Unit 12 Volume of Cones, Spheres, and Cylinders

Pre-Algebra
EMS 8th Grade Math Department / Dates: March 28–
Math Florida Standard(s)
Benchmarks, Descriptions
and DOK levels / MAFS.8.G.3.9 (DOK 2):
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Identify and define vocabulary: cone, cylinder, sphere, radius, diameter, circumference, area, volume, pi, base, height.
Know formulas for volume of cones, cylinders, and spheres.
Compare the volume of cones, cylinders, and spheres.
Determine and apply appropriate volume formulas in order to solve mathematical and real-world problems for the given shape.
Given the volume of a cone, cylinder, or sphere, find the radii, height, or approximate usingπ.
Learning Goal / Students will be able to understand the relationship between the volume of cylinders cones and spheres in order to solve real world problems.
Essential Question(s) / Explain the significance of how the formula of a cone relates to a cylinder?
How does the relationship of the volume of a sphere apply to a cylinder?
Assessments / Pre-Assessments / Create a tree map and tell me everything you know about cones, spheres, and spheres.
Formative Assessments / Cornell Notes, Cooperative exercises, Observation,
Summative Assessments / Quiz on volume formulas
Quiz on real world application
Unit test
Progress Monitoring/ Feedback Loop / If a student scores less than 70 on a quiz, cooperative exercise, or unit test they may come in and take an equivalent test for full credit. They may come in after school on Tuesdays and Thursdays, or during lunch on Mondays or Wednesdays.
Higher Order Question(s) / How can the formula for volume help when making a conjecture about the volume of a cylinder?
How did you determine the appropriate volume formula?
How can we compare the volumes of 2 or more cones, cylinders, and spheres?
Key Vocabulary / Vol7ume, Cone, Cylinder, Sphere, Radius, Diameter, Circumference, Area
Monday, March 28, 2016 / Unpack Standards and Pre-Assess / DOK 1-3
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will be introduced to the unit on Volume by: taking the pre assessment, unpacking the standards, completing the vocabulary and preview the learning scale

BELL RINGER
( 5 minutes) / Create a tree map and tell me everything you know about cones, spheres, and spheres.
I DO: /
  • Assess and Monitor student progress.

WE DO: /
  • Bell Ringer
  • Unpack the standard
  • Vocabulary.
  • Learning Scale Preview

YOU DO: /
  • Assess yourself on the learning scale.

EXIT TICKET:
(5 minutes) /
  • What is this unit going to be about?

Tuesday, March 29, 2016 / Volume of Cylinders / DOK 1-3
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will learn to derive volume formula for a Cylinder and a cone using Cornell
  • Notes and use that to practice finding the volume of cylinders.

BELL RINGER
( 5 minutes) /
  • What does a cylinder look like? What are the various parts of a cylinder?

I DO: /
  • Assess and monitor

WE DO: /
  • Bell Ringer
  • Cornell Notes. How do I derive the formula for a cylinder and how can I apply it to the real world?
  • Cylinder worksheet done with partner

YOU DO: /
  • Assess yourself on the learning scale

EXIT TICKET:
(5 minutes) /
  • What is the volume of a cylinder and how can you remember it?

Wednesday, March 30, 2016 / Volume of Cones / DOK 1
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will learn to derive volume formula for a cone and a cone using Cornell
  • Notes and use that to practice finding the volume of cone.

BELL RINGER
( 5 minutes) /
  • What does a cylinder look like? What are the various parts of a cone?
  • How are a cylinder and a cone alike?

I DO: /
  • Assess and monitor

WE DO: /
  • Bell Ringer
  • Cornell Notes. How do I derive the formula for a cone and how can I apply it to the real world?
  • Cone worksheet done with partner

YOU DO: /
  • Assess yourself on the learning scale

EXIT TICKET:
(5 minutes) /
  • What is the volume of a Cone and how can you remember it?

Thursday, March 31, 2016 / Volume of Spheres / DOK 1-3
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will learn to derive volume formula for a sphere and a cone using Cornell
  • Notes and use that to practice finding the volume of spheres.

