Download 4th Nine Weeks

8th Grade Mathematics Quarter 4 Curriculum Map
Unit: Geometry and Measurement
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4th Nine Weeks
2013-2014
Suggested Number of Days: 14 18
Unit Summary (Learning Target/Goal):
• Develop an understanding of the congruence and similarity of two-dimensional figures; use informal arguments to establish
facts about the sum of the angles of a triangle, the exterior angle of triangles, and the angles created when parallel lines are cut
by a transversal.
• Solve real-world and mathematical problems involving the volume of cylinders, cones, and spheres; apply understanding of
Pythagorean Theorem to find unknown side lengths of right triangles when determining the volume of three-dimensional
figures.
CCSS for Mathematical Content:
Key Vocabulary:
Geometry—Understand congruence and similarity using physical models, transparencies, or
angle of rotation
geometry software.
center of rotation
dilation
enlargement
8.G.1. Verify experimentally the properties of rotations, reflections, and translations:
image
line of reflection
8.G.1.a. Lines are taken to lines, and line segments to line segments of the same length.
line of symmetry
reduction
8.G.1.b. Angles are taken to angles of the same measure.
reflection
reflection symmetry
8.G.1.c. Parallel lines are taken to parallel lines.
rotation
rotational symmetry
8.G.2. Understand that a two-dimensional figure is congruent to another if the second can be
scale factor
obtained from the first by a sequence of rotations, reflections, and translations; given two congruent transformation
figures, describe a sequence that exhibits the congruence between them.
translation
Examples:
• Is Figure A congruent to Figure A’? Explain how you know.
Grade 8 Quarter 4 1
8th Grade Mathematics Quarter 4 Curriculum Map
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2013-2014
Describe the sequence of transformations that results in the transformation of Figure A to
Figure A’.
8.G.3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional
figures using coordinates.
A dilation is a transformation that moves each point along a ray emanating from a fixed center, and
multiplies distances from the center by a common scale factor. In dilated figures, the dilated figure
is similar to its pre-image.
Translation: A translation is a transformation of an object that moves the object so that every point
of the object moves in the same direction as well as the same distance. In a translation, the translated
object is congruent to its pre-image.
• ΔABC has been translated 7 units to the right and 3 units up. To get from A (1,5) to A’ (8,8),
move A 7 units to the right (from x = 1 to x = 8) and 3 units up (from y = 5 to y = 8). Points
B + C also move in the same direction (7 units to the right and 3 units up).
Grade 8 Quarter 4 2
8th Grade Mathematics Quarter 4 Curriculum Map
2013-2014
Reflection: A reflection is a transformation that flips an object across a line of reflection (in a
coordinate grid the line of reflection may be the x or y axis). In a rotation, the rotated object is
congruent to its pre-image
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.
Examples:
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Is Figure A similar to Figure A’? Explain how you know.
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Describe the sequence of transformations that results in the transformation of Figure A to
Grade 8 Quarter 4 3
8th Grade Mathematics Quarter 4 Curriculum Map
2013-2014
Figure A’.
Geometry--- 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. *Suggested math practices #1,4.
.
Example-Mr. Hernandez leans a 10' ladder against the side of his house. Because of the shrubs, the
foot of the ladder must be 6 feet away from the house. How far up the side of the house does the
ladder go?
Grade 8 Quarter 4 4
8th Grade Mathematics Quarter 4 Curriculum Map
Geometry--- 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.
*Suggested math practice #2
2013-2014
Key Vocabulary:
cone
cylinder
polyhedron
prism
pyramid
similar solids
skew lines
solids
sphere
volume
Example-As Barbara was eating breakfast one day, she realized
that there were several geometric shapes on the table. Her plate is in the shape of a circle, her juice
glass is a cylinder and her cereal box is a rectangular prism. Given the dimensions of her cereal box,
what is the volume of the box?
