Nicole Butcher Mimi Gulick AMTNYS 2010 Lesson

Transcription

1 Nicole Butcher Mimi Gulick AMTNYS 2010 Lesson Introduction This lesson is designed to expand student s knowledge of proportions. s are asked to choose a proportion project which will give them an opportunity to see how proportions work. s will have a choice between Math on Me, Monument measures, and International Dough. NCTM Principals and Standards: Understand and use ratios and proportions to represent quantitative relationships Understand numbers, ways of representing numbers, relationships among numbers, and number systems Compute fluently and make reasonable estimates Understand relationships among units and convert from one unit to another within the same system NYS Core Curriculum Standards: 6.N.7 Express equivalent ratios as a proportion 6.N.9 Solve proportions using equivalent fractions 6.N.10 Verify the proportionality using the product of the means equals the product of the extremes 6.A.5 Solve simple proportions within context Major Instructional Goals: Math on me: Feeling comfortable with proportions Figuring out the proportions of their own bodies Be able to draw their own bodies in proportion Monument measures: Be able to take the pictures of the monuments of the country they were given and find the different proportions of the buildings. Draw their own monument in a realistic scale, labeling what scale (in ratio form) they used on the side. International Dough Each student should be able to use conversion to complete the questions provided.

2 Math on Me! This project requires students to explore the measurements of their body and see how they measure up compared to the idealized human figure. They are instructed to measure each other s head and height in inches, and find it s proportion to various sections of their body. The Viturvian Man by Leonardo DaVinci is based on the ideal body proportions of men. These ideal proportions include: Man s total height = 8 heads Hip height = 4 heads Total arm span = total height = 8 heads Elbow to fingertip = 2 heads Wrist to fingertip = 1 head After taking measurements and calculating the required proportions, students are required to draw a picture of themselves, using the proportions they found- no stick figures! On-task? Grading Rubric failed to participate in class Measurements took no measurements Proportions Picture completed no proportions drew no picture Participated, but after repeatedly asked did not complete all measurements completed some proportions, with errors submitted incomplete picture required minimal teacher encouragement took measurements, multiple errors s completed all proportions with little error s picture was not proportionally correct required only one reminder to stay on task took measurements, little errors s completed all proportions with one error s picture was slightly out of proportion stayed on task took all measurements with no error correctly completed the proportions s picture was in the correct proportion Total

3 Name: Math on Me Worksheet The Viturvian Man by Leonardo DaVinci is based on the ideal body proportions of men. These ideal proportions include: Man s total height = 8 heads Hip height = 4 heads Total arm span = total height = 8 heads Elbow to fingertip = 2 heads Wrist to fingertip = 1 head Instructions: With a friend, use the ruler provided to fill out the chart below, in inches. Total height Head height Hip Height Arm span Elbow to fingertip Wrist to fingertip 1. Ratio of head height to total height: Does your own ratio come close to the ratio of the Vitruvian man?

4 2. Ratio of head height to hip height: How does it compare to Vitruvian man? 3. Ratio of head height to arm span: Is it the same as the ratio to total height? Does that make your total height = your arm span? 4. Ratio of head height to the elbow to fingertip length: How does it compare to vitruvian man? 5. Ratio of head height to the wrist to fingertip length: Is it the same?

5 Monumental Measures Part 1: Directions: In this project you are to pick one of the countries listed. Once you have chosen a country, you will have the option of choosing two monuments from that country to answer questions on, and to draw. France o Eiffel Tower (1,063 ft tall) o Arc de Triomphe (160 ft tall ) o Notre Dame de Paris ( 420 ft long, 226 ft tall: the towers) India o o Taj Mahal (561ft tall) Humanyun Tomb (85 ft tall) Italy o o Leaning Tower of Pisa (186 ft tall: the taller side) The Arch of Constantine (85ft wide, 69 ft tall) United States o Statue of Liberty (305ft tall) o White House (70ft tall) o Washington Monument (555ft tall) To get full credit for this project you must make yourself a chart of the different objects in the monument that you wish to find the height of. Keep in mind that these measurements are going to help you with the second part of the project. Part 2: This part of the project is requiring you to get into your artsy mode. Create a well drawn (to scale) picture of one of the two monuments you found the measurements of. Include the scale you used, and also the list measurements you found for this monument in pencil on the back of your drawing.

6 International Dough This project requires students to convert several U.S. dollar values into values of foreign currency. They are to use their knowledge of proportions to figure the cost of several desirable items, tickets, ect. A list of several different foreign currency values, compared to our U.S. dollar will be kept by the teacher, and once students choose their desired destination, they will be given that countries equivalence to one of our dollars. The table below gives the currency values for several countries, compared to ONE U.S. dollar. Country, Currency Name Equivalence to 1 dollar European EURO.72 Brazilian REAL 1.70 British POUND.62 Mexican PESO Turkish LIRA 1.43 Egyptian POUND 5.77 Russian RUBLES Indian RUPEE Chinese YUAN 6.68 Fijian DOLLAR 1.85 These values we found using GOOGLE currency converter. Amounts may not be exact.

7 Name International Dough Worksheet Instructions: Circle one of the listed countries below, so you can begin planning your trip! Europe - EURO Brazil - REAL Britain - POUND Mexico - PESO Turkey - LIRA Egypt - POUND Russia - RUBLES India - RUPEE China YUAN Fiji - DOLLAR Selected countries equivalence to One U.S. Dollar = Write this as a ratio (you will be using it often) **Time for Vacation** Give your answers with your countries currency name. 1. Plane ticket to your country costs $ How much is this in your countries system? 2. You have made it to your destination! It is time for lunch, which costs $7.75. How much is this in your countries system? 3. The Hotel you wish to stay at is $76.00 a night. How much is this in your countries system? 4. Dinner at the hotel is $ How much is this in your countries system?

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