8th grade: Volume and Architecture
Learning Module
- Creator(s):
Abstract
A learning module meant to build on a student's knowledge of volume and complex 3D shapes. Includes three lessons and two activities!
A learning module meant to build on a student's knowledge of volume and complex 3D shapes. Includes three lessons and two activities!
Overview: This is a unit with eight concrete days of instruction, meant to be spread over two to three weeks of remote learning plans. As I am a Chicago Public Schools teacher, I'm writing this module with the intention of using it during our remote learning transition. Governor Pritzker announced that schools are cancelled through the end of the year, thus my intention is to carry out this lesson using both online and paper materials that the students have in their possession. This unit is a continuation of the geometry strand that we have worked on for the previous two weeks. In 6th grade, this class was re-introduced to area and perimeter of shapes, a topic that has been present in instruction initiating in third grade. This class (who I also taught in sixth grade) learned about volume and surface area of rectangular prisms, cubes, and pyramids; only advanced students learned about the volume of cones, spheres, and cylinders at that time. Now that these students are in 8th grade, they were introduced to the Pythagorean Theorem, a notion by the Greek mathematician Pythagoreas whose equation can be used to find the length of unknown sides and applied to find missing sides and heughts of 3D figures in this unit.
Target Population: 8th grade students or Geometry students (if applicable) who are completing remote learning or ubiquitous learning. Degrees of difficulty can be varied by number of shapes, or units/numbers used to make the unit apply to a wider grade range.
8th Grade Curriculum Standards: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
CCSS.MATH.CONTENT.8.G.C.9
CCSS.MATH.PRACTICE.MP4
CCSS.MATH.PRACTICE.MP5
Daily Objectives:
| Day | Student Objectives |
|---|---|
| Day 1-2 | SWBAT: Find the volume of cones, pyramids, prisms, cylinders and spheres using given formulas and a calculator with 80% accuracy. |
| Day 3 | SWBAT: Find the volume of truncated cones and truncated pyramids pyramids using given formulas and a calculator with 80% accuracy. |
| Day 4 | SWBAT: Find the volume of composite figures (two or more 3D shapes combined or stacked) using given formulas and a calculator with 80% accuracy. |
| Day 5 | SWBAT: Find the total volume of a castle comprised of composite 3D shapes using given formulas and a calculator with 80% accuracy. |
| Day 6-7 |
SWBAT: Draw a blueprint of a 3D castle include six 3D shapes, two composite shapes and one truncated shape. SWBAT: Find the volume of each shape, composite shape, and truncated shape as well as the total volume of the castle using given formulas and a calculator with 80% accuracy. |
| Day 8 |
SWBAT: Follow feedback suggestions to revise or review calculations and resubmit their project using the creator tool. Students will be able to provide clear and constructive feedback on a numerical rubric to offer peers constructive criticism during the editing process. |
Materials:
Intended Outcomes:
Assessment Plan:
|
Day # |
Assessment Measure/Strategy | Type of Assessment |
|---|---|---|
| Day 1-2 |
|
Formative |
| Day 3 |
|
Formative |
| Day 4 |
|
Formative |
| Day 5 |
|
Summative |
| Day 6-7 |
|
Summative with recursive peer feedback |
| Day 8 |
|
Summative with recursive peer feedback AND formative |
Daily Objectives: SWBAT: Find the volume of cones, pyramids, prisms, cylinders and spheres using given formulas and a calculator with 80% accuracy.
Before beginning this unit, we need to access what you know and what you need to work on. In this 5-question quiz, you will be surveyed of your knowledge of finding the volume of 3D solids. The link to partake in this survey is: Survey
Today, you will be learning about finding the volume of 3D figures including: reviewing rectangular prisms, pyramids, cones, spheres and cylinders. For the first part of your lesson, please have your Engage NY textbook open to Module 7, Lesson 19. You will need a pencil and calculator to complete this lesson.
