Download 8th grade Mathematics Curriculum Guide – Unit 3 Geometry

8th grade Mathematics Curriculum Guide – Unit 3 Geometry
2016 – 2017
Unit 3: Geometry
(Pythagorean Theorem, Similarity: Angles, Parallel lines, and Triangles, Transformations, and Volume)
Time Frame: 36 – 42 days
Connections to Previous Learning:
In Unit 1, students learned to evaluate expressions and equations with exponents. Unit 2 is about solved equations. In previous grades, students have
worked with triangles and classifying triangles. In previous grades, students made scale drawings of geometric figures and solved problems involving
angle measure, surface area, and volume. In Grade 7, students found the volume of prisms and pyramids. In Grade 8, students expand on the general
concept of volume to explore the volume of rounded objects (specifically cylinders, cones and spheres). Moreover, students draw on their knowledge of
exponents (particularly squares and cubes) from Unit 1 when finding missing sides of a right triangle and the volume and utilize their knowledge of
solving equations to solve for the radius given a volume.
Focus within the Grade Level:
Students will apply their knowledge of squares, cubes, square roots, cube roots, and solving to solve problems like 𝑥 2 = 𝑝 and 𝑥 3 = 𝑝. Students will
apply their prior knowledge of triangles to the specific qualities of right triangles and find the missing side lengths of right triangles in various real world
2-D and 3-D situations. They will also apply the concepts of squares and square roots. Students will apply the concept of the Pythagorean Theorem to
find the height or radius of a cone given the slant height and either the height or radius, while studying volume. Geometric sense allows students to
comprehend space and shape. Students analyze the characteristics and relationships of shapes and structures; engage in logical reasoning, and use tools
and techniques to determine measurement. Students learn that geometry and measurement are useful in representing and solving problems in the real
world as well as in mathematics. Through application in real-world contexts, students learn the volume formulas for cylinders, cones and spheres. They
then apply these formulas to not only find the volume of objects, but also missing dimensions such as the radius or height.
Part A: Solve 𝑥 2 = 𝑝 and Pythagorean Theorem
Part B: Similarity
Part C: Transformations
Part D: Solve 𝑥 3 = 𝑝 and Volume
Connections to Subsequent Learning:
Students will extend the concept of similar triangles to find sloe of linear lines. Students will extend these concepts to trigonometry. At the high school
level, students will apply transformations to numbers, functional representations, and data. They will experiment with transformations in the plane
where they will do rigid motion transformations, transformations in terms of a function, and transformations such as stretches that lead to shapes that
are not similar or congruent. Students will use this understanding in high school when they use volume formulas of cylinders, pyramids, cones and
spheres to solve problems, use geometric shapes to model real-life objects, apply concepts of density based on volume, and solve design problems using
geometric methods.
Unit 1
Clover Park School District 6/20/16
Page 1
8th grade Mathematics Curriculum Guide – Unit 3 Geometry
2016 – 2017
Common Core Standards in this unit:
 Indicates was presented to students in the 7th grade curriculum in the Clover Park School District.
Work with radical and integer exponents.
8.EE.2
Use square root and cube root symbols to represent solutions to equations of the form 𝑥 2 = 𝑝 and 𝑥 3 = 𝑝, where p is a positive rational number.
Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
Understand and apply the Pythagorean Theorem.
8.G.B.6:
Explain a proof of the Pythagorean Theorem and its converse.
8.G.B.7:
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three
dimensions.
8.G.B.8:
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Understand congruence and similarity using physical models, transparencies, or geometry software.
 8.6.A.1
8.6.A.1.A
8.6.A.1.B
8.6.A.1.C
 8.G.A.2
 8.G.A.3
 8.G.A.4
 8.G.A.5
Verify experimentally the properties of rotations, reflection, and translations:
Lines are taken to lines, and line segments to line segments of the same length
Angles are taken to angles of the same measure.
Parallel lines are taken to parallel lines.
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.
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of
rotations, reflection, translations, and dilations: given two similar two-dimensional figures, describe a sequence that exhibits the
similarity between them.
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.
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
 8.G.C.9
Unit 1
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Clover Park School District 6/20/16
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8th grade Mathematics Curriculum Guide – Unit 3 Geometry
2016 – 2017
Mathematical Practices
1.
3.
5.
7.
Unit 1
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Use appropriate tools strategically.
Look for and make sure of structure.
