Three Math Field Trips At School III

From telling time to measuring the height of a tree, here are three outdoor lessons to reinforce mathematical learning about measurement.

Telling Time: Whole and Half Hours*

Preparations
Materials:

• Hula hoops
• Sidewalk chalk
• Ten worksheets with six times printed on it; eg.  6:30, half past 10, 5 o'clock, etc.  Note: Each of the ten sheets are different, but there are to be no more than ten different times-on-the-clock total printed on the ten sheets, six of those ten in random order on each sheet.
  

Print out the worksheets, one for each group. These could be laminated for re-use. Gather the other necessary materials, and lay them out in the designated location.

Ready...

In the classroom, teach whole and half hours on an analog clock. Divide the class into ten groups. After that, the class can go outside and you can explain the first task.

Go! 

Task 1 

Gather your class in a central location. Each group gets a hoop, some sidewalk chalk and a worksheet with six descriptions of time from you (see Materials). 

Each group finds a place on the paved area of the school yard to lay their hula hoop.  Inside the hoop, the group writes the numbers on the clock, from 1 to 12.  Then they draw the hands on the clock, according to the first time on their worksheet. Once every group is done, quick check whether each clock is drawn correctly.

Task 2

On the pavement, there are now ten different clocks.  Each group will now go and look for the clock that matches their second time description.  Once each group has done that, they stay by that clock until you have checked for accuracy.  Then the groups find the third clock, and so on, until all six times have been found.  

Reflection

Gather students together in a central location. Ask them how it went. Were the correct clocks difficult to find?

Tree Triangulation I*

Preparations

Materials

• Cards with letters A to J or however many trees there are on the school property
• Sheet of graph paper and clipboard for every group
  
• Tape measure,  1 yard lengths of rope and other tools for measuring 
• Sheets of paper to fold into a triangle, one for every group
  

Prepare the worksheet, one for every group:  Make a graph with an x and y axis.  Along the y axis, graph 'number of feet' from 1 to 40.  Along the x axis, write the letters A to J, or as many letters as there are trees on the property. 

Hang the letter cards on the trees, one letter for every tree up until J, or more if there are more tree, or however many trees you want to measure.

Gather all the materials; you could ask students to bring a measuring tape from home. Try folding the paper into a triangle according to the instructions, so that you'll have an exemplar for your students (see graphic below).

Ready...

Challenge the children to measure the height of the schoolyard trees.  How high are they actually?  How do you measure them when you can't reach the top of them. Does anyone have an idea?  What about estimating?  Give time to try out some estimates, and compare the estimates.  What works and what doesn't work? Explain that there is a way, and go back inside. 

Go!

Watch this video together as a class:

source: Kenton Library

 Give each student a sheet of paper, and have students fold it into a triangle according to your instructions. 

After that, divide students in to groups of three, and let them decide in their groups which of their triangles is folded best for measurement.  Then give them the following step-by-step instructions:

• As a group, choose a tree.
• Measure the tree. It goes like this:  Hold the triangle in front of your eyes so that you are looking at the top of the tree across the diagonal side of the triangle. Walk back and forth until the top of the tree is exactly at the top of the diagonal side of the triangle.
• Your group members check whether you are holding the triangle properly.
• Now your group members measure the distance from you to the tree along the ground.
• Add the distance from you until the tree (A) and your height (B) together: A+B=C.
• Graph the height of your tree on your graph.
• Do it again for every tree on the property, taking turns within the group to do the different tasks.

Reflection
Discuss afterwards the results of each group. Did everyone get the same results for each tree? If there were differences, why was that?

*Both ideas are from buitenlesdag.nl

 

Tree Triangulation II**

What if the tree that you want to measure is across a road or a river? Teach your students this Pace-Angle Method.

• Locate a tree on the opposite side of the road or river (A)
  
• Place a stick on this side exactly opposite the tree (B)
  
• Walk along the shore or road at a right angle to AB. Take 20 paces (Note: one pace equals two steps.)  At this point, place another stick (C).
• Continue walking along the shore or road in the same direction another 10 paces.  Place another stick at this point (D).
  
•  Turn away from the road or river at D, and walk at a right angle to DB until you can sight through stick C to tree A. Stop and mark this point (E).
• Line DE is half the distance across the river or road. Pace this distance and double it to determine the width of the river at points AB.
  

artofmanliness.com

 **Teaching in the Outdoors, fifth edition. Donald R. Hammerman, William M. Hammerman, Elizabeth L. Hammerman, 2001