*Disclaimer: I know the video is LONG! However it covers the entire lesson form the book. You do not have to watch the full video, but watch a few minutes before attempting independently. You can watch as much or as little of this video to help you.
Video Lesson:
Media retreived from: 8Th Math Module 7 Lesson 19. (2015). Retrieved from https://www.youtube.com/watch?v=iQkVUMCL2m8
Are you still feeling a bit uncertain of finding the volume. These shorter videos are great resources to use while completing the problem set and quiz.
Need extra help?
Media retreived from:
Volume of a Pyramid. (2012). Retrieved from https://www.youtube.com/watch?v=e7-am8JtREI&t=1s
Volumes of Cylinders, Cones and Spheres. (2019). Retrieved from https://www.youtube.com/watch?v=bLEH02cGL_o
Now that you have reviewed finding the volume of 3D figures, it's time to assess your knowledge. Please click this Quiz for your assessment. You have three attempts to complete the quiz, and will know which questions you get wrong after each attempt. In between trying this quiz, you are encouraged to contact your teacher or peers for help.
Exit ticket: Reply to this update and answer one or more of the following questions:
Reply to at least two peers' responses to receive full credit. You may agree or disagree, ask questions, make suggestions, respond to their questions, or give kind concrete feedback if they have posted their own work.
Curriculum Standards:
CCSS.MATH.CONTENT.8.G.C.9
CCSS.MATH.PRACTICE.MP4
CCSS.MATH.PRACTICE.MP5
Materials:
Generally, when given the formulas and content in video instruction, students are able to understand finding the volume. Engage NY suggests the following as an option for a closing discussion. If you are holding lessons online or by video call they could be incorporated into instruction or student questioning:
"Summarize, or ask students to summarize, the main points from the lesson. The main points could be described as:
Source: https://www.engageny.org/resource/grade-8-mathematics-module-7-topic-d-lesson-19/file/49786
Daily Objectives: SWBAT: Find the volume of truncated cones and truncated pyramids pyramids using given formulas and a calculator with 80% accuracy.
Today, you will be learning about finding the volume of 3D figures that look a little different. This section includes truncated figures, or frustums (a shape with the top cut off). For the first part of your lesson, please have your Engage NY textbook open to Module 7, Lesson 20. You will need a pencil and calculator to complete this lesson.
*Disclaimer: I know the video is LONG! However it covers the entire lesson form the book. You do not have to watch the full video, but watch a few minutes before attempting independently. You can watch as much or as little of this video to help you.
Video Lesson:
Media retrieved from: 8Th Math Module 7 Lesson 20. (2015). Retrieved from https://www.youtube.com/watch?v=iQkVUMCL2m8
Did you complete the lesson but are still feeling stuck? Truncated shapes can be difficult, so these additional videos are here to review prior or during the quiz:
Media retrieved from:
Volume of a Truncated Cone. (2018). Retrieved from https://www.youtube.com/watch?v=hc9Efi-GjMs&t=4s
Volume of a Frustrum (2017) retreived from https://www.youtube.com/watch?v=1v1Pp-lJSKY&t=14s
Now that you have reviewed finding the volume of 3D truncated shapes, it's time to assess your knowledge. Please click this Quiz for your assessment. You have three attempts to complete the quiz, and will know which questions you get wrong after each attempt. In between trying this quiz, you are encouraged to contact your teacher or peers for help. Quiz
Exit ticket: You must reply to this post by responding to one or more of the following questions:
What is the greek/latin root of truncate? If you don''t know, you can use an online thesaurus to find out. How can you use this to explain the meaning of the word?
How could you explain this word using symbols or pictures to someone who may not speak english? How can you demonstrate what "truncate" means?
Come up with your own question about truncated shapes. Select between a pryamid and a cone and write a problem for your peers to solve.
Respond to two or more peers or receive full credit. You may agree or disagree, ask questions, make suggestions, respond to their questions, or give kind concrete feedback if they have posted their own work.
