Middle School Content Academy Geometry SOL 6.11, 6.12, 6.13, 7.7, 7.8, 8.8, 8.9, 8.10, 8.11 February 12, 2015

Curriculum framework Geometry strand information!

Reporting Category: Measurement and Geometry Let’s examine the SOL in this reporting category strand. Which are in the Geometry reporting category?

Curriculum framework – Unpack the standard What are the verbs?

Henrico Curriculum Guide http://blogs.henrico.k12.va.us/math/courses/

Pacing SOL 6.11, 6.12, 6.13 SOL 7.7, 7.8 SOL 8.8, 8.9, 8.10, 8.11

Reporting Category: Measurement and Geometry Grade 6 2011-12 2012-13 2013-14 Grade 7 Grade 8 Look for trends!

Formulas What formulas do students need to know related to the Geometry strand? What formulas are provided on the formula sheet related to the Geometry strand?

Vertical Articulation of Content Focus: Problem Solving with 2- and 3-Dimensional Figures Focus: Properties and Relationships Focus: Relationships between Figures

2014 SPBQ Data – 6.11, 7.8, 8.8 Grade Description of Question % Correct in Division 6 Assign points to the correct quadrants or axes without graphing. 59 Use coordinates to graph points on the coordinate plane. 76 Assign points to the correct quadrants or axes. 88 7 Apply a transformation to the graph or coordinates of a figure and determine the graph or coordinates for the image. 50 Identify and recognize congruent images resulting from transformations. 63 Identify the resulting image of a transformation. 64 8 Apply transformations to plane figures and identify applications of transformations. 77 Identify the resulting image of a transformation 62 Apply transformations to plane figures. 67

Performance Analysis Comparison SOL 6.11, 7.8, 8.8 2012 SOL 6.11 identify the coordinates of a point in a coordinate plane; and graph ordered pairs in a coordinate plane. SOL 7.8 - The student, given a polygon in the coordinate plane, will represent transformations (reflections, dilations, rotations, and translations) by graphing in the coordinate plane. SOL 8.8 - None 2013 SOL 6.11 – None SOL 8.8 apply transformations to plane figures; and identify applications of transformations. 2013: The next standard being highlighted is SOL 7.8. This standard reads: The student, given a polygon in the coordinate plane, will represent transformations (reflections, dilations, rotations, and translations) by graphing in the coordinate plane. The next Standard of Learning being highlighted is SOL 8.8. In particular, student performance was inconsistent on questions that assessed bullet a, which states: The student will apply transformations to plane figures.

2012 - Suggested Practice for SOL 6.11 Students need additional practice recognizing the location of points that lie on the x- or y-axis. 1. Identify the location of the point (10,0). In Quadrant I In Quadrant III On the x-axis On the y-axis 2. Select the two points that are located on the y-axis. (0,0) (0,1) (1,1) (-1,-1) (1,0) Common Errors? Misconceptions?

2012 - Suggested Practice for SOL 7.8 Students need additional practice applying transformations to a given figure on a coordinate plane. A (-7,3) B (-7,-2) C (-1,-2) A C B Identify the coordinates of the image of triangle ABC after a dilation about the origin by a factor of 2. Identify the coordinates of the image of triangle ABC after a rotation of 180 degrees counterclockwise about the origin. Identify the coordinates of the image of triangle ABC after a reflection over the y-axis. Identify the coordinates of the image of triangle ABC after a translation 5 units to the right. Common Errors? Misconceptions?

2013 - Suggested Practice for SOL 7.8 A (-2,4) B (-2,-3) C (-4,-3) y x A B C Students need additional practice applying transformations to a given figure on a coordinate plane. Identify the coordinates of the image of triangle ABC after a dilation about the origin by a factor of 2. Identify the coordinates of the image of triangle ABC after a rotation of 180 degrees clockwise about the origin. Identify the coordinates of the image of triangle ABC after a reflection over the y-axis. For this standard, students need additional practice applying transformations to a given figure on a coordinate plane. Students need additional practice identifying the image of a figure when given the pre-image on the coordinate plane, and they also need additional practice identifying the vertices of the image of a figure, as in the examples on the screen. Students did better on multiple choice items that required identification of a vertex of the image, but did not do as well on a technology enhanced item when asked to plot the points on the coordinate plane. The answers to these questions are shown on the screen. Common Errors? Misconceptions?

2013 - Suggested Practice for SOL 8.8a Students need additional practice determining the coordinates of a figure after it is rotated about the origin in the counterclockwise direction. D This polygon is rotated 270° counterclockwise about the origin. Plot the image of point D (-4, 5) and name the coordinates. D ’ (5, 4) Students need to focus on understanding how a figure is affected when it is rotated in the counterclockwise direction. Teachers are encouraged to include opportunities for students to plot the resulting image of one or more vertices on a coordinate plane. The answer to this example is shown on the screen. Common Errors? Misconceptions?

Vertical Articulation of Content Focus: Problem Solving with 2- and 3-Dimensional Figures Focus: Properties and Relationships Focus: Relationships between Figures

2014 SPBQ Data – 6.13, 7.7 Grade Description of Question % Correct in Division 6 Use attributes of quadrilaterals to solve problems. 74 7 Classify quadrilaterals based on properties. 82 Use properties to compare and contrast quadrilaterals. 46 72

Performance Analysis Comparison SOL 6.13, 7.7 2012 SOL 6.13 – The student will describe and identify properties of quadrilaterals. SOL 7.7 – The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid. 2013 SOL 6.13 – None SOL 7.7 – The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid. The next standard being highlighted is SOL 7.7. This standard reads: The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid. In particular, students had difficulty comparing and contrasting the properties of rhombi with the properties of parallelograms and squares.