2. Reason abstractly and quantitatively.
4. Model with mathematics.
6. Attend to precision.
8. Look for and express regularity in repeated reasoning.
Clover Park School District 6/20/16
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8th grade Mathematics Curriculum Guide – Unit 3 Geometry
2016 – 2017
Stage 1 Desired Results
Transfer Goals
Students will be able to independently use their learning to…
- Understand and apply the Pythagorean Theorem.
- Understand congruence and similarity using physical models, transparencies, or geometry software.
- Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
Meaning Goals
UNDERSTANDINGS
Students will understand that…
 Right triangles have a special relationship among the side lengths which can be
represented by a model and a formula.
 The Pythagorean Theorem can be used to find the missing side lengths in a
coordinate plane and real-world situations.
 The Pythagorean Theorem and its converse can be proven.
 Reflections, translations, and rotations are actions that produce congruent
geometric objects.
 Dilation is a transformation that changes the size of a figure but not the shape.
 If the scale factor of a dilation is greater than 1, the image resulting from the
dilation is an enlargement, and if the scale factor is less than 1, the image is a
reduction.
 A two-dimensional figure is similar to another if the second can be obtained from
the first by a sequence of transformations.
 Two shapes are similar if the lengths of all the corresponding sides are
proportional and all the corresponding angles are congruent.
 Two similar figures are related by a scale factor, which is the ratio of the lengths
of corresponding sides.
 Congruent figures have the same size and shape. If the scale factor of a dilation is
equal to 1, the image resulting from the dilation is congruent to the original
figure.
Unit 1
ESSENTIAL QUESTIONS
Clover Park School District 6/20/16
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





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
Why does the Pythagorean Theorem apply only to
right triangles?
How does the knowledge of how to use right
triangles and the Pythagorean Theorem enable the
design and construction of such structures as a
properly pitched roof, handicap ramps to meet code,
structurally stable bridges, and roads?
How can the Pythagorean Theorem be used for
indirect measurement?
How do indirect measurement strategies allow for
the measurement of items in the real world such as
playground structures, flagpoles, and buildings?
What are transformations and what effect do they
have on an object?
What does the scale factor of a dilation convey?
How can transformations be used to determine
congruency or similarity?
What angle relationships are formed by a
transversal?
How do we determine the volume of rounded
objects?
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8th grade Mathematics Curriculum Guide – Unit 3 Geometry



2016 – 2017
When parallel lines are cut by a transversal, corresponding angles, alternate
interior angles, alternate exterior angles, and vertical angles are congruent.
Rounded object volume can be calculated with specific formulas.
Pi is necessary when calculating volume of rounded objects.
Acquisition Goals
Students will know…
 The Pythagorean Theorem.
 When to apply the Pythagorean Theorem.
 Properties of rotations, reflections and translations
 Exterior angle and angle sum of triangles.
 The names and properties of angles created when parallel
lines are cut by a transversal.
 Angle-angle criterion for similarity of triangles.
 The volume formulas for cylinders, cones and spheres.
Students will be skilled at…
 Explaining a proof of the Pythagorean Theorem and its converse. (8.G.6)
 Using the Pythagorean Theorem to solve for a missing side of a right
triangle given the other 2 sides in both 2-D and 3-D problems. (8.G.7)
 Applying the Pythagorean Theorem to solve problems in real-world
contexts. (8.G.7)
 Applying the Pythagorean Theorem to find the distance between two
points in the coordinate system. (8.G.8)
 Describing a series of transformations that exhibits congruence between
two congruent figures. (8.G.2)
 Describing transformations (dilations, translations, rotations, and
reflections) with words and with coordinates. (8.G.3)
 Describing a series of transformations that exhibits similarity between two
similar figures. (8.G.4)
 Finding the measures of angles using transversals, the sum of angles in a
triangle, the exterior angles of triangles. (8.G.5)
 Determining if triangles are similar using the angle-angle criterion. (8.G.5)
 Justifying congruence or similarity of figures using a series of
transformations. (8.G.2 and 8.G.4)
 Finding the volume of rounded objects in real-world contexts. (8.G.9)


Unit 1
Giving volume in terms of 3.14 or 𝜋 (8.G.9)
Finding a missing dimension given the volume of rounded object. (8.G.9)
Clover Park School District 6/20/16
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8th grade Mathematics Curriculum Guide – Unit 3 Geometry
2016 – 2017
Stage 1 Established Goals: Common Core State Standards for Mathematics
Students will be able to independently use their learning to…
Part A: Solve 𝒙𝟐 = 𝒑 and Pythagorean Theorem
8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form 𝑥 2 = 𝑝 and 𝑥 3 = 𝑝, where p is a positive rational
number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
Understand and apply the Pythagorean Theorem.
