Concrete Thematic Unit

UNIT TITLE: Is Concrete Really Hard?

Author: Debbie Grace
E-Mail Address: Gracedb@aol.com
School: St. Mary Nativity School : Joliet, Illinois
School Home Page URL: Stmarynativity.org

THEME : Concrete Work

BROAD CONCEPT: Working Cooperatively, Persistence, Cautious, Patience

GRADES: Grades 7 - 8

INTEGRATED SUBJECTS: Mathematics, English, Science, Social Science, Technology

UNIT GOALS AND PURPOSE: Students will learn how geometry is used in concrete work. They will explore perimeter, area, volume and the Pythagorean Theorem and see why accuracy is so important. The computer will be incorporated into the unit by using the Internet for research, Interactive sites for exploring concepts, a Spreadsheet for organizing information, and Microsoft Word for the final activity. The instructor will evaluate the activities and a rubric will be used to evaluate the final activity.

TIME FRAME: about 10 days

OBJECTIVES:

In this lesson, students will:

Calculate perimeter of a polygon
Calculate area of a polygon
Calculate volume of a rectangular prism
Convert cubic feet to cubic yards
Explore the Pythagorean Theorem
Find a number when a percent of it is given

MATERIALS:

General materials and equipment

graph paper, rulers, protractors, calculators

Technology tools:

Computer

Software Used in this Unit

Brainstorming (Inspiration)

Word Processing (MS Word)

Spreadsheet (MS Excel)

Multimedia (Power Point)

STATE STANDARDS ADDRESSED BY THIS UNIT:
                   Mathematics
                    6.B.3c Identify and apply properties of real numbers including pi, squares, and square roots.
                          6.C.3a Select computational procedures and solve problems with whole numbers, fractions, decimals, percents and proportions.
                    7.A.3a Measure length, capacity, weight/mass and angles using sophisticated instruments (e.g., compass, protractor, trundle, wheel).
                          7.A.3b Apply the concepts and attributes of length, capacity, weight, perimeter, area, volume, time, temperature and angle measures in practical situations.
                          7.C.3a Construct a simple scale drawing for a given situation.
                          9.C.3a Construct, develop and communicate logical arguments (informal proofs) about geometric figures and patterns.
                          9.D.3    Compute distance, lengths and measures of angles using proportions, the Pythagorean Theorem and it's converse.

Language Arts
1.C.3c Compare, contrast and evaluate ideas and information from various sources and genres.
1C.3d Summarize and make generalizations from content and relate them to purpose of the material.
3C.3b Using available technology, produce compositions and multimedia works for specified audiences.
5A.3a Choose and analyze informational sources for individual, academic and functional purposes.

Science
13B.3c Describe how occupations use scientific and technological knowledge and skills.

Social Science
15A.3c Describe the relationship between consumer purchases and businesses paying for productive resources.

N.C.T.M. STANDARDS ADDRESSED BY THIS UNIT:

Number and Operations

work flexibly with fractions, decimals, and percents to solve problems

understand and use the inverse relationship of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems

Geometry

understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects
create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.
recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.

Measurement

understand relationships among units and convert from one unit to another within the same system

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision

develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes

Problem Solving

build new mathematical knowledge through problem solving

Reasoning and Proof

recognize reasoning and proof as fundamental aspects of mathematics;

Communication

organize and consolidate their mathematical thinking through communication;
communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
analyze and evaluate the mathematical thinking and strategies of others;
use the language of mathematics to express mathematical ideas precisely.

Connections

Recognize and apply mathematics in contexts outside of mathematics.

Representation

Select, apply, and translate among mathematical representations to solve problems

STUDENT ACTIVITIES WHICH WILL PROMOTE ENGAGED LEARNING:

Activity 1: (about 45 minutes) The teacher will give students instruction about using Inspiration by doing an example. Students will then work in groups to brainstorm and organize a diagram and an outline showing components involved in building a house.

Activity 2: (about 30 minutes) In this unit students will only work on the concrete portion of building a house. After the excavator has dug the hole for the house the footing and the foundation will be framed and poured. Working in the same groups students will do some research on the internet. Students are to find out what footings and foundations are and find some information about framing and pouring them (pictures or diagrams can be very helpful). Students will then share their findings with the class. [A footing is 20" wide and 10" deep and it is necessary to support the foundation wall. Foundation walls are usually 9' high and 10" thick and they are placed in the middle of the footing so that there is about 5" of the footing showing on each side of the foundation wall.]

