior angles of a triangle related?
geometry VERTICAL ALIGNMENT 5 TH GRADE 6 TH GRADE 7 th GRADE Model area formulas for parallelograms, trapezoids, and triangles (6.8B). Represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b (7.7A). Represent and solve problems related to perimeter and/or area and related to volume (5.4H) Graph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and real-world problems (5.8C). Write equations (6.8C) and determine solutions that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms, where dimensions are positive rational numbers (6.8D). Extend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle (6.8A). Graph points in all four quadrants using ordered pairs of rational numbers (6.11A). Determine the area of composite figures (7.9C); solve problems involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid by determining the area of the shape's net (7.9D). Write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships (7.11C). KEY VOCABULARY area: coordinate plane: origin: parallelogram: quadrant: rectangular prism: trapezoid: triangle: quadrilateral: volume: the covering of a two-dimensional shape the plane containing the x- and y-axes the point (0, 0); where the x- and y-axes intersect a quadrilateral with opposite sides parallel and opposite sides congruent four regions on the coordinate plane a three-dimensional object with two rectangular bases a quadrilateral with one set of parallel sides a three-sided polygon with a sum of 180 o in the angle measures a four-sided polygon the amount of space a three-dimensional object occupies
geometry COMMON MISCONCEPTIONS Students may use the incorrect formula. Students may mistake the height of the triangle and the height of the parallelogram for the side length. Students may mistake the x- and y-coordinates when plotting a point. Students may confuse the various quadrants or may struggle with roman numerals.
GEOMETRY PAC ING GU I DE DAY 1 DAY 2 DAY 3 DAY 4 DAY 5 Angle Relationships and Triangles Area of Rectangles and Parallelograms Area of Triangles and Trapezoids Measurement and Area Angles and Area Quiz Student Handout 1 Homework 1 Student Handout 2 Homework 2 Student Handout 3 Homework 3 Student Handout 4 Homework 4 Quiz 1 DAY 6 DAY 7 DAY 8 Day 9 Day 10 Volume of Rectangular Prisms Volume with Rational Lengths Graphing on the Coordinate Plane Geometry Unit Study Guide Geometry Unit Test Student Handout 5 Homework 5 Student Handout 6 Homework 6 Student Handout 7 Homework 7 Unit Study Guide Unit Test
geometry TOPIC Angle Relationships and Triangles Area of Quadrilaterals TEACHING TIPS This is one of my most favorite topics! Have students work in groups of three. Give them a long piece of string that has been tied to form a circle. Each student will hold the string and form a vertex. As a review, you could call out the various triangle classifications and have students move to create that type of triangle. Oftentimes during the STAAR exam students are asked to bubble these types of responses. Consider practicing bubbling the correct value or even showing the answers bubbled incorrectly. I love teaching area as a covering of a 2D object. This could be as simple as using graph paper to color various shapes with various dimensions. Students could create a picture with various shapes or even spell out their name. Cheez-Its are also great ways for students to physically cover an object. Consider giving students a specific number of Cheez-Its, and then ask them the various dimensions that can be created with that area. Area of Triangles Search www.illuminations.nctm.org for the Area Tool to find an interactive tool that allows you to draw the height of the triangle (and trapezoid) to see various changes. This helps to see the height of the triangle even on an obtuse triangle. I would suggest printing a TEKS Mathematics Chart from the TEA website and then laminating it for everyday use throughout the unit. I did this and students were able to practice using the reference materials. Measurement and Area Reference materials: https://tea.texas.gov/student.assessment/staar/math/ The main purpose of the lesson is for students to practice using the math chart to measure and then use the formula. If students are doing well, then you might consider supplementing this lesson with more hands-on objects instead of the images on the student handouts. Examples include: the window on your classroom door, any posters hanging on the wall, etc.
geometry TOPIC Volume of Rectangular Prisms TEACHING TIPS Since volume is the space that a 3D object occupies, there are lots of great hands-on options. From a Rubix s cube to filling an object with unit cubes, have students explore with their hands. Search www.pbslearningmedia.org for Volume of Prisms to find a few short videos to share. This will be students first experience with all four quadrants of the coordinate plane. Students are now putting both the vertical number line and the horizontal number line together to form a coordinate plane. Graphing on the Coordinate Plane Consider pulling up Google Maps or Google Earth and putting in intersections of streets near you. Ask students to explain why this is important and how it applies to the coordinate plane. If you have a large space outside, use masking tape to mark off a basic coordinate plane. Ask students to place various objects at specific ordered pairs.