8.G.B.6: Explain a proof of the Pythagorean Theorem and its converse.
8.G.B.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two
and three dimensions.
8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Explanations, Examples, and Comments
Previous learning
-
Vocabulary Cards
Points, Lines, Planes, and Angles (Holt Course 3: 7-1)
Angles in Triangles (Holt Course 3: 7-3)
Explanations:
 Students should verify, using a model, that the sum of the squares of the legs is equal
to the square of the hypotenuse in a right triangle. Students should also understand
that if the sum of the squares of the 2 smaller legs of a triangle is equal to the square
of the third leg, then the triangle is a right triangle.
 Through authentic experiences and exploration, students should use the Pythagorean
Theorem to solve problems. Problems can include working in both two and three
dimensions. Students should be familiar with the common Pythagorean triplets.
ALD
Target H: Understand and apply the Pythagorean theorem
Unit 1
Clover Park School District 6/20/16
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Acute angle (4th)
Angle (4th)
Distance (4th)
Measure (4th)
Obtuse angle (4th)
Right angle (4th)
Right Triangle (4th)
Coordinates (5th)
Measurement (5th)
Ordered pairs (5th)
Coordinate plan (6th)
Edge length (6th)
Vertices (6th)
Graph (7th)
Triangle (right, scalene, acute, obtuse, equilateral,
isosceles) (7th)
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8th grade Mathematics Curriculum Guide – Unit 3 Geometry
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Level 1 student should be able to identify the hypotenuse and the legs of a right triangle
given the side lengths or an image of a right triangle.
Level 2 student should be able to apply the Pythagorean theorem to determine whether or
not a given triangle is a right triangle, given its side lengths. They should be able to find the
distance between two points on a horizontal or vertical line in a two-dimensional coordinate
system.
Level 3 students should be able to apply the Pythagorean theorem to determine the
unknown side lengths of right triangles and to find the distance between two points in a
coordinate system in two dimensions.
Level 4 students should be able to apply the Pythagorean theorem to find the distance
between two points in a coordinate system in three dimensions.
2016 – 2017
Converse (8th)
Degree (8th)
Height (8th)
Hypotenuse (8th)
Leg (pertaining to the Pythagorean theorem) (8th)
Origin (8th)
Power (8th)
Pythagorean theorem (8th)
Square root (8th)
X-coordinate (8th)
Y-coordinate (8th)
Item Specs Version 2.0
- Target H
Item Specs Version 3.0
- Target H
Stage 1 Established Goals: Common Core State Standards for Mathematics
Students will be able to independently use their learning to…
Part B: Similarity
Understand congruence and similarity using physical models, transparencies, or geometry software.
8.G.A.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.
Explanations, Examples, and Comments
Previous learning
-
Vocabulary Cards and some more geometry Cards
Ratios and Proportions (Holt Course 3: 5-1and 5-4)
Point, Line, line segment, ray, triangle
Explanations
Students can informally prove relationships with transversals.

Unit 1
Show that m 3 + m  4 + m 5 = 180˚ if l and m are parallel lines and t1 & t2 are
transversals.
Clover Park School District 6/20/16
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Acute angle (4th)
Angle (4th)
Line (4th)
Obtuse angle (4th)
Point (4th)
Protractor (4th)
Ray (4th)
Right angle (4th)
Straight angle (4th)
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8th grade Mathematics Curriculum Guide – Unit 3 Geometry
1 + 2 + 3 = 180˚. Angle 1 and Angle 5 are congruent because they are
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˚

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 to the right, 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.
Unit 1
Clover Park School District 6/20/16
-
2016 – 2017
Vertex (4th)
Line segments (5th)
Parallel (5th)
Perpendicular (5th)
Adjacent angles (7th)
Complementary angles (7th)
Linear pairs of angles (7th)
Supplementary angles (7th)
Triangle (right, scalene, acute, obtuse, equilateral,
isosceles) (7th)
Vertical angles (7th)
Angle-angle criterion (8th)
Congruent (8th)
Converse (8th)
Exterior angles of triangles (8th)
Measure of an angle (8th)
Measure of a line segment (8th)
Similar (8th)
Similar Triangles (8th)
Transversal (8th)
Page 8
8th grade Mathematics Curriculum Guide – Unit 3 Geometry
2016 – 2017
Stage 1 Established Goals: Common Core State Standards for Mathematics
Students will be able to independently use their learning to…
Part C: Transformations
Understand congruence and similarity using physical models, transparencies, or geometry software.
