6th Grade Geometry PBL

Contact Information:Valerie RobertsTitle:Using Geometry to Solve Real World ProblemsPrimary Subject Area and Grade Level:6th Grade GeometryOverview:Lesson aims at teaching students area, surface area, and volume by having the students complete a project in which they must design a vertical planter for people that live a big cities. They will be researching, creating a presentation to share with class members, and creating a design plan to share online. State Standards being addressed are:

MAFS.6.G.1.1 - Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

MAFS.6.G.1.2 - Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

MAFS.6.G.1.3 - Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

MAFS.6.G.1.4 - Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

This lesson could also incorporate standards from other content areas if used as a Thematic Unit. Approximate Duration:This lesson will require two weeks (10, 45 min class periods) to completeClass Format:This lesson will be face-to-face, but require students to collaborate online in and outside of class.

Danielson, 1b

Common Core Educational Technology Standards Addressed: MAFS.6.G.1.1, MAFS.6.G.1.2, MAFS.6.G.1.3, MAFS.6.G.1.4 Interdisciplinary Connections:Science, social studies, & language arts are all be incorporated in this lesson

Prior Knowledge:Students must have prior knowledge of shapes, multiplication/division, addition/subtraction, fractions, and some knowledge of computers and how to use the internet, knowledge and log in information for EDPuzzle.com, Google Docs, Prezi.com, Aurasma.com, and optional access to the Aurasma app on smartphone/tablet. Outcomes/Objectives: Given a time limit of two weeks and a rubric to follow/be graded on, students will be able to apply knowledge of area, surface area, and volume to design simple building plans, research and create a plan to solve a real-world problem, and create a presentation about what they did to solve the problem.

Technologies and Other Materials /Resources: Lesson Notes – Provided at end of Lesson PlanTeacher Notes – Provided at end of Lesson PlanStop Sign – Provided at end of Lesson PlanWorksheet – retrieved from K5Learning.com

http://www.k5learning.com/worksheets/math/grade-6-rectangular-prism-volume-surface-area-fractions-a.pdf Project Instructions – Provided at end of Lesson PlanRubric – Provided at the end of the Lesson PlanProjector – Use of Projector needed for Lesson NotesEDPuzzle.com – Teacher must have account set up and a class set up for students to log into, with the videos assigned to the class.

https://edpuzzle.com/ (Log-in/Sign-up)

Area of a Parallelogram Day 1 Homeworko https://edpuzzle.com/media/575043e6e37454f56e6b40e8

Area of a Trapezoid Day 1 Homeworko https://edpuzzle.com/media/575046f0e37454f56e6b59d3

Area of Polygons Day 1 Homeworko https://edpuzzle.com/media/57504cafd68c932a5da82dff

Surface area of rectangular prism Day 1 Homeworko https://edpuzzle.com/media/57505470d68c932a5da86506

Surface area of triangular prism Day 1 Homeworko https://edpuzzle.com/media/575056ffe37454f56e6bd2a9

Volume of rectangular prism Day 2 Homeworko https://edpuzzle.com/media/575059cbd68c932a5da88c69

Drawing polygons in the coordinate plane Day 2 Homeworko https://edpuzzle.com/media/57505d47d68c932a5da89f75

Finding area of polygons in coordinate plane Day 2 Homeworko https://edpuzzle.com/media/57505ee9e37454f56e6c0730

Prezi.com – Teacher and students must have accounts on Prezi.com. I have provided a link to the Prezi needed by the teacher. https://prezi.com/ (Log-in/Sign-up) http://prezi.com/_mzd6m4lf09i/?utm_campaign=share&utm_medium=copy&rc=ex0share (Project Presentation)

Google Docs – Teacher and students must have accounts for Google Docs. I have provided a link to sign up for Google. https://accounts.google.com/SignUp?service=wise&continue=https%3A%2F%2Fdocs.google.com%2Fdocument%2F

%3Fusp%3Ddocs_alc%26pref%3D2%26pli%3D1&hl=en (Log-in/Sign-up)Aurasma.com – Teacher must have account with Aurasma. Students must have an account, it is optional for them to have the app on a smartphone/tablet.

https://studio.aurasma.com/login (Log-in/Sign-up) Auras have been made public and can be found by searching robertsvalerie Pictures connected to auras provided at bottom of lesson (all pictures used are labeled for reuse) Pictures can only be scanned if you are “following” my profile (robertsvalerie)

