Middle School Content Academy Measurement SOL 6.9, 6.10, 7.5, 7.6, 8.6, 8.7 March 11, 2015

Curriculum framework Measurement strand information!

Reporting Category: Measurement and Geometry Let’s examine the SOL in this reporting category strand. Which are in the Measurement reporting category? *SOL 8.6b cannot be appropriately assessed within the current format and is excluded from testing. 

Curriculum framework – Unpack the standard What are the verbs?

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

Pacing SOL 6.9, 6.10 SOL 7.5, 7.6 SOL 8.6, 8.7

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 Measurement strand? What formulas are provided on the formula sheet related to the Measurement strand?

Vertical Articulation of Content Grade 6 Focus: Problem Solving with Area, Perimeter, Volume, and Surface Area Grade 7 Focus: Proportional Reasoning Grade 8 Focus: Problem Solving

2014 SPBQ Data – 6.9, 6.10 SOL Description of Question % Correct in Division 6.9 Use ballpark comparisons between U.S. Customary System and metric system to estimate measurement 70 26 6.10d Find the volume of a rectangular prism 83 6.10b Solve practical problems involving circumference of a circle using the diameter and the definition of pi Solve practical problems involving the circumference of a circle 60 6.10c Solve practical problems involving the area of triangles 52 6.10a Apply the definition of pi to a practical problem 58

Performance Analysis Comparison SOL 6.9, 6.10 2012 SOL 6.9 – None SOL 6.10 – The student will define pi (π) as the ratio of the circumference of a circle to its diameter; solve practical problems involving circumference and area of a circle, given the diameter or radius; solve practical problems involving area and perimeter; and describe and determine the volume and surface area of a rectangular prism. 2013 define pi as the ratio of the circumference of a circle to its diameter; 2014

2014 SPBQ Data – 7.5, 8.7 SOL Description of Question % Correct in Division 7.5ab Describe volume and surface area of cylinders and rectangular prisms 26 7.5c Describe or solve practical problems where an attribute of the figure has been changed 78 7.5b Solve practical problems involving volume and surface area of rectangular prisms and cylinders 54 7b Use the dimensions of rectangular prisms or cylinders to describe or compare volume and surface areas 72 8.7a Investigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids 69 45

Performance Analysis Comparison SOL 7.5, 8.7 2012 SOL 7.5 – The student will describe volume and surface area of cylinders; solve practical problems involving the volume and surface area of rectangular prisms and cylinders; and describe how changing one measured attribute of a rectangular prism affects its volume and surface area. SOL 8.7 – The student will investigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids; and describe how changing one measured attribute of the figure affects the volume and surface area. 2013 SOL 7.5c – The student will SOL 8.7a – The student will describe how changing one measured attribute of a figure affects the volume and surface area. 2014 SOL 8.7 – None

2012 - Suggested Practice for SOL 6.10bc Students need additional practice finding circumference, perimeter, and area when figures are not included. Clinton purchased a circular rug to cover part of a floor. The diameter of the rug is 8 feet. Rounded to the nearest whole number, what area of the floor will the rug cover? 50 square feet A circular pool has a radius of 12 feet. What is the approximate distance around the pool, rounded to the nearest foot? Approximately 75 feet Dana has a rectangular garden that she wishes to fence in. If the dimensions of the garden are 15 feet by 13 feet, what is the minimum amount of fencing that she needs to enclose her garden? 56 feet Common Errors? Misconceptions?

2013 - Suggested Practice for SOL 6.10b Students need additional practice solving practical problems involving circumference and area, particularly when a figure is not provided. Leo is designing a circular table top with a diameter of 10 feet. 1. Which is closest to the circumference of this table top? 314.2 feet 78.5 square feet 31.4 feet 15.7 square feet 2. Which is closest to the area of this table top? a) 314.2 feet b) 78.5 square feet c) 31.4 feet d) 15.7 square feet 2013 - For SOL 6.10b, students need additional practice solving practical problems involving circumference and area, particularly when a figure is not provided. Student performance also indicates that students do not know whether the diameter or radius should be used in a calculation, and whether the resulting units are linear or square units. Questions like the ones on the screen give students practice finding circumference and area when given a diameter, as well as deciding the appropriate unit of measure for their answers. The answers are shown on the screen. Common Errors? Misconceptions?

2013 - Suggested Practice for SOL 6.10c Students need additional practice solving practical problems involving area and perimeter. This triangle represents a section of a garden. (Figure is not drawn to scale.) What are the area and perimeter of the garden? Area = 25.5 m² Perimeter = 35.3 m 5 m 4 m 3 m 13 m 13.3 m 2013 - For SOL 6.10c, students need additional practice solving practical problems involving area and perimeter. Student performance was inconsistent when students had to determine which information to use to answer the question. For instance, in this example, students need to determine which measurements to use to find the area, and which measurements to use to find the perimeter. As in the previous example, students also need practice determining the correct unit of measure to use when labeling the answers. The answers are shown on the screen. Common Errors? Misconceptions?

