1. MIDDLE SCHOOL CONTENT ACADEMY Measurement SOL 6.9, 6.10, 7.5, 7.6, 8.6, 8.7 March 11, 2015

2. Grade 6 Focus: Problem Solving with Area, Perimeter, Volume, and Surface Area Grade 7 Focus: Proportional Reasoning Grade 8 Focus: Problem Solving VERTICAL ARTICULATION OF CONTENT

3. 2014 SPBQ DATA – 6.9, 6.10 SOLDescription of Question% Correct in Division 6.9Use ballpark comparisons between U.S. Customary System and metric system to estimate measurement 70 6.9Use ballpark comparisons between U.S. Customary System and metric system to estimate measurement 26 6.10dFind the volume of a rectangular prism83 6.10bSolve practical problems involving circumference of a circle using the diameter and the definition of pi 70 6.10bSolve practical problems involving the circumference of a circle60 6.10cSolve practical problems involving the area of triangles52 6.10aApply the definition of pi to a practical problem58

4. 2014 SPBQ DATA – 7.5, 8.7 SOLDescription of Question% Correct in Division 7.5abDescribe volume and surface area of cylinders and rectangular prisms 26 7.5cDescribe or solve practical problems where an attribute of the figure has been changed 78 7.5bSolve practical problems involving volume and surface area of rectangular prisms and cylinders 54 7bUse the dimensions of rectangular prisms or cylinders to describe or compare volume and surface areas 72 8.7aInvestigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids 69 8.7aInvestigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids 45

5. 2012 - SUGGESTED PRACTICE FOR SOL 6.10BC Common Errors ? Misconceptions? Students need additional practice finding circumference, perimeter, and area when figures are not included. a)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? b)A circular pool has a radius of 12 feet. What is the approximate distance around the pool, rounded to the nearest foot? c)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?

6. 2013 - SUGGESTED PRACTICE FOR SOL 6.10B Common Errors ? Misconceptions? 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? a)314.2 feet b)78.5 square feet c)31.4 feet d)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

7. 2013 - SUGGESTED PRACTICE FOR SOL 6.10C Common Errors ? Misconceptions? 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? 5 m 4 m 3 m 13 m 13.3 m

8. 2014 - SUGGESTED PRACTICE FOR SOL 6.10B Common Errors ? Misconceptions? 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? a)17.3 square inches b)34.6 square inches c)95.0 square inches d)380.1 square inches

9. 2012 - SUGGESTED PRACTICE FOR SOL 7.5C Common Errors ? Misconceptions? Students need additional practice determining what effect changing an attribute of a rectangular prism has on its volume and surface area. a)What effect does doubling the width, length, OR height of a prism have on its volume? b)A rectangular prism has a volume of 16 cm 3. If the height of the prism is tripled and the other dimensions stay the same, what is the volume of the new prism?

10. 2012 - SUGGESTED PRACTICE FOR SOL 7.5C Common Errors ? Misconceptions? 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 cm 2. If the height of the prism is increased to 15 cm and the other dimensions remain the same, the surface area – a)Triples b)Increases by 20 cm 2 c)Increases by 30 cm 2 d)Increases by 140 cm 2 Length = 4 cm Width = 3 cm Height = 5 cm

11. 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. Common Errors ? Misconceptions? Which method would result in tripling the volume of this rectangular prism? a)Add three to each dimension of the prism b)Add three to the height of the prism and keep the other dimensions the same c)Multiply each dimension of the prism by three d)Multiply the width of the prism by three and keep the other dimensions the same height=5 cm width=2 cm length=10 cm

12. Students need additional practice describing the surface area of a cylinder. One way to determine the surface area of this cylinder is to – a)add the areas of both bases to the rectangular area around the cylinder b)add the areas of both bases c)multiply the area of the base by the height d)multiply the rectangular area around the cylinder by pi 2014 - SUGGESTED PRACTICE FOR SOL 7.5A Common Errors ? Misconceptions?

13. 2014 - SUGGESTED PRACTICE FOR SOL 7.5B Common Errors ? Misconceptions? 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? cubic inches

14. 2014 - SUGGESTED PRACTICE FOR SOL 7.5C Common Errors ? Misconceptions? 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 – a)twice the volume of Prism A b)one-half the volume of Prism A c)one-fourth the volume of Prism A d)four times the volume of Prism A h = 5 cm w = 3 cm l = 4 cm

15. 2012 - SUGGESTED PRACTICE FOR SOL 8.7 Common Errors ? Misconceptions? 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? 4 inches

16. 2012 - SUGGESTED PRACTICE FOR SOL 8.7 Common Errors ? Misconceptions? 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?

17. 2012 - SUGGESTED PRACTICE FOR SOL 8.7 Common Errors ? Misconceptions? 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? 4 inches

18. 2012 - SUGGESTED PRACTICE FOR SOL 8.7 Common Errors ? Misconceptions? 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. a)How does the volume of the two prisms compare? b)How does the surface area of the two prisms compare? c)Find the volume and surface area of Prism A and Prism B. 18 inches h 2h Prism A Prism B 18 inches

19. 2013 - SUGGESTED PRACTICE FOR SOL 8.7A Common Errors ? Misconceptions? 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? 2.5 ft 1.5 ft

20. Grade 6 Focus: Problem Solving with Area, Perimeter, Volume, and Surface Area Grade 7 Focus: Proportional Reasoning Grade 8 Focus: Problem Solving VERTICAL ARTICULATION OF CONTENT

21. 2014 SPBQ DATA – MISCELLANEOUS SOL SOLDescription of Question% Correct in Division 7.6Use properties and proportions of quadrilaterals and triangles to determine corresponding sides and angles of similar figures 81 7.6Use properties and proportions of quadrilaterals and triangles to determine corresponding sides and angles of similar figures 82 7.6Use properties and proportions of quadrilaterals and triangles to determine corresponding sides and angles of similar figures 80 8.6Describe and verify angle relationships among vertical, adjacent, supplementary, and complementary angles 49

22. 2013 - SUGGESTED PRACTICE FOR SOL 7.6 Common Errors ? Misconceptions? 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

23. 2012 - SUGGESTED PRACTICE FOR SOL 8.6 Common Errors ? Misconceptions? Students need additional practice recognizing angle relationships, given a diagram. 1 2 3 4 5 6 a)Name the pairs of vertical angles in the figure. b)Which two angles are supplementary? c)Name an angle in the figure that is adjacent to angle 2. d)Which pairs of angles are complementary?

24. 2013 - SUGGESTED PRACTICE FOR SOL 8.6A Common Errors ? Misconceptions? Students need additional practice identifying angle relationships among multiple angles. Name pairs of vertical, adjacent, supplementary, and complementary angles. a e b d c Vertical Angles Adjacent AnglesSupplementary Angles Complementary Angles

25. RESOURCES 1.ExamView BanksExamView Banks 2.NextLesson.orgNextLesson.org 3.HCPS Math Website - http://teachers.henrico.k12.va.us/math/courses/http://teachers.henrico.k12.va.us/math/courses/  VDOE Enhanced Scope and Sequence  Skills - JMU Pivotal Items 4.ExploreLearning Teaching Strategies Student Engagement Activities