“Test the water” usually means to see if the water is too hot or cold to swim in. There is a popular joke involving teachers.
   
“Q: Why did the teacher go to the beach?  A: He wanted to test the waters” was printed in Class Act: Riddles for School (1995) by John Jansen. “Why did the teacher go to the beach? To test the water!” was printed in the Sudbury (ON) Star on December 6, 2005. “Sam just told me a joke for the 57th time (4yo) why did the teacher go to the beach? Answer - to test the water!!” was posted on Twitter by Darren Kitto on May 20, 2009.
 
“Why did the teacher jump in the lake? She wanted to test the waters” was printed in the Los Angeles (CA) Times on January 18, 2005. “Why did the teacher jump in the lake? She wanted to test the water” was printed in Newsday (Long Island, NY) on February 21, 2009. “#kidsjokes: why did the teacher jump in the lake? || because she wanted to test the waters” was posted on Twitter by Bill Uko on April 22, 2010.
 
“So my science teacher likes jokes. His joke for the 1st day of school was ‘Why did the teacher jump in the pool? TO TEST THE WATER!’” was posted on Twitter by “ig ↠ ＿ｌｏｖｅｓｅａｉｒａ” on August 6, 2011. “Why did the teacher jump in the school swimming pool? She wanted to test the water!” was printed in Silly School Jokes (2017) by Sally Lindley. “Why did the teacher jump into the pool? He/She wanted to test the water! #LaughoftheDay” was posted on Twitter by Jimmy RevJim Olsen on July 2, 2023.
 
   
Google Books
Class Act:
Riddles for School
By John Jansen
Minneapolis, MN: Lerner Publications
1995
Pg. ?:
Q: Why did the teacher go to the beach?
A: He wanted to test the waters.
     
Newspapers.com
18 January 2005, Los Angeles (CA) Times, ‘The Kids’ Reading Room: Jokes & Riddles,” pg. E18, col. 3:
Why did the teacher jump in the lake?
She wanted to test the waters.
Angela, 11
Los Feliz Elementary
Los Angeles
 
Google Groups: alt.humor.puns
Kids Puns of the Weak 01-25-05
Stan Kegel
Jan 25, 2005, 1:54:45 PM
(...)
Why did the teacher jump in the lake?
She wanted to test the waters. (Angella, 11)
         
6 December 2005, Sudbury (ON) Star, “Smile of the Day,” pg. A1:
Why did the teacher go to the beach? To test the water!—Anonymous.
 
Newspapers.com
21 February 2009, Newsday (Long Island, NY), “Kidsday,” pg. B20, col. 1:
Why did the teacher jump in the lake?
She wanted to test the water.
Yasin Spiteri
     
Twitter
Darren Kitto
@Darrenkitto
Sam just told me a joke for the 57th time (4yo) why did the teacher go to the beach? Answer - to test the water!! He has good delivery too.
7:01 AM · May 20, 2009
 
Twitter
Bill Uko
@billuko
#kidsjokes: why did the teacher jump in the lake? || because she wanted to test the waters
5:27 AM · Apr 22, 2010
   
Twitter
Q101 FM - Merritt
@Q101Merritt
Brian’s Joke of the Day: Why did the teacher jump into the lake? Because she wanted to test the waters!
12:39 PM · Sep 29, 2010
   
Twitter
ig ↠ ＿ｌｏｖｅｓｅａｉｒａ
@xbummerrr
So my science teacher likes jokes. His joke for the 1st day of school was “Why did the teacher jump in the pool? TO TEST THE WATER!” #Ba ...
5:25 PM · Aug 6, 2011
   
Twitter
Jeffrey Power
@Hefpow
JOTD…
Why did the teacher jump into the ocean?
...she wanted to test the waters…
10:23 AM · Oct 5, 2011
 
Google Books
Friend or Foe:
Which side are you on?
By Brian Gallagher
Dublin, Ireland; The O’Brien Press
2015
Pg. ?:
‘Why did the teacher jump into the river?’
 
‘Why?’ asked Joan.
 
‘She wanted to test the water!’

Google Books
Silly School Jokes
By Sally Lindley
New York, NY: Windmill Books
2017
Pg. 47:
Why did the teacher jump in the school swimming pool? She wanted to test the water!
 
Reddit—Dadjokes
Posted by u/ZappBrannigansLaw February 1, 2018
Why did the teacher jump in the lake?
Because she wanted to test the water!
 
Reddit—WiserRead
Posted by u/WiserRead October 3, 2022
Why did the teacher jump in the pool?
It’s always mysterious why people do strange things. To this day, nobody knows what exactly caused the teacher to plunge into the water.
 
Twitter
Jimmy RevJim Olsen
@mybuddyjimmy
Why did the teacher jump into the pool? He/She wanted to test the water! #LaughoftheDay
10:20 AM · Jul 2, 2023