Lesson 1

Tremendous Trees

Grade Levels: 5-8

Learner Outcomes: Students will use ratios and proportions to solve problems involving the unknown height of trees.

Duration of Lesson:  one week

Materials: 

• cm ruler
• physician scale with height rod
• digital camera
• extra disks for digital camera

Technology Tools:  digital camera, computer, photo software

Teacher Notes:

• This activity can be used to find the height of any object (i.e. buildings, people, cars, fences, playground equipment).
• Emphasis must be given on making accurate measurements.
• Measurements can be made in either standard or metric units, however, metric units will be the easier unit to work with.
• If a digital camera is not available, a Polaroid instant camera may be used. 
• A regular camera may be used, but extra time must be provided to allow time for the film to get developed.
• Students must be knowledgeable in operating a digital camera.
• You may wish to involve another staff member or volunteer to assist students when they are taking photographs outside.
• Students must be knowledgeable in solving one step problems for a given variable.

1. Begin lesson by reviewing multiplication and division of decimals. This may be done at  http://www.blarg.net/~math/FDU15.HTM and http://www.blarg.net/~math/FDU16.HTM 
2. Introduce the terms ratio and proportion.
3. Use equivalent fractions to demonstrate how the product of the means equals the product of the extremes.  See Means = Extremes Worksheet.
4. Demonstrate how to use cross-multiplication in a proportion to solve for an unknown variable.
5. Provide practice using whole numbers.  See Means = Extremes Worksheet.
6. Having students work with a partner, give group a digital camera.
7. Allow each group of students 10 minutes to go outside onto school grounds and take a picture of each other next to a tree.  Make sure that the student taking the picture gets the entire tree in the picture. Camera lens must be held parallel to tree to avoid distortion. (In other words, don't tilt the camera.)  These are both musts!
8. Groups not taking picture may go to   http://www.edhelper.com/ratios.htm   & http://www.math.com/school/subject1/practice/S1U2L2/S1U2L2Pract.html to practice solving ratios and proportions.
9. Once students have taken their pictures, they will download each picture onto a computer using the photo software needed for the camera.  Make sure students do not edit their photographs in any way.  This is a must!
10. Students must print their photo from the computer.
11. Students need to use a centimeter ruler to accurately measure their height and the height of the tree in the picture, and then record the data on the Tremendous Trees Worksheet.
12. Using a physician's scale with height rod, each partner accurately measures their actual height and records it on the worksheet..
13. Using words, students must set up a proportion to be used to find the actual height of the tree. Space is provided on the worksheet.
14. Students must then substitute the known information in their proportion and solve.  All work must be completed on the Tremendous Trees Worksheet.
15. Write a paragraph explaining how to use ratios and proportions to solve a similar problem.

• Assign students to work with a peer helper.
• Provide a calculator for students to use while solving equations.
• Make any necessary adaptations as stated in individual IEPs.

• Students may take pictures of themselves next to any item.  If they use an item that can be accurately measured with a cm measuring tape, they can easily check their own measurements and accuracy.

Evaluation/Assessment:

Students need to turn in photograph and the Tremendous Trees Worksheet. The following rubric may be used to assess students' work: Tremendous Tree Assessment Rubric

WV IGOs:  

National Standards:  

Job/Career Clusters:  Natural Science

References:

 http://cne.gmu.edu/modules/dau/algebra/fractions/frac5_bdy.html
 http://www.math.com/school/subject1/lessons/S1U2L2GL.html
 http://users.erols.com/toftness/BasicMath/ratios_nf.html
 http://www.edhelper.com/ratios.htm

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