Pinterest.com – The teacher must have a Pinterest account with a page for each of his/her classes to upload content to. https://www.pinterest.com/ (Log-in/Sign-up)

Math4childrenplus.com – Geometry games for children in K-7 http://www.math4childrenplus.com/games/geometry/

Activities/Tasks (Lesson Procedure):

Lesson Procedure: Day 1 Monday Introduction/Gain Attention/Ice Breaker – 5 min

o TTW hold up a square stop sign and wait for the students to stop talking and have eyes on him/her.o TTW ask, “What is wrong with this stop sign?”o TSW respond.o TTW say, “You knew what was wrong with this stop sign because you see them every day. Geometry is all around

you and involved in our lives all day every day. Outcomes and Relevance – 3 min

o TTW say, “This week we are going to learn how to solve real-world problems using geometry skills. Today we will start with learning about area and surface area. Tomorrow we will learn about volume and drawing polygons in the coordinate plane. Throughout the rest of the next two weeks we will be practicing these skills and working in groups to create a solution for a problem faced by many people across the world.”

Motivating Introduction – 2 mino TTW say, “By the end of the week you will have used your knowledge of geometry to create something that will

make the world a better place.” Content of Lesson – 30 min

o TTW hand out pre-printed lesson notes to the students. o TTW work through the notes, following the set of teacher notes provided, highlighting special words/phrases and

working through the example problems with the students, allowing them to try some of them on their own.o TTW only go over area and surface area today. Volume and drawing polygons in the coordinate plane will be

focused on tomorrow.o TSW follow along with the teacher and the notes, highlighting where necessary and working through the example

problems.o TTW draw a Venn diagram on the board.

o TTW have students compare and contrast area and surface area. Closure and Review: - 5 min

TTW say, “Today we have learned important skills that will help you to solve problems and make the world a better place. Tomorrow we will continue to learn important geometry skills. Tonight your homework will be to log-in to your EDPuzzle.com account and watch the assigned videos and answer the questions.”

Note:The videos used are available online and can be accessed through EDPuzzle.com. Links are provided in the Materials/Resources section of the Lesson Plan.

Higher Level Thinking Skills Notedo “Compare and contrast area and surface area.”

Lesson Procedure: Day 2 Tuesday Introduction/Gain Attention/Ice Breaker – 5 min

o TTW say, “Bakers, Chemists, Doctors, Engineers, and Mechanics, what do all of the professionals have in common?

o TTW wait for student response.o TSW respond.o TTW say, “All of these professionals need to know how to calculate volume.”

Outcomes and Relevance – 3 mino TTW say, “Yesterday we learned about area and surface area, how they are alike and different, and how to

calculate them. Today we will be learning about volume and how to draw polygons in the coordinate plane.” Motivating Introduction – 2 min

o TTW say, “Today we will continue to learn about very important aspects of geometry!” Content of Lesson – 30 min

o TTW ask students to pull out their pre-printed notes from the day before. o TTW continue to work through the notes, following the set of teacher notes provided, highlighting special

words/phrases and working through the example problems with the students, allowing them to try some of them on their own.

o TSW follow along with the teacher and the notes, highlighting where necessary and working through the example problems.

Closure and Review: - 5 minTTW say, “We have finished with content, and now we can move on to applying our new knowledge! Tonight for homework, you will log into your EDPuzzle.com accounts and watch the assigned videos and answer the questions.”

Note:The videos used are available online and can be accessed through EDPuzzle.com or YouTube.com. Links are provided in the Materials/Resources section of the Lesson Plan.

Higher Level Thinking Skills Notedo “What do you think of when you hear the word volume?”

Lesson Procedure: Day 3 Wednesday Introduction/Gain Attention/Ice Breaker – 2 min

o TTW say, “How many of you want to do something to change the world?” Outcomes and Relevance – 2 min

o TTW say, “Today we are going to practice what we learned in the last two days about area, surface area, and volume, and learn how we can apply that knowledge to solve a real world problem.”

Motivating Introduction – 1 mino TTW say, “Today you will start a project that will help people across the world!”