2012 - Suggested Practice for SOL 6.13 Students need additional practice describing and identifying properties of quadrilaterals. Name each figure using the given attributes with its most precise name. What term most accurately classifies all of these figures? What term most accurately classifies figures 1, 3, 4, and 6? What term most accurately classifies figures 1 and 3? quadrilateral parallelogram rhombus square trapezoid rhombus rectangle kite parallelogram 1 2 3 4 5 6 Each angle is 90° Common Errors? Misconceptions?

2012 - Suggested Practice for SOL 7.7 The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid. Identify the classifications to which this figure belongs. Parallelogram Trapezoid Quadrilateral Rhombus Rectangle Select each figure that appears to be a rectangle. All angles in this figure are 90 degrees. Common Errors? Misconceptions?

2013 - Suggested Practice for SOL 7.7 Students need additional practice classifying an image of a rhombus. Which classifications describe this figure? Parallelogram Trapezoid Quadrilateral Square Rhombus Rectangle For SOL 7.7, students need additional practice classifying an image of a rhombus. A common student error is to identify the image of a rhombus as a square. The answers are shown on the screen. Common Errors? Misconceptions?

2013 - Suggested Practice for SOL 7.7 Students need additional practice differentiating between an image of a rhombus and a parallelogram. Which classifications appear to describe both of these figures? Parallelogram Trapezoid Quadrilateral Square Rhombus Rectangle For this SOL, students also need additional practice differentiating between an image of a rhombus and a parallelogram. A common student error is for students to identify both of these figures as rhombi. The answers are shown on the screen. Common Errors? Misconceptions?

2013 - Suggested Practice for SOL 7.7 Students need additional practice identifying the properties of a rhombus. Select each property that is true for any rhombus. There is exactly one pair of parallel sides. There are exactly two pairs of parallel sides. There are exactly four congruent sides. There are exactly four right angles. There are exactly two pairs of congruent opposite angles. There are exactly four congruent angles. For SOL 7.7, students also need additional practice identifying the properties of a rhombus. Common misconceptions are that a rhombus must have four right angles and/or four congruent angles. The answers to the example are shown on the screen. Common Errors? Misconceptions?

Vertical Articulation of Content Focus: Problem Solving with 2- and 3-Dimensional Figures Focus: Properties and Relationships Focus: Relationships between Figures

2014 SPBQ Data – 6.12, 8.10 Grade Description of Question % Correct in Division 6 Use attributes to identify congruent polygons. 67 8 Verify and apply the Pythagorean Theorem to find any missing side of a right triangle. 46 36 59

Performance Analysis Comparison SOL 6.12, 8.10 2012 SOL 6.12 – None SOL 8.10 – None 2013 SOL 8.10 – None – Really???

Vertical Articulation of Content Focus: Problem Solving with 2- and 3-Dimensional Figures Focus: Properties and Relationships Focus: Relationships between Figures

2014 SPBQ Data – 8.11 Grade Description of Question % Correct in Division 8 Solve practical area and perimeter problems involving composite plane figures. 44 23

Performance Analysis Comparison SOL 8.11 2012 SOL 8.11 – The student will solve practical area and perimeter problems involving composite plane figures. 2013 2013: The next Standard of Learning being highlighted is SOL 8.11. Student performance data indicate that students need additional practice solving practical area and perimeter problems involving composite plane figures.

2012 - Suggested Practice for SOL 8.11 Students need additional practice using addition and subtraction to calculate area and perimeter in problems involving composite plane figures. 4 cm 6 cm 10 cm 9 cm 2 cm Find the area and perimeter of this composite figure. A semicircle with a diameter of 2 centimeters is added to the side of the figure labeled 2 cm. Find the approximate area and perimeter of the new figure after this addition. Common Errors? Misconceptions?

2012 - Suggested Practice for SOL 8.11 Students need additional practice solving practical area problems involving composite plane figures. An artist created a geometric design on a wall. She began by painting a blue circle and then painting a yellow isosceles right triangle on top of the blue circle. This figure shows the artist’s beginning steps. Point A is the center of the circle. Points B and C lie on the circle. The diameter of the circle is 12 feet. What is the area of the interior of the circle not covered by triangle ABC, rounded to the nearest whole number? Common Errors? Misconceptions?

2012 - Suggested Practice for SOL 8.11 Students need additional practice finding the area and perimeter of composite figures. Bobby is painting a figure on a banner for a homecoming parade. The figure he is painting consists of an isosceles triangle, a rectangle, and a semicircle, as shown. What is the total area of the figure, rounded to the nearest tenth? What is the total perimeter of the figure, rounded to the nearest tenth? 3ft 10 ft 8 ft 5ft Students find items that involve finding the area and/or perimeter of composite figures challenging. The answers to the examples are shown on the screen. 117.1 sq ft 42.6 ft Common Errors? Misconceptions?

Resources ExamView Banks NextLesson.org HCPS Math Website - http://teachers.henrico.k12.va.us/math/courses/ VDOE Enhanced Scope and Sequence Skills - JMU Pivotal Items ExploreLearning Teaching Strategies Student Engagement Activities