Download sample tasks - Deep Curriculum Alignment Project for Mathematics

Common Core Learning Standards
GRADE 8 Mathematics
GEOMETRY
Common Core Learning
Standards
Understand congruence and
similarity using physical models,
transparencies, or geometry
software.
8.G.1.
Verify experimentally the properties of
rotations, reflections, and translations:
8.G.1a.
Lines are taken to lines, and line segments to
line segments of the same length.
Concepts
Embedded Skills
Transformations Translate, rotate, and reflect figures.
Explain the preservation of the sides of a figure
through a given transformation.
Identify corresponding parts between a figure and
its image using prime notation.
Show that lines are taken to lines and line
segments are taken to line segments.
Vocabulary
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Rotation
Reflection
Translation
Congruence
Transformation
Corresponding
parts
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Understand congruence and
similarity using physical models,
transparencies, or geometry
software.
8.G.1.
Verify experimentally the properties of
rotations, reflections, and translations:
8.G.1b.
Angles are taken to angles of the same
measure.
Concepts
Embedded Skills
Transformations Translate, rotate, and reflect geometric shapes on
a coordinate plane.
Measure angles using a protractor.
Identify corresponding parts between a figure and
its image using prime notation.
Show that angles are taken to angles of the same
measure.
Vocabulary
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Rotation
Reflection
Translation
Congruence
Properties
Transformation
Corresponding
parts
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Understand congruence and
similarity using physical models,
transparencies, or geometry
software.
8.G.1.
Verify experimentally the properties of
rotations, reflections, and translations:
8.G.1c.
Parallel lines are taken to parallel lines.
Concepts
Embedded Skills
Transformations Translate, rotate, and reflect geometric shapes on
a coordinate plane.
Explain what happens to parallel lines after a
given transformation.
Identify corresponding parts between a figure and
its image using prime notation.
Show that parallel lines are taken to parallel lines.
Vocabulary
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Parallel lines
Rotation
Reflection
Translation
Transformation
Slope/rate of
change
Corresponding
parts
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Understand congruence and
similarity using physical models,
transparencies, or geometry
software.
Concepts
Congruent
figures
Embedded Skills
Explain the preservation of congruence when a
figure is rotated, reflected, and/or translated.
Describe the sequence of transformations that
occurred from the original 2D figure to the image.
8.G.2.
Understand that a two-dimensional figure is
congruent to another if the second can be
obtained from the first by a sequence of
rotations, reflections, and translations; given
two congruent figures, describe a sequence
that exhibits the congruence between them.
Vocabulary
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Transformation
Reflection
Rotation
Translation
Congruence
Corresponding
parts
sequence
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Understand congruence and
similarity using physical models,
transparencies, or geometry
software.
8.G.3.
Describe the effect of dilations, translations,
rotations, and reflections on two-dimensional
figures using coordinates.
Concepts
Embedded Skills
Transformations Dilate a two-dimensional figure using coordinates.
Describe the effect of dilating a two-dimensional
figure using coordinates.
Rotate a two-dimensional figure using coordinates.
Describe the effect of rotating a two-dimensional
figure using coordinates.
Translate a two-dimensional figure using
coordinates.
Describe the effect of translating a twodimensional figure using coordinates.
Reflect a two-dimensional figure using
coordinates.
Describe the effect of reflecting a two-dimensional
figure using coordinates.
Vocabulary
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Coordinate
Figure
Ordered pair
Reflect
Translate
Dilate
Rotate
Transformation
Prime
Image
X-axis
Y-axis
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Understand congruence and
similarity using physical models,
transparencies, or geometry
software.
Concepts
Embedded Skills
Similarity with Explain the preservation of similarity when a figure
transformations is dilated, rotated, reflected, and/or translated.
Describe the sequence of transformations that
occurred from the original 2D figure to the image
to show the similarity.
8.G.4.
Understand that a two-dimensional figure is
similar to another if the second can be
obtained from the first by a sequence of
rotations, reflections, translations, and
dilations; given two similar two-dimensional
figures, describe a sequence that exhibits the
similarity between them.
Vocabulary
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Rotation
Reflection
Translation
Dilation
Transformation
Similarity
Congruent
Similar
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Concepts
Embedded Skills
Understand congruence and
similarity using physical models,
transparencies, or geometry
software.
Prove/explain why the three angles of a triangle
equal 180°.
Prove/explain the exterior angle theorem of a
triangle.
8.G.5.
Use informal arguments to establish facts
about the angle sum and exterior angle of
triangles, about the angles created when
parallel lines are cut by a transversal, and the
angle-angle criterion for similarity of triangles.
For example, arrange three copies of the same
triangle so that the sum of the three angles
appears to form a line, and give an argument
in terms of transversals why this is so.
Prove/explain why alternate interior angles are
congruent.
Prove/explain why alternate exterior angles are
congruent.
Prove/explain why corresponding angles are
congruent.
Prove/explain why angle-angle criterion works to
prove similarity of two triangles.
Vocabulary
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Triangle
Similar
Parallel lines
Transversal
Congruent
Supplementary
Linear pair
Corresponding
Vertical
Alternate,
exterior,
interior angles
SAMPLE TASKS
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Given AC DE . Prove that the angles of
BED add up to 180 .
A
B
C
58 62
D
E
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.