Content of Lesson – 35 mino TTW separate students into groups of 3 or 4 depending on size of class. If possible, divide students in group by

ability, matching higher and lower ability students together so that groups are evenly dispersed.o TTW open a Prezi that explains the problem that the students will be solving and how.o TTW say, “Across the world, people that live in big cities are all dealing with the problem of, not having the space

to grow their own produce. Many people are choosing organic produce because they fear the use of pesticides and genetically engineered produce, but it is often expensive. The only other way to get produce that is not affected by these factors is to grow your own, but most of the time when you live in a big city, you don’t have the space for a garden. What we are going to do this week is give these people a solution. What are some ways you think that we could help solve this problem with our knowledge of geometry?”

o TTW wait for student responses.

o TTW say, “Those are all great ideas and maybe something you could look into further at home. What we are going to do to help solve this problem is to design a vertical planter that will help people grow their own produce in a small amount of space.”

o TTW say, “As a group, you will be choosing a city from a list that I have provided. You will research the climate of that city, and what kind of produce grows well in that city’s climate. You will then need to research what these plants need to grow, how much soil they need, and the space they need to grow, in order to figure out the dimensions you will need to design a vertical planter to grow them in. You will then design your planter and share that design on the internet for other people to use. Finally, you will make a presentation on your findings, and the planter that you designed to share with the class. There is a rubric for you to follow, and I will be available to help you along the way with any questions you have.

o TTW say, “Before we pick the cities that you will be researching, I am going to put a problem on the board. The first group that finds the correct surface area, and volume of the 3D object will get first pick of their city.

o TTW go to the slide on the Prezi which has the problem for the students to solve. The next slide has the problem solved.

o TTW allow students time to solve the problem.o TTW say, “I have pictures of the cities that you can chose from. When your group chooses a city, you can use the

picture and your Aurasma app to access sites you can use for research. If you do not have the app, you can log into Aurasma.com and view the Aura from there, I have provided instructions for this in your project instructions.

*Note – the teacher must have printed pictures of each of the cities that the students can choose from. These pictures are given in the auras that I have created and these pictures are the ones that must be used.*Note – students must be “following” my profile (robertsvalerie) to be able to scan the pictures with Aurasma app. If teacher creates his/her own videos, students must be “following” the teacher’s profile to be able to scan Auras.o TTW allow groups to pick their cities and hand out the pre-printed instructions for the project.o TTW help the students log into their Google Docs accounts and help them set up a google doc for each group.

Closure and Review: 3 mino TTW say, “Today we have started a project that will help people across the world. Your homework tonight is to

research the climate of the city that your group chose and the types of produce that grows well in that climate, using the websites that I have provided in your instructions. You will share your research with the rest of your group using your Google Doc. Tomorrow we will continue our research and start to formulate a design.”

Higher Level Thinking Skills Noted“What are some ways you think that we could help solve this problem (lack of space in cities for people to grow their own produce) with our knowledge of geometry?”

Lesson Procedure: Day 4 Thursday Introduction/Gain Attention/Ice Breaker – 2 min

o TTW say, Research is necessary in all fields of work. It is important to be knowledgeable and have up-to-date information about any topic you choose to specialize in.

Outcomes and Relevance – 2 mino TTW say, “Today we will continue our work on researching our topics. It is important that you learn how to gather

accurate information and learn how to organize that information to accurately represent your findings and insights.”

Motivating Introduction – 1 mino TTW say, “Continue to work hard and you will end up with wonderful results!”

Content of Lesson – 35 mino TTW have the students break into their groups to continue researching their topics and organizing their

information.o TTW work with each group individually to make sure that they are on the right path and answer any questions.o TTW make sure that students are finding information about the climate of their chosen city, what plants work well

in that climate, and what those plants need to survive. This is to include, the size of the plants, how much soil, water, and space the plants need to grow, whether or not they need to be attached to a support, whether they spread out on the ground or grow vertically, etc.

Closure and Review: - 5 minTTW say, “You have all done very well with your research. Tonight for homework you will complete a worksheet for practice with your geometry skills. I have a question I want you to think about and come to class ready for a discussion. The question is, How are the geometry skills that you have learned going to help you design a planter?”

Higher Level Thinking Skills Notedo “How are the geometry skills that you have learned going to help you design a planter?”

Lesson Procedure: Day 5 Friday Introduction/Gain Attention/Ice Breaker – 1 min

o TTW say, “Are we ready to help change the world?!” Outcomes and Relevance – 2 min

o TTW say, “Today we are going to use the research that you have collected and your knowledge of area, surface area, and volume, to help you design your planters.”

