Download Math Student Assessment Gr 6 Measurement and Geometry

6th Grade Measurement and Geometry
Name
Items aligned to core and extended core GLCEs
1. A rectangle has sides of 2 feet and 3 feet. Its area is 6 square feet. What is the area of this
rectangle in square inches?
3 ft
a)
b)
c)
d)
60 square inches
120 square inches
144 square inches
864 square inches
2 ft
A = 6 sq ft
2. These two rhombuses are congruent. Therefore the measure of angle x is
a) 30o
b) 60o
c) 115o
d) 120o
12 cm
6 cm
60o
Jackson Co. ISD & Mid-Michigan Consortium
x
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3. Which transformation moves rectangle A into rectangle B?
L
A
P
B
a) two translations: first down, and then to the right
b) a rotation around point P
c) a reflection through the line
d) an expansion from quadrant 2 to quadrant 1
4. Part 1: In the figure below, first draw the rotation of the square 90o around point Q.
Q
Part 2: Then draw the translation of the rectangle six units downward.
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Item
1
2
3
4
Correct Answer
d
b
c
GLCE
M.UN.06.01
G.GS.06.02
G.TR.06.03
G.TR.06.04
The student
could rotate the
rectangle in the
other direction
(counterclockwis
e) and then
translate
downward. Either
approach is
acceptable. See
figure at right.
rotation
P
translation
P
5
6
7
8
9
10
11
12
13
14
15
16
Students’ answers should show 6 square faces, connected
appropriately.
c
d
a and c, b and d
c
a and b, b and c, c and d, d and a
d
q and p, r and s, q and r, p and s
c
a
Angles g and h are supplementary (their sum is 180o). The
sum of all the interior angles of the triangle is 180o also.
Therefore, since h + g = 180 o and h + j + k = 180 o, then g = j
+ k.
Angle r is one external angle. Each vertex has another
external angle, for a total of 6 external angles. All would be
the same measure. Since there are 6 external angles, and
their sum is 360 o, then each external angle is 60 o. Since
angle p and r are supplementary, p = 120 o.
p
M.PS.06.02
M.TE.06.03
M.TE.06.03
G.GS.06.01
G.GS.06.01
G.GS.06.01
G.GS.06.01
G.GS.06.01
G.GS.06.01
G.GS.06.01
G.GS.06.01
G.GS.06.01
r
There are no items for this GLCE. It will not be assessed on
the MEAP.
G.SR.06.05
GLCEs in grey are designated as “future core” by MEAP.
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MEASUREMENT
• Units and systems of measurement (UN)
• Techniques and formulas for measurement (TE)
• Problem solving involving measurement (PS)
Convert within measurement systems
M.UN.06.01
Convert between basic units of measurement within a single measurement system, e.g., square inches to square
feet. [Core]
Find volume and surface area
M.PS.06.02
Draw patterns (of faces) for a cube and rectangular prism that, when cut, will cover the solid exactly (nets). [Fut]
M.TE.06.03
Compute the volume and surface area of cubes and rectangular prisms given the lengths of their sides using
formulas. [Fut]
GEOMETRY
• Geometric shape and properties, and mathematical arguments (GS)
• Location and spatial relationships (LO)
• Spatial reasoning and geometric modeling (SR)
• Transformation and Symmetry (TR)
Understand and apply basic properties
G.GS.06.01
Understand and apply basic properties of lines, angles, and triangles, including:
—triangle inequality
—relationships of vertical angles, complementary angles, supplementary angles
—congruence of corresponding and alternate interior angles when parallel lines
—are cut by a transversal, and that such congruences imply parallel lines
—locate interior and exterior angles of any triangle, and use the property that an exterior
—angle of a triangle is equal to the sum of the remote (opposite) interior angles
—know that the sum of the exterior angles of a convex polygon is 360º. [Fut]
G.GS.06.02
Understand that for polygons, congruence means corresponding sides and angles have equal measures. [Core]
G.TR.06.03
Understand the basic rigid motions in the plane (reflections, rotations, translations), relate these to congruence, and
apply them to solve problems. [Core]
G.TR.06.04
Understand and use simple compositions of basic rigid transformations, e.g., a translation followed by a reflection.
[Core]
Construct geometric shapes
G.SR.06.05
Use paper folding to perform basic geometric constructions of perpendicular lines, midpoints of line segments and
angle bisectors; justify informally. [NASL]
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6th Grade Measurement and Geometry
Name
Items aligned to future core GLCEs
5. Which pattern of squares could be folded to make a cube, so that no square overlaps any
others?
a)
b)
c)
d)
6. Find the volume of this rectangular prism with sides of 2 inches, 4 inches and 3 inches.
a)
b)
c)
d)
9 cubic inches
18 cubic inches
24 cubic inches
27 cubic inches
3 in.
2 in.
4 in.
7. Find the surface area of the rectangular prism above. The surface area is how many square
inches of wrapping paper would be needed to cover all of the sides without overlapping.
a)
b)
c)
d)
12 square inches
16 square inches
24 square inches
52 square inches
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8. In the parallelogram shown below, the diagonals intersect each other and make four angles,
a, b, c and d. Name two pairs of vertical angles:
Pair 1: angle ___ and angle ___
b
a
Pair 2: angle ___ and angle ___
c
d
9. In the parallelogram above, which of the following is true?
a) measure of angle a = measure of angle b
b) measure of angle a = measure of angle c + measure of angle d
c) measure of angle a = measure of angle c
d) measure of angle c + measure of angle d = 90˚
10. In the parallelogram for #8, name two angles that are supplementary:
a) angle a and angle b
b) angle a and angle c
c) angle a and angle d
d) angle b and angle d
Explain your answer:
11. If these two horizontal lines are parallel, what is true about angles p and r?
p
q
r
s
a) measure of angle p + measure of angle r = 90˚
b) measure of angle p + measure of angle r = 180˚
c) measure of angle p > measure of angle r
d) measure of angle p = measure of angle r
12. In the drawing in #11 of parallel lines, name two angles that are supplementary.
a) angle p and angle r
b) angle p and angle s
c) angle q and angle s
d) angle q and angle r
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13. Joan was making a box as a gift. She wanted the box to be a perfect rectangle. To see if the
opposite sides were parallel, she drew one of the diagonals on the top of the box. The
diagonal made several angles, as shown.
e
a
c
d
b
Which angles have to be equal in order for the opposite sides to be parallel?
a)
b)
c)
d)
<a and <b
<a and <c
<a and <d
<a and <e
14. In the rectangle for #13, identify two angles that are complimentary.
a) < a and < b
b) < b and < c
c) < c and < e
d) < d and < e
15. In this triangle, explain why the measure of angle g equals the sum of the measures of
angle j + angle k.
j
k
h
g
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16. Draw one external angle at each of the vertices of this regular hexagon.
p
Use the fact that the sum of the external angles of any convex polygon (including this
hexagon) equals 360o to determine the measure of angle p. Show how you got your answer.
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