LESSON PLAN

Name:  Itzel Suárez

Title of lesson:  Ratios, Proportions, & Floor Plans

Grade level:  10th grade Geometry

Length of Lesson:  1 class period (50 minutes)

Sources of the lesson:                                                                                                         

Discovery Channel’s Education Website:  Architects in Action

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

Amy Cunningham and Sabriel Foster’s Lesson Plan for PBI http://www.uteach.utexas.edu/%7Egdickinson/pbi/pbifall02/House/content/Lesson5.htm      

Math-Kitecture:  Floorplan Your Classroom                                                             

http://www.math-kitecture.com/floor.htm                                                                                   

Common Blueprint Symbols & Abbreviations http://www.edu.pe.ca/montaguehigh/grass/housing/kitchen/LEG1.HTM      

TEKS addressed:

1.    The relationship between geometry, other mathematics, and other disciplines. Geometry can be used to model and represent many mathematical and real-world situations. Students perceive the connection between geometry and the real and mathematical worlds and use geometric ideas, relationships, and properties to solve problems.

2.    The student uses numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles.

I.  Overview:  The student will be introduced to the concept of scaling using ration and proportions.

II.   Performance or learner outcomes

The students will be able to:                                                                                                             Ÿ       Understand that ratios are used to create scale models of buildings and structures.                  Ÿ       Understand the principles of ratio and apply these principles in the solution of problems     Ÿ       Understand how to calculate scale using ratio.

III. Resources, materials and supplies needed

- 0.25-inch graph paper                                                                                                                  - Map(s) of the United States                                                                                                           - Pencils                                                                                                                                            - Ruler (metric or inches)                                                                                                       - Tape measure

Five-E Organization

Teacher Does                                                             Student Does

Engage: (10-15 mins.)

Writes the word scale on the board and has the students brainstorm examples of where scales are found and what they measure.  For example, we use scales to measure the weight of an object, the temperature of air, the length of an object, and so on..

Briefly talk about the scaling on the map of the United States.

Explain that scale models can represent objects that are too big, like the United States, and objects that are too small, like atoms.

Explain that a scale is a ratio used to determine the size of a model of a real object. A ratio is a relationship between two objects in quantity, size, or amount. (i.e. the ratio of quarters to dollar is 4 to 1).  Ask students to think of other examples of how money can be turned into a scale.

Illustrate how to draw an object to scale. Use a ruler to draw a square on the board with sides that equal 10 inches in length. Ask students how they might use this square to draw another that is half its size. Explain that an object is not simply cut in half when it is scaled down. The whole object is shrunk proportionally, meaning that it doesn’t change shape but is reduced to a smaller size.

Explain that when an object is scaled down, the length of its sides must be reduced by the same amount. So, the ratio of the small square to the large square can be expressed in three ways:5:10, 5 to 10, or 5/10, which is a fraction that reduces to 1/2. Also, if an object has been scaled down proportionally, the perimeter of the object will scale down by the same ratio.

Questions:

So what can y’all tell me about drawing your dream home and scaling?  Will you draw it to scale, meaning will you draw it to its actual size?  What will happen if you draw it on paper to the actual size of your dream home?

Students give examples of where scales are found and what they measure.

Students learn about scales and ratios.

Students gives examples of how money can be turned into a scale.

Students watch teacher as a square is drawn. 

Students tell how they would use the square to draw another square that is half its size.

 Expected student answers:

If you draw your house to scale, you use too much paper.

By drawing your house at a smaller scale, you can carry it with you, as with architects.  It’s more practical.

 

Evaluate:  The teacher should call on various students to answer questions about scales and ratios.

Teacher Does                                                       Student Does

Explore: (20 mins.)

Explain that students will use ratio to make a scale drawing of the classroom floor plan.

First explain what a floor plan is.

A floor plan is a drawing that shows a room as seen from above. Everything in a floor plan appears flat. Architects use floor plans to show what a room or building will look like. Anyone who draws (or drafts) a floor plan is called a draftsperson.

Floor plans may be drafted to scale, which means reducing the size of a drawing so the whole room can fit on a piece of paper. A common scale is 1/4 inch equals 1 foot. This means that if something is drawn 1/4 inch long in a floor plan, it is 1 foot long in real life.

Floor plans may be drafted by hand with a pencil (to draw thick or thin lines), ruler (to draw straight lines to a specific length), a protractor (to draw the angles where walls meet), and graph paper (which usually has 1/4 inch boxes, to make floor plans easier to draft in 1/4"=1' scale).

Divide students into teams of four. Have students come and pick up their measuring tools.  The class will use English measurements.

Construct a class data table on the board with three columns labeled “object,” “measurement,” and “scaled measurement.”  Tell them that each group will have write that table on their paper and record their measurements of the room.

Once teams have recorded all their data, they will decide on the scale of their floor plan.

Students form a group of four with access to a tape measure, pencils, and paper to record their measurements.

Students copy the table in their notebooks and fill in the answers as they measure the objects.

Student groups decide on the scale of their floor plans.

Evaluate:  The teacher should walk around and make sure all students are on task and participating in the activity.

Teacher Does                                                    Student Does

Explain: (25 mins.)

Pass out graphing paper.

With the class, discuss the proportions that would allow students to draw the entire room on one sheet of 8.5" × 11" graph paper. For example, if the longest wall in the classroom is 16 feet long, then a scale of 1" = 1’ will not work because the graph paper is not 16” long. But 0.5" = 1’ will work perfectly and you end up using 8” of the paper.  Also, using 1 square to equal ½ foot, 2 squares to equal ½ foot could work easier because then they would be using the graph paper.

Use the agreed-upon ratio to create the proportion for your classroom. Then have groups convert their measurements into scaled equivalents.  Emphasize that they whole plan must be kept at the same scale or else it will be out of proportion, so if you decide to do 0.5”, all the objects in the room will be drawn to that same scale.

For example, if a desktop measures 2 feet in width and the scale is 0.5" = 1’, use the following equation to figure out how large the scaled drawing of the desktop should be.

0.5 inches divided by 1 foot = the scaled down length of the object divided by 2 feet

Or, written as an equation of two ratios:

0.5 inches

=

y inches

1 foot

 

2 feet

y = 1 inch

Have students use their scaled measurement, rulers, and graph paper to draw the floor plan their team measured.

Students discuss the proportions to use in order to draw the entire room.

Student groups convert their measurement into scaled equivalents.

Student groups create their floor plans of the room.

Evaluate:  The teacher listens attentively to the students ideas for which proportion to use in order to draw the entire room on 8.5" × 11" graph paper.  The teacher walks around as each groups converts their measurements into scaled equivalents and create their floor plans and helps students as needed.

                        Teacher Does                                                  Student Does

Extend / Elaborate: (5-10 mins.)

As students complete their drawings, encourage them to calculate the perimeter of their classrooms.

(For homework):  Tell students to start with the floor plans of their dream homes.  Tell them to start off with the scale of their own homes that they currently live in and look at how the rooms are structured.  Hand out blueprint symbols resource sheet.

Questions

1. What is the relationship between the perimeter of the drawing and the perimeter of the actual classroom?

What the students are doing:

Students are finishing up their drawings.  Those who are finished with their drawings are calculating the perimeter of the classroom. 

Expected answers:

Relationship between the perimeter of the drawing and the perimeter of the actual classroom is a ratio.

Evaluate:  The teacher should have each group turn in their floor plan drawings.