Triangle XYZ and its exterior angles are shown below.
1
X
Y
2
Z
Part A: What is
Part B: What is
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mÐ1?
mÐ2 ? Explain how you found your answer?
In the figure below, mÐ2 = 118 and mÐ5 = 72 .
1
3
7
5
8
4
2
r
6
s
Part A: Name a pair of corresponding angles.
Part B: Are lines r and s parallel? Explain how you know.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.

The measure of two angles of
ABC are given as 40 and 80 . The measure of two angles of FED are given as 80 and 60 .
E
D
F
Part A: Are ABC and FED similar?
Part B: Explain how you are able to tell whether or not the two triangles are similar.
Common Core Learning
Standards
Understand and apply the
Pythagorean Theorem.
8.G.6.
Explain a proof of the Pythagorean Theorem
and its converse.
Concepts
Embedded Skills
Pythagorean
theorem
Explain a proof of Pythagorean theorem. (If a
triangle is a right triangle, then a2 + b2 = c2)
Explain a proof of the converse of Pythagorean
theorem. (If a2 + b2 = c2, then a triangle is a right
triangle)
Identify the legs and hypotenuse of a right triangle.
Solve multi-step equations.
Vocabulary
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Pythagorean
theorem
Converse
Proof
Legs
Hypotenuse
SAMPLE TASKS
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Given triangle ABC with side lengths of 10 cm, 8 cm, and 5 cm prove whether or not the sides form a right triangle.
The inside edges of three fields meet to form a right triangle. The first field has an edge of 30 yards, the second field has an edge of
40 yards, and the third field has an edge of 50 yards. Use this to show the Pythagorean Theorem is true.
Jacob needs to construct a right triangle using drinking straws. If he has straw lengths of 5 cm, 12 cm and 15 cm, can he construct a
right triangle? Explain why or why not.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Understand and apply the
Pythagorean Theorem.
8.G.7.
Apply the Pythagorean Theorem to determine
unknown side lengths in right triangles in realworld and mathematical problems in two and
three dimensions.
Concepts
Embedded Skills
Pythagorean
theorem
Calculate the length of a leg of a right triangle using
Pythagorean theorem.
Calculate the length of the hypotenuse of a right
triangle using Pythagorean theorem.
Calculate the diagonal of a three-dimensional figure
using Pythagorean Theorem.
Read and interpret a word problem involving
Pythagorean Theorem.
Solve word problems involving Pythagorean
Theorem.
Solve multi-step equations.
Identify the legs and hypotenuse of a right triangle.
Round to given place value.
Vocabulary
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Leg
Hypotenuse
Right angle
Pythagorean
theorem
Square root
Radical
Diagonals
SAMPLE TASKS
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In Juanita’s Little League championship game the bases are all 60 feet apart forming a square. Juanita is on first base planning on
stealing second, how far does the catcher need to throw the ball from home plate to second base in order to make the out?
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Simon leans a 20-foot ladder against the side of his house so that the base of the ladder is 5 feet from the house. About how high up
the side of the house does the ladder reach? Round your answer to the nearest tenth of a foot.
A cylindrical can of soda has a height of 5 inches and a diameter of 2 inches as shown. What is the shortest straw that can be used in
this can so that it doesn’t fall into the can?

5 in
2 in
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Concepts
Understand and apply the
Pythagorean Theorem.
8.G.8.
Apply the Pythagorean Theorem to find the
distance between two points in a coordinate
system.
Pythagorean
theorem on a
coordinate
plane
Embedded Skills
Calculate the distance between two points in a
coordinate plane using the Pythagorean Theorem.
Plot points in a coordinate plane
Solve multi-step equations
Identify the legs and hypotenuse of a right triangle
Solve Pythagorean Theorem
Vocabulary
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Leg
Hypotenuse
Right angle
Pythagorean
theorem
Ordered pair
Coordinate
plane
Square root
Distance
formula
SAMPLE TASKS
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Line segment XY has endpoints at (6, 1) and (-6, 6). What is the length of XY ?
A team of archaeologists fenced off an ancient ruin they are exploring. They created a grid to represent the area, so they could label
the locations of several artifacts. If each unit on the grid represents 2 meters, approximately how many meters apart were the
pitcher and the pot found.
A
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What is the approximate length of
AB shown on the right?
B
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Concepts
Embedded Skills
Write and solve using the formula for the volume
of a cone.
Write and solve using the formula for the volume of
a cylinder.
Write and solve using the formula for the volume of
a sphere.
Solve word problems involving the volume of cones,
cylinders, and spheres.
Solve a multi-step equation for a missing variable.
Solve real-world and mathematical
problems involving volume of
cylinders, cones, and spheres.
8.G.9.
Know the formulas for the volumes of cones,
cylinders, and spheres and use them to solve
real-world and mathematical problems.
Vocabulary
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Volume
Cone
Cylinder
Sphere
Area
Base
Formula
SAMPLE TASKS
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How much ice cream can fit exactly inside a cone that has a diameter of 8 centimeters and a height of 9 centimeters?
A pitcher holds 1,614.7 in3 of liquid. Each can of punch is 15 inches tall with a diameter of 8 inches. How many full cans will the
pitcher hold? Explain.
A cylindrical can has a height of 24 inches and a volume of 864 p cubic inches. What is its diameter?
To the nearest cubic inch, how much space is there inside a hamster ball with a diameter of 10 inches?
Two companies manufacture tanks that store water. Company A sells cylindrical tanks like the one shown below for $500, and
company B sells spherical tanks like the one shown below also for $500. Which company should you purchase your tank from in
order to maximize your water storage?
r = 2.5
ft
8 ft
3 ft
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.