Planning Guide

Creating Learner-Focused
Schools

* Madison-Oneida BOCES- This document may not be reproduced in any form without the expressed written consent of the District Superintendent or his designee.

 

LU Title: Area, Surface Area and Volume of 3-D shapes.

Author(s): Barbara R. McCoy

Grade Level: Grade 7-8

School Address: Heuvelton Central School District
P.O. Box 375, Heuvelton, NY 13654

Subject Area: Mathematics

School Phone/Fax 315-344-2414

 

CONTENT KNOWLEDGE

Declarative

Procedural
  • Learn formulas for the area of squares, rectangles, triangles, parallelograms, trapezoids, circles
  • Use formulas to calculate the area of squares, rectangles, parallelograms, triangles, trapezoids, circles
  • Learn a method to find surface area of prisms, pyramids, and cylinders
  • Demonstrate the ability to calculate the surface area of a prism, pyramid, and cylinders
  • Learn formulas for finding the area of prisms, cylinders, pyramids, and cones
  • Use formulas to calculate the volume of prisms, cylinders, pyramids and cones.
  • Students will know how to use a spreadsheet to create a budget
  • Students will create a production budget using a spread sheet

ESSENTIAL QUESTIONS

 

INITIATING ACTIVITY

The teacher will present an assortment of packages, prisms, cylinders, cubes, any available package. Students will circulate in pairs and order the boxes from the least to the greatest for volume and the amount of surface area. Students may verify results using popcorn and graduated cylinders or beakers. Boxes can be opened so that students can see the size and shape of a package's "Net". Predictions will be posted on a chart to be verified with calculations as students learn to find volume and surface area.

 

Connection to State Learning Standards

Content Area: Mathematics

Level: Intermediate 7-8

Benchmarks: visualize, represent, and transform two and three dimensional shapes

 

Benchmarks: Understand the attributes of area, length, volume

Standard: Standard #3: Modeling/multiple representations

 

Standard: Standard # 3

Measurement

 

Standard: ELA #1 Language for information and understanding

 

Standard: ELA #3 Language for critical analysis and evaluation

Benchmarks: organize information according to an identifiable structure such as compare/contrast

 

Benchmarks: Use standard English, precise vocabulary, and presentational strategies effectively to influence an audience.

 

Learning Experiences

Declarative Knowledge

What declarative knowledge should studentsbe in the process of acquiring & integrating? As a result of the unit, the student will know or understand…

What experiences or activities will be used to help students acquire & integrate this knowledge?

What strategies will be used to help students construct meaning, organize and/or store the knowledge?

Describe what will be done.

Concept: Memorize area formulas for square, rectangles, triangle, trapezoid, circles. 

 

 

 

Concept: Apply area formulas to find Surface Area of prisms, cylinders, pyramids

 

 

 

 

 

Concept: Learn formulas to find volume and cones

Flash cards

Concentration Game

 

 

 

 

Students will create a net for a rectangular prism

Find surface areas of packages

 

 

 

 

 

Name 3-D shapes

Use popcorn of  prisms, cylinders, pyramids to measure and compare the volumes of cones and cylinders, pyramids and prisms.

Geoboards or dot paper to demonstrate area formulas

T-Table comparing similarities and differences between the formulas

 

Describe the process used to find surface area

Create a graphic organizer to demonstrate process

 

 

 

 

Create a graphic organizer to name polyhedrons

Extend T -Table to compare similarities and differences between volume formulas

Teacher will lead class activity with geoboards, dot paper or graph paper to derive area formulas. Students will create flashcards with formulas and use these to play concentration with a partner.

Students will create a T-Table to find the similarities and differences between the formulas 

Student pairs will use graph paper, pencil, pen, scissors, tape to create a net for a cube and a rectangular prism

Teacher will lead the discussion on the process of finding surface area.

Student pairs will create a bubble map to show the process

Class will generate a flow chart or template to find surface area

Partners will use a placemat to create a graphic organizer to name polyhedrons

Teacher demonstrates volume of prisms using plastic manipulatives and water or popcorn

Students will create a cone and cylinder and discover the relationships between the volumes

Learning Experiences

Procedural Knowledge

What procedural knowledge will students be in the process of acquiring & integrating? As a result of this unit, students will be able to:

What will be done to help students construct models, shape & internalize the knowledge?

Describe what will be done.

 Use formulas to find the Area of a rectangle, square, triangle, trapezoid and circles

Apply area formulas to prisms and 3-D shapes to find the surface area of prisms, cylinders, cones and pyramids

 

 

 

Apply volume formulas to find the volume of prisms, cylinders, cones, pyramids

 Derive formulas using geoboards, dot paper or graph paper

 

Construct nets for prisms and pyramids and cylinders to link area concepts to a 3-D shape

 

 

Students will create a paper cone and corresponding cylinder. Using popcorn, students will discover the relationship between the volume of a cone and cylinder having the same radius

 Teacher will lead the class in deriving the area formulas by using dot or graph paper.

Students will use graph paper to construct a net for a prism or pyramid or cylinder. Using the nets, pairs will write a process statement for finding surface area. Teacher will lead class discussion to develop a chart or graphic organizer that can be used to find surface area

Teacher will demonstrate the concept of volume of prisms and cylinders using plastic manipulative and water or popcorn. Teacher will demonstrate how to construct a paper cone and cylinder having the same radius. Students will work with a partner to construct the cone and cylinder, then use popcorn to discover the relationship between the volume of a cone and cylinder. The teacher will lead the class in a discussion of the results, thus deriving the volume formula of a cone.