Motivating Introduction – 2 mino TTW say, “Today you will all be engineers using your knowledge of geometry to help change the world!”

Content of Lesson – 35 mino TTW say, “What are some examples that you can think of, of jobs that might need the use of geometry skills?”o TSW give examples of jobs that use geometry skills.o TTW say, “There are many jobs out there that require the use of geometry skills. Today you will be using your

geometry skills to act as engineers and designers to create a vertical planter.”o TTW say, “Yesterday, along with your homework, I asked you to think about how the geometry skills you have

learned are going to help you design your planters. Now I would like to hear your ideas.”o TSW participate in the discussion.o TTW say, “Now I want you to use the ideas we have discussed to design your planters.”o TTW have students log in to their Google Docs.o TTW have the students start discussing with each other what they found and what produce they want to grow in

their planters.o TTW go to each group and check to see that they have done the appropriate research and are headed in the right

direction.o TTW say, “Now that you know what plants you want to grow in your planter, you need to discuss as a group the

size of the plants and how much soil they will need so that you can figure out the dimensions you will need for your planters and how many plants you can put in each box. I will be visiting each group to help them with their plans.

o TSW work in groups to design their planters.o TTW visit each group and help them to design their planters.

Closure and Review: - 5 minTTW say, “Today you have used your research to help you design your planters, just like engineers! For homework, you will design a box of your choosing. It can be a jewelry box, a safe, or anything else that you can think of. The only requirements are that if has a total volume of ____ and you must calculate the surface area of the box after you have completed it. I look forward to seeing what you have come up with on Monday.”

Higher Level Thinking Skills Notedo “What are some examples that you can think of, of jobs that might need the use of geometry skills?”o Design a box of your choosing, the only requirements are that is has a total volume of _____ and you must

calculate the surface area of the box after you have completed it.

Lesson Procedure: Day 6 Monday Introduction/Gain Attention/Ice Breaker – 1 min

o TTW say, “I am very excited to see all of your geometry skills at use in your box designs!” Outcomes and Relevance – 2 min

o TTW say, “Today we are going to use our geometry skills to check one another’s designs for accuracy.” Motivating Introduction – 2 min

o TTW say, “Part of an engineer’s work is to check designs for accuracy and stability. Today you will be doing just that!”

Content of Lesson – 35 mino TTW have students turn in their homework box designs.o TTW have students get into their groups.o TSW have 10 minutes to check their planter designs and refine them.o TTW have students switch designs with another group and check the designs for accuracy.o TSW have 10 min to check that the correct measurements have been used and that the volumes of each of the

boxes on the planters were calculated accurately.o TTW have students return the designs to the other groups.o TSW have 10 min to correct any changes that need to be made and create a final copy of their designs.o TSW turn their designs in so that the teacher may upload them to Pinterest.com under their class page.

Closure and Review: - 5 minTTW say, “Today you have used your geometry skills to check the accuracy of each other’s work. Tomorrow you will start

your presentations. For homework tonight I want you to go over the research that you have found in your groups. I want you to create an outline of what you think should be included in your presentations. Use your rubric as a guideline.”

Lesson Procedure: Day 7 Tuesday Introduction/Gain Attention/Ice Breaker – 2 min

o TTW say, “How many of you know what you want to be when you grow up?”o TSW raise their hands.o TTW say, “In our world of growing technology, creating presentations and presenting them is a skill that many of

you will need to have.” Outcomes and Relevance – 2 min

o TTW say, “Today you will be working in your groups to create a presentation to showcase your project. The research that you’ve done, how you used this research to design your planters, how these planters will help people, and how geometry has helped you accomplish this, will all be showcased in your presentation to show what you have learned.”

Motivating Introduction – 1 mino TTW say, “Today you will be cultivating skills that will be very important in your future careers.”

Content of Lesson – 35 mino TTW say, “How do you think having the knowledge and skills of creating a presentation will help you in your

future careers?”o TSW respond.o TTW say, “What do you think are important aspects of a successful presentation?”o TSW respond.o TTW write their ideas on the board.o TTW say, “You have now made your own guideline to follow while making your presentations.”o TTW have students log into their Prezi accounts.o TTW help students share a Prezi within their groups so that everyone may work on it together.o TSW work together to create their presentations.o TTW visit each group answering any questions that they may have and guiding them through the process of

creating a presentation. Closure and Review: - 5 min

TTW say, “Today you have collaborated with each other and cultivated skills that will be necessary in your future careers. You are well on your way to becoming successful in anything you choose to do! Tonight for homework you will log into your EDPuzzle.com accounts, watch the assigned videos, and answer the questions in the videos.”