Activity 3: (about 20 minutes) When concrete is purchased it comes in units called a cubic yard. I want students to get an understanding of the big picture before I break it down into pieces, so I will refer them to an activity at
http://www.pbs.org/teachersource/mathline/concepts/architecture/activity1.shtm. This activity explains measuring and ordering concrete on a very small scale.

Activity 4: (about 30 minutes) Discuss perimeter and area and why knowing these are very important in concrete work. Perimeter and area are very much related so students will explore this concept at an interactive website http://www.shodor.org/interactivate/activities/permarea/index.html.

Activity 5: (about 20 minutes) As shown in the PBS activity the dimensions are given in feet but concrete in ordered in cubic yards. Working in small groups, students will solve problems regarding ordering concrete. The problems were from mathcentral.uregina.ca/QQ/database/QQ.09.01/michael1.html and mathcentral.uregina.ca/QQ/database/QQ.09.03/john2.html.

Activity 6: (about 45 minutes) How can a we be sure that an angle is 90 degrees? Students will investigate proofs of the Pythagorean Theorem by looking for information on the internet. This activity will be followed by exploring an interactive site http://www.ies.co.jp/math/java/geo/pythagoras.html .

Activity 7: (about 45 minutes) Students will work in groups and devise a plan for a house foundation, basement and a garage. Students will use an Interactive Geoboard to help them develop the dimensions needed to provide the appropriate amount of concrete for footings, foundation, basement and garage floors. When information is complete it should be put on graph paper and a scale for the model must be included. [Basement is 4" thick and garage is 5" thick]

Activity 8: (about 45 minutes) Students will use measurements from Activity 7 to develop a Spreadsheet that shows dimensions and formulas for calculating the number of cubic yards of concrete needed for the job. The Spreadsheet should also include a formula for total job charge if concrete is 40% of the total cost of the job. [Concrete is about $80 per cubic yard]

Activity 9: (2 days) Students will work in groups to design a Power Point slide show. There should be a minimum of three slides and it should consist of some information about concrete. This activity will require some research.

                        Activity 10: (2 days) Students will make a job proposal that would be given to a customer, based on information from activities 7 and 8.                                 This proposal will be done on Microsoft Word.

SHARE YOUR IDEAS:
The culminating project will be the job proposal (Activity 10). Students should design a letterhead including a company name and graphics as well as measurements and prices for a foundation, basement and garage floors. They should be able to explain their proposals to other students and the instructor.

                        Rubric for culminating project:

                                                                                            Job Proposal

Category	4 points	3 points	2 points	1 point
Attractiveness & Organization	The proposal is exceptionally attractive and well organized.	The proposal is somewhat attractive and well organized.	The proposal is not very attractive but well organized.	The proposal is not very organized.
Knowledge Gained	The students in the group can accurately answer all questions related to the facts in the proposal and to technical processes used to create the proposal.	The students in the group can accurately answer most questions related to the facts in the proposal and to technical processes used to create the proposal.	The students in the group can accurately answer some questions related to the facts in the proposal and to technical processes used to create the proposal.	The students in the group can accurately answer very few questions related to the facts in the proposal and to technical processes used to create the proposal.
Mathematical Accuracy	All mathematical calculations in the proposal are correct.	There are 1-2 mathematical mistakes in the proposal.	There are 3-4 mathematical mistakes in the proposal.	There are more than 4 mathematical mistakes in the proposal.
Grammar & Spelling	There are 0-1 grammatical or spelling mistakes in the proposal.	There are 2-3 grammatical or spelling mistakes in the proposal	There are 4-5 grammatical or spelling mistakes in the proposal	There are more than 5 grammatical or spelling mistakes in the proposal

STUDENT AND TEACHER ROLES:
        The teacher will serve as facilitator by creating the activities and providing resources for students. The teacher will also guide students through questioning and discussions.
        The students will serve as researchers and investigators by looking for information. Students will be explorers when they discover concepts presented in different ways and creators through the making a sideshow and a job proposal.