 

Learning Experiences

Extending and Refining

What knowledge will students be extending and refining? Specifically, they will be extending and refining their understanding of…

What reasoning process will they be using?

Describe what will be done.

 The relationships that exist between the area, volume and surface areas of 3-D shapes

[ ]Comparing

[ ]Classifying

[ ]Inductive Reasoning

[ ]Deductive Reasoning

[ ]Error Analysis

[ ]Analyzing Perspectives

[ ] Constructing Support

[ ]Abstracting

[ ]Other:

 Students will create a graphic organizer to map the relationships between the formulas for area, surface area and volume. The teacher will lead class discussion to create a T-Table to compare the similarities and differences between the formulas for 2 and 3dimensional shapes.

Planning Guide for Mighty McCoy Manufacturing Company

Unit: Area, Surface Area Volume

Step 1

Step 2

Step 3

What knowledge will students be using meaningfully? Specifically, they will be demonstrating their understanding of and ability to...........

What reasoning process will they be using?

Describe student's products and performances and the criteria for evaluation.

Find the dimensions of a 3-D shape given the volume

Create a 3-D package with a specific volume

Calculate the surface area

[ X] Decision Making
(selecting from seemingly equal alternatives or examining the decisions of others)
[x ] Problem Solving
(seeking to achieve a goal by overcoming constraints or limiting conditions)
[ x] Invention
(creating something to meet a need or improve on a situation)
[ ] Experimental Inquiry
(generating an explanation for a phenomenon and testing the explanation)
[ ] Investigation
(resolving confusions or contradictions related to a historical event, a hypothetical past or future event, or to the defining characteristics of something)
[ ] Systems Analysis
(analyzing the parts of a system and how they interact)
[ ] Other:

Products/Performances

Students will create a 3-D package design for a student chosen product. The package will have a specific, teacher chosen volume. Students will generate a budget for the production of their package by creating a spreadsheet and following the cost guidelines given to the students. After designing and creating their package, students will use a spreadsheet to create a production budget including cost per sq. inch, printing costs, labor, and profit. Students will then use a word processing program to write a business letter explaining the process they followed to find the volume and surface area, and an explanation of how they calculated to cost per box and the total cost of production.

 

Name___________________________

 

PROJECT: VOLUME AND SURFACE AREA

You are a world renowned packaging design engineer. A major conglomerate has hired your firm to design the packaging for a new environmentally safe product which will soon be marketed nationally.

THE MIGHTY MCCOY MANUFACTURING COMPANY

 

Product specifications:

$.01 per square inch cardboard

$.01 per color per box used in printing

$.01 per box for labor

You must submit your package design and present your design to the class. Include your product's special features, production costs per box, total production costs, your profit and the total costs to the Mighty McCoy Manufacturing Company.

Hand in the following:

1. Completed Box showing your packaging Logo.

2. Written presentation and oral presentation ( This will be your advertising campaign)

3. Budget Sheet including all costs and projected profits.

4. Completed Rubric(see attached)

 

RUBRIC FOR MUT

NAME:

 

Group

 

Teacher

PEER EVALUATOR:
YES

NO

NEEDS WORK

 

YES

NO

NEEDS WORK

ACCURACY
  1. Volume: Measurements must be accurate.

 

 

 

 

 

 

 
  • Formulas and computation are 100% correct.

 

 

 

 

 

 

 
  • Surface area is accurately and neatly calculated.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RESEARCH
  1. Log is a complete history of groups theory and research.

REPORT
  1. The model and report are interesting and attractive.

 

 

 

 

 

 

 
  • This report would convince anyone that the container you propose is the right one for the job.

 

 

 

 

 

 

 
  • All group members are equally knowledgeable to write and speak about the model chosen.

 

 

 

 

 

 

 

4. Turned in on time.

SPREADSHEET
  1. Correct formulas.

  • Well organized.

LETTER

Business letter is word processed, spell checked and grammar checked

 

{short description of image}
SAMPLE SPREADSHEET FOR MIGHTY MCCOY MANUFACTURING

REFLECTION

Students were grouped in pairs or groups of three. Students can submit recommendations for grouping to the teacher prior to the project. It is important that students work well with their partners during the 3-4 weeks that this unit encompasses. Prior to starting the project the teacher should review the rubric and peer evaluation process with the students. It is important that groups review their project using the rubric prior to submitting their final project. Groups that go through peer review and revision are always successful during the presentation stage.

Each group is given a Blue Book to maintain a log of the groups' progress and process. Every package should be sketched and formulas and correct calculations shown. If the group decides not to use a particular design they should explain this decision in their logbook.

Students' level of concern may be heightened by incorporating a videotape or by inviting a guest reviewer. Video taping a workgroup can become a valuable role model for other groups to view and discuss during the project phase. Students' presentations can be video taped and reviewed by the students to analyze presentation skills and improve future presentations. Parents, teachers, or the principal may be invited to participate in the presentation process. Students work toward an excellent project when they know they will perform for a guest.

A traditional test on area, volume and surface area may be given at the conclusion of this unit. Individual accountability can be measured by using a traditional skill format.