## Shadow Chasing

### Christina Keeler

#### Description

This activity is a fun way to introduce proportions and reinforce measuring in centimeters. The students compare themselves and their shadows to various objects big and small. They then use their data to set up proportions to solve.

#### Objectives

Relates the concepts of measurement to similarity and proportionality in real-world situations.

#### Materials

-1 Meter stick per pair of students
-Pencil and paper (supplied by student)
-Paper clip (to be used by the teacher)
-Shadow Chasing lab sheet (See Associated File)

#### Preparations

1. Make sure you have enough meter sticks for either groups of two or three.
2. Find an outside area that will cast good shadows for the time of your class that also has various size objects.
3. Make enough copies of the lab sheet provided in the associated file.
4. Make sure to get the administration's approval to go outside on the premises.

#### Procedures

Note: The students should have prior knowledge of the metric and standard measurement systems. The students should also have prior knowledge of multi-step equations.

DAY 1
1. Ask, “Is there anyone who likes to build things? Anyone want to be an architect when they get out of school? Well, then we have to think about math and proportions.” Wait for responses to each question then discuss how architects use proportions to build scale models of an actual building.

2. Ask, “Who thinks they are twenty times as big as this paper clip? Who thinks they are twenty-five times as big? Does anyone think they are a hundred times as big?” As a student raises his/her hand, have that student come to the front of the class. If more than one person raises a hand, choose one for each question.

3. Have those three students stand up in front of the class to have their heights measured.

4. Show the meter stick to the class.

5. Discuss the different measurements on each side, centimeters and inches (metric system vs. standard).

6. Inform the students that they will be using centimeters for our measurements.

7. Put the measurements of the three students' heights on the board.

8. Now have all of the students line up in order of height (tallest to shortest). Then have them partner up with the person to the left to measure each other's height, and record.

9. Have each student find five different objects that are the same length or as close to their heights in a designated area outside. Have the students list the objects that are the same height on their papers. The students should measure the objects to double-check their measurements.

10. Talk about how all of the objects that they found are similar, due to their lengths being the same.

DAY 2
11. Discuss that they are going to find out how tall trees and other objects are without measuring them, but by using the shadows of the objects to set up proportions.

12. Give each group a designated area with five objects to measure the shadows of and record. The student should write the names of the objects on their lab sheets (See Associated File) and put the measurement of the object's shadow on their sheets.

13. Have each pair measure each other's shadows and record.

14. When all of the measuring is finished, they then go inside to finish the discussion of how to set up proportions (heights vs. shadows). Their variable will be the height of the object.

15. Now show the students how to set up a proportion by using either
Their height/object's height = Their shadow/object's shadow
or
Their height/Their shadow = Object's height/object's shadow

16. Demonstrate how to solve by just cross-multiplying and dividing. They should find it to be easy.

17. Allow students to solve the proportions to discuss the next day. They may finish for homework is necessary.

#### Assessments

EVIDENCE
Students should successfully fill out the lab sheet (See Associated File) with the measurements of their heights and shadows, and lengths of various objects and their shadows. The students also solve proportions using the data found.

CRITERIA
1. Proper measurement in centimeters of their height and shadow, and outside objects and their shadows.
2. Proper set up of proportions.
3. The student finds five different objects that are the same length as their height.
4. The student calculates the heights of various objects from setting up proportions and using the shadows of the objects.

#### Attached Files

This file contains the Shadow Chasing lab sheet.     File Extension: pdf