CCSS for Mathematical Practice:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
4. Model with mathematics
Explanation/Examples:
-Name solids and their parts
- Recognize solids
- Identify skew line segments
- Find volume of triangular prism
- Find volume of cylinder
- Find volume of square pyramid
- Use volume formulas
- Find surface area and volume of sphere
- Find dimensions of similar solids
Resources:
Assessment:
Prentice Hall Mathematics Common
Core Course 3
www.basic-mathematics.com
www.sascurriculumpathways.com
www.kidsmathgamesonline.com
www.discoveryeducation.com/streaming
- Classwork/Homework
- Lesson quizzes
- Unit test
- District Common Formative
Assessment
Grade 8 Quarter 4 5
8th Grade Mathematics Quarter 4 Curriculum Map
2013-2014
- Surface area and volume of similar solids
Reflection/Notes:
4th Nine Weeks
Suggested Number of Days: 14 - 18
Unit: Geometry
Unit Summary (Learning Target/Goal):
Develop an understanding of the congruence and similarity of two-dimensional figures; use informal arguments to establish facts
about the sum of the angles of a triangle, the exterior angle of triangles, and the angles created when parallel lines are cut by a
transversal.
CCSS for Mathematical Content:
Key Vocabulary:
Geometry---Understand congruence and similarity using physical models, transparencies,
adjacent angles
or geometry software.
alternate interior angles
. complementary
8.G.5. Use informal arguments to establish facts about the angle sum and exterior angle of
congruent angles
triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle congruent polygons
criterion for similarity of triangles. For example, arrange three copies of the same triangle so that corresponding angles
the sum of the three angles appears to form a line, and give an argument in terms of transversals exterior angle
why this is so.
interior angle
perpendicular lines
Examples: Students can informally prove relationships with transversals.
similar figures
similar polygons
• Show that m ∠3 + m ∠4 + m ∠5 = 180˚ if l and m are parallel lines and t1 & t2 are
supplementary
transversals.
transversal
∠1 + ∠2 + ∠3 = 180˚. Angle 1 and Angle 5 are congruent because they are
vertical angles
corresponding angles ( ∠5 ≅ ∠1 ). ∠1 can be substituted for ∠5 .
∠4 ≅ ∠2 : because alternate interior angles are congruent.
∠4 can be substituted for ∠2 .
Therefore m ∠3 + m ∠4 + m ∠5 = 180˚
Grade 8 Quarter 4 6
8th Grade Mathematics Quarter 4 Curriculum Map
2013-2014
Students can informally conclude that the sum of a triangle is 180o (the angle-sum theorem) by
applying their understanding of lines and alternate interior angles.
• In the figure below, line x is parallel to line yz:
Angle a is 35 o because it alternates with the angle inside the triangle that measures 35 o. Angle c
is 80 o because it alternates with the angle inside the triangle that measures 80 o. Because lines
have a measure of 180 o, and angles a + b + c form a straight line, then angle b must be 65 o (180
– 35 + 80 = 65). Therefore, the sum of the angles of the triangle are
35 o + 65 o + 80 o.
CCSS for Mathematical Practice:
1. Make sense of problems and persevere in solving them
3. Construct arguments and critique the reasoning of others
5. Use appropriate tools strategically.
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
Explanation/Examples:
-Identify adjacent and vertical angles
- Find supplementary angles
- Find angle measures
- Identify angles
- Identify parallel lines
Resources:
Assessment:
Prentice Hall Mathematics
Common Core Course 3
- Classwork/Homework
- Lesson quizzes
- Unit test
- District Common Formative
Connected Mathematics
Grade 8 Quarter 4 7
8th Grade Mathematics Quarter 4 Curriculum Map
- Write congruence statements
- Congruent triangles
- Identify similar polygons
- Identify similar triangles
- Sum of the interior angle measures
- Angle measures of a polygon
- Fine measure of exterior angle
Program (CMP)
2013-2014
Assessment
Teacher Resource
Prentice Hall Mathematics
Common Core Course 3 Online resources
Reflection/Notes:
Grade 8 Quarter 4 8