BELL RINGER
( 5 minutes) /
  • What does a cylinder look like? What are the various parts of a spheres?

I DO: /
  • Assess and monitor

WE DO: /
  • Bell Ringer
  • Cornell Notes. How do I derive the formula for a sphere and how can I apply it to the real world?
  • Sphere worksheet done with partner

YOU DO: /
  • Assess yourself on the learning scale

EXIT TICKET:
(5 minutes) /
  • What is the volume of a spherer and how can you remember it?

Friday ,April 1 2016 / Quiz 1 / DOK 1
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will show mastery of deriving the formula for volume of cylinders, cones and spheres and will show mastery of calculating the volume of such figures.

BELL RINGER
( 5 minutes) /
  • Pre assessment

I DO: /
  • Assess and Monitor student progress

WE DO: /
  • Bell Ringer
  • Quiz
  • Self assessment.

YOU DO: /
  • Assess yourself on the learning scale

Homework /
  • None

EXIT TICKET:
(5 minutes) /
  • How do you think you did on the quiz?

Monday , April 4 / Finding a dimension / DOK 3
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will learn to calculate for a dimension (height, radii, length, etc) of the 3-D object when given the volume

BELL RINGER
( 5 minutes) /
  • Bell Ringer. 3 algebraic equations

I DO: /
  • Assess and Monitor student progress

WE DO: /
  • Bell Ringer
  • Return of quizzes
  • Cornell Notes Finding a dimension
  • Worksheet on dimensions – Do with a partner

YOU DO: /
  • Assess yourself on the learning scale

Homework /
  • Finish worksheet on Dimensions

EXIT TICKET:
(5 minutes) /
  • How do you find a dimension when given the volume of a 3D object? Explain and show example.

Tuesday, April 5, / Finding a dimension / DOK 2
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will learn to calculate for a dimension (height, radii, length, etc) of the 3-D object when given the volume

BELL RINGER
( 5 minutes) /
  • Bell Ringer. 3 algebraic equations

I DO: /
  • Assess and Monitor student progress

WE DO: /
  • Bell Ringer
  • Return of quizzes
  • Worksheet on dimensions – Do with a partner

YOU DO: /
  • Assess yourself on the learning scale

Homework /
  • Finish worksheet on Dimensions

EXIT TICKET:
(5 minutes) /
  • How do you find a dimension when given the volume of a 3D object? Explain and show example.

Wednesday, / Comparing 3D objects / DOK 2
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will learn to compare and analyze 2 or more 3D objects using Cornell Notes and guided work.

BELL RINGER
( 5 minutes) /
  • Find a dimension

I DO: /
  • Assess and Monitor student progress

WE DO: /
  • Bell ringer
  • Go over finding a dimension
  • Cornell Notes
  • Guided Practice of Comparing 3D objects.

YOU DO: /
  • Assess yourself on the learning scale

Homework /
  • Finish comparison of 3D objects.

EXIT TICKET:
(5 minutes) /
  • When given two cylinders how can you tell which one will how mare? How can you calculate how much more will it hold?

Thursday, / Comparing 3D objects / DOK 1-3
Daily Objective /
  • Students will learn to compare and analyze 2 or more 3D objects using Cornell Notes and guided work.

BELL RINGER
( 5 minutes) /
  • Find a dimension

I DO: /
  • Assess and Monitor student progress

WE DO: /
  • Bell ringer
  • Go over comparing 3D object worksheets
  • Class discussion of comparing 3D objects
  • Guided Practice of Comparing 3D objects.

YOU DO: /
  • Assess yourself on the learning scale

Homework /
  • Finish comparison of 3D objects.

EXIT TICKET:
(5 minutes) /
  • When given two cylinders how can you tell which one will how mare? How can you calculate how much more will it hold?

Friday, / End Product / DOK 1
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will show mastery of the unit with pencil and paper test

BELL RINGER
( 5 minutes) /
  • Are you ready?