8.G.A.1: Verify experimentally the properties of rotations, reflection, and translations:
- 8.G.A.1a: Lines are taken to lines, and line segments to line segments of the same length.
- 8.G.A.1b: Angles are taken to angles of the same measure.
- 8.G.A.1c: Parallel lines are taken to parallel lines.
8.G.A.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.
8.G.A.3: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
8.G.A.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,
reflection, translations, and dilations: given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
Explanations, Examples, and Comments
Vocabulary Cards
ALD
Target G: Understand congruence and similarity using physical models, transparencies, o geometry
software.
Level 1 students should be able to identify reflections, rotations, and translations and the result of these
right motions on figures.
Level 2 students should be able to construct reflections and translations of figures in a coordinate plane and
identify dilations and the results of dilations on figures.
Level 3 students should be able to understand and describe the impact of a transformation on a figure and
its component parts with or without coordinates. They should be able to use or describe a sequence of
Unit 1
Clover Park School District 6/20/16
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Polygon (3rd)
Rectangle (3rd)
Rhombus (3rd)
Square (3rd)
Acute angle (4th)
Angle (4th)
Distance (4th)
Figure (4th)
Line (4th)
Measure (4th)
Obtuse angle (4th)
Point (4th)
Page 9
8th grade Mathematics Curriculum Guide – Unit 3 Geometry
transformations to determine or exhibit the congruence of two figures. They should also be able to
construct rotations and dilations of figures in a coordinate plane.
Level 4 students should be able to describe a sequence that exhibits the similarity between two shapes and
understand that the angle measures are unchanged.
Item Specs Version 2.0
-
Target G
Item Specs Version 3.0
-
Target G
2016 – 2017
-
Unit 1
Clover Park School District 6/20/16
Protractor (4th)
Ray (4th)
Right angle (4th)
Straight angle (4th)
Vertex (4th)
Coordinates (5th)
Line segments (5th)
Measurement (5th)
Ordered Pairs (5th)
Parallel (5th)
Perpendicular (5th)
Sequence (5th)
Coordinate plane (6th)
Edge length (6th)
Vertices (6th)
Adjacent angles (7th)
Complementary angles (7th)
Graph (7th)
Linear pairs of angles (7th)
Parallelogram (7th)
Supplementary angles (7th)
Trapezoid (7th)
Triangle (right, scalene, acute, obtuse,
equilateral, isosceles) (7th)
Vertical angles (7th)
Congruent (8th)
Converse (8th)
Dilate (8th)
Dilation (8th)
Measure of an angle (8th)
Measure of a line segment (8th)
Proportional relationship (8th)
Reflect (8th)
Reflection (8th)
Rotate (8th)
Rotation (8th)
Similar (8th)
Similar Triangles (8th)
Page 10
8th grade Mathematics Curriculum Guide – Unit 3 Geometry
2016 – 2017
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Transformations (8th)
Translate (8th)
Translation (8th)
Stage 1 Established Goals: Common Core State Standards for Mathematics
Students will be able to independently use their learning to…
Part D: Solve 𝒙𝟑 = 𝒑 and Volume
8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form 𝑥 2 = 𝑝 and 𝑥 3 = 𝑝, where p is a positive rational
number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
8.G.C.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Explanations, Examples, and Comments
Vocabulary
Previous learning
-
Circle
Radius
Diameter
Chord
Circumference
Area
Explanations
 Students should verify, using a model, that the sum of the squares of the legs is
equal to the square of the hypotenuse in a right triangle. Students should also
understand that if the sum of the squares of the 2 smaller legs of a triangle is
equal to the square of the third leg, then the triangle is a right triangle.
Unit 1
-
Clover Park School District 6/20/16
Volume (4th)
Surface area (6th)
Base of 3-D figures (7th)
Circle (7th)
Circumference (7th)
Diameter (7th)
Pi (7th)
Radius (7th)
Cone (8th)
Cube (8th)
Cube root (8th)
Cylinder (8th)
Height (8th)
Sphere (8th)
Square (8th)
Square root (8th)
Slant height
Page 11
8th grade Mathematics Curriculum Guide – Unit 3 Geometry
Stage 2 - Evidence
SAMPLE Assessment Evidence
PERFORMANCE TASK(S):
See Day 32, Day 35, and Matchsticks: lesson, resource
Evaluative Criteria:
Common Assessment
See Sample Assessments for Unit 3.
