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Finding Unknown Heights of Objects Using Ratio and Proportion
7th Grade
Ellen Cole

Oklahoma PASS Objectives
Mathematics Process Standards
I. Problem Solving
A.
Develop and test strategies to solve practical, everyday problems which may have single or multiple answers.
B.
Use technology to generate and analyze data to solve problems.
C. Formulate problems from situations within and outside of mathematics and generalize solutions and strategies to new problem situations.
D. Evaluate results to determine their reasonableness.
IV. Connections
A.
Apply mathematical strategies to solve problems that arise from other disciplines and the real world.
B. Connect one area or idea of mathematics to another (e.g., relate equivalent number representations to each other, relate experiences with geometric shapes to understanding ratio and proportion).
V. Representations
D.
Use a variety of representations to model and solve physical, social, and mathematical problems (e.g., geometric objects, pictures, charts, tables, graphs).
Mathematics Content Skills
II. Number Sense and Computation
B. Ratio, Proportion, and Percents
1. Understand the concept of ratio and proportion and be able to demonstrate it with models (e.g., similar geometric shapes, growth patterns, scale models).
2. Identify and write problems using ratio and proportion (e.g., find equivalent ratios).

NPS Curriculum
3.1.2 Number Operations
3.1.4 Computation
5.1.4 Metric Application
6.1.2 Range, mode, median, mean in problem solving situation

NPS Technology
Scope & Sequence Objectives

Students import digital images into other documents.

Students use formulas in a spreadsheet

Students use a spreadsheet to analyze trends and test hypotheses.

Students collaborate with peers and others to solve problems and develop solutions using technology tools and resources.

Students use multiple resources, tools, and technologies to solve complex problems and present solutions.

Description: Students use digital cameras to take pictures to find heights using ratio and proportion. This activity helps students to transfer knowledge of ratio and proportion to the real-life skill of finding the height of an object.

Lesson :

1. Use a digital camera to take a pictures of another student standing next to a tall object (such as a stop sign, flag pole, tree, football goal, etc.).

2. Import the digital image into MS Word or PowerPoint, and resize the image to 8.5 by 11 inches.

3. Print the image. Measure the image of the student and the object in standard or metric measurement.

4. Measure the student's actual physical height in standard or metric measurement.

5. Open MS Excel and set up a proportion problem (equation/formula) using the ratio of the actual student height to the student's height in the picture. Do the same for the (unknown) actual object height to the height of the object in the picture.*

6. Solve problem using cross products.

*This can also be done as a whole class spreadsheet if an Averkey and TV or a projector is available, and each student group types in their data (measurements).

Extentions:

  • Graph the data using the Excel Chart Wizard
  • As a class find the range for each object. Use mean, median, or mode as "reasonable." Identify unreasonable outliers.

Online Resources
http://illuminations.nctm.org/imath/6-8/pooltable/
http://score.kings.k12.ca.us/lessons/popratio.htm

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Last updated Wednesday, August 28, 2002
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