MIDDLE SCHOOL CONTENT ACADEMY

MeasurementSOL 6.9, 6.10, 7.5, 7.6, 8.6, 8.7 March 11, 2015

Grade 6 Focus: Problem Solving with Area, Perimeter, Volume, and Surface AreaGrade 7 Focus: Proportional Reasoning Grade 8 Focus: Problem Solving

VERTICAL ARTICULATION OF CONTENT

2014 SPBQ DATA – 6.9, 6.10SOL Description of Question % Correct in

Division

6.9 Use ballpark comparisons between U.S. Customary System and metric system to estimate measurement

70

6.9 Use ballpark comparisons between U.S. Customary System and metric system to estimate measurement

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

70

6.10b 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

2014 SPBQ DATA – 7.5, 8.7SOL 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

8.7a Investigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids

45

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?

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 feetb)78.5 square feetc)31.4 feetd)15.7 square feet

2. Which is closest to the area of this table top?a) 314.2 feetb) 78.5 square feetc) 31.4 feetd) 15.7 square feet

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

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 inchesb) 34.6 square inchesc) 95.0 square inchesd) 380.1 square inches

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 cm3. If the height of the prism is tripled and the other dimensions stay the same, what is the volume of the new prism?

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 cm2.

If the height of the prism is increased to 15 cm and the other dimensions remain the same, the surface area – a) Triplesb) Increases by 20 cm2

c) Increases by 30 cm2

d) Increases by 140 cm2

Length = 4 cmWidth = 3 cm

Height = 5 cm

2013 - SUGGESTED PRACTICE FOR SOL 7.5CStudents 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 prismb) Add three to the height of the prism and keep the other dimensions the samec) Multiply each dimension of the prism by threed) Multiply the width of the prism by three and keep the other dimensions the same

height=5 cm

width=2 cmlength=10 cm

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 basesc)multiply the area of the base by the heightd)multiply the rectangular area around the cylinder by pi

2014 - SUGGESTED PRACTICE FOR SOL 7.5A

Common Errors? Misconceptions?

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

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

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

4 inches

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?

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

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

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

Grade 6 Focus: Problem Solving with Area, Perimeter, Volume, and Surface AreaGrade 7 Focus: Proportional Reasoning Grade 8 Focus: Problem Solving

VERTICAL ARTICULATION OF CONTENT

2014 SPBQ DATA – MISCELLANEOUS SOL 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

7.6 Use properties and proportions of quadrilaterals and triangles to determine corresponding sides and angles of similar figures

82

7.6 Use properties and proportions of quadrilaterals and triangles to determine corresponding sides and angles of similar figures

80

8.6 Describe and verify angle relationships among vertical, adjacent, supplementary, and complementary angles

49

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

810

65

x3

2012 - SUGGESTED PRACTICE FOR SOL 8.6

Common Errors? Misconceptions?

Students need additional practice recognizing angle relationships, given a diagram.

1

23

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?

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.

ae

b

d

c

Vertical Angles

Adjacent AnglesSupplementary Angles

Complementary Angles

RESOURCES

1. ExamView Banks

2. NextLesson.org

3. HCPS Math Website - http://teachers.henrico.k12.va.us/math/courses/

VDOE Enhanced Scope and Sequence Skills - JMU Pivotal Items

4. ExploreLearning

Teaching Strategies

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