ADDITIONAL REFERENCE PRINT RESOURCES STUDENTS MAY USE :

            Homeowner's Encyclopedia of House Construction
            Illustrated Encyclopedic Dictionary of Building and Construction Terms
            Encarta Encyclopedia 99

        THE FOLLOWING BOOKS CONTAIN INFORMATION ABOUT THIS TOPIC:

             Foundations and Concrete Work by the editors of Fine Homebuilding
            Concrete and Formwork by T.W. Lowe

FOR ADDITIONAL ONLINE INFORMATION AND MEDIA PERTAINING TO THIS UNIT, TEACHERS MAY WANT TO USE THE FOLLOWING INTERNET ARTICLES:

                                       Title1: The Concrete Net

                                             URL1: www.concretenetwork.com/concrete/foundations.htm

                                             Description1: This page gives an excellent diagram of a footing and a foundation wall and how they are positioned.

                                           Title2: Formco Concrete Foundation

                                             URL2: www.formcofoundations.com

                                               Description2: This site has pictures of footings and foundations being constructed. It also provides some information about the                                                         equipment that is used.

                                       Title3: Building Materials - Pouring a foundation

                                           URL3: www.pbs.org/teachersource/mathline/concepts/architecture/activity1.shtm

                                           Description3: This activity describes calculating measurements for ordering concrete. The dimensions are on a much smaller scale                                                   than an actual house.

                                          Title4: Quandaries and Queries - Cubic yards of Concrete

URL4: mathcentral.uregina.ca/QQ/database/QQ.09.01/michael1.html and

                                               mathcentral.uregina.ca/QQ/database/QQ.09.03/john2.html.

                                               Description4: These two sites each describe a scenerio where someone is trying to calculate the number of cubic yards of concrete                                                  yards that is needed. They know the dimensions but they do not know how much concrete to order.

Title5: The Pythagorean Theorem

URL5: www.Jimloy.com/geometry/pythag.htm

Description5: This site contains examples of proofs of the Pythagorean Theorem, including a proof by President Garfield.

Title6: Architects in Action

URL6: school.discovery.com/lessonplans/programs/architectsinaction/

Description6: This site provides activities to help students understand how ratios are used in scale models of building.

RELEVANT INFORMATION, STUDENTS WILL VISIT THE FOLLOWING WEB SITES:

Title1: The Concrete Network

URL1: www.concretenetwork.com/concrete/foundations.htm

Purpose of Use1: After students have investigated footings and foundations in their groups, this site can be shared with them.

Description1: This page gives an excellent diagram of a footing and a foundation wall and how they are positioned.

Title2: Building Materials - Pouring a foundation

URL2: www.pbs.org/teachersource/mathline/concepts/architecture/activity1.shtm .

Purpose of Use2: This site gives students a diagram of a very small foundation, but some very important information. It also gives them some things to think about for the next step (pouring the basement floor).

Description2: This activity describes calculating measurments for ordering concrete. The dimensions are on a much smaller scale than an actual house.

Title3: Perimeter Explorer

URL3: www.shodor.org/interactivate/activities/permarea/index.html

Purpose of Use3: Perimeter and area are related and play an important part in construction. When two shapes have the same area that does not mean that they will have the same perimeter.

Description3: This is an Interactive site that allows students to input a value for the area and a shape will be constructed. The student then has to find the perimeter. The shapes can be irregular.

Title4: Quandaries and Queries - Cubic yards of concrete

URL4: mathcentral.uregina.ca/QQ/database/QQ.09.01/michael1.html and mathcentral.uregina.ca/QQ/database/QQ.09.03/john2.html

Purpose of Use4: Good real-life situations for finding volume and converting to cubic yards.

Description4: These two sites each describe a scenario where someone is trying to calculate the number of cubic yards of concrete yards that is needed. They know the dimensions but they do not know how much concrete to order.

Title5: Pythagorean Thereom

URL5: www.ies.co.jp/math/java/geo/pythagoras.html

Purpose of Use5: The Pythagorean Theorem is used quite often in framing to make sure things are square. Students should know why it works.

Description5: This Interactive site allows students to explore the Pythagorean Theorem in different ways by moving pieces, similar to a puzzle.

Title6: Interactive Geoboard

URL6: nlvm.usu.edu/en/nav/vm1_asid_172.html

Purpose of Use6: Students will use the Interactive Geoboard to design a small scale plan of a house. Then they will calculate the amount of concrete needed and the amount to charge the customer.

Description6: An Interactive Geoboard is a Geoboard on the computer where students can create and explore angles, polygons, and space figures.