2014 - Suggested Practice for SOL 6.10b Students need additional practice finding the area of a circle. A circular plate has a diameter of 11 inches. Which is closest to the area of this plate? 17.3 square inches 34.6 square inches 95.0 square inches 380.1 square inches Most common error 2014 - For SOL 6.10b, students did very well finding the circumference of a circle but did not do as well when finding the area. For the question shown on the screen, students are asked to find the area of a circular plate, given its diameter. The most common error (multiplying pi by the diameter) and the answer are shown on the screen. The common error indicates that many students are applying the formula for circumference to an area problem, or it is possible that they are using the correct area formula, but incorrectly calculating the square of the radius as the radius times two. Common Errors? Misconceptions?

2012 - Suggested Practice for SOL 7.5c Students need additional practice determining what effect changing an attribute of a rectangular prism has on its volume and surface area. What effect does doubling the width, length, OR height of a prism have on its volume? The volume of the new prism is double the volume of the original prism. A rectangular prism has a volume of 16 cm3. If the height of the prism is tripled and the other dimensions stay the same, what is the volume of the new prism? 48 cm3 Common Errors? Misconceptions?

2012 - Suggested Practice for SOL 7.5c Students need additional practice determining what effect changing an attribute of a rectangular prism has on its volume and surface area. The rectangular prism shown has a surface area of 94 cm2. If the height of the prism is increased to 15 cm and the other dimensions remain the same, the surface area – Triples Increases by 20 cm2 Increases by 30 cm2 Increases by 140 cm2 Length = 4 cm Width = 3 cm Height = 5 cm Common Errors? Misconceptions?

2013 - Suggested Practice for SOL 7.5c Students need additional practice determining the effect of changing an attribute of a rectangular prism on its volume. Which method would result in tripling the volume of this rectangular prism? Add three to each dimension of the prism Add three to the height of the prism and keep the other dimensions the same Multiply each dimension of the prism by three Multiply the width of the prism by three and keep the other dimensions the same height=5 cm width=2 cm length=10 cm 2013 - For SOL 7.5c, students need additional practice determining the effect of changing an attribute of a rectangular prism on its volume. The example on the screen asks: Which method would result in tripling the volume of this rectangular prism? Student performance on questions requiring this type of analysis was lower than on questions in which students were given the attribute change and asked to determine the effect on the volume. The answer to the question is shown on the screen. Common Errors? Misconceptions?

2014 - Suggested Practice for SOL 7.5a Students need additional practice describing the surface area of a cylinder. One way to determine the surface area of this cylinder is to – add the areas of both bases to the rectangular area around the cylinder add the areas of both bases multiply the area of the base by the height multiply the rectangular area around the cylinder by pi 2014 - For SOL 7.5a, students need additional practice describing the surface area of a cylinder. The most common errors for an item similar to the one shown are for students to choose answer choices c and d. This may be because students recognize that area involves multiplication and they select an option with the key word “multiply” without making sense of the entire answer choice. Conceptually, students may not recognize that the shape around the cylinder can be a rectangle. Working with a net of a cylinder may help students understand the shapes that are involved. Working with nets, in conjunction with a discussion about what each term in the surface area formula represents, may help students connect the parts of the net and the surface area formula. Common Errors? Misconceptions?

2014 - Suggested Practice for SOL 7.5b Students need additional finding the volume of a cube, given its edge length. A container in the shape of a cube will be completely filled with sand. The container has an edge length of 8 inches. What is the exact number of cubic inches of sand needed to completely fill the container? 2014 - For SOL 7.5b, students need additional practice finding the volume of a cube, given its edge length. There are several misconceptions on items similar to the one shown on the screen. The most common misconception is to square the edge length. In this example, that error would result in an answer of 64 cubic inches. Another common error is to multiply the edge length by 6, which is the number of sides of a cube. Still, other students will multiply the edge length by three, rather than finding the value of the edge length to the third power. cubic inches Common Errors? Misconceptions?

2014 - Suggested Practice for SOL 7.5c Students need additional practice describing how a change in one measured attribute of a rectangular prism impacts volume. Rectangular Prism A is shown. Rectangular Prism B has the same height and width as rectangular Prism A but its length is 8 inches. The volume of Prism B is – twice the volume of Prism A one-half the volume of Prism A one-fourth the volume of Prism A four times the volume of Prism A h = 5 cm w = 3 cm l = 4 cm 2014 - For SOL 7.5c, students need additional practice describing how a change in a measured attribute of a rectangular prism impacts volume. The most common error for an item similar to the one shown on the screen is the selection of option B. The correct answer is shown on the screen. Most common error Common Errors? Misconceptions?