Higher Level Thinking Skills Notedo “How do you think having the knowledge and skills of creating a presentation will help you in your future

careers?”

Lesson Procedure: Day 8 Wednesday Introduction/Gain Attention/Ice Breaker – 1 min

o TTW say, “Your presentations are coming along nicely!” Outcomes and Relevance – 3 min

o TTW say, “Today you will be continuing your work on your presentations. These presentations will show what you have learned and how hard you have worked.”

Motivating Introduction – 1 mino TTW say, “I know that all of your hard work will pay off.”

Content of Lesson – 35 mino TTW have students break into their groups.o TSW continue working on their presentations.o TTW visit each group checking their progress and answering any questions they may have.

Closure and Review: - 5 minTTW say, “We are in the home stretch! Tonight for homework you will finish your presentations and prepare for your presentation to the class.”

Lesson Procedure: Day 9 Thursday Introduction/Gain Attention/Ice Breaker – 1 min

o TTW say, “Today is the day you will showcase all of your hard work!” Outcomes and Relevance – 3 min

o TTW say, “Today you will be presenting your projects to the class. You will present the Prezi presentations that you have created”

Motivating Introduction – 1 mino TTW say, “I am very excited to see all of your hard work!.”

Content of Lesson – 30 mino TTW say, “You will have 10 minutes to present your project to the class. We will get as many groups done today

as we can and tomorrow the rest of the groups will present.”o TSW present their projects while the rest of the students watch.o TTW allow the students to ask questions after each presentation.o TTW grade the projects based on the rubric provided.

Closure and Review: - 5 minTTW say, “I have seen some wonderful presentations today. You have all done very good work. I cannot wait to see what the rest of you have accomplished tomorrow. No homework today!”

Lesson Procedure: Day 10 Friday Introduction/Gain Attention/Ice Breaker – 1 min

o TTW say, “Today we will see the last of your presentations!” Outcomes and Relevance – 3 min

o TTW say, “Today you will be presenting your projects to the class. You will present the Prezi presentations that you have created”

Motivating Introduction – 1 mino TTW say, “I am very excited to see all of your hard work!”

Content of Lesson – 30 mino TTW say, “You will have 10 minutes to present your project to the class.”o TSW present their projects while the rest of the students watch.o TTW allow the students to ask questions after each presentation.o TTW grade the projects based on the rubric provided.o If there is time remaining after all of the presentations are completed the students may play geometry games at

math4children.com Closure and Review: - 5 min

TTW say, “You have all had wonderful presentations and I am very proud of the hard work that you have done to get this far! No homework today!”

Relevance/Rationale: In this unit students have learned about area, surface area, volume, and drawing polygons in the coordinate plane, which are all standards addressed by the state as mandatory for learning. Students have also learned about conducting research, using this research to solve a problem using their geometry skills, and creating a presentation to show what they have learned and what they did to solve a problem, which is important because they are skills that will be used in future learning and in the real world.Assessment Criteria for Success:Content knowledge, student knowledge, and appropriate resources aligned to instructional outcomes.

Formative assessments throughout the unit will be through the use of EDPuzzle.com, the worksheet completed for homework, and teacher observation of class discussions and group work.

The teacher and students will know if they have successfully met the outcomes by following the project instructions and the rubric provided.

The specific criteria to be met in a successful product are listed in the project instructions and the rubric. Success in this unit would mean that students are accurately using their knowledge of area, surface area, and volume to

design a vertical planter, that they have done the proper research to know what they need their planter to accommodate, and that they have created a successful presentation to showcase what they have learned, the research they have done, and how it is going to help people.

Summative assessment will be their final presentation and the final design that the students come up with.

Explorations and Extensions:1. EXPLORATION: For students that are early finishers, we will challenge them with higher order geometry questions.

Questions that involve more than just using the formulas, but require the identification of the problem and multiple steps to complete. Such as:

Adam is building a rectangular planter without a top. The planter will be 7 inches wide, 16 inches long, and 10 inches high. How much wood is needed to make the bottom and sides of the planter?

