"Figure This!"

 I am always on the lookout for activities designed to encourage critical thinking or conversation.  Too many times, the activities I find are based on filling out a worksheet but I found a website with problems rather than just worksheets.

The site "Figure This" created by the National Council of Mathematics for families to use together.  It appears the site has not been updated since 2004 but the problems are still able to be accessed. Although the site is listed for grades 6 to 8, I believe the material could easily be used in high school.

The problems are listed in two ways on the website.  The first listing is the challenge index which lists all 80 problems with a small description of each.  The other listing is via the math index which classifies the same activities as either Algebra, Geometry, measurement, numbers, or statistics and probability.  Many problems are listed in more than one category.

One such problem is titled "Stamps".  It shows up under Algebra, Geometry, and Numbers.  According to the list under Algebra, this problem deals with linear equations, graphs of lines, and representing patterns.  This activity also covers coordinate geometry, solving problems with percentages, decimals, and fractions.

Every problem has a hint button with the problem, and the site has the full answer.  When I say full answer, it shows four different ways to solve this particular problem so it is not one with only one way to get to the solution.

In case you are interested, the stamps problem states that you've found an old roll of 15 cent stamps before asking how many 33 cent stamps must you mix with the 15 cent stamps to find exactly $1.77 so you can mail a package.  The hint suggests students use as many 33 cent stamps with the difference made up of 15 cent stamps but the hint does not show unless the student clicks on the word.

The site also allows the challenges to be printed off complete with answers and hints should you want to use several different ones at math stations or they can be read from online.  It is possible to print the challenges off, separate the problems from the explanations and the answers so you could place the challenges at a station and the explanations in a different place.

The way these problems are designed, it is quite easy to have students explain their thinking process via video or flip grid once they've found solution.  If students get stuck while working on it, the teacher can ask students to share their thinking when they ask for help.  What did they try that got them to the point they got stuck.

The problems cover a variety of topics such as how long it takes the Arctic Tern to fly from the Arctic to the Antarctic and back again, or calculating BMI (Body Mass Index) to determine if someone is over weight, or life expectancy, or which windshield wiper cleans the most area.  So many of the challenges are based on real life.

Check it out to see if you can use it in your classroom.  Let me know what you think, I'd love to hear. Have a great day.