Curriculum Standards:
CCSS.MATH.CONTENT.8.G.C.9
CCSS.MATH.PRACTICE.MP4
CCSS.MATH.PRACTICE.MP5
Materials:
This lesson can be a bit difficult for students. I would encourage individual appointments if students struggle to visualize truncated shapes. Cutting a piece of paper into a 2-D cone shape, then cutting off the top is a strong way to prove the deviation between a cone and a truncated cone. Reviewing the formulas as well as giving additional opportunities to practice using implified uunits or scaffolding may assist students who struggle with the multi-step nature of these problems. To avoid frustration, and keep students in their zone of proximal development, make sure that students are FIRST able to find the volume of a cone independently. Then, through this supplemental instruction they should be able to use the additional outlined steps to subtract a smaller cone and fund the volume of a truncated shape.
It is important to note that finding the volume of a truncated cone is not technically or explicitly stated as an 8th grade standard. Howeber, this skill provides students a chance to expand their geometric repertoire as well as combine skills learned in this unit. This lesson, and particularly this unit, builds off of volume as well as the Pythagorean theorem which is needed for parts of this lesson to determine radius, height or slant height.
It is important that students have a working knowledge of how to use the Pythagorean theorem to find the missing sides for some of the problems demonstrated in this problem set. Being spatially aware is the best thing to help students in this unit, so providing kinesthetic, visual (or a mix of both) would be the best option to assist students who may be struggling.
Daily Objectives: SWBAT: Find the volume of composite figures (two or more 3D shapes joint or stacked) using given formulas and a calculator with 80% accuracy.
Today, you will be learning about finding the volume of 3D figures that look a little different. This section includes composite figures, or two or more shapes joint or stacked. For the first part of your lesson, please have your Engage NY textbook open to Module 7, Lesson 21. You will need a pencil and calculator to complete this lesson.
*Disclaimer: I know the video is LONG! However it covers the entire lesson form the book. You do not have to watch the full video, but watch a few minutes before attempting independently. You can watch as much or as little of this video to help you.
Video Lesson:
Media retrieved from: 8h Math Module 7 Lesson 21. (2015). Retrieved from https://www.youtube.com/watch?v=p59KgLb7W8c&t=2s
Need extra help?
Media retreived from:Calculating the Volume of Composite Solids. (2014). Retrieved from https://www.youtube.com/watch?v=pQCrugPzsU0
Volume of Composite Solids. (2015). Retrieved from https://www.youtube.com/watch?v=6STXYGaBtW8
After watching the lesson videos and completing the lesson and problem set in your book, please click this link to complete the Quiz!
CONGRATULATIONS, MY DEAR STUDENT, YOUR BOOK WORK FOR THIS MINI-MODULE HAS BEEN COMPLETED.
Exit ticket: Please reply to this post by answering one or more of the following questions:
Draw your own mini skyline for your peers to solve. Include two or more composite shapes as well as measurements.
Pretend you are teaching this lesson to your younger brother or sister who is in Kindergarten. How would you explain composite volume or volume in general to this much younger student? What might you need to think about so that your younger sibling understands?
Please reply to two or more peers to receive full credit on your exit ticket. You may agree or disagree, ask questions, make suggestions, respond to their questions, or give kind concrete feedback if they have posted their own work.
Curriculum Standards:
CCSS.MATH.CONTENT.8.G.C.9
CCSS.MATH.PRACTICE.MP4
CCSS.MATH.PRACTICE.MP5
Materials:
This lesson is simple once students understand that the formulas remain constant, as does the way they solve the problem. Some suggestions for students that may need differentiation include:
Daily Objectives: SWBAT: Find the total volume of a castle consisted of composite 3D shapes using given formulas and a calculator with 80% accuracy.