2. EXTENSIONS: For students that are not successful with independent activity: One-on-one teacher/student time. Extra EDPuzzle.com videos Extra worksheets Pair with high achieving student

Modifications/Accommodations and Access for All:ESE:

Cooperative learning groups Using multimedia and/or supplemental materials Check often for understanding and review Individualized instruction Peer tutoring

ESOL: Alternate responses Advanced notes Teacher modeling Simplified written and verbal instructions eDictionaries

Behavioral: Preventive classroom management Breaks between tasks Daily feedback to student Positive Reinforcement

Meaningful technology Integration Explanation:This lesson integrates technology in an educational manner because it addresses both Social Constructivism and

Connectivism Learning Theories. The students work together in groups to solve a real world problem. They use technology to conduct research, collaborate, create a presentation, and share their work, as well as receiving content. Technology is also used for both formative and summative assessments. In this lesson, students are receiving interaction from the content and technology as well as adding to it.

For example, for homework students are required to watch videos assigned on EDPuzzle.com. The videos assigned to them are not simply videos to watch, but to interact with. During the video, questions will appear and students must answer them before the video can continue. Secondly, Students are using their knowledge of the content to create a solution to a real world problem. In order to accomplish this, they must use technology to conduct research and use this research in their design. Next, students are sharing their designs on the internet which grows the knowledge base online. Also, students are using technology to create a presentation on what they have learned to share with other students in their class.

In conclusion, this lesson uses meaningful technology integration to not only teach geometry skills, but to give students practice with using this knowledge to solve a problem. During this lesson, students must use technology to research, create, and share. Students are not only receiving content through technology, but using technology to add to the content.

Vertical Planter Project Instructions

Across the world, people that live in big cities often have the problem of lack of space to have a garden to grow produce in. During this project you will be researching a city’s climate, what produce grows well in this climate, and what these plants need to survive. You will use your knowledge of area, surface area, and volume to design a vertical planter that will enable people to grow produce in a small space. You will then create a presentation about your research and design to share with the class.

ResearchYou will use the links provided from the Aura based on your city’s picture for your research.Your research must include:

The city’s population The city’s climate Produce that grows well in this climate including

o What time of year they growo How big the plants get (roots and above ground)o How much spacing the plants needo Whether the plants grow on vines that spread across the ground or need to be attached to a trelliso Etc.

DesignAfter you have gathered all of your research, you must use this research to design a vertical planter to accommodate plants of your choosing.Your design must have certain specifications:

Planter must take up no more than 12 f t 2

Planter must be no taller than 6 ft Planter must have at least 2 levels Planter must be made out of real materials and materials must be specified.

The goal is for people to actually be able to make a vertical planter using you design.

PresentationYou will be creating a presentation to show the class the research that you conducted and the design that you came up with.Your presentation is to include:

Research about your city Research about the plants that you chose Your planter design including specifications about why you designed it the way you did How geometry has helped you with your design and ideas as to how these skills can help you in the

future. 10-15 meaningful frames

You will be graded on several categories:

Fulfillment of requirements Content covered (research and math skills) Organization of ideas

Mechanics Originality Attractiveness of presentation Presentation (how well you present your project to the class Workload (how well you shared the work within your group)

Vertical Planter Design

Teacher Name: Mrs. RobertsCATEGORY 4 3 2 1Requirements All requirements are

met and exceeded.All requirements are met.

One requirement was not completely met.

More than one requirement was not completely met.

Content Covers topic in-depth with details and examples. Subject knowledge is excellent.

Includes essential knowledge about the topic. Subject knowledge appears to be good.

Includes essential information about the topic but there are 1-2 factual errors.

Content is minimal OR there are several factual errors.

Organization Content is well organized using headings or bulleted lists to group related material.

Uses headings or bulleted lists to organize, but the overall organization of topics appears flawed.

Content is logically organized for the most part.

There was no clear or logical organizational structure, just lots of facts.

Mechanics No misspellings or grammatical errors.

Three or fewer misspellings and/or mechanical errors.

Four misspellings and/or grammatical errors.

More than 4 errors in spelling or grammar.

Originality Product shows a large amount of original thought. Ideas are creative and inventive.

Product shows some original thought. Work shows new ideas and insights.

Uses other people\'s ideas (giving them credit), but there is little evidence of original thinking.

Uses other people\'s ideas, but does not give them credit.

