Ways to Introduce Variables.

  The other day, at the family Christmas gathering with people from 2 to 93 years old present, the topic of math always comes up because I'm there.  One of my nieces told me she loved her last math class while another one told me she was ok with one letter but not two.  She couldn't even use the term variable.

I know that there is a recent trend to use emoji's or characters instead of variables in three equations so the first equation is one equation, the second equation is two variables and the third equation has three variables.  Usually there is a fourth equation that students use the values from the earlier three equations.

Another way to introduce multiple variables into equations is using Marilyn Burns Math Solutions lesson by Carrie DeFrancisco who created a lovely lesson based on Dr Suess's Green Eggs and Ham.  The idea is using a menu based on certain choices from the book such as green eggs, regular eggs, bacon, ham, etc.  Each item is represented by a single letter so green eggs is G, the special is x, ham is H, etc. 

The lesson has students calculate the cost for various orders such as G + B + S =? or 2G + H =? at first but the orders become more complex as they move through the lesson. Students are encouraged to explain their thinking throughout the whole process.  Although this lesson is listed for grades 6 to 8, I plan to use it with my pre-algebra class in January.  I need new ways to present the information. This looks like a fun way to do it.

The Utah Education network has a nice lesson designed to introduce the concept of variables to students.  It begins having students determine whether certain equations such as 5 + 7 = 12 are true or false.  They indicate their choice using a thumbs up or thumbs down. The lesson has several activities which take a student from translating verbal equations into numerical equations which are then solved,  while the second activity helps them set up expressions using variables with shapes first before using the actual letters.  The final step is to create verbal sentences for an equation such as x + 4.

NCTM Illuminations has a nice variable machine activity using a code machine which aligns the alphabet to numbers to find the value of their first and last names.  They get to calculate the difference between the two names.  This is extended by having students find words equal to certain values.

All of these activities have an element giving a total which they have to find the equation which will give that number or give part of an equation where they have to find the missing value.  I love activities with open ended questions so they have to think more.

I love using whiteboards, either digital or real, with students because they can do their work, hold it up and with a glance, I know if they understand the concept.  I can also go around the class with a marker and draw a smiley or frowny face that provides an immediate feedback.  If its a frowny face, they have to figure out why its incorrect and make corrections.  They can ask table mates to help them.

Let me know what you think.  I'd love to hear.