2012 - Suggested Practice for SOL 8.7 Students need additional practice calculating the surface area and volume of a three-dimensional figure. Brian purchased a trophy in the shape of a square pyramid for the most valuable player on his lacrosse team. The trophy had a slant height of 4 inches, and each side of its base measured 4 inches. Brian wanted to engrave text on the four sides of the trophy, but not on the base of the trophy. How many square inches of the trophy were available for engraving? 32 square inches 4 inches Common Errors? Misconceptions?

2012 - Suggested Practice for SOL 8.7 Students need additional practice calculating the surface area and volume of a three-dimensional figure. A paper weight mold in the shape of a square pyramid is filled with molten glass. How many cubic inches of molten glass are needed to fill the paper weight? 12 cubic inches Common Errors? Misconceptions?

2012 - Suggested Practice for SOL 8.7 Students need additional practice calculating the surface area and volume of a three-dimensional figure. Megan wrapped a present inside a cube-shaped box. The box had an edge length of 4 inches. How many square inches of paper were needed to wrap the box, if there was no overlap? 96 square inches 4 inches Common Errors? Misconceptions?

2012 - Suggested Practice for SOL 8.7 Students need additional practice calculating the surface area and volume of a three-dimensional figure. Anna built a prism (Prism A) in the shape of a cube out of wood. The side length of the cube measured 18 inches in length. Anna built another prism (Prism B) with the same dimensions as the cube, except she doubled its height. How does the volume of the two prisms compare? The volume of Prism B is twice the volume of Prism A. How does the surface area of the two prisms compare? The surface area of Prism B is greater than the surface area of Prism A. The surface area of the four sides of Prism B are twice the surface area of the four sides of Prism A, and the surface area of the two bases of Prism A and the two bases of Prism B are the same. Find the volume and surface area of Prism A and Prism B. 18 inches h 2h Prism A Prism B Common Errors? Misconceptions?

2013 - Suggested Practice for SOL 8.7a Students need additional practice determining surface area of a square- based pyramid. Timothy built a wooden square-based pyramid for a history class project on Egypt. He needs to buy enough gold paper to cover the entire surface. The base length is 2.5 ft and the slant height is 1.5 ft. What is the minimum amount of gold paper he needs to purchase? 13.75 sq ft 2.5 ft 1.5 ft 2013 - Students need additional practice determining the surface area of a square-based pyramid. Teachers are encouraged to provide practice with both multiple-choice and open-response formats and to include measurements that are decimals. The answer to the example is shown on the screen. Common Errors? Misconceptions?

Vertical Articulation of Content Grade 6 Focus: Problem Solving with Area, Perimeter, Volume, and Surface Area Grade 7 Focus: Proportional Reasoning Grade 8 Focus: Problem Solving

2014 SPBQ Data – Miscellaneous SOL Description of Question % Correct in Division 7.6 Use properties and proportions of quadrilaterals and triangles to determine corresponding sides and angles of similar figures 81 82 80 8.6 Describe and verify angle relationships among vertical, adjacent, supplementary, and complementary angles 49

Performance Analysis Comparison SOL 2012 SOL 7.6 – None SOL 8.6 – The student will verify by measuring and describe the relationships among vertical angles, adjacent angles, supplementary angles, and complementary angles; and measure angles of less than 360°. 2013 SOL 7.6 – The student will determine whether plane figures—quadrilaterals and triangles—are similar and write proportions to express the relationships between corresponding sides of similar figures. SOL 8.6 – The student will 2014 SOL 7.6 – None SOL 8.6 – None

2013 - Suggested Practice for SOL 7.6 Students need additional practice identifying a proportion that can be used to determine the missing side length of a triangle, when given similar triangles. Triangle JKL is similar to triangle PQR. Which three proportions can be used to find the value of x? K L P Q R 8 10 6 5 x 3 2013 - For SOL 7.6, students need additional practice identifying a proportion that can be used to determine the missing side length of a triangle, when given similar triangles. It is important for students to recognize that many different proportions can be written to solve for a missing side. Students must be able to recognize any one of the correct proportions among the answer options in a multiple choice item. Questions such as the example provided will give students practice identifying multiple correct proportions that can be used to solve for a missing side. The answers are shown on the screen. Common Errors? Misconceptions?

2012 - Suggested Practice for SOL 8.6 Students need additional practice recognizing angle relationships, given a diagram. 1 2 3 4 5 6 Name the pairs of vertical angles in the figure. Which two angles are supplementary? Name an angle in the figure that is adjacent to angle 2. Which pairs of angles are complementary? 2012 Common Errors? Misconceptions?

2013 - Suggested Practice for SOL 8.6a Students need additional practice identifying angle relationships among multiple angles. Name pairs of vertical, adjacent, supplementary, and complementary angles. Vertical Angles Complementary Angles a e b d c a and c e and d Supplementary Angles Adjacent Angles 2012 a and b b and c c and d d and e a and e a and b b and c a and c 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