As we saw on day 4, 3D shapes including composite and truncated shapes are frequent features in today's skyline. Let's take a trip back to medieval times or to Hogwarts, whichever magical adventure inspires you. Please enjoy these flyovers of British castles for inspiration!
Media retreived from: Castle Flyover. (2017). Retrieved from https://www.youtube.com/watch?v=c_945pky8Lg
Drone Flyover of Bodiam Castle. (2014). Retrieved from https://www.youtube.com/watch?v=2Px8JgD0h_k
Note the presence of 3D figures in each of the castles above. It's important to know the volume of these castles in order to understand the amount of space or rooms can fit in the castle as well as the amount of building materials such as concrete or sand will be needed to take up space in construction. While buildings look different today, knowing how much material is needed is crucial for the construction and design process. Today, you will practice finding the total volume of a structure, in this case a castle, such as the one above.
In this castle investigation, you must use your knowledge of finding volume of 3D shapes in order to find the volume of the castle. To help you stay organized, the castle is color coded and all sides are labeled.
Find the volume of the castle below:
You must:
For help, please use this list of formulas:
Source: http://mrscolpittswss.weebly.com/unit-3-surface-area-and-volume.html
Exit ticket: Please reply to one or more of the following questions!
Please reply to two or more peers to receive full credit on your exit ticket. You may agree or disagree, ask questions, make suggestions, respond to their questions, or give kind concrete feedback if they have posted their own work.
Curriculum Standards:
CCSS.MATH.CONTENT.8.G.C.9
CCSS.MATH.PRACTICE.MP4
CCSS.MATH.PRACTICE.MP5
Materials:
Use the videos to your advantage. Some students haven't seen what a castle can look like; consider the cultural context and ensure that your students understand. Use the flyovers (using drone technology) to spark interest in all of the intricacies possible in each of these figures. When it comes time to explore the castle, students may find that they recognize features from the video in the castle they are tasked to find the volume in. This is with the intention that students make historical connections to their daily work.
I used my name to make this castle for students to use, but using any photo editing software it is easy to make your own. Although I only used one version, you are able to easily create simpler or more intricate castles using a variety of programs such as Adobe or Microsoft 3D paint in order to create works like this for your students.
Making a castle more simple or including smaller units helps students who do not have a solid grasp on the material. To assist my students, I used color coding to group shapes by type and help students match the shapes to the formulas. I would encourage students to use a formula reference sheet as well as a calculator to check their work. Although some of this module is online, I would recommend students write their equations, including the information they are plugging in on a piece of paper or whiteboard.
Daily Objectives:
SWBAT: Draw a blueprint of a 3D castle include six 3D shapes, two composite shapes and one truncated shape.
SWBAT: Find the volume of each shape, composite shape, and truncated shape as well as the total volume of the castle using given formulas and a calculator with 80% accuracy.
You are excited about entering in the yearly castle design competition; however, this year’s competition comes with a geometric twist!
You must have:
The competition also requires that you find the volume of your figures!
To enter the contest you must submit a two-dimensional blueprint of your design. You must draw it to the best of your ability (see images below for examples). In addition to your drawing, you must include calculations for all 3d shapes used in the project (total of 9 total shapes or more).
Geometric Figure Details: Include answers in a table or on a piece of paper. All work including formulas used should be shown for full credit. (Note: you are not limited to a total of four figures. Please use a separate sheet of paper to complete the table if more room is needed).
Your castle may be as simple as this style:
Your castle may also be as complicated as:
You may also need the following formulas to help you:
The above formula sheet was retrieved from: http://mrscolpittswss.weebly.com/unit-3-surface-area-and-volume.html
How will you be graded on this project?
How to complete a Scholar work in Creator:
For this project, open up a document and add the images of your castle as well as all calculations using the insert media tool. Please write 2-3 paragraphs explaining your castle, why you created it to look a certain way, and your process during blueprinting.