Attractiveness Makes excellent use of font, color, graphics, effects, etc. to enhance the presentation.

Makes good use of font, color, graphics, effects, etc. to enhance to presentation.

Makes use of font, color, graphics, effects, etc. but occasionally these detract from the presentation content.

Use of font, color, graphics, effects etc. but these often distract from the presentaion content.

Presentation Well-rehearsed with smooth delivery that holds audience attention.

Rehearsed with fairly smooth delivery that holds audience attention most of the time.

Delivery not smooth, but able to maintain interest of the audience most of the time.

Delivery not smooth and audience attention often lost.

Workload The workload is divided and shared equally by all team members.

The workload is divided and shared fairly by all team members, though workloads may vary from person to person.

The workload was divided, but one person in the group is viewed as not doing his/her fair share of the work.

The workload was not divided OR several people in the group are viewed as not doing their fair share of the work.

London, England

Delhi, India

New York City, NY

Los Angeles, CA

Sydney, Australia

Area, Surface Area, and Volume Lesson Notes

Finding the Area of Right Triangles

Decompose – to break down a shape into different smaller shapes.

Area of a Rectangle = (length × width)

Area of a Triangle =

Compose – to make a shape by adding other shapes

We can add the reflection of this triangle in order to make a rectangle.

You can also use these concepts with more complicated shapes to break them down into easier shapes to calculate.

The area of this trapezoid can be found by decomposing it into a rectangle and two triangles. Then we just add up the areas of the smaller shapes to get the area of the trapezoid.

The area of this hexagon can be found by decomposing it into a rectangle and three triangles.

Surface Area of 3D Objects

The Surface Area on an object is the total area of all of the faces of the object.

To find the surface area, we simply find the area of each face on the object and add them all together.

Ex. 1

Ex. 2

5 yd.

4 yd.2 yd.

2.2 ft.

3 ft.

2 ft. 2 yd.

Volume

When you hear the word volume what do you think of?

When we talk about the volume of an object, we are talking about the amount of space inside the object, or how much you can fill the object with, whether it be with liquids or solids.

When we calculate the volume of an object there are three dimensions that we need to consider, length, width, and height.

There are two formulas we can use to calculate volume.

1. V=l × w ×h

2. V=B x h where B is area of the base of the object

Example 1

Find the volume of the rectangular prism.

V=____________________

Example 2

Find the volume of the Rectangular prism.

34

m

12

m12

m

V=______________________

You can also find the measurement of a missing dimension when given the total Volume.

Example 3

Write and solve an equation to find the missing dimension of the prism.

Volume = 72 i n3

L=_____________________

Example 4

Write and solve an equation to find the missing dimension of the prism.

Volume = 1735 c m3

2 in

6 in

L

W=___________________________

Drawing Polygons in the Coordinate Plane

What is the Coordinate Plane?

The Coordinate Plane is a plane spanned by the (x) and (y) axis.

An ordered pair is a set of coordinates corresponding to the (x) and (y) values counting away from the origin.

The origin is the point of intersection of the (x) and (y) axis and is valued at (0,0).

We can draw polygons in the coordinate plane by plotting coordinates and connecting the points.

Example 1

Plot the points and connect the points in the order that they are listed to create a polygon

(-3,3); (3,3); (3,-3); (-3,-3)

Example 2

Plot the points and connect the points in the order that they are listed to create a polygon

(-4,3); (-1,0); (3,0); (0,3)

Finding the Area of Polygons in the Coordinate Plane

The first step to finding the area of polygons in the coordinate plane is to know the lengths of the sides.

You can count the length, or if two points share the same (x) or (y) coordinate, we can find the length of that side by looking at the other coordinates in the point.

Example 1

Find the length of the line from (2,-3) to (2,3).

Once you know how to find the length of the sides of a polygon in the coordinate plane you can find the area.

*You may need to may need to decompose the polygon into rectangles and triangles.

Example 2

Plot the points and connect them in the order listed to create a polygon and find the area of the polygon.

(-2,3); (2,3); (4,0); (2,-3); (-2,-3); (-4,0)

Step 1 – plot the points and connect them to create the polygon Step 2 – decompose the polygon into triangles and rectangles Step 3 – find the lengths of the sides of each of the rectangles and triangles Step 4 – find the areas of each of the rectangles and triangles Step 5 – add the areas together to find the total area.

Teacher Notes