Name: _________________________________            Date: __________________

 

Using Proportions To Solve

Impossible Heights

Hands-on Activity

GOAL:

- The students will calculate the measurements of different objects that have heights that are impossible to measure.

OBJECTIVES:

- Given a tape measure and a data-recording sheet, the students will take the measurement of their own height, the measurement of their shadows, and the measurement of the shadows of objects that are impossible to measure.

- Given the measurements taken, the students will set up proportions to find the height of objects that are impossible to measure.

MATERIALS:

- Tape measure

- Worksheet with data-recording sheet

- Pencil

- Calculator

 

REVIEW:

Proportion: ____________________________________________________________

 

         Ratio: ____________________________________________________________

 

 

Three forms of writing ratios:

 

1.                                                   2.                                                               3.

 

 

Proportions are two ratios set equal to each other.

 

                                     Example:   

 

 

STEP 1:

 

�      You and your partner will each measure your own height in inches using the tape measure

�      Then, standing where you can clearly see your shadow (your back to the sun), your partner will measure your shadow from your toes to the top of your head on your shadow in inches. Take turns doing this with your partner.

o   Record your findings on the data-recording sheet in the correct box.

                        

                           

 

STEP 2:

 

�      Next, you and your partner will measure the shadow of the basketball hoop on the playground. You should start at the bottom of the hoop (where it meets the ground) to the top of the hoop�s shadow.

�      Record your findings on the data-recording sheet in the correct box.

                     

        

 

 

 

 

 

 

 

 

 

 

 

 

 

STEP 3:

 

�      Then, you and your partner will measure the shadow of the flagpole near the playground. You should start at the bottom of the pole (where it meets the ground) to the top of the flagpole�s shadow.

o   Record your findings on the data-recording sheet in the correct box.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

STEP 4:

 

�      Lastly, you and your partner will measure the shadow of a tree by the playground. You should start at the bottom of the tree�s trunk (where it meets the ground) to the top of the tree�s shadow.

o   Record your findings on the data-recording sheet in the correct box.

 

 

 

 

 

 

 

 

 

 

STEP 5:

 

�      After you record all the measurements that you need in the data chart, use the equation below to set up the proportions to find the height of the objects that cannot be measured.

 

 

 

 

 

 

�      Use the chart below to write and solve the proportions for each object. Find x (the height).

 

Basketball Hoop Proportion	Flagpole Proportion	Tree Proportion
x = ____	x = ____	x = ____

 

 

STEP 6:

 

�      Write your conclusion on the bottom of the data-recording sheet. You should convert the inches to feet (remember divide the number by 12)

Data Recording Sheet

 

 

Name: ______________	Height of Shadow	Actual Height
You
Basketball Hoop
Flag Pole
Tree

 

 

*CONCLUSIONS:

 

 

Extra Practice with Proportions

 

1.)                                          2.)

 

 

 

 

 

 

 

 

 

 

 

 

3.)                                          4.)