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:
Understand that ratios are used to create scale models of buildings and
structures.
Understand the principles of ratio and apply these principles in the
solution of problems
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
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:
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.