I DO: /
  • Assess and Monitor student progress

WE DO: /
  • Bell Ringer
  • Go over comparing 3D worksheet
  • Unit test

YOU DO: /
  • Assess yourself on the learning scale

Homework /
  • None

EXIT TICKET:
(5 minutes) /
  • How did you do on this unit ?

Note: Learning Scales, Accommodations, and Math Practice Standards are below.

Learning Goal Scale
Level / Date / Skill
4 / □
3 / □
2 / □
1 / □
WICR Strategies used during each unit.
Writing
Writing activities that help
students understand the
content / Inquiry
Questioning strategies
that help students
understand the content / Collaboration
Working together with a
partner or in a group of
students to understand, to
problem solve, or to
complete a task/project / Reading
Any strategies in reading
that help students
understand
Writing-to-Learn
• summaries
Process Writing
• using a rubric as evaluation
On-Demand/Timed-Writing
• writing that is completed in class within a set amount of time
• grade is evaluated using a rubric
Cornell Notes
• taking notes on the most important information
• summarizing
• using the notes to study
Reflective Writing
• students write about what they have learned and what they still need / Higher-Level Questioningin Classes
• Costa’s Level 1: Studentsfind the answers right therein the text.
• Costa’s Level 2: Studentsmust figure out the answerfrom information in thetext.
• Costa’s Level 3: Studentsapply what they havelearned or use what theyhave learned to evaluate orcreate. / Think Pair Share
Sharing Ideas With a Partner or in a Group
Carousel or Gallery Walk
Problem Solving in Groups
Projects in Groups / Before Reading Activities
• vocabulary activities
• accessing prior knowledge
• making predictions
During Reading Activities
• marking the text
• Cornell notes
• graphic organizers
After Reading Strategies
• summarizing
• group projects
Accommodations used daily on an individual basis in accordance with IEP and 504 plans and ELL Students
  • Read directions for the student
  • Check for understanding
  • Allow to leave class for assistance
  • Extra time for exams
  • Daily agenda
/
  • Allow student time to step out to de-escalate
  • Testing in small groups
  • Use of a planner/binder for organization
  • English Language Dictionary
/
  • Extended time on assignments =1 day
  • Preferential seating
  • Written direction given
  • Break directions into chunks
/
  • Read Aloud to Students
  • Visual manipulatives
  • Cooperative Learning,
  • Vocabulary, Description, Introduction,
.
Student Friendly Mathematical Practice Statements
MAFS.K12.MP.1.1 Make Sense of Problems and Persevere in Solving Them
• Make a plan! • Try different approaches when your problem is hard. • Solve your problem in more than one way. • Check whether your solution makes sense.
MAFS.K12.MP.2.1 Reason Abstractly and Quantitatively
• Explain the meanings of the numbers, words, pictures, symbols, and objects you and others use.
MAFS.K12.MP.3.1 Construct Viable Arguments and Critique the Reasoning of Others.
• Explain both what to do and why it works. • Work to make sense of others’ mathematical thinking.
MAFS.K12.MP.4.1 Model with Mathematics
• Apply math to real-world situations. • Use models such as graphs, drawings, tables, symbols, numbers, and diagrams to solve problems.
MAFS.K12.MP.5.1 Use appropriate Tools Strategically
• Choose appropriate tools for your problem. • Use mathematical tools correctly and efficiently. • Estimate and use what you know to check the answers you find using tools.
MAFS.K12.MP.6.1 Attend to Precision
• Communicate your mathematical thinking clearly and precisely. • Use the level of precision you need for your problem. • Be accurate when you count, measure, and calculate.
MAFS.K12.MP.7.1 Look for and Make Use of Structure
• Find, extend, analyze, and create patterns. • Use patterns and structures to solve problems.
MAFS.K23.MP.8.1 Look for and Express Regularity in Repeated Reasoning
• Use patterns and structures to create and explain rules and shortcuts. • Use properties, rules, and shortcuts to solve problems. • Reflect on your thinking before, during, and after you solve a problem.