Within one week:
8th Grade project rubric is as follows:
Curriculum Standards:
CCSS.MATH.CONTENT.8.G.C.9
CCSS.MATH.PRACTICE.MP4
CCSS.MATH.PRACTICE.MP5
Materials:
You must assign this Work through Creator for students to get started. This is meant as a culminating project where pairs reflect on what they have learned in Days 1-5 to prepare for their own construction.
Be clear to students that they do not need to use outside resources to complete this project, but they are optional if students would like to explore further.
Students who require more structure could benefit from a graphic organizer, or specific steps to ensure that they are able to progress through the prompts and the rubric. Students may need assistance using the tools on Creator such as viewing the rubric, or using Structure to create headings. As students begin their writing process, it may be positive to hold writers workshops or circulate to ensure that students are comprehending the technical aspects of Scholar. Encourage students to add videos as well as the piece of required media
Daily Objectives: SWBAT: Follow feedback suggestions to revise or review calculations and resubmit their project using the creator tool.
Students will be able to provide clear and constructive feedback on a numerical rubric to offer peers constructive criticism during the editing process.
Now that we have reached the end of our 3D shapes mini-unit, it is important to re-take our pre-unit assessment. You should have a much better understanding of how to use formulas to find the volume of shapes including truncated and composite shapes. Please make sure you complete the Survey!
You will have received revision requests from creator. This means that there may be some changes you need to make in your overall design of your castle or your calculations.
In a private message to your teacher, please state whether you feel you have met the learning objective for the day and why.
Lesson Objective:
Curriculum Standards:
CCSS.MATH.CONTENT.8.G.C.9
CCSS.MATH.PRACTICE.MP4
CCSS.MATH.PRACTICE.MP5
Materials:
This is the last day of the unit. By now, students will have had time to make revisions to their work using Creator. You may choose to assess each student on their abilities to:
Teachers should look to give the post test as a small formative asssessment here. While this assessment is very short, it gives a small skills based portion to a rather project-based ending. Many students like this circular trajectory where they can see their final product as well as a score change between pre and post quizzes.
8th Math Module 7 Lesson 19. (2015). Retrieved from https://www.youtube.com/watch?v=iQkVUMCL2m8
8th Math Module 7 Lesson 21. (2015). Retrieved from https://www.youtube.com/watch?v=p59KgLb7W8c&t=2s
Calculating the Volum eof Composite Solids. (2014). Retrieved from https://www.youtube.com/watch?v=pQCrugPzsU0
Castle Flyover. (2017). Retrieved from https://www.youtube.com/watch?v=c_945pky8Lg
Drone Flyover of Bodiam Castle. (2014). Retrieved from https://www.youtube.com/watch?v=2Px8JgD0h_k
Enagge NY. (2014, April 17). Grade 8 Mathematics. Retrieved April 21, 2020, from https://www.engageny.org/resource/grade-8-mathematics-module-7-topic-d-overview
How to find the volume of a Frustum. (2012). Retrieved from https://www.youtube.com/watch?v=1v1Pp-lJSKY&t=14s
Scolpitts. (n.d.). Unit 3: Surface Area and Volume. Retrieved April 21, 2020, from http://mrscolpittswss.weebly.com/unit-3-surface-area-and-volume.html
Thompson, A. (2020, April). Ch 19 Quiz. Retrieved April 21, 2020, from https://quizizz.com/admin/quiz/5d9cf63c8aaa11001beabb64?studentShare=true
Volume of a Pyramid. (2012). Retrieved from https://www.youtube.com/watch?v=e7-am8JtREI&t=1s
Volume of a Truncated Cone. (2018). Retrieved from https://www.youtube.com/watch?v=hc9Efi-GjMs&t=4s
Volume of Composite Solids. (2015). Retrieved from https://www.youtube.com/watch?v=6STXYGaBtW8
Volumes of Cylinders, Cones and Spheres. (2019). Retrieved from https://www.youtube.com/watch?v=bLEH02cGL_o