Common Core Mathematics Unit Lesson Sequence
8th grade Unit 7: Geometric Formula Application
Disclaimer:
The following sample unit is intended to provide an example of a possible flow of instruction. Consider this a work in progress. As a sample instructional
plan, it should invite discussion and development. It is not intended to be prescriptive, only suggestive. It may provide ideas and guidance in the
development of conceptual understanding through a sample sequence of lessons. This UNIT can be adapted, modified, expanded, delivered as-is, or not
used at all. Lessons are not time bound and may extend beyond a day. It simply provides an example unit of instruction which incorporates:
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Integration of the 8 Mathematical Practices
Investigative tasks
Formative assessment and performance assessments
In this unit, you will find that specific standards are NOT listed within each lesson, as lessons integrate multiple standards to better address conceptual
understanding.
Previous Concepts
Understand and apply the Pythagorean
Theorem.
8. G.6 Explain a proof of the Pythagorean
Theorem and its converse.
8. G.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.8 Apply the Pythagorean Theorem to find
the distance between two points in a coordinate
system.
Understand congruence and similarity using
Grade Level Standard(s)
Central to Lesson
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.
Upcoming Concept
Integrated End of the Year Modeling
Project
Common Core Mathematics Unit Lesson Sequence
8th grade Unit 7: Geometric Formula Application
physical models, transparencies, or
geometry software.
8.G.1 Verify experimentally the properties of
rotations, reflections, and translations:
a. Lines are taken to lines, and line segments to
line segments of the same length.
b. Angles are taken to angles of the same
measure.
c. Parallel lines are taken to parallel lines.
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.
8. G.3 Describe the effect of dilations,
translations, rotations, and reflections on twodimensional figures using coordinates.
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.
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 angleangle criterion for similarity of triangles.
Lesson
Title of Lesson & Description
Resources
Common Core Mathematics Unit Lesson Sequence
8th grade Unit 7: Geometric Formula Application
Number
0
PRE-REQUISITES FROM 6th Grade Common Core
Introduction Lesson Developing Concepts on the Circle
McDougal Littell Mathematics Concepts and Skills
http://www.tncurriculumcenter.org/resource/2005/go Interactive 3d
resources for SMARTboard.
Pages 509-510 in resources
0
Developing concepts: Lesson 10.1 Circumference and Area
of a Circle
McDougal Littell Mathematics Concepts and Skills
http://www.ixl.com/math/grade-8 Interactive resources for 8th grade
standards.
Pages 511-515 in resources
0
John A. Van De Walle: Mathematics Teaching
Developmentally: Activity 20.28 Finding Area of a Triangle.
http://www.nctm.org/standards Side Length and Area of Similar Figures
0
Introduction of 3-Dimensional Figures. Lesson 10-2
McDougal Littell Mathematics Concepts and Skills
0
1
Developing the Concept of Surface Area
McDougal Littell Mathematics Concepts and Skills
Surface Area of Prisms and Cylinders. Lesson 10-3
McDougal Littell Mathematics Concepts and Skills
Pages 517-521 in resources
Page 522 in resources
Pages 523-526 in resources
2
Illuminations Activity: Fishing for the Best Prism
Students use the concept of nets to discover surface area.
8th grade Common Core Lessons: 6 Nets and solids 8th grade Common
Core: downloadable nets and activities.
3
Developing Concepts: Volume of a Prism
McDougal Littell Mathematics Concepts and Skills
Pages 528-529 in resources
4
John A. Van De Walle: Mathematics Teaching
Developmentally: Activity 20.29 Volume of Boxes
http://www.nctm.org/standards Learning about Length, Perimeter, Area, and
Volume of Similar Objects Using Interactive Figures
5
Illuminations Activity: Soda Cans. Students use arrays to
conceptually see the net of a cylinder.
Common Core Mathematics Unit Lesson Sequence
8th grade Unit 7: Geometric Formula Application
Lesson Title of Lesson & Description
Number
Resources
6
John A. Van De Walle: Mathematics Teaching
Developmentally: Activity 20.29 Volume of Boxes
7
Volume of a Cylinder Lesson 10-5
McDougal Littell Mathematics Concepts and Skills
Pages 535-537 in resources
Volumes of Pyramids and Cones Lesson 10-6
McDougal Littell Mathematics Concepts and Skills
Pages 539-541
9
MARS Task: Glasses. Students calculate the volume of
various types of drinking glasses.
http://www.nctm.org/standards Side Length, Volume, and Surface Area of
Similar Solids
10
Illuminations Task: Cubed Cans
Students will use formulas for cylinders and convert them
to same volume for various rectangular prisms.
11
Volume of a Sphere Lesson 10-7
McDougal Littell Mathematics Concepts and Skills
8
12
13
Assess
Assess
Comparing Spheres and Cylinders based on Volume
Learning task.
Illuminations Activity Tetrahedral Kites
Students construct a tetrahedron and describes the linear,
area, and volume and compare the relationships to others.
Formative Assessment Lesson: Modeling: Making
Matchsticks.
http://map.mathshell.org/materials/Volume of
Compound Objects Formative and Summative
Assessment.
Pages 543-545 in resources
Common Core Mathematics Unit Lesson Sequence
8th grade Unit 7: Geometric Formula Application
Illustrative Math Tasks: The following tasks are standard specific and may be used when applicable within this unit.
8. G.9 Comparing Snow Cones
8. G.9 Glasses
8. G.9 Flower Vases
8. G.9 Shipping Rolled Oats