Washington State: Materials to help districts and others understand the
organization and content of the standards and the content and evidence
base used to support the standards:
http://mathpractices.edc.org/pdf/Rational_Exponents.pdf
Washington State: Instructional materials, Resources and Course
Support: http://www.k12.wa.us/Mathematics/Resources.aspx
Washington State: Professional Learning Support:
http://www.k12.wa.us/Mathematics/profdev.aspx
Washington State: General Assessment Resources:
http://www.k12.wa.us/Mathematics/Assessment.aspx
2016 – 2017
OTHER ASSESSMENT EVIDENCE:
SBA Sample Items
8.G.2 (G.141)
8.G.3 (G.142)
8.G.5 (G.129)
8.G.2 (G.146)
8.G.7 (H.002)
8.G.8 (H.143)
8.G.9 (A.001)
8.G.4 (G.321)
8.G.9 (B.128)
8.G.9 (B.132)
8.G.4 (B.010)
8.G.3 (B.059)
8.G.7 (B.433)
8.G.9 (F.011)
8.G.7 (F.016)
8.G.3 (F.559)
8.G.9 (A.271)
SBA Review by Target
SBA Review Target G
SBA Review Target H1
Unit 1
Clover Park School District 6/20/16
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8th grade Mathematics Curriculum Guide – Unit 3 Geometry
2016 – 2017
SBA Review Target H2
SBA Review Target I
Stage 3 – Learning Plan Sample
Summary of Key Learning Events and Instruction that serves as a guide to a detailed lesson planning
LEARNING ACTIVITIES:
Additional Resources:
A suggested guide to layout of unit by days
Part A: Pythagorean theorem 8.EE.2 and 8.G.B.6, 7, and 8
Day 1: Lab: What is the Pythagorean Theorem?
Day 2: Discovering the Pythagorean Theorem: lesson, resources
Day 3: Holt Course 3: 4-8 The Pythagorean Theorem and
- Watson Saves: from Yummy math problem
Day 4: Holt Course 3 Companion Guide: 4-9A
Day 5: Tunnel Vision: from Making Sense of Problem Solving and
- Holt Geometry: 5-7 The Pythagorean Theorem
Part A: 8.EE.2 and 8.G.B.6, 7, and 8
Stations Activity: Properties of Right Triangles
Comparing TVs: Task from Georgia
Steep Hikes: from Yummy math
Pythagorean Theorem: more practice
worksheets
Proving Triangles are Right Triangles: more
practice worksheets
Pythagorean Triples: more practice worksheets
Using the Pythagorean Theorem to Find
Missing Dimensions: more practice worksheets
Think Tac Toe Pythagorean Theorem
Day 6: Holt Geometry: 5-8 Applying Special Right Triangles
- Fish Tale: from Yummy math problem
Day 7 : additional day if needed
- Holt Algebra 1: 1-5 challenge
- School Yard: lesson, resources
Part B: Similarity 8.G.A.5
Day 8: Lines and Angles
- Properties of Angle Pairs: Station Activity (Discovery of rules)
- Holt Geometry: 3-1 Lines and Angles
Unit 1
Clover Park School District 6/20/16
Part B: Similarity 8.G.A.5
Properties of Angle Pairs: Station Activity
Properties of Lines Cut by Transversals: Station
Activity
Page 13
8th grade Mathematics Curriculum Guide – Unit 3 Geometry
2016 – 2017
Stage 3 – Learning Plan Sample
Day 9: Parallel Lines and Angles
- Holt Course 3: 7-2 Parallel and Perpendicular Lines
Parallel Lines and Transversals: worksheet
Angles in Triangles: worksheet
Similar Triangles worksheet
Day 10: Parallel Lines and Angles
- Holt Geometry: 3-2 Angles Formed by Parallel Lines and Transversals
Stage 3 MATERIALS BY STANDARD(S):
Day 11: Parallel Lines and Angles
- Angles, draw the picture: Activity PowerPoint (review of angle pairs/notes)
- Holt Geometry: 3-3 Proving Lines Parallel
Day 12: Parallel Lines and Angles
- City Design: Activity PowerPoint
Day 13: Parallel Lines and Angles
- City Design: Activity day 2 and review
Day 14: Triangles
- Holt Course 3: 7-3 Angles in Triangles
Day 15: Triangles
- Holt Geometry: 4-2 Angle Relationships in Triangles
Estimate days 11-13
Holt Course 3: 7-6 Congruence
Holt Course 3 Curriculum Companion: 7-6A
Hands-On Lab: Explore congruence
Holt Geometry: 12-1 Reflections
Holt Geometry: 12-2 Translations
Holt Geometry: 12-3 Rotations
Holt Course 3: 7-7 Transformations
Holt Geometry: 12-4 Compositions of
Transformations
Holt Course 3: 5-6 Dilations
Holt Geometry: Dilations
Holt Course 3 Curriculum Companion: 7-7A
Similarity & Congruence Transformations
Holt Course 3 Curriculum Companion: 7-7B
Identifying Combined Transformations
Day 16: Triangles
- What’s Your Angle Activity: from Making Sense of Problem Solving
Day 17: Similar Figures
- Holt Course 3: 5-5 Similar Figures
Day18: Similar Figures
- Holt Course 3: 5-7 Indirect Measurement
Day 19: Similar Triangles
- Holt Geometry: 7-3 Triangle Similarity: AA, SSS, SAS
Unit 1
Clover Park School District 6/20/16
Page 14
8th grade Mathematics Curriculum Guide – Unit 3 Geometry
2016 – 2017
Stage 3 – Learning Plan Sample
Day 20: Similar Triangles
- This is Similar Activity: from Making Sense of Problem Solving or
- Identifying Similar Triangles: lesson, resources
Part C: Transformations 8.G.A 1, 8.G.A.2, 8.G.A.3, and 8.G.A.4
Day 21: Congruence of Figures
- Holt Course 3: 7-6 Congruence
- Holt Course 3 Curriculum Companion: 7-6A Hands-On Lab: Explore congruence
Day 22: Transformations Reflections
- Holt Geometry: 12-1 Reflections
Part C: Transformations 8.G.A 1, 8.G.A.2,
8.G.A.3, and 8.G.A.4
Transformations: Station Activity
Translations and Rotations: Station Activity
Aaron’s Design: problem
Transformations: small activity or little quiz
Day 23: Transformations Translations
- Holt Geometry: 12-2 Translations
Day 24: Transformations Rotations
- Holt Geometry: 12-3 Rotations
Day 25: Transformations
- Holt Course 3: 7-7 Transformations and/or
- Holt Geometry: 12-4 Compositions of Transformations
Day 26: Transformations
- Representing and Combining Transformations: lesson, resources
Day 27: Dilations
- Holt Course 3: 5-6 Dilations
Day 28: Dilations
- Holt Geometry: Dilations
Day 29: Transformations
- Holt Course 3 Curriculum Companion: 7-7A Similarity & Congruence Transformations
- Combining Transformations: worksheet
Unit 1
Clover Park School District 6/20/16
Page 15
8th grade Mathematics Curriculum Guide – Unit 3 Geometry
2016 – 2017
Stage 3 – Learning Plan Sample
Day 30: Transformations
- Holt Course 3 Curriculum Companion: 7-7B Identifying Combined Transformations
Part D: Volume 8.G.C.9
Day 31: Circles and 𝜋
- What is 𝜋? Activity : The Mystery Ratio Activity (review from 7th, but good lab activity to reviw)
Day 32: Volume of Cylinders
- Which glass of soda would you pick (good opener to get students thinking about volume)
- http://mrmeyer.com/threeacts/youpourichoose/
- Holt Course 1 Lesson 10-8 Volume of Cylinders
Day 33: Volume of Cylinders
- Holt Course 3 Lesson 8-5 Volume of Prisms and Cylinders
Part D: Volume 8.G.C.9
Comparing Spheres and Cylinders (Georgia
Task)
Making Sense of Problem Solving H.12 Picking
up the Garbage
How full is your glass? (Georgia Task)
Gift Box Dilemma (North Carolina Task)
Volume of Cylinders, Cones, and Spheres:
Station Activity
Day 34: Volume of Cones
- Holt Course 3 Lesson 8-6 Volumes of Pyramids and Cones
Day 35: Volume of Spheres
- Holt Course 3 lesson 8-9 Spheres
Day 36: Volume of Cylinders, Cones, and Spheres
- Meltdown (North Carolina Task) good problem or
- I Scream for Ice Cream and Hank’s Tanks: worksheet
Common Assessment
Semester Cumulative Assessment
Unit 1
Clover Park School District 6/20/16
Page 16