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Rigorous Curriculum Design

Unit Planning Organizer

Subject(s) / Middle Grades Mathematics
Grade/Course / 8th
Unit of Study / Unit 8: Volume
Unit Type(s) / ❑Topical X Skills-based ❑ Thematic
Pacing / 8 days
Unit Planning Organizer Content
Unit Abstract
NCSCOS State Standards
Standards for Mathematical Practice
“Unpacked Standards”
Concepts/Skills/DOK’s / EQ’s/ Corresponding Big Ideas
Vocabulary
Language Objectives
Information and Technology Standards
Instructional Resources and Materials
Unit Abstract
Students will develop formulas for the volume of cylinders, cones, and spheres and use these formulas to solve problems. They will extend what they have learned about volume formulas when they use the formulas to solve for other variables, such as radius or base radius. Students will be able to solve equations by taking the square root or cube root of each side
Vertical Articulation:In the seventh grade students calculated the area and circumference of a circle and found the volume of right square pyramids. In Math I students will use the volume formulas to solve for a missing measurement.
NCSCOS
Domains:Geometry (8.G)
Clusters: Solve real world and mathematical problems involving volume of cylinders,
cones and spheres.
Standards:
8.G.9KNOW the formulas for the volumes of cones, cylinders, and spheres and USE them to solve real world and mathematical problems.
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2.Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics. / 5.Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Unpacked Standard
8.G.9 Students build on understandings of circles and volume from 7th grade to find the volume of cylinders, finding the area of the base ∏r2 and multiplying by the number of layers (the height).

find the area of the base and multiply by the number of layers
Students understand that the volume of a cylinder is 3 times the volume of a cone having the same base area and height or that the volume of a cone is the volume of a cylinder having the same base area and height.



A sphere can be enclosed with a cylinder, which has the same radius and height of the sphere (Note: the height of the cylinder is twice the radius of the sphere). If the sphere is flattened, it will fill of the cylinder. Based on this model, students understand that the volume of a sphere is the volume of a cylinder with the same radius and height. The height of the cylinder is the same as the diameter of the sphere or 2r. Using this
information, the formula for the volume of the sphere can be derived in the following way:
V =∏r2h cylinder volume formula
V = ∏r2h multiply by since the volume of a sphere is the cylinder’s
volume
V = ∏r22r substitute 2r for height since 2r is the height of the sphere
V =∏r3 simplify
Students find the volume of cylinders, cones and spheres to solve real world and mathematical problems. Answers could also be given in terms of Pi.
Example 1:
James wanted to plant pansies in his new planter. He wondered how much potting soil he should buy to fill it. Use the measurements in the diagram below to determine the planter’s volume.

Solution:
V = ∏r2h
V = 3.14 (40)2(100)
V = 502,400 cm3
The answer could also be given in terms ofл: V = 160,000л
Example 2:
How much yogurt is needed to fill the cone to the right? Express your answers in terms of Pi.
Solution:
V =∏r2h
V =∏32)(5)
V =∏(45)
V = 15 ∏ cm3
Example 3:
Approximately, how much air would be needed to fill a soccer ball with a radius of 14 cm?
Solution:
V =∏r3
V = (3.14)(143)
V = 11.5 cm3
“Know the formula” does not mean memorization of the formula. To “know” means to have an understanding of why the formula works and how the formula relates to the measure (volume) and the figure. This understanding should be for all students.
Note: At this level composite shapes will not be used and only volume will be calculated.
“Unpacked” Concepts
(students need to know) / “Unwrapped” Skills
(students need to be able to do) / Cognition
(DOK)
8.G.9
  • Volume of cones, cylinders and spheres
/
  • I can explore patterns among the volumes of cylinders, cones and spheres.
  • I can develop strategies for finding volumes of cones, cylinders and spheres.
  • I can use volume to solve a variety of real-world problems.
/ 2
2
3
Essential Questions / Corresponding Big Ideas
8.G.9
  • How can I find the volume of cylinders, cones and spheres?
  • How can I compare the volume of different 3-D figures?
  • How can I apply finding volume toreal life situations?
/
  • Students will develop formulas to find the volume of cones, cylinders and spheres.
  • Students will develop strategies to compare volumes of different 3-D figures.
  • Students will solve real life problems by identifying shape of figures referred to and applying volume formulas.

Vocabulary
Tier 2 / Tier 3
cone, cylinder, sphere, Pi, radius, volume, height
Language Objectives
Key Vocabulary
8.G9 / SWBAT Define and give examples of the specific vocabulary for this standardcone, cylinder, sphere, Pi, radius, volume, height.
Language Function
8.G.9 / SWBAT explain the relationship of the area of the base (circle) to the volume of the cylinder.
Language Skills
8.G.9 / SWBAT apply the appropriate formula to solve real-world and mathematical word problems related to cones, cylinders, spheres.
Language Structures
8.G.9 / SWBAT explain the relationship of a sphere enclosed in a cylinder with the same radius and height and apply the appropriate formula. (V=⅔r2h)
Language Tasks
8.G.9 / SWBAT identify, label, find, and create cones, cylinders, and spheres.
8.G.9 / SWBAT using a drawing or a model, explain the formula for finding the volume of a cone.
8.G.9 / SWBAT using a drawing or a model, explain the formula for finding the volume of a sphere.
8.G.9 / SWBAT express the answers to problems involving volume in terms of Pi (). (V=502,400cm3 = 160,000)
Language Learning Strategies
8.G.9 / SWBAT identify and interpret language that provides key information to solve real-world and mathematical word problems using visual and graphical supports.
Information and Technology Standards
8.TT.1.2 Use appropriate technology tools and other resources to organize information (e.g. graphic organizers, databases, spreadsheets, and desktop publishing).
8.RP.1.1 Implement a project-based activity collaboratively.
8.RP.1.2 Implement a project-based activity independently.
Instructional Resources and Materials
Physical / Technology-Based
Discovery Education
  • Unit 11: Volume of Solid Figures
Connected Math 2 Series
  • Common Core Investigation 4
Partners in Math
  • Paper Cylinder Task
  • Geometry
Lessons for Learning (DPI)
  • Gift Box Dilemma
  • Meltdown
Mathematics Assessment Project (MARS)
  • Modeling: Making Matchsticks
  • Matchsticks, task
  • Circles & Squares, HS task
/ WSFCS Math Wiki
NCDPI Wikispaces Eighth Grade
MARS
Georgia Unit
Illustrative Math
Illuminations

Rev’d 7/19/16