Transcript Geometry Content Academy

MIDDLE SCHOOL CONTENT ACADEMY
Measurement
SOL 6.9, 6.10, 7.5, 7.6, 8.6, 8.7
March 11, 2015
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
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, 8.7
SOL
7.5ab
Description of Question
% Correct in Division
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
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
7b
2012 - SUGGESTED PRACTICE FOR SOL 6.10BC
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?
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.
a)
b)
c)
d)
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
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.)
13.3 m
5m
3m
4m
13 m
What are the area and perimeter of the garden?
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?
a)
b)
c)
d)
17.3 square inches
34.6 square inches
95.0 square inches
380.1 square inches
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.
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?
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.
Height = 5 cm
Width = 3 cm
Length = 4 cm
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 cm2
c) Increases by 30 cm2
Common Errors? Misconceptions?
d) Increases by 140 cm2
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?
height=5 cm
width=2 cm
length=10 cm
a)
b)
c)
d)
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
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 –
a)
b)
c)
d)
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
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?
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.
h = 5 cm
l = 4 cm
w = 3 cm
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
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.
4 inches
4 inches
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?
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?
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.
4 inches
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?
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.
a)
How does the volume of the two prisms compare?
h
b)
How does the surface area of the two prisms compare?
2h
18 inches
Prism A
18 inches
Prism B
c)
Find the volume and surface area of Prism A and Prism B.
Common Errors? Misconceptions?
2013 - SUGGESTED PRACTICE FOR SOL 8.7A
Students need additional practice determining surface area of a squarebased 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.
1.5 ft
2.5 ft
What is the minimum amount of gold paper he needs to purchase?
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
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
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.
Q
8
10
3
R
K
6
x
5
L
P
Which three proportions can be used to find the value of x?
Common Errors? Misconceptions?
2012 - SUGGESTED PRACTICE FOR SOL 8.6
Students need additional practice recognizing angle relationships, given a
diagram.
a) Name the pairs of vertical angles in the figure.
b) Which two angles are supplementary?
6
c) Name an angle in the figure that is adjacent to angle 2.
1
5
4
2
3
d) Which pairs of angles are complementary?
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
d
c
e
Supplementary Angles
Complementary Angles
Adjacent Angles
a
b
Common Errors? Misconceptions